From 09db2adcb4e8535b590d9fa92cf4adce34fbcf7e Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Mon, 16 Oct 2023 21:39:36 +0000 Subject: [PATCH] build based on 3f5f22a --- previews/PR387/barotropic/index.html | 2 +- previews/PR387/extending/index.html | 20 +- previews/PR387/functions/index.html | 286 +++++------ previews/PR387/installation/index.html | 2 +- previews/PR387/jablonowski.png | Bin 23741 -> 23744 bytes .../PR387/lowertriangularmatrices/index.html | 4 +- previews/PR387/output/index.html | 2 +- previews/PR387/parameterizations/index.html | 2 +- previews/PR387/ringgrids/index.html | 466 +++++++++--------- previews/PR387/run_0001/progress.txt | 44 +- previews/PR387/run_0002/progress.txt | 44 +- previews/PR387/run_0003/progress.txt | 32 +- previews/PR387/run_0004/progress.txt | 32 +- previews/PR387/run_0005/output.nc | Bin 3799561 -> 3799392 bytes previews/PR387/run_0005/progress.txt | 38 +- previews/PR387/run_0005/restart.jld2 | Bin 321662 -> 321662 bytes previews/PR387/run_test/progress.txt | 44 +- previews/PR387/speedytransforms/index.html | 64 +-- 18 files changed, 541 insertions(+), 541 deletions(-) diff --git a/previews/PR387/barotropic/index.html b/previews/PR387/barotropic/index.html index 77882368a..be682007a 100644 --- a/previews/PR387/barotropic/index.html +++ b/previews/PR387/barotropic/index.html @@ -9,4 +9,4 @@ w_{i+1} &= u_{i-1} + 2\Delta tF(v_i) \\ u_i &= v_i + \frac{\nu\alpha}{2}(w_{i+1} - 2v_i + u_{i-1}) \\ v_{i+1} &= w_{i+1} - \frac{\nu(1-\alpha)}{2}(w_{i+1} - 2v_i + u_{i-1}) -\end{aligned}\]

with the Williams filter parameter $\alpha \in [0.5,1]$. For $\alpha=1$ we're back with the Robert-Asselin filter (the first two lines).

The Laplacian in the parentheses is often called a displacement, meaning that the filtered value is displaced (or corrected) in the direction of the two surrounding time steps. The Williams filter now also applies the same displacement, but in the opposite direction to the next time step $i+1$ as a correction step (line 3 above) for a once-filtered value $v_{i+1}$ which will then be twice-filtered by the Robert-Asselin filter on the next iteration. For more details see the referenced publications.

The initial Euler step (see Time integration, Table) is not filtered. Both the the Robert-Asselin and Williams filter are then switched on for all following leapfrog time steps.

References

+\end{aligned}\]

with the Williams filter parameter $\alpha \in [0.5,1]$. For $\alpha=1$ we're back with the Robert-Asselin filter (the first two lines).

The Laplacian in the parentheses is often called a displacement, meaning that the filtered value is displaced (or corrected) in the direction of the two surrounding time steps. The Williams filter now also applies the same displacement, but in the opposite direction to the next time step $i+1$ as a correction step (line 3 above) for a once-filtered value $v_{i+1}$ which will then be twice-filtered by the Robert-Asselin filter on the next iteration. For more details see the referenced publications.

The initial Euler step (see Time integration, Table) is not filtered. Both the the Robert-Asselin and Williams filter are then switched on for all following leapfrog time steps.

References

diff --git a/previews/PR387/extending/index.html b/previews/PR387/extending/index.html index 3c40d6d84..2bdb91fca 100644 --- a/previews/PR387/extending/index.html +++ b/previews/PR387/extending/index.html @@ -131,22 +131,22 @@ model = BarotropicModel(;spectral_grid,initial_conditions,forcing=stochastic_stirring) simulation = initialize!(model) run!(simulation)
                         Surface relative vorticity                          
-       ┌────────────────────────────────────────────────────────────┐4.0f-5  
+       ┌────────────────────────────────────────────────────────────┐5.0f-5  
     90 ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ┌──┐   
        ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
        ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
        ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
        ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
        ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-    ˚N ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
-   -90 ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ └──┘   
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
+    ˚N ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄   
+   -90 ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ └──┘   
        └────────────────────────────────────────────────────────────┘-4.0f-5 
         0                           ˚E                           360         

Yay! As you can see the vorticity does something funky on the southern hemisphere but not on the northern, as we do not force there. Awesome! Adding new components other than forcing works surprisingly similar. We briefly discuss how to add a custom drag to illustrate the differences but there are not really many.

Custom drag

From the barotropic vorticity equation in Custom forcing: define we omitted the drag term $-r\zeta$ which however can be defined in a strikingly similar way. This section is just to outline some differences.

SpeedyWeather defines AbstractForcing and AbstractDrag, both are only conceptual supertypes, and in fact you could define a forcing as a subtype of AbstractDrag and vice versa. So for a drag, most straight-forwardly you would do

struct MyDrag <: AbstractDrag
     # parameters and arrays
diff --git a/previews/PR387/functions/index.html b/previews/PR387/functions/index.html
index f873a7524..215b6efe0 100644
--- a/previews/PR387/functions/index.html
+++ b/previews/PR387/functions/index.html
@@ -1,102 +1,102 @@
 
-Function and type index · SpeedyWeather.jl

Function and type index

SpeedyWeather.BarotropicModelType

The BarotropicModel struct holds all other structs that contain precalculated constants, whether scalars or arrays that do not change throughout model integration.

  • spectral_grid::SpectralGrid: dictates resolution for many other components

  • planet::SpeedyWeather.AbstractPlanet: contains physical and orbital characteristics

  • atmosphere::SpeedyWeather.AbstractAtmosphere

  • forcing::SpeedyWeather.AbstractForcing{NF} where NF<:AbstractFloat

  • drag::SpeedyWeather.AbstractDrag{NF} where NF<:AbstractFloat

  • initial_conditions::SpeedyWeather.InitialConditions

  • time_stepping::SpeedyWeather.TimeStepper{NF} where NF<:AbstractFloat

  • spectral_transform::SpectralTransform

  • horizontal_diffusion::SpeedyWeather.HorizontalDiffusion{NF} where NF<:AbstractFloat

  • implicit::SpeedyWeather.AbstractImplicit{NF} where NF<:AbstractFloat

  • geometry::Geometry

  • constants::DynamicsConstants

  • device_setup::SpeedyWeather.DeviceSetup

  • output::SpeedyWeather.AbstractOutputWriter

  • feedback::SpeedyWeather.AbstractFeedback

source
SpeedyWeather.ClockType

Clock struct keeps track of the model time, how many days to integrate for and how many time steps this takes

  • time::Dates.DateTime: current model time

  • n_days::Float64: number of days to integrate for, set in run!(::Simulation)

  • n_timesteps::Int64: number of time steps to integrate for, set in initialize!(::Clock,::TimeStepper)

.

source
SpeedyWeather.ClockMethod
Clock(
+Function and type index · SpeedyWeather.jl

Function and type index

SpeedyWeather.BarotropicModelType

The BarotropicModel struct holds all other structs that contain precalculated constants, whether scalars or arrays that do not change throughout model integration.

  • spectral_grid::SpectralGrid: dictates resolution for many other components

  • planet::SpeedyWeather.AbstractPlanet: contains physical and orbital characteristics

  • atmosphere::SpeedyWeather.AbstractAtmosphere

  • forcing::SpeedyWeather.AbstractForcing{NF} where NF<:AbstractFloat

  • drag::SpeedyWeather.AbstractDrag{NF} where NF<:AbstractFloat

  • initial_conditions::SpeedyWeather.InitialConditions

  • time_stepping::SpeedyWeather.TimeStepper{NF} where NF<:AbstractFloat

  • spectral_transform::SpectralTransform

  • horizontal_diffusion::SpeedyWeather.HorizontalDiffusion{NF} where NF<:AbstractFloat

  • implicit::SpeedyWeather.AbstractImplicit{NF} where NF<:AbstractFloat

  • geometry::Geometry

  • constants::DynamicsConstants

  • device_setup::SpeedyWeather.DeviceSetup

  • output::SpeedyWeather.AbstractOutputWriter

  • feedback::SpeedyWeather.AbstractFeedback

source
SpeedyWeather.ClockType

Clock struct keeps track of the model time, how many days to integrate for and how many time steps this takes

  • time::Dates.DateTime: current model time

  • n_days::Float64: number of days to integrate for, set in run!(::Simulation)

  • n_timesteps::Int64: number of time steps to integrate for, set in initialize!(::Clock,::TimeStepper)

.

source
SpeedyWeather.ClockMethod
Clock(
     time_stepping::SpeedyWeather.TimeStepper;
     kwargs...
 ) -> SpeedyWeather.Clock
-

Create and initialize a clock from time_stepping

source
SpeedyWeather.ColumnVariablesType

Mutable struct that contains all prognostic (copies thereof) and diagnostic variables in a single column needed to evaluate the physical parametrizations. For now the struct is mutable as we will reuse the struct to iterate over horizontal grid points. Every column vector has nlev entries, from [1] at the top to [end] at the lowermost model level at the planetary boundary layer.

  • nlev::Int64

  • nband::Int64

  • n_stratosphere_levels::Int64

  • jring::Int64

  • lond::AbstractFloat

  • latd::AbstractFloat

  • land_fraction::AbstractFloat

  • u::Vector{NF} where NF<:AbstractFloat

  • v::Vector{NF} where NF<:AbstractFloat

  • temp::Vector{NF} where NF<:AbstractFloat

  • humid::Vector{NF} where NF<:AbstractFloat

  • ln_pres::Vector{NF} where NF<:AbstractFloat

  • pres::Vector{NF} where NF<:AbstractFloat

  • u_tend::Vector{NF} where NF<:AbstractFloat

  • v_tend::Vector{NF} where NF<:AbstractFloat

  • temp_tend::Vector{NF} where NF<:AbstractFloat

  • humid_tend::Vector{NF} where NF<:AbstractFloat

  • geopot::Vector{NF} where NF<:AbstractFloat

  • flux_u_upward::Vector{NF} where NF<:AbstractFloat

  • flux_u_downward::Vector{NF} where NF<:AbstractFloat

  • flux_v_upward::Vector{NF} where NF<:AbstractFloat

  • flux_v_downward::Vector{NF} where NF<:AbstractFloat

  • flux_temp_upward::Vector{NF} where NF<:AbstractFloat

  • flux_temp_downward::Vector{NF} where NF<:AbstractFloat

  • flux_humid_upward::Vector{NF} where NF<:AbstractFloat

  • flux_humid_downward::Vector{NF} where NF<:AbstractFloat

  • sat_humid::Vector{NF} where NF<:AbstractFloat

  • sat_vap_pres::Vector{NF} where NF<:AbstractFloat

  • dry_static_energy::Vector{NF} where NF<:AbstractFloat

  • moist_static_energy::Vector{NF} where NF<:AbstractFloat

  • humid_half::Vector{NF} where NF<:AbstractFloat

  • sat_humid_half::Vector{NF} where NF<:AbstractFloat

  • sat_moist_static_energy::Vector{NF} where NF<:AbstractFloat

  • dry_static_energy_half::Vector{NF} where NF<:AbstractFloat

  • sat_moist_static_energy_half::Vector{NF} where NF<:AbstractFloat

  • conditional_instability::Bool

  • activate_convection::Bool

  • cloud_top::Int64

  • excess_humidity::AbstractFloat

  • cloud_base_mass_flux::AbstractFloat

  • precip_convection::AbstractFloat

  • net_flux_humid::Vector{NF} where NF<:AbstractFloat

  • net_flux_dry_static_energy::Vector{NF} where NF<:AbstractFloat

  • entrainment_profile::Vector{NF} where NF<:AbstractFloat

  • precip_large_scale::AbstractFloat

  • wvi::Matrix{NF} where NF<:AbstractFloat

  • tau2::Matrix{NF} where NF<:AbstractFloat

  • dfabs::Vector{NF} where NF<:AbstractFloat

  • fsfcd::AbstractFloat

  • st4a::Matrix{NF} where NF<:AbstractFloat

  • flux::Vector{NF} where NF<:AbstractFloat

  • fsfcu::AbstractFloat

  • ts::AbstractFloat

  • fsfc::AbstractFloat

  • ftop::AbstractFloat

  • stratc::Vector{NF} where NF<:AbstractFloat

  • tyear::AbstractFloat

  • csol::AbstractFloat

  • topsr::AbstractFloat

  • fsol::AbstractFloat

  • ozupp::AbstractFloat

  • ozone::AbstractFloat

  • zenit::AbstractFloat

  • stratz::AbstractFloat

  • albsfc::AbstractFloat

  • ssrd::AbstractFloat

  • ssr::AbstractFloat

  • tsr::AbstractFloat

  • tend_t_rsw::Vector{NF} where NF<:AbstractFloat

  • norm_pres::AbstractFloat

  • icltop::Int64

  • cloudc::AbstractFloat

  • clstr::AbstractFloat

  • qcloud::AbstractFloat

  • fmask::AbstractFloat

  • rel_hum::Vector{NF} where NF<:AbstractFloat

  • grad_dry_static_energy::AbstractFloat

source
SpeedyWeather.DeviceSetupType
DeviceSetup{S<:AbstractDevice}

Holds information about the device the model is running on and workgroup size.

  • device::AbstractDevice: Device the model is running on
  • device_KA::KernelAbstractions.Device: Device for use with KernelAbstractions
  • n: workgroup size
source
SpeedyWeather.DynamicsConstantsType

Struct holding constants needed at runtime for the dynamical core in number format NF.

  • radius::AbstractFloat: Radius of Planet [m]

  • rotation::AbstractFloat: Angular frequency of Planet's rotation [s^-1]

  • gravity::AbstractFloat: Gravitational acceleration [m/s^2]

  • layer_thickness::AbstractFloat: shallow water layer thickness [m]

  • R_dry::AbstractFloat: specific gas constant for dry air [J/kg/K]

  • R_vapour::AbstractFloat: specific gas constant for water vapour [J/kg/K]

  • μ_virt_temp::AbstractFloat: used in Tv = T(1+μq) for virt temp Tv(T,q) calculation

  • cₚ::AbstractFloat: specific heat at constant pressure [J/K/kg]

  • κ::AbstractFloat: = R_dry/cₚ, gas const for air over heat capacity

  • water_density::AbstractFloat: water density [kg/m³]

  • f_coriolis::Vector{NF} where NF<:AbstractFloat: coriolis frequency [s^-1], scaled by radius as is vorticity = 2Ωsin(lat)radius

  • σ_lnp_A::Vector{NF} where NF<:AbstractFloat: σ-related factor A needed for adiabatic conversion term

  • σ_lnp_B::Vector{NF} where NF<:AbstractFloat: σ-related factor B needed for adiabatic conversion term

  • Δp_geopot_half::Vector{NF} where NF<:AbstractFloat: = R*(ln(pk+1) - ln(pk+1/2)), for half level geopotential

  • Δp_geopot_full::Vector{NF} where NF<:AbstractFloat: = R*(ln(pk+1/2) - ln(pk)), for full level geopotential

  • temp_ref_profile::Vector{NF} where NF<:AbstractFloat: reference temperature profile

source
SpeedyWeather.ColumnVariablesType

Mutable struct that contains all prognostic (copies thereof) and diagnostic variables in a single column needed to evaluate the physical parametrizations. For now the struct is mutable as we will reuse the struct to iterate over horizontal grid points. Every column vector has nlev entries, from [1] at the top to [end] at the lowermost model level at the planetary boundary layer.

  • nlev::Int64

  • nband::Int64

  • n_stratosphere_levels::Int64

  • jring::Int64

  • lond::AbstractFloat

  • latd::AbstractFloat

  • land_fraction::AbstractFloat

  • u::Vector{NF} where NF<:AbstractFloat

  • v::Vector{NF} where NF<:AbstractFloat

  • temp::Vector{NF} where NF<:AbstractFloat

  • humid::Vector{NF} where NF<:AbstractFloat

  • ln_pres::Vector{NF} where NF<:AbstractFloat

  • pres::Vector{NF} where NF<:AbstractFloat

  • u_tend::Vector{NF} where NF<:AbstractFloat

  • v_tend::Vector{NF} where NF<:AbstractFloat

  • temp_tend::Vector{NF} where NF<:AbstractFloat

  • humid_tend::Vector{NF} where NF<:AbstractFloat

  • geopot::Vector{NF} where NF<:AbstractFloat

  • flux_u_upward::Vector{NF} where NF<:AbstractFloat

  • flux_u_downward::Vector{NF} where NF<:AbstractFloat

  • flux_v_upward::Vector{NF} where NF<:AbstractFloat

  • flux_v_downward::Vector{NF} where NF<:AbstractFloat

  • flux_temp_upward::Vector{NF} where NF<:AbstractFloat

  • flux_temp_downward::Vector{NF} where NF<:AbstractFloat

  • flux_humid_upward::Vector{NF} where NF<:AbstractFloat

  • flux_humid_downward::Vector{NF} where NF<:AbstractFloat

  • sat_humid::Vector{NF} where NF<:AbstractFloat

  • sat_vap_pres::Vector{NF} where NF<:AbstractFloat

  • dry_static_energy::Vector{NF} where NF<:AbstractFloat

  • moist_static_energy::Vector{NF} where NF<:AbstractFloat

  • humid_half::Vector{NF} where NF<:AbstractFloat

  • sat_humid_half::Vector{NF} where NF<:AbstractFloat

  • sat_moist_static_energy::Vector{NF} where NF<:AbstractFloat

  • dry_static_energy_half::Vector{NF} where NF<:AbstractFloat

  • sat_moist_static_energy_half::Vector{NF} where NF<:AbstractFloat

  • conditional_instability::Bool

  • activate_convection::Bool

  • cloud_top::Int64

  • excess_humidity::AbstractFloat

  • cloud_base_mass_flux::AbstractFloat

  • precip_convection::AbstractFloat

  • net_flux_humid::Vector{NF} where NF<:AbstractFloat

  • net_flux_dry_static_energy::Vector{NF} where NF<:AbstractFloat

  • entrainment_profile::Vector{NF} where NF<:AbstractFloat

  • precip_large_scale::AbstractFloat

  • wvi::Matrix{NF} where NF<:AbstractFloat

  • tau2::Matrix{NF} where NF<:AbstractFloat

  • dfabs::Vector{NF} where NF<:AbstractFloat

  • fsfcd::AbstractFloat

  • st4a::Matrix{NF} where NF<:AbstractFloat

  • flux::Vector{NF} where NF<:AbstractFloat

  • fsfcu::AbstractFloat

  • ts::AbstractFloat

  • fsfc::AbstractFloat

  • ftop::AbstractFloat

  • stratc::Vector{NF} where NF<:AbstractFloat

  • tyear::AbstractFloat

  • csol::AbstractFloat

  • topsr::AbstractFloat

  • fsol::AbstractFloat

  • ozupp::AbstractFloat

  • ozone::AbstractFloat

  • zenit::AbstractFloat

  • stratz::AbstractFloat

  • albsfc::AbstractFloat

  • ssrd::AbstractFloat

  • ssr::AbstractFloat

  • tsr::AbstractFloat

  • tend_t_rsw::Vector{NF} where NF<:AbstractFloat

  • norm_pres::AbstractFloat

  • icltop::Int64

  • cloudc::AbstractFloat

  • clstr::AbstractFloat

  • qcloud::AbstractFloat

  • fmask::AbstractFloat

  • rel_hum::Vector{NF} where NF<:AbstractFloat

  • grad_dry_static_energy::AbstractFloat

source
SpeedyWeather.DeviceSetupType
DeviceSetup{S<:AbstractDevice}

Holds information about the device the model is running on and workgroup size.

  • device::AbstractDevice: Device the model is running on
  • device_KA::KernelAbstractions.Device: Device for use with KernelAbstractions
  • n: workgroup size
source
SpeedyWeather.DynamicsConstantsType

Struct holding constants needed at runtime for the dynamical core in number format NF.

  • radius::AbstractFloat: Radius of Planet [m]

  • rotation::AbstractFloat: Angular frequency of Planet's rotation [s^-1]

  • gravity::AbstractFloat: Gravitational acceleration [m/s^2]

  • layer_thickness::AbstractFloat: shallow water layer thickness [m]

  • R_dry::AbstractFloat: specific gas constant for dry air [J/kg/K]

  • R_vapour::AbstractFloat: specific gas constant for water vapour [J/kg/K]

  • μ_virt_temp::AbstractFloat: used in Tv = T(1+μq) for virt temp Tv(T,q) calculation

  • cₚ::AbstractFloat: specific heat at constant pressure [J/K/kg]

  • κ::AbstractFloat: = R_dry/cₚ, gas const for air over heat capacity

  • water_density::AbstractFloat: water density [kg/m³]

  • f_coriolis::Vector{NF} where NF<:AbstractFloat: coriolis frequency [s^-1], scaled by radius as is vorticity = 2Ωsin(lat)radius

  • σ_lnp_A::Vector{NF} where NF<:AbstractFloat: σ-related factor A needed for adiabatic conversion term

  • σ_lnp_B::Vector{NF} where NF<:AbstractFloat: σ-related factor B needed for adiabatic conversion term

  • Δp_geopot_half::Vector{NF} where NF<:AbstractFloat: = R*(ln(pk+1) - ln(pk+1/2)), for half level geopotential

  • Δp_geopot_full::Vector{NF} where NF<:AbstractFloat: = R*(ln(pk+1/2) - ln(pk)), for full level geopotential

  • temp_ref_profile::Vector{NF} where NF<:AbstractFloat: reference temperature profile

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SpeedyWeather.DynamicsConstantsMethod
DynamicsConstants(
     spectral_grid::SpectralGrid,
     planet::SpeedyWeather.AbstractPlanet,
     atmosphere::SpeedyWeather.AbstractAtmosphere,
     geometry::Geometry
 ) -> Any
-

Generator function for a DynamicsConstants struct.

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SpeedyWeather.EarthType

Create a struct Earth<:AbstractPlanet, with the following physical/orbital characteristics. Note that radius is not part of it as this should be chosen in SpectralGrid. Keyword arguments are

  • rotation::Float64: angular frequency of Earth's rotation [rad/s]

  • gravity::Float64: gravitational acceleration [m/s^2]

  • daily_cycle::Bool: switch on/off daily cycle

  • length_of_day::Float64: [hrs] in a day

  • seasonal_cycle::Bool: switch on/off seasonal cycle

  • length_of_year::Float64: [days] in a year

  • equinox::Dates.DateTime: time of spring equinox (year irrelevant)

  • axial_tilt::Float64: angle [˚] rotation axis tilt wrt to orbit

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SpeedyWeather.EarthAtmosphereType

Create a struct EarthAtmosphere<:AbstractPlanet, with the following physical/chemical characteristics. Note that radius is not part of it as this should be chosen in SpectralGrid. Keyword arguments are

  • mol_mass_dry_air::Float64: molar mass of dry air [g/mol]

  • mol_mass_vapour::Float64: molar mass of water vapour [g/mol]

  • cₚ::Float64: specific heat at constant pressure [J/K/kg]

  • R_gas::Float64: universal gas constant [J/K/mol]

  • R_dry::Float64: specific gas constant for dry air [J/kg/K]

  • R_vapour::Float64: specific gas constant for water vapour [J/kg/K]

  • water_density::Float64: water density [kg/m³]

  • latent_heat_condensation::Float64: latent heat of condensation [J/g] for consistency with specific humidity [g/Kg], also called alhc

  • latent_heat_sublimation::Float64: latent heat of sublimation [J/g], also called alhs

  • stefan_boltzmann::Float64: stefan-Boltzmann constant [W/m²/K⁴]

  • lapse_rate::Float64: moist adiabatic temperature lapse rate $-dT/dz$ [K/km]

  • temp_ref::Float64: absolute temperature at surface $z=0$ [K]

  • temp_top::Float64: absolute temperature in stratosphere [K]

  • ΔT_stratosphere::Float64: for stratospheric lapse rate [K] after Jablonowski

  • σ_tropopause::Float64: start of the stratosphere in sigma coordinates

  • σ_boundary_layer::Float64: top of the planetary boundary layer in sigma coordinates

  • scale_height::Float64: scale height for pressure [km]

  • pres_ref::Float64: surface pressure [hPa]

  • scale_height_humid::Float64: scale height for specific humidity [km]

  • relhumid_ref::Float64: relative humidity of near-surface air [1]

  • water_pres_ref::Float64: saturation water vapour pressure [Pa]

  • layer_thickness::Float64: layer thickness for the shallow water model [km]

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SpeedyWeather.EarthOrographyType

Earth's orography read from file, with smoothing.

  • path::String: path to the folder containing the orography file, pkg path default

  • file::String: filename of orography

  • file_Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}: Grid the orography file comes on

  • scale::Float64: scale orography by a factor

  • smoothing::Bool: smooth the orography field?

  • smoothing_power::Float64: power of Laplacian for smoothing

  • smoothing_strength::Float64: highest degree l is multiplied by

  • smoothing_truncation::Int64: resolution of orography in spectral trunc

  • orography::SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat: height [m] on grid-point space.

  • geopot_surf::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: surface geopotential, height*gravity [m²/s²]

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SpeedyWeather.EarthType

Create a struct Earth<:AbstractPlanet, with the following physical/orbital characteristics. Note that radius is not part of it as this should be chosen in SpectralGrid. Keyword arguments are

  • rotation::Float64: angular frequency of Earth's rotation [rad/s]

  • gravity::Float64: gravitational acceleration [m/s^2]

  • daily_cycle::Bool: switch on/off daily cycle

  • length_of_day::Float64: [hrs] in a day

  • seasonal_cycle::Bool: switch on/off seasonal cycle

  • length_of_year::Float64: [days] in a year

  • equinox::Dates.DateTime: time of spring equinox (year irrelevant)

  • axial_tilt::Float64: angle [˚] rotation axis tilt wrt to orbit

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SpeedyWeather.EarthAtmosphereType

Create a struct EarthAtmosphere<:AbstractPlanet, with the following physical/chemical characteristics. Note that radius is not part of it as this should be chosen in SpectralGrid. Keyword arguments are

  • mol_mass_dry_air::Float64: molar mass of dry air [g/mol]

  • mol_mass_vapour::Float64: molar mass of water vapour [g/mol]

  • cₚ::Float64: specific heat at constant pressure [J/K/kg]

  • R_gas::Float64: universal gas constant [J/K/mol]

  • R_dry::Float64: specific gas constant for dry air [J/kg/K]

  • R_vapour::Float64: specific gas constant for water vapour [J/kg/K]

  • water_density::Float64: water density [kg/m³]

  • latent_heat_condensation::Float64: latent heat of condensation [J/g] for consistency with specific humidity [g/Kg], also called alhc

  • latent_heat_sublimation::Float64: latent heat of sublimation [J/g], also called alhs

  • stefan_boltzmann::Float64: stefan-Boltzmann constant [W/m²/K⁴]

  • lapse_rate::Float64: moist adiabatic temperature lapse rate $-dT/dz$ [K/km]

  • temp_ref::Float64: absolute temperature at surface $z=0$ [K]

  • temp_top::Float64: absolute temperature in stratosphere [K]

  • ΔT_stratosphere::Float64: for stratospheric lapse rate [K] after Jablonowski

  • σ_tropopause::Float64: start of the stratosphere in sigma coordinates

  • σ_boundary_layer::Float64: top of the planetary boundary layer in sigma coordinates

  • scale_height::Float64: scale height for pressure [km]

  • pres_ref::Float64: surface pressure [hPa]

  • scale_height_humid::Float64: scale height for specific humidity [km]

  • relhumid_ref::Float64: relative humidity of near-surface air [1]

  • water_pres_ref::Float64: saturation water vapour pressure [Pa]

  • layer_thickness::Float64: layer thickness for the shallow water model [km]

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SpeedyWeather.EarthOrographyType

Earth's orography read from file, with smoothing.

  • path::String: path to the folder containing the orography file, pkg path default

  • file::String: filename of orography

  • file_Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}: Grid the orography file comes on

  • scale::Float64: scale orography by a factor

  • smoothing::Bool: smooth the orography field?

  • smoothing_power::Float64: power of Laplacian for smoothing

  • smoothing_strength::Float64: highest degree l is multiplied by

  • smoothing_truncation::Int64: resolution of orography in spectral trunc

  • orography::SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat: height [m] on grid-point space.

  • geopot_surf::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: surface geopotential, height*gravity [m²/s²]

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SpeedyWeather.EarthOrographyMethod
EarthOrography(
     spectral_grid::SpectralGrid;
     kwargs...
 ) -> Any
-

Generator function pulling the resolution information from spectral_grid.

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SpeedyWeather.FeedbackType
Feedback() -> Feedback
 Feedback(verbose::Bool) -> Feedback
 Feedback(verbose::Bool, debug::Bool) -> Feedback
-

Generator function for a Feedback struct.

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SpeedyWeather.FeedbackType

Feedback struct that contains options and object for command-line feedback like the progress meter.

  • verbose::Bool: print feedback to REPL?

  • debug::Bool: check for NaRs in the prognostic variables

  • output::Bool: write a progress.txt file? State synced with OutputWriter.output

  • id::Union{Int64, String}: identification of run, taken from ::OutputWriter

  • run_path::String: path to run folder, taken from ::OutputWriter

  • progress_meter::ProgressMeter.Progress: struct containing everything progress related

  • progress_txt::Union{Nothing, IOStream}: txt is a Nothing in case of no output

  • nars_detected::Bool: did Infs/NaNs occur in the simulation?

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SpeedyWeather.GeometryType

Construct Geometry struct containing parameters and arrays describing an iso-latitude grid <:AbstractGrid and the vertical levels. Pass on SpectralGrid to calculate the following fields

  • spectral_grid::SpectralGrid: SpectralGrid that defines spectral and grid resolution

  • Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}: grid of the dynamical core

  • nlat_half::Int64: resolution parameter nlat_half of Grid, # of latitudes on one hemisphere (incl Equator)

  • nlon_max::Int64: maximum number of longitudes (at/around Equator)

  • nlon::Int64: =nlon_max, same (used for compatibility), TODO: still needed?

  • nlat::Int64: number of latitude rings

  • nlev::Int64: number of vertical levels

  • npoints::Int64: total number of grid points

  • radius::AbstractFloat: Planet's radius [m]

  • colat::Vector{Float64}: array of colatitudes in radians (0...π)

  • latd::Vector{Float64}: array of latitudes in degrees (90˚...-90˚)

  • lond::Vector{Float64}: array of longitudes in degrees (0...360˚), empty for non-full grids

  • londs::Vector{NF} where NF<:AbstractFloat: longitude (-180˚...180˚) for each grid point in ring order

  • latds::Vector{NF} where NF<:AbstractFloat: latitude (-90˚...˚90) for each grid point in ring order

  • sinlat::Vector{NF} where NF<:AbstractFloat: sin of latitudes

  • coslat::Vector{NF} where NF<:AbstractFloat: cos of latitudes

  • coslat⁻¹::Vector{NF} where NF<:AbstractFloat: = 1/cos(lat)

  • coslat²::Vector{NF} where NF<:AbstractFloat: = cos²(lat)

  • coslat⁻²::Vector{NF} where NF<:AbstractFloat: # = 1/cos²(lat)

  • σ_levels_half::Vector{NF} where NF<:AbstractFloat: σ at half levels, σ_k+1/2

  • σ_levels_full::Vector{NF} where NF<:AbstractFloat: σ at full levels, σₖ

  • σ_levels_thick::Vector{NF} where NF<:AbstractFloat: σ level thicknesses, σₖ₊₁ - σₖ

  • ln_σ_levels_full::Vector{NF} where NF<:AbstractFloat: log of σ at full levels, include surface (σ=1) as last element

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SpeedyWeather.GeometryMethod
Geometry(spectral_grid::SpectralGrid) -> Any
-

Generator function for Geometry struct based on spectral_grid.

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SpeedyWeather.HeldSuarezType

Struct that defines the temperature relaxation from Held and Suarez, 1996 BAMS

  • nlat::Int64: number of latitude rings

  • nlev::Int64: number of vertical levels

  • σb::Float64: sigma coordinate below which faster surface relaxation is applied

  • relax_time_slow::Float64: time scale [hrs] for slow global relaxation

  • relax_time_fast::Float64: time scale [hrs] for faster tropical surface relaxation

  • Tmin::Float64: minimum equilibrium temperature [K]

  • Tmax::Float64: maximum equilibrium temperature [K]

  • ΔTy::Float64: meridional temperature gradient [K]

  • Δθz::Float64: vertical temperature gradient [K]

  • κ::Base.RefValue{NF} where NF<:AbstractFloat

  • p₀::Base.RefValue{NF} where NF<:AbstractFloat

  • temp_relax_freq::Matrix{NF} where NF<:AbstractFloat

  • temp_equil_a::Vector{NF} where NF<:AbstractFloat

  • temp_equil_b::Vector{NF} where NF<:AbstractFloat

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SpeedyWeather.HeldSuarezMethod
HeldSuarez(SG::SpectralGrid; kwargs...) -> Any
-

create a HeldSuarez temperature relaxation with arrays allocated given spectral_grid

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SpeedyWeather.HyperDiffusionType

Struct for horizontal hyper diffusion of vor, div, temp; implicitly in spectral space with a power of the Laplacian (default=4) and the strength controlled by time_scale. Options exist to scale the diffusion by resolution, and adaptive depending on the current vorticity maximum to increase diffusion in active layers. Furthermore the power can be decreased above the tapering_σ to power_stratosphere (default 2). For Barotropic, ShallowWater, the default non-adaptive constant-time scale hyper diffusion is used. Options are

  • trunc::Int64: spectral resolution

  • nlev::Int64: number of vertical levels

  • power::Float64: power of Laplacian

  • time_scale::Float64: diffusion time scales [hrs]

  • resolution_scaling::Float64: stronger diffusion with resolution? 0: constant with trunc, 1: (inverse) linear with trunc, etc

  • power_stratosphere::Float64: different power for tropopause/stratosphere

  • tapering_σ::Float64: linearly scale towards power_stratosphere above this σ

  • adaptive::Bool: adaptive = higher diffusion for layers with higher vorticity levels.

  • vor_max::Float64: above this (absolute) vorticity level [1/s], diffusion is increased

  • adaptive_strength::Float64: increase strength above vor_max by this factor times max(abs(vor))/vor_max

  • ∇²ⁿ_2D::Vector

  • ∇²ⁿ_2D_implicit::Vector

  • ∇²ⁿ::Array{Vector{NF}, 1} where NF

  • ∇²ⁿ_implicit::Array{Vector{NF}, 1} where NF

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SpeedyWeather.FeedbackType

Feedback struct that contains options and object for command-line feedback like the progress meter.

  • verbose::Bool: print feedback to REPL?

  • debug::Bool: check for NaRs in the prognostic variables

  • output::Bool: write a progress.txt file? State synced with OutputWriter.output

  • id::Union{Int64, String}: identification of run, taken from ::OutputWriter

  • run_path::String: path to run folder, taken from ::OutputWriter

  • progress_meter::ProgressMeter.Progress: struct containing everything progress related

  • progress_txt::Union{Nothing, IOStream}: txt is a Nothing in case of no output

  • nars_detected::Bool: did Infs/NaNs occur in the simulation?

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SpeedyWeather.GeometryType

Construct Geometry struct containing parameters and arrays describing an iso-latitude grid <:AbstractGrid and the vertical levels. Pass on SpectralGrid to calculate the following fields

  • spectral_grid::SpectralGrid: SpectralGrid that defines spectral and grid resolution

  • Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}: grid of the dynamical core

  • nlat_half::Int64: resolution parameter nlat_half of Grid, # of latitudes on one hemisphere (incl Equator)

  • nlon_max::Int64: maximum number of longitudes (at/around Equator)

  • nlon::Int64: =nlon_max, same (used for compatibility), TODO: still needed?

  • nlat::Int64: number of latitude rings

  • nlev::Int64: number of vertical levels

  • npoints::Int64: total number of grid points

  • radius::AbstractFloat: Planet's radius [m]

  • colat::Vector{Float64}: array of colatitudes in radians (0...π)

  • latd::Vector{Float64}: array of latitudes in degrees (90˚...-90˚)

  • lond::Vector{Float64}: array of longitudes in degrees (0...360˚), empty for non-full grids

  • londs::Vector{NF} where NF<:AbstractFloat: longitude (-180˚...180˚) for each grid point in ring order

  • latds::Vector{NF} where NF<:AbstractFloat: latitude (-90˚...˚90) for each grid point in ring order

  • sinlat::Vector{NF} where NF<:AbstractFloat: sin of latitudes

  • coslat::Vector{NF} where NF<:AbstractFloat: cos of latitudes

  • coslat⁻¹::Vector{NF} where NF<:AbstractFloat: = 1/cos(lat)

  • coslat²::Vector{NF} where NF<:AbstractFloat: = cos²(lat)

  • coslat⁻²::Vector{NF} where NF<:AbstractFloat: # = 1/cos²(lat)

  • σ_levels_half::Vector{NF} where NF<:AbstractFloat: σ at half levels, σ_k+1/2

  • σ_levels_full::Vector{NF} where NF<:AbstractFloat: σ at full levels, σₖ

  • σ_levels_thick::Vector{NF} where NF<:AbstractFloat: σ level thicknesses, σₖ₊₁ - σₖ

  • ln_σ_levels_full::Vector{NF} where NF<:AbstractFloat: log of σ at full levels, include surface (σ=1) as last element

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SpeedyWeather.GeometryMethod
Geometry(spectral_grid::SpectralGrid) -> Any
+

Generator function for Geometry struct based on spectral_grid.

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SpeedyWeather.HeldSuarezType

Struct that defines the temperature relaxation from Held and Suarez, 1996 BAMS

  • nlat::Int64: number of latitude rings

  • nlev::Int64: number of vertical levels

  • σb::Float64: sigma coordinate below which faster surface relaxation is applied

  • relax_time_slow::Float64: time scale [hrs] for slow global relaxation

  • relax_time_fast::Float64: time scale [hrs] for faster tropical surface relaxation

  • Tmin::Float64: minimum equilibrium temperature [K]

  • Tmax::Float64: maximum equilibrium temperature [K]

  • ΔTy::Float64: meridional temperature gradient [K]

  • Δθz::Float64: vertical temperature gradient [K]

  • κ::Base.RefValue{NF} where NF<:AbstractFloat

  • p₀::Base.RefValue{NF} where NF<:AbstractFloat

  • temp_relax_freq::Matrix{NF} where NF<:AbstractFloat

  • temp_equil_a::Vector{NF} where NF<:AbstractFloat

  • temp_equil_b::Vector{NF} where NF<:AbstractFloat

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SpeedyWeather.HeldSuarezMethod
HeldSuarez(SG::SpectralGrid; kwargs...) -> Any
+

create a HeldSuarez temperature relaxation with arrays allocated given spectral_grid

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SpeedyWeather.HyperDiffusionType

Struct for horizontal hyper diffusion of vor, div, temp; implicitly in spectral space with a power of the Laplacian (default=4) and the strength controlled by time_scale. Options exist to scale the diffusion by resolution, and adaptive depending on the current vorticity maximum to increase diffusion in active layers. Furthermore the power can be decreased above the tapering_σ to power_stratosphere (default 2). For Barotropic, ShallowWater, the default non-adaptive constant-time scale hyper diffusion is used. Options are

  • trunc::Int64: spectral resolution

  • nlev::Int64: number of vertical levels

  • power::Float64: power of Laplacian

  • time_scale::Float64: diffusion time scales [hrs]

  • resolution_scaling::Float64: stronger diffusion with resolution? 0: constant with trunc, 1: (inverse) linear with trunc, etc

  • power_stratosphere::Float64: different power for tropopause/stratosphere

  • tapering_σ::Float64: linearly scale towards power_stratosphere above this σ

  • adaptive::Bool: adaptive = higher diffusion for layers with higher vorticity levels.

  • vor_max::Float64: above this (absolute) vorticity level [1/s], diffusion is increased

  • adaptive_strength::Float64: increase strength above vor_max by this factor times max(abs(vor))/vor_max

  • ∇²ⁿ_2D::Vector

  • ∇²ⁿ_2D_implicit::Vector

  • ∇²ⁿ::Array{Vector{NF}, 1} where NF

  • ∇²ⁿ_implicit::Array{Vector{NF}, 1} where NF

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SpeedyWeather.HyperDiffusionMethod
HyperDiffusion(
     spectral_grid::SpectralGrid;
     kwargs...
 ) -> Any
-

Generator function based on the resolutin in spectral_grid. Passes on keyword arguments.

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SpeedyWeather.ImplicitPrimitiveEqType

Struct that holds various precomputed arrays for the semi-implicit correction to prevent gravity waves from amplifying in the primitive equation model.

  • trunc::Int64: spectral resolution

  • nlev::Int64: number of vertical levels

  • α::Float64: time-step coefficient: 0=explicit, 0.5=centred implicit, 1=backward implicit

  • temp_profile::Vector{NF} where NF<:AbstractFloat: vertical temperature profile, obtained from diagn

  • ξ::Base.RefValue{NF} where NF<:AbstractFloat: time step 2α*Δt packed in RefValue for mutability

  • R::Matrix{NF} where NF<:AbstractFloat: divergence: operator for the geopotential calculation

  • U::Vector{NF} where NF<:AbstractFloat: divergence: the -RdTₖ∇² term excl the eigenvalues from ∇² for divergence

  • L::Matrix{NF} where NF<:AbstractFloat: temperature: operator for the TₖD + κTₖDlnps/Dt term

  • W::Vector{NF} where NF<:AbstractFloat: pressure: vertical averaging of the -D̄ term in the log surface pres equation

  • L0::Vector{NF} where NF<:AbstractFloat: components to construct L, 1/ 2Δσ

  • L1::Matrix{NF} where NF<:AbstractFloat: vert advection term in the temperature equation (below+above)

  • L2::Vector{NF} where NF<:AbstractFloat: factor in front of the divsumabove term

  • L3::Matrix{NF} where NF<:AbstractFloat: sumabove operator itself

  • L4::Vector{NF} where NF<:AbstractFloat: factor in front of div term in Dlnps/Dt

  • S::Matrix{NF} where NF<:AbstractFloat: for every l the matrix to be inverted

  • S⁻¹::Array{NF, 3} where NF<:AbstractFloat: combined inverted operator: S = 1 - ξ²(RL + UW)

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SpeedyWeather.ImplicitPrimitiveEqType

Struct that holds various precomputed arrays for the semi-implicit correction to prevent gravity waves from amplifying in the primitive equation model.

  • trunc::Int64: spectral resolution

  • nlev::Int64: number of vertical levels

  • α::Float64: time-step coefficient: 0=explicit, 0.5=centred implicit, 1=backward implicit

  • temp_profile::Vector{NF} where NF<:AbstractFloat: vertical temperature profile, obtained from diagn

  • ξ::Base.RefValue{NF} where NF<:AbstractFloat: time step 2α*Δt packed in RefValue for mutability

  • R::Matrix{NF} where NF<:AbstractFloat: divergence: operator for the geopotential calculation

  • U::Vector{NF} where NF<:AbstractFloat: divergence: the -RdTₖ∇² term excl the eigenvalues from ∇² for divergence

  • L::Matrix{NF} where NF<:AbstractFloat: temperature: operator for the TₖD + κTₖDlnps/Dt term

  • W::Vector{NF} where NF<:AbstractFloat: pressure: vertical averaging of the -D̄ term in the log surface pres equation

  • L0::Vector{NF} where NF<:AbstractFloat: components to construct L, 1/ 2Δσ

  • L1::Matrix{NF} where NF<:AbstractFloat: vert advection term in the temperature equation (below+above)

  • L2::Vector{NF} where NF<:AbstractFloat: factor in front of the divsumabove term

  • L3::Matrix{NF} where NF<:AbstractFloat: sumabove operator itself

  • L4::Vector{NF} where NF<:AbstractFloat: factor in front of div term in Dlnps/Dt

  • S::Matrix{NF} where NF<:AbstractFloat: for every l the matrix to be inverted

  • S⁻¹::Array{NF, 3} where NF<:AbstractFloat: combined inverted operator: S = 1 - ξ²(RL + UW)

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SpeedyWeather.ImplicitShallowWaterType

Struct that holds various precomputed arrays for the semi-implicit correction to prevent gravity waves from amplifying in the shallow water model.

  • trunc::Int64

  • α::Float64: coefficient for semi-implicit computations to filter gravity waves

  • H::Base.RefValue{NF} where NF<:AbstractFloat

  • ξH::Base.RefValue{NF} where NF<:AbstractFloat

  • g∇²::Vector{NF} where NF<:AbstractFloat

  • ξg∇²::Vector{NF} where NF<:AbstractFloat

  • S⁻¹::Vector{NF} where NF<:AbstractFloat

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SpeedyWeather.ImplicitShallowWaterType

Struct that holds various precomputed arrays for the semi-implicit correction to prevent gravity waves from amplifying in the shallow water model.

  • trunc::Int64

  • α::Float64: coefficient for semi-implicit computations to filter gravity waves

  • H::Base.RefValue{NF} where NF<:AbstractFloat

  • ξH::Base.RefValue{NF} where NF<:AbstractFloat

  • g∇²::Vector{NF} where NF<:AbstractFloat

  • ξg∇²::Vector{NF} where NF<:AbstractFloat

  • S⁻¹::Vector{NF} where NF<:AbstractFloat

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SpeedyWeather.JablonowskiRelaxationMethod
JablonowskiRelaxation(SG::SpectralGrid; kwargs...) -> Any
-

create a JablonowskiRelaxation temperature relaxation with arrays allocated given spectral_grid

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SpeedyWeather.JetStreamForcingType

Forcing term for the Barotropic or ShallowWaterModel with an idealised jet stream similar to the initial conditions from Galewsky, 2004, but mirrored for both hemispheres.

  • nlat::Int64: Number of latitude rings

  • latitude::Float64: jet latitude [˚N]

  • width::Float64: jet width [˚], default ≈ 19.29˚

  • speed::Float64: jet speed scale [m/s]

  • time_scale::Float64: time scale [days]

  • amplitude::Vector: precomputed amplitude vector [m/s²]

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SpeedyWeather.KeepbitsType

Number of mantissa bits to keep for each prognostic variable when compressed for netCDF and .jld2 data output.

  • u::Int64

  • v::Int64

  • vor::Int64

  • div::Int64

  • temp::Int64

  • pres::Int64

  • humid::Int64

  • precip_cond::Int64

  • precip_conv::Int64

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SpeedyWeather.LandSeaMaskType

Land-sea mask, fractional, read from file.

  • path::String: path to the folder containing the land-sea mask file, pkg path default

  • file::String: filename of land sea mask

  • file_Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}: Grid the land-sea mask file comes on

  • land_sea_mask::SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat: Land-sea mask [1] on grid-point space. Land=1, sea=0, land-area fraction in between.

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SpeedyWeather.LandSeaMaskMethod
LandSeaMask(spectral_grid::SpectralGrid; kwargs...) -> Any
-

Generator function pulling the resolution information from spectral_grid.

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SpeedyWeather.LeapfrogType

Leapfrog time stepping defined by the following fields

  • trunc::Int64: spectral resolution (max degree of spherical harmonics)

  • Δt_at_T31::Float64: time step in minutes for T31, scale linearly to trunc

  • radius::Any: radius of sphere [m], used for scaling

  • robert_filter::Any: Robert (1966) time filter coefficeint to suppress comput. mode

  • williams_filter::Any: Williams time filter (Amezcua 2011) coefficient for 3rd order acc

  • Δt_sec::Int64: time step Δt [s] at specified resolution

  • Δt::Any: time step Δt [s/m] at specified resolution, scaled by 1/radius

  • Δt_hrs::Float64: convert time step Δt from minutes to hours

source
SpeedyWeather.LeapfrogMethod
Leapfrog(spectral_grid::SpectralGrid; kwargs...) -> Any
-

Generator function for a Leapfrog struct using spectral_grid for the resolution information.

source
SpeedyWeather.LinearDragType

Linear boundary layer drag Following Held and Suarez, 1996 BAMS

  • σb::Float64

  • time_scale::Float64

  • nlev::Int64

  • drag_coefs::Vector{NF} where NF<:AbstractFloat

source
SpeedyWeather.MagnusCoefsType

Parameters for computing saturation vapour pressure using the August-Roche-Magnus formula,

eᵢ(T) = e₀ * exp(Cᵢ * (T - T₀) / (T - Tᵢ)),

where T is in Kelvin and i = 1,2 for saturation with respect to water and ice, respectively.

  • e₀::AbstractFloat: Saturation vapour pressure at 0°C [Pa]

  • T₀::AbstractFloat: 0°C in Kelvin

  • T₁::AbstractFloat

  • T₂::AbstractFloat

  • C₁::AbstractFloat

  • C₂::AbstractFloat

source
SpeedyWeather.NoOrographyType

Orography with zero height in orography and zero surface geopotential geopot_surf.

  • orography::SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat: height [m] on grid-point space.

  • geopot_surf::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: surface geopotential, height*gravity [m²/s²]

source
SpeedyWeather.NoOrographyMethod
NoOrography(spectral_grid::SpectralGrid) -> NoOrography
-

Generator function pulling the resolution information from spectral_grid.

source
SpeedyWeather.OutputWriterType

NetCDF output writer. Contains all output options and auxiliary fields for output interpolation. To be initialised with OutputWriter(::SpectralGrid,::Type{<:ModelSetup},kwargs...) to pass on the resolution information and the model type which chooses which variables to output. Options include

  • spectral_grid::SpectralGrid

  • output::Bool

  • path::String: [OPTION] path to output folder, run_???? will be created within

  • id::String: [OPTION] run identification number/string

  • run_path::String

  • filename::String: [OPTION] name of the output netcdf file

  • write_restart::Bool: [OPTION] also write restart file if output==true?

  • pkg_version::VersionNumber

  • startdate::Dates.DateTime

  • output_dt::Float64: [OPTION] output frequency, time step [hrs]

  • output_dt_sec::Int64: actual output time step [sec]

  • output_vars::Vector{Symbol}: [OPTION] which variables to output, u, v, vor, div, pres, temp, humid

  • missing_value::Union{Float32, Float64}: [OPTION] missing value to be used in netcdf output

  • compression_level::Int64: [OPTION] lossless compression level; 1=low but fast, 9=high but slow

  • shuffle::Bool: [OPTION] shuffle/bittranspose filter for compression

  • keepbits::SpeedyWeather.Keepbits: [OPTION] mantissa bits to keep for every variable

  • output_every_n_steps::Int64

  • timestep_counter::Int64

  • output_counter::Int64

  • netcdf_file::Union{Nothing, NCDatasets.NCDataset}

  • input_Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}

  • as_matrix::Bool: [OPTION] sort grid points into a matrix (interpolation-free), for OctahedralClenshawGrid, OctaHEALPixGrid only

  • quadrant_rotation::NTuple{4, Int64}

  • matrix_quadrant::NTuple{4, Tuple{Int64, Int64}}

  • output_Grid::Type{<:SpeedyWeather.RingGrids.AbstractFullGrid}: [OPTION] the grid used for output, full grids only

  • nlat_half::Int64: [OPTION] the resolution of the output grid, default: same nlat_half as in the dynamical core

  • nlon::Int64

  • nlat::Int64

  • npoints::Int64

  • nlev::Int64

  • interpolator::SpeedyWeather.RingGrids.AbstractInterpolator

  • u::Matrix{NF} where NF<:Union{Float32, Float64}

  • v::Matrix{NF} where NF<:Union{Float32, Float64}

  • vor::Matrix{NF} where NF<:Union{Float32, Float64}

  • div::Matrix{NF} where NF<:Union{Float32, Float64}

  • temp::Matrix{NF} where NF<:Union{Float32, Float64}

  • pres::Matrix{NF} where NF<:Union{Float32, Float64}

  • humid::Matrix{NF} where NF<:Union{Float32, Float64}

  • precip_cond::Matrix{NF} where NF<:Union{Float32, Float64}

  • precip_conv::Matrix{NF} where NF<:Union{Float32, Float64}

source
SpeedyWeather.PrimitiveDryModelType

The PrimitiveDryModel struct holds all other structs that contain precalculated constants, whether scalars or arrays that do not change throughout model integration.

  • spectral_grid::SpectralGrid: dictates resolution for many other components

  • planet::SpeedyWeather.AbstractPlanet: contains physical and orbital characteristics

  • atmosphere::SpeedyWeather.AbstractAtmosphere

  • initial_conditions::SpeedyWeather.InitialConditions

  • orography::SpeedyWeather.AbstractOrography{NF} where NF<:AbstractFloat

  • land_sea_mask::SpeedyWeather.AbstractLandSeaMask{NF} where NF<:AbstractFloat

  • physics::Bool

  • boundary_layer_drag::SpeedyWeather.BoundaryLayerDrag{NF} where NF<:AbstractFloat

  • temperature_relaxation::SpeedyWeather.TemperatureRelaxation{NF} where NF<:AbstractFloat

  • static_energy_diffusion::SpeedyWeather.VerticalDiffusion{NF} where NF<:AbstractFloat

  • vertical_advection::SpeedyWeather.VerticalAdvection{NF} where NF<:AbstractFloat

  • time_stepping::SpeedyWeather.TimeStepper{NF} where NF<:AbstractFloat

  • spectral_transform::SpectralTransform

  • horizontal_diffusion::SpeedyWeather.HorizontalDiffusion{NF} where NF<:AbstractFloat

  • implicit::SpeedyWeather.AbstractImplicit{NF} where NF<:AbstractFloat

  • geometry::Geometry

  • constants::DynamicsConstants

  • device_setup::SpeedyWeather.DeviceSetup

  • output::SpeedyWeather.AbstractOutputWriter

  • feedback::SpeedyWeather.AbstractFeedback

source
SpeedyWeather.PrimitiveWetModelType

The PrimitiveDryModel struct holds all other structs that contain precalculated constants, whether scalars or arrays that do not change throughout model integration.

  • spectral_grid::SpectralGrid: dictates resolution for many other components

  • planet::SpeedyWeather.AbstractPlanet: contains physical and orbital characteristics

  • atmosphere::SpeedyWeather.AbstractAtmosphere

  • initial_conditions::SpeedyWeather.InitialConditions

  • orography::SpeedyWeather.AbstractOrography{NF} where NF<:AbstractFloat

  • land_sea_mask::SpeedyWeather.AbstractLandSeaMask{NF} where NF<:AbstractFloat

  • physics::Bool

  • thermodynamics::SpeedyWeather.Thermodynamics{NF} where NF<:AbstractFloat

  • boundary_layer_drag::SpeedyWeather.BoundaryLayerDrag{NF} where NF<:AbstractFloat

  • temperature_relaxation::SpeedyWeather.TemperatureRelaxation{NF} where NF<:AbstractFloat

  • static_energy_diffusion::SpeedyWeather.VerticalDiffusion{NF} where NF<:AbstractFloat

  • large_scale_condensation::SpeedyWeather.AbstractCondensation{NF} where NF<:AbstractFloat

  • vertical_advection::SpeedyWeather.VerticalAdvection{NF} where NF<:AbstractFloat

  • time_stepping::SpeedyWeather.TimeStepper{NF} where NF<:AbstractFloat

  • spectral_transform::SpectralTransform

  • horizontal_diffusion::SpeedyWeather.HorizontalDiffusion{NF} where NF<:AbstractFloat

  • implicit::SpeedyWeather.AbstractImplicit{NF} where NF<:AbstractFloat

  • geometry::Geometry

  • constants::DynamicsConstants

  • device_setup::SpeedyWeather.DeviceSetup

  • output::SpeedyWeather.AbstractOutputWriter

  • feedback::SpeedyWeather.AbstractFeedback

source
SpeedyWeather.PrognosticLayerTimestepsType

Collect the n time steps of PrognosticVariablesLayer of an n-step time integration (leapfrog=2) into a single struct.

  • timesteps::Array{SpeedyWeather.PrognosticVariablesLayer{NF}, 1} where NF<:AbstractFloat

.

source
SpeedyWeather.PrognosticSurfaceTimestepsType

Collect the n time steps of PrognosticVariablesSurface of an n-step time integration (leapfrog=2) into a single struct.

  • timesteps::Array{SpeedyWeather.PrognosticVariablesSurface{NF}, 1} where NF<:AbstractFloat

.

source
SpeedyWeather.PrognosticVariablesLayerType

A layer of the prognostic variables in spectral space.

  • trunc::Int64: Spectral resolution as max degree of spherical harmonics

  • vor::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: Vorticity of horizontal wind field [1/s]

  • div::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: Divergence of horizontal wind field [1/s]

  • temp::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: Absolute temperature [K]

  • humid::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: Specific humidity [kg/kg]

source
SpeedyWeather.PrognosticVariablesSurfaceType

The spectral and gridded prognostic variables at the surface.

  • trunc::Int64: Spectral resolution as max degree of spherical harmonics

  • pres::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: log of surface pressure [log(Pa)] for PrimitiveEquation, interface displacement [m] for ShallowWaterModel

source
SpeedyWeather.RandomWavesType

Parameters for random initial conditions for the interface displacement η in the shallow water equations.

  • A::Float64

  • lmin::Int64

  • lmax::Int64

source
SpeedyWeather.ShallowWaterModelType

The ShallowWaterModel struct holds all other structs that contain precalculated constants, whether scalars or arrays that do not change throughout model integration.

  • spectral_grid::SpectralGrid: dictates resolution for many other components

  • planet::SpeedyWeather.AbstractPlanet: contains physical and orbital characteristics

  • atmosphere::SpeedyWeather.AbstractAtmosphere

  • forcing::SpeedyWeather.AbstractForcing{NF} where NF<:AbstractFloat

  • drag::SpeedyWeather.AbstractDrag{NF} where NF<:AbstractFloat

  • initial_conditions::SpeedyWeather.InitialConditions

  • orography::SpeedyWeather.AbstractOrography{NF} where NF<:AbstractFloat

  • time_stepping::SpeedyWeather.TimeStepper{NF} where NF<:AbstractFloat

  • spectral_transform::SpectralTransform

  • horizontal_diffusion::SpeedyWeather.HorizontalDiffusion{NF} where NF<:AbstractFloat

  • implicit::SpeedyWeather.AbstractImplicit{NF} where NF<:AbstractFloat

  • geometry::Geometry

  • constants::DynamicsConstants

  • device_setup::SpeedyWeather.DeviceSetup

  • output::SpeedyWeather.AbstractOutputWriter

  • feedback::SpeedyWeather.AbstractFeedback

source
SpeedyWeather.SimulationType

Simulation is a container struct to be used with run!(::Simulation). It contains

  • prognostic_variables::PrognosticVariables: define the current state of the model

  • diagnostic_variables::DiagnosticVariables: contain the tendencies and auxiliary arrays to compute them

  • model::SpeedyWeather.ModelSetup: all parameters, constant at runtime

source
SpeedyWeather.SpectralGridType

Defines the horizontal spectral resolution and corresponding grid and the vertical coordinate for SpeedyWeather.jl. Options are

  • NF::Type{<:AbstractFloat}: number format used throughout the model

  • trunc::Int64: horizontal resolution as the maximum degree of spherical harmonics

  • Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}: horizontal grid used for calculations in grid-point space

  • dealiasing::Float64: how to match spectral with grid resolution: dealiasing factor, 1=linear, 2=quadratic, 3=cubic grid

  • radius::Float64: radius of the sphere [m]

  • nlat_half::Int64: number of latitude rings on one hemisphere (Equator incl)

  • npoints::Int64: total number of grid points in the horizontal

  • nlev::Int64: number of vertical levels

  • vertical_coordinates::SpeedyWeather.VerticalCoordinates: coordinates used to discretize the vertical

nlat_half and npoints should not be chosen but are derived from trunc, Grid and dealiasing.

source
SpeedyWeather.SpeedyCondensationType

Large scale condensation as in Fortran SPEEDY with default values from therein.

  • nlev::Int64: number of vertical levels

  • threshold_boundary_layer::Float64: Relative humidity threshold for boundary layer

  • threshold_range::Float64: Vertical range of relative humidity threshold

  • threshold_max::Float64: Maximum relative humidity threshold [1]

  • time_scale::Float64: Relaxation time for humidity [hrs]

  • n_stratosphere_levels::Base.RefValue{Int64}

  • humid_tend_max::Vector{NF} where NF<:AbstractFloat

  • relative_threshold::Vector{NF} where NF<:AbstractFloat

source
SpeedyWeather.JablonowskiRelaxationMethod
JablonowskiRelaxation(SG::SpectralGrid; kwargs...) -> Any
+

create a JablonowskiRelaxation temperature relaxation with arrays allocated given spectral_grid

source
SpeedyWeather.JetStreamForcingType

Forcing term for the Barotropic or ShallowWaterModel with an idealised jet stream similar to the initial conditions from Galewsky, 2004, but mirrored for both hemispheres.

  • nlat::Int64: Number of latitude rings

  • latitude::Float64: jet latitude [˚N]

  • width::Float64: jet width [˚], default ≈ 19.29˚

  • speed::Float64: jet speed scale [m/s]

  • time_scale::Float64: time scale [days]

  • amplitude::Vector: precomputed amplitude vector [m/s²]

source
SpeedyWeather.KeepbitsType

Number of mantissa bits to keep for each prognostic variable when compressed for netCDF and .jld2 data output.

  • u::Int64

  • v::Int64

  • vor::Int64

  • div::Int64

  • temp::Int64

  • pres::Int64

  • humid::Int64

  • precip_cond::Int64

  • precip_conv::Int64

source
SpeedyWeather.LandSeaMaskType

Land-sea mask, fractional, read from file.

  • path::String: path to the folder containing the land-sea mask file, pkg path default

  • file::String: filename of land sea mask

  • file_Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}: Grid the land-sea mask file comes on

  • land_sea_mask::SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat: Land-sea mask [1] on grid-point space. Land=1, sea=0, land-area fraction in between.

source
SpeedyWeather.LandSeaMaskMethod
LandSeaMask(spectral_grid::SpectralGrid; kwargs...) -> Any
+

Generator function pulling the resolution information from spectral_grid.

source
SpeedyWeather.LeapfrogType

Leapfrog time stepping defined by the following fields

  • trunc::Int64: spectral resolution (max degree of spherical harmonics)

  • Δt_at_T31::Float64: time step in minutes for T31, scale linearly to trunc

  • radius::Any: radius of sphere [m], used for scaling

  • robert_filter::Any: Robert (1966) time filter coefficeint to suppress comput. mode

  • williams_filter::Any: Williams time filter (Amezcua 2011) coefficient for 3rd order acc

  • Δt_sec::Int64: time step Δt [s] at specified resolution

  • Δt::Any: time step Δt [s/m] at specified resolution, scaled by 1/radius

  • Δt_hrs::Float64: convert time step Δt from minutes to hours

source
SpeedyWeather.LeapfrogMethod
Leapfrog(spectral_grid::SpectralGrid; kwargs...) -> Any
+

Generator function for a Leapfrog struct using spectral_grid for the resolution information.

source
SpeedyWeather.LinearDragType

Linear boundary layer drag Following Held and Suarez, 1996 BAMS

  • σb::Float64

  • time_scale::Float64

  • nlev::Int64

  • drag_coefs::Vector{NF} where NF<:AbstractFloat

source
SpeedyWeather.MagnusCoefsType

Parameters for computing saturation vapour pressure using the August-Roche-Magnus formula,

eᵢ(T) = e₀ * exp(Cᵢ * (T - T₀) / (T - Tᵢ)),

where T is in Kelvin and i = 1,2 for saturation with respect to water and ice, respectively.

  • e₀::AbstractFloat: Saturation vapour pressure at 0°C [Pa]

  • T₀::AbstractFloat: 0°C in Kelvin

  • T₁::AbstractFloat

  • T₂::AbstractFloat

  • C₁::AbstractFloat

  • C₂::AbstractFloat

source
SpeedyWeather.NoOrographyType

Orography with zero height in orography and zero surface geopotential geopot_surf.

  • orography::SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat: height [m] on grid-point space.

  • geopot_surf::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: surface geopotential, height*gravity [m²/s²]

source
SpeedyWeather.NoOrographyMethod
NoOrography(spectral_grid::SpectralGrid) -> NoOrography
+

Generator function pulling the resolution information from spectral_grid.

source
SpeedyWeather.OutputWriterType

NetCDF output writer. Contains all output options and auxiliary fields for output interpolation. To be initialised with OutputWriter(::SpectralGrid,::Type{<:ModelSetup},kwargs...) to pass on the resolution information and the model type which chooses which variables to output. Options include

  • spectral_grid::SpectralGrid

  • output::Bool

  • path::String: [OPTION] path to output folder, run_???? will be created within

  • id::String: [OPTION] run identification number/string

  • run_path::String

  • filename::String: [OPTION] name of the output netcdf file

  • write_restart::Bool: [OPTION] also write restart file if output==true?

  • pkg_version::VersionNumber

  • startdate::Dates.DateTime

  • output_dt::Float64: [OPTION] output frequency, time step [hrs]

  • output_dt_sec::Int64: actual output time step [sec]

  • output_vars::Vector{Symbol}: [OPTION] which variables to output, u, v, vor, div, pres, temp, humid

  • missing_value::Union{Float32, Float64}: [OPTION] missing value to be used in netcdf output

  • compression_level::Int64: [OPTION] lossless compression level; 1=low but fast, 9=high but slow

  • shuffle::Bool: [OPTION] shuffle/bittranspose filter for compression

  • keepbits::SpeedyWeather.Keepbits: [OPTION] mantissa bits to keep for every variable

  • output_every_n_steps::Int64

  • timestep_counter::Int64

  • output_counter::Int64

  • netcdf_file::Union{Nothing, NCDatasets.NCDataset}

  • input_Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}

  • as_matrix::Bool: [OPTION] sort grid points into a matrix (interpolation-free), for OctahedralClenshawGrid, OctaHEALPixGrid only

  • quadrant_rotation::NTuple{4, Int64}

  • matrix_quadrant::NTuple{4, Tuple{Int64, Int64}}

  • output_Grid::Type{<:SpeedyWeather.RingGrids.AbstractFullGrid}: [OPTION] the grid used for output, full grids only

  • nlat_half::Int64: [OPTION] the resolution of the output grid, default: same nlat_half as in the dynamical core

  • nlon::Int64

  • nlat::Int64

  • npoints::Int64

  • nlev::Int64

  • interpolator::SpeedyWeather.RingGrids.AbstractInterpolator

  • u::Matrix{NF} where NF<:Union{Float32, Float64}

  • v::Matrix{NF} where NF<:Union{Float32, Float64}

  • vor::Matrix{NF} where NF<:Union{Float32, Float64}

  • div::Matrix{NF} where NF<:Union{Float32, Float64}

  • temp::Matrix{NF} where NF<:Union{Float32, Float64}

  • pres::Matrix{NF} where NF<:Union{Float32, Float64}

  • humid::Matrix{NF} where NF<:Union{Float32, Float64}

  • precip_cond::Matrix{NF} where NF<:Union{Float32, Float64}

  • precip_conv::Matrix{NF} where NF<:Union{Float32, Float64}

source
SpeedyWeather.PrimitiveDryModelType

The PrimitiveDryModel struct holds all other structs that contain precalculated constants, whether scalars or arrays that do not change throughout model integration.

  • spectral_grid::SpectralGrid: dictates resolution for many other components

  • planet::SpeedyWeather.AbstractPlanet: contains physical and orbital characteristics

  • atmosphere::SpeedyWeather.AbstractAtmosphere

  • initial_conditions::SpeedyWeather.InitialConditions

  • orography::SpeedyWeather.AbstractOrography{NF} where NF<:AbstractFloat

  • land_sea_mask::SpeedyWeather.AbstractLandSeaMask{NF} where NF<:AbstractFloat

  • physics::Bool

  • boundary_layer_drag::SpeedyWeather.BoundaryLayerDrag{NF} where NF<:AbstractFloat

  • temperature_relaxation::SpeedyWeather.TemperatureRelaxation{NF} where NF<:AbstractFloat

  • static_energy_diffusion::SpeedyWeather.VerticalDiffusion{NF} where NF<:AbstractFloat

  • vertical_advection::SpeedyWeather.VerticalAdvection{NF} where NF<:AbstractFloat

  • time_stepping::SpeedyWeather.TimeStepper{NF} where NF<:AbstractFloat

  • spectral_transform::SpectralTransform

  • horizontal_diffusion::SpeedyWeather.HorizontalDiffusion{NF} where NF<:AbstractFloat

  • implicit::SpeedyWeather.AbstractImplicit{NF} where NF<:AbstractFloat

  • geometry::Geometry

  • constants::DynamicsConstants

  • device_setup::SpeedyWeather.DeviceSetup

  • output::SpeedyWeather.AbstractOutputWriter

  • feedback::SpeedyWeather.AbstractFeedback

source
SpeedyWeather.PrimitiveWetModelType

The PrimitiveDryModel struct holds all other structs that contain precalculated constants, whether scalars or arrays that do not change throughout model integration.

  • spectral_grid::SpectralGrid: dictates resolution for many other components

  • planet::SpeedyWeather.AbstractPlanet: contains physical and orbital characteristics

  • atmosphere::SpeedyWeather.AbstractAtmosphere

  • initial_conditions::SpeedyWeather.InitialConditions

  • orography::SpeedyWeather.AbstractOrography{NF} where NF<:AbstractFloat

  • land_sea_mask::SpeedyWeather.AbstractLandSeaMask{NF} where NF<:AbstractFloat

  • physics::Bool

  • thermodynamics::SpeedyWeather.Thermodynamics{NF} where NF<:AbstractFloat

  • boundary_layer_drag::SpeedyWeather.BoundaryLayerDrag{NF} where NF<:AbstractFloat

  • temperature_relaxation::SpeedyWeather.TemperatureRelaxation{NF} where NF<:AbstractFloat

  • static_energy_diffusion::SpeedyWeather.VerticalDiffusion{NF} where NF<:AbstractFloat

  • large_scale_condensation::SpeedyWeather.AbstractCondensation{NF} where NF<:AbstractFloat

  • vertical_advection::SpeedyWeather.VerticalAdvection{NF} where NF<:AbstractFloat

  • time_stepping::SpeedyWeather.TimeStepper{NF} where NF<:AbstractFloat

  • spectral_transform::SpectralTransform

  • horizontal_diffusion::SpeedyWeather.HorizontalDiffusion{NF} where NF<:AbstractFloat

  • implicit::SpeedyWeather.AbstractImplicit{NF} where NF<:AbstractFloat

  • geometry::Geometry

  • constants::DynamicsConstants

  • device_setup::SpeedyWeather.DeviceSetup

  • output::SpeedyWeather.AbstractOutputWriter

  • feedback::SpeedyWeather.AbstractFeedback

source
SpeedyWeather.PrognosticLayerTimestepsType

Collect the n time steps of PrognosticVariablesLayer of an n-step time integration (leapfrog=2) into a single struct.

  • timesteps::Array{SpeedyWeather.PrognosticVariablesLayer{NF}, 1} where NF<:AbstractFloat

.

source
SpeedyWeather.PrognosticSurfaceTimestepsType

Collect the n time steps of PrognosticVariablesSurface of an n-step time integration (leapfrog=2) into a single struct.

  • timesteps::Array{SpeedyWeather.PrognosticVariablesSurface{NF}, 1} where NF<:AbstractFloat

.

source
SpeedyWeather.PrognosticVariablesLayerType

A layer of the prognostic variables in spectral space.

  • trunc::Int64: Spectral resolution as max degree of spherical harmonics

  • vor::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: Vorticity of horizontal wind field [1/s]

  • div::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: Divergence of horizontal wind field [1/s]

  • temp::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: Absolute temperature [K]

  • humid::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: Specific humidity [kg/kg]

source
SpeedyWeather.PrognosticVariablesSurfaceType

The spectral and gridded prognostic variables at the surface.

  • trunc::Int64: Spectral resolution as max degree of spherical harmonics

  • pres::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: log of surface pressure [log(Pa)] for PrimitiveEquation, interface displacement [m] for ShallowWaterModel

source
SpeedyWeather.RandomWavesType

Parameters for random initial conditions for the interface displacement η in the shallow water equations.

  • A::Float64

  • lmin::Int64

  • lmax::Int64

source
SpeedyWeather.ShallowWaterModelType

The ShallowWaterModel struct holds all other structs that contain precalculated constants, whether scalars or arrays that do not change throughout model integration.

  • spectral_grid::SpectralGrid: dictates resolution for many other components

  • planet::SpeedyWeather.AbstractPlanet: contains physical and orbital characteristics

  • atmosphere::SpeedyWeather.AbstractAtmosphere

  • forcing::SpeedyWeather.AbstractForcing{NF} where NF<:AbstractFloat

  • drag::SpeedyWeather.AbstractDrag{NF} where NF<:AbstractFloat

  • initial_conditions::SpeedyWeather.InitialConditions

  • orography::SpeedyWeather.AbstractOrography{NF} where NF<:AbstractFloat

  • time_stepping::SpeedyWeather.TimeStepper{NF} where NF<:AbstractFloat

  • spectral_transform::SpectralTransform

  • horizontal_diffusion::SpeedyWeather.HorizontalDiffusion{NF} where NF<:AbstractFloat

  • implicit::SpeedyWeather.AbstractImplicit{NF} where NF<:AbstractFloat

  • geometry::Geometry

  • constants::DynamicsConstants

  • device_setup::SpeedyWeather.DeviceSetup

  • output::SpeedyWeather.AbstractOutputWriter

  • feedback::SpeedyWeather.AbstractFeedback

source
SpeedyWeather.SimulationType

Simulation is a container struct to be used with run!(::Simulation). It contains

  • prognostic_variables::PrognosticVariables: define the current state of the model

  • diagnostic_variables::DiagnosticVariables: contain the tendencies and auxiliary arrays to compute them

  • model::SpeedyWeather.ModelSetup: all parameters, constant at runtime

source
SpeedyWeather.SpectralGridType

Defines the horizontal spectral resolution and corresponding grid and the vertical coordinate for SpeedyWeather.jl. Options are

  • NF::Type{<:AbstractFloat}: number format used throughout the model

  • trunc::Int64: horizontal resolution as the maximum degree of spherical harmonics

  • Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid}: horizontal grid used for calculations in grid-point space

  • dealiasing::Float64: how to match spectral with grid resolution: dealiasing factor, 1=linear, 2=quadratic, 3=cubic grid

  • radius::Float64: radius of the sphere [m]

  • nlat_half::Int64: number of latitude rings on one hemisphere (Equator incl)

  • npoints::Int64: total number of grid points in the horizontal

  • nlev::Int64: number of vertical levels

  • vertical_coordinates::SpeedyWeather.VerticalCoordinates: coordinates used to discretize the vertical

nlat_half and npoints should not be chosen but are derived from trunc, Grid and dealiasing.

source
SpeedyWeather.SpeedyCondensationType

Large scale condensation as in Fortran SPEEDY with default values from therein.

  • nlev::Int64: number of vertical levels

  • threshold_boundary_layer::Float64: Relative humidity threshold for boundary layer

  • threshold_range::Float64: Vertical range of relative humidity threshold

  • threshold_max::Float64: Maximum relative humidity threshold [1]

  • time_scale::Float64: Relaxation time for humidity [hrs]

  • n_stratosphere_levels::Base.RefValue{Int64}

  • humid_tend_max::Vector{NF} where NF<:AbstractFloat

  • relative_threshold::Vector{NF} where NF<:AbstractFloat

source
SpeedyWeather.SpeedyTransforms.SpectralTransformMethod
SpectralTransform(
     spectral_grid::SpectralGrid;
     recompute_legendre,
     one_more_degree,
     kwargs...
 ) -> SpectralTransform
-

Generator function for a SpectralTransform struct pulling in parameters from a SpectralGrid struct.

source
SpeedyWeather.StartFromFileType

Restart from a previous SpeedyWeather.jl simulation via the restart file restart.jld2 Applies interpolation in the horizontal but not in the vertical. restart.jld2 is identified by

  • path::String: path for restart file

  • id::Union{Int64, String}: run_id of restart file in run_????/restart.jld2

source
SpeedyWeather.StartWithRandomVorticityType

Start with random vorticity as initial conditions

  • power::Float64: Power of the spectral distribution k^power

  • amplitude::Float64: (approximate) amplitude in [1/s], used as standard deviation of spherical harmonic coefficients

source
SpeedyWeather.StaticEnergyDiffusionType

Diffusion of dry static energy: A relaxation towards a reference gradient of static energy wrt to geopotential, see Fortran SPEEDY documentation.

  • time_scale::Float64: time scale [hrs] for strength

  • static_energy_lapse_rate::Float64: [1] ∂SE/∂Φ, vertical gradient of static energy SE with geopotential Φ

  • Fstar::Base.RefValue{NF} where NF<:AbstractFloat

source
SpeedyWeather.TendenciesType
Tendencies{Grid<:AbstractGrid,NF<:AbstractFloat}

Struct holding the tendencies of the prognostic spectral variables for a given layer.

source
SpeedyWeather.ZonalJetType

Create a struct that contains all parameters for the Galewsky et al, 2004 zonal jet intitial conditions for the shallow water model. Default values as in Galewsky.

  • latitude::Float64: jet latitude [˚N]

  • width::Float64: jet width [˚], default ≈ 19.29˚

  • umax::Float64: jet maximum velocity [m/s]

  • perturb_lat::Float64: perturbation latitude [˚N], position in jet by default

  • perturb_lon::Float64: perturbation longitude [˚E]

  • perturb_xwidth::Float64: perturbation zonal extent [˚], default ≈ 19.1˚

  • perturb_ywidth::Float64: perturbation meridinoal extent [˚], default ≈ 3.8˚

  • perturb_height::Float64: perturbation amplitude [m]

source
SpeedyWeather.ZonalRidgeType

Zonal ridge orography after Jablonowski and Williamson, 2006.

  • η₀::Float64: conversion from σ to Jablonowski's ηᵥ-coordinates

  • u₀::Float64: max amplitude of zonal wind [m/s] that scales orography height

  • orography::SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat: height [m] on grid-point space.

  • geopot_surf::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: surface geopotential, height*gravity [m²/s²]

source
SpeedyWeather.ZonalRidgeMethod
ZonalRidge(spectral_grid::SpectralGrid; kwargs...) -> Any
-

Generator function pulling the resolution information from spectral_grid.

source
SpeedyWeather.ZonalWindType

Create a struct that contains all parameters for the Jablonowski and Williamson, 2006 intitial conditions for the primitive equation model. Default values as in Jablonowski.

  • η₀::Float64: conversion from σ to Jablonowski's ηᵥ-coordinates

  • u₀::Float64: max amplitude of zonal wind [m/s]

  • perturb_lat::Float64: perturbation centred at [˚N]

  • perturb_lon::Float64: perturbation centred at [˚E]

  • perturb_uₚ::Float64: perturbation strength [m/s]

  • perturb_radius::Float64: radius of Gaussian perturbation in units of Earth's radius [1]

  • ΔT::Float64: temperature difference used for stratospheric lapse rate [K], Jablonowski uses ΔT = 4.8e5 [K]

  • Tmin::Float64: minimum temperature [K] of profile

  • pressure_on_orography::Bool: initialize pressure given the atmosphere.lapse_rate on orography?

source
Base.copy!Method
copy!(progn_new::PrognosticVariables, progn_old::PrognosticVariables)

Copies entries of progn_old into progn_new. Only copies those variables that are present in the model of both progn_new and progn_old.

source
SpeedyWeather.DeviceMethod
Device()

Return default used device for internal purposes, either CPUDevice or GPUDevice if a GPU is available.

source
SpeedyWeather.DeviceArrayMethod
DeviceArray(device::AbstractDevice, x)

Adapts x to a CuArray when device<:GPUDevice is used, otherwise a regular Array. Uses adapt, thus also can return SubArrays etc.

source
SpeedyWeather.DeviceArrayNotAdaptMethod
DeviceArrayNotAdapt(device::AbstractDevice, x)

Returns a CuArray when device<:GPUDevice is used, otherwise a regular Array. Doesn't uses adapt, therefore always returns CuArray/Array

source
SpeedyWeather.StartFromFileType

Restart from a previous SpeedyWeather.jl simulation via the restart file restart.jld2 Applies interpolation in the horizontal but not in the vertical. restart.jld2 is identified by

  • path::String: path for restart file

  • id::Union{Int64, String}: run_id of restart file in run_????/restart.jld2

source
SpeedyWeather.StartWithRandomVorticityType

Start with random vorticity as initial conditions

  • power::Float64: Power of the spectral distribution k^power

  • amplitude::Float64: (approximate) amplitude in [1/s], used as standard deviation of spherical harmonic coefficients

source
SpeedyWeather.StaticEnergyDiffusionType

Diffusion of dry static energy: A relaxation towards a reference gradient of static energy wrt to geopotential, see Fortran SPEEDY documentation.

  • time_scale::Float64: time scale [hrs] for strength

  • static_energy_lapse_rate::Float64: [1] ∂SE/∂Φ, vertical gradient of static energy SE with geopotential Φ

  • Fstar::Base.RefValue{NF} where NF<:AbstractFloat

source
SpeedyWeather.TendenciesType
Tendencies{Grid<:AbstractGrid,NF<:AbstractFloat}

Struct holding the tendencies of the prognostic spectral variables for a given layer.

source
SpeedyWeather.ZonalJetType

Create a struct that contains all parameters for the Galewsky et al, 2004 zonal jet intitial conditions for the shallow water model. Default values as in Galewsky.

  • latitude::Float64: jet latitude [˚N]

  • width::Float64: jet width [˚], default ≈ 19.29˚

  • umax::Float64: jet maximum velocity [m/s]

  • perturb_lat::Float64: perturbation latitude [˚N], position in jet by default

  • perturb_lon::Float64: perturbation longitude [˚E]

  • perturb_xwidth::Float64: perturbation zonal extent [˚], default ≈ 19.1˚

  • perturb_ywidth::Float64: perturbation meridinoal extent [˚], default ≈ 3.8˚

  • perturb_height::Float64: perturbation amplitude [m]

source
SpeedyWeather.ZonalRidgeType

Zonal ridge orography after Jablonowski and Williamson, 2006.

  • η₀::Float64: conversion from σ to Jablonowski's ηᵥ-coordinates

  • u₀::Float64: max amplitude of zonal wind [m/s] that scales orography height

  • orography::SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat: height [m] on grid-point space.

  • geopot_surf::LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat: surface geopotential, height*gravity [m²/s²]

source
SpeedyWeather.ZonalRidgeMethod
ZonalRidge(spectral_grid::SpectralGrid; kwargs...) -> Any
+

Generator function pulling the resolution information from spectral_grid.

source
SpeedyWeather.ZonalWindType

Create a struct that contains all parameters for the Jablonowski and Williamson, 2006 intitial conditions for the primitive equation model. Default values as in Jablonowski.

  • η₀::Float64: conversion from σ to Jablonowski's ηᵥ-coordinates

  • u₀::Float64: max amplitude of zonal wind [m/s]

  • perturb_lat::Float64: perturbation centred at [˚N]

  • perturb_lon::Float64: perturbation centred at [˚E]

  • perturb_uₚ::Float64: perturbation strength [m/s]

  • perturb_radius::Float64: radius of Gaussian perturbation in units of Earth's radius [1]

  • ΔT::Float64: temperature difference used for stratospheric lapse rate [K], Jablonowski uses ΔT = 4.8e5 [K]

  • Tmin::Float64: minimum temperature [K] of profile

  • pressure_on_orography::Bool: initialize pressure given the atmosphere.lapse_rate on orography?

source
Base.copy!Method
copy!(progn_new::PrognosticVariables, progn_old::PrognosticVariables)

Copies entries of progn_old into progn_new. Only copies those variables that are present in the model of both progn_new and progn_old.

source
SpeedyWeather.DeviceMethod
Device()

Return default used device for internal purposes, either CPUDevice or GPUDevice if a GPU is available.

source
SpeedyWeather.DeviceArrayMethod
DeviceArray(device::AbstractDevice, x)

Adapts x to a CuArray when device<:GPUDevice is used, otherwise a regular Array. Uses adapt, thus also can return SubArrays etc.

source
SpeedyWeather.DeviceArrayNotAdaptMethod
DeviceArrayNotAdapt(device::AbstractDevice, x)

Returns a CuArray when device<:GPUDevice is used, otherwise a regular Array. Doesn't uses adapt, therefore always returns CuArray/Array

source
SpeedyWeather.SpeedyTransforms.gridded!Method
gridded!(
     diagn::DiagnosticVariables,
     progn::PrognosticVariables,
     lf::Int64,
     model::SpeedyWeather.ModelSetup
 )
-

Propagate the spectral state of progn to diagn using time step/leapfrog index lf. Function barrier that calls gridded! for the respective model.

source
SpeedyWeather.SpeedyTransforms.gridded!Method
gridded!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     progn::SpeedyWeather.PrognosticLayerTimesteps,
     lf::Int64,
     model::Barotropic
 )
-

Propagate the spectral state of the prognostic variables progn to the diagnostic variables in diagn for the barotropic vorticity model. Updates grid vorticity, spectral stream function and spectral and grid velocities u,v.

source
SpeedyWeather.SpeedyTransforms.gridded!Method
gridded!(
+

Propagate the spectral state of the prognostic variables progn to the diagnostic variables in diagn for the barotropic vorticity model. Updates grid vorticity, spectral stream function and spectral and grid velocities u,v.

source
SpeedyWeather.SpeedyTransforms.gridded!Method
gridded!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     progn::SpeedyWeather.PrognosticLayerTimesteps,
     lf::Int64,
     model::PrimitiveEquation
 )
-

Propagate the spectral state of the prognostic variables progn to the diagnostic variables in diagn for primitive equation models. Updates grid vorticity, grid divergence, grid temperature, pressure (pres_grid) and the velocities u,v.

source
SpeedyWeather.SpeedyTransforms.gridded!Method
gridded!(
+

Propagate the spectral state of the prognostic variables progn to the diagnostic variables in diagn for primitive equation models. Updates grid vorticity, grid divergence, grid temperature, pressure (pres_grid) and the velocities u,v.

source
SpeedyWeather.SpeedyTransforms.gridded!Method
gridded!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     progn::SpeedyWeather.PrognosticLayerTimesteps,
     lf::Int64,
     model::ShallowWater
 )
-

Propagate the spectral state of the prognostic variables progn to the diagnostic variables in diagn for the shallow water model. Updates grid vorticity, grid divergence, grid interface displacement (pres_grid) and the velocities u,v.

source
SpeedyWeather.bernoulli_potential!Method
bernoulli_potential!(
+

Propagate the spectral state of the prognostic variables progn to the diagnostic variables in diagn for the shallow water model. Updates grid vorticity, grid divergence, grid interface displacement (pres_grid) and the velocities u,v.

source
SpeedyWeather.bernoulli_potential!Method
bernoulli_potential!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer{NF, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF},
     S::SpectralTransform
 ) -> LowerTriangularMatrix{Complex{NF}} where NF
-

Computes the Laplace operator ∇² of the Bernoulli potential B in spectral space.

  1. computes the kinetic energy KE = ½(u²+v²) on the grid
  2. transforms KE to spectral space
  3. adds geopotential for the Bernoulli potential in spectral space
  4. takes the Laplace operator.

This version is used for both ShallowWater and PrimitiveEquation, only the geopotential calculation in geopotential! differs.

source
SpeedyWeather.boundary_layer_drag!Method
boundary_layer_drag!(
+

Computes the Laplace operator ∇² of the Bernoulli potential B in spectral space.

  1. computes the kinetic energy KE = ½(u²+v²) on the grid
  2. transforms KE to spectral space
  3. adds geopotential for the Bernoulli potential in spectral space
  4. takes the Laplace operator.

This version is used for both ShallowWater and PrimitiveEquation, only the geopotential calculation in geopotential! differs.

source
SpeedyWeather.boundary_layer_drag!Method
boundary_layer_drag!(
     column::ColumnVariables,
     scheme::LinearDrag
 )
-

Compute tendency for boundary layer drag of a column and add to its tendencies fields

source
SpeedyWeather.coriolisMethod
coriolis(
     grid::SpeedyWeather.RingGrids.AbstractGrid;
     rotation
 ) -> Any
-

Return the Coriolis parameter f on a grid like grid on a planet of ratation [1/s]. Default rotation of Earth.

source
SpeedyWeather.coriolisMethod
coriolis(
+

Return the Coriolis parameter f on a grid like grid on a planet of ratation [1/s]. Default rotation of Earth.

source
SpeedyWeather.coriolisMethod
coriolis(
     grid::SpeedyWeather.RingGrids.AbstractGrid;
     rotation
 ) -> Any
-

Return the Coriolis parameter f on the grid Grid of resolution nlat_half on a planet of ratation [1/s]. Default rotation of Earth.

source
SpeedyWeather.create_output_folderMethod
create_output_folder(
+

Return the Coriolis parameter f on the grid Grid of resolution nlat_half on a planet of ratation [1/s]. Default rotation of Earth.

source
SpeedyWeather.create_output_folderMethod
create_output_folder(
     path::String,
     id::Union{Int64, String}
 ) -> String
-

Creates a new folder run_* with the identification id. Also returns the full path run_path of that folder.

source
SpeedyWeather.default_sigma_coordinatesMethod
default_sigma_coordinates(nlev::Integer) -> Any
-

Vertical sigma coordinates defined by their nlev+1 half levels σ_levels_half. Sigma coordinates are fraction of surface pressure (p/p0) and are sorted from top (stratosphere) to bottom (surface). The first half level is at 0 the last at 1. Evaluate a generalised logistic function with coefficients in P for the distribution of values in between. Default coefficients follow the L31 configuration historically used at ECMWF.

source
SpeedyWeather.drag!Method
drag!(
+

Creates a new folder run_* with the identification id. Also returns the full path run_path of that folder.

source
SpeedyWeather.default_sigma_coordinatesMethod
default_sigma_coordinates(nlev::Integer) -> Any
+

Vertical sigma coordinates defined by their nlev+1 half levels σ_levels_half. Sigma coordinates are fraction of surface pressure (p/p0) and are sorted from top (stratosphere) to bottom (surface). The first half level is at 0 the last at 1. Evaluate a generalised logistic function with coefficients in P for the distribution of values in between. Default coefficients follow the L31 configuration historically used at ECMWF.

source
SpeedyWeather.drag!Method
drag!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     drag::QuadraticDrag{NF},
     C::DynamicsConstants
 )
-

Quadratic drag for the momentum equations.

F = -c_D/H*|(u,v)|*(u,v)

with c_D the non-dimensional drag coefficient as defined in drag::QuadraticDrag. Layer thickness H is taken from the Atmosphere via DynamicsConstants, as defined for the ShallowWaterModel.

source
SpeedyWeather.dry_static_energy!Method
dry_static_energy!(
+

Quadratic drag for the momentum equations.

F = -c_D/H*|(u,v)|*(u,v)

with c_D the non-dimensional drag coefficient as defined in drag::QuadraticDrag. Layer thickness H is taken from the Atmosphere via DynamicsConstants, as defined for the ShallowWaterModel.

source
SpeedyWeather.dry_static_energy!Method
dry_static_energy!(
     column::ColumnVariables,
     constants::DynamicsConstants
 )
-

Compute the dry static energy SE = cₚT + Φ (latent heat times temperature plus geopotential) for the column.

source
SpeedyWeather.dynamics_tendencies!Function
dynamics_tendencies!(
     diagn::DiagnosticVariables,
     progn::PrognosticVariables,
     model::PrimitiveEquation
@@ -107,25 +107,25 @@
     model::PrimitiveEquation,
     lf::Int64
 ) -> Any
-

Calculate all tendencies for the PrimitiveEquation model (wet or dry).

source
SpeedyWeather.dynamics_tendencies!Method
dynamics_tendencies!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     time::Dates.DateTime,
     model::Barotropic
 )
-

Calculate all tendencies for the BarotropicModel.

source
SpeedyWeather.dynamics_tendencies!Method
dynamics_tendencies!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     surface::SpeedyWeather.SurfaceVariables,
     pres::LowerTriangularMatrix,
     time::Dates.DateTime,
     model::ShallowWater
 )
-

Calculate all tendencies for the ShallowWaterModel.

source
SpeedyWeather.first_timesteps!Method
first_timesteps!(
     progn::PrognosticVariables,
     diagn::DiagnosticVariables,
     model::SpeedyWeather.ModelSetup,
     output::SpeedyWeather.AbstractOutputWriter
 ) -> typeof(time)
-

Performs the first two initial time steps (Euler forward, unfiltered leapfrog) to populate the prognostic variables with two time steps (t=0,Δt) that can then be used in the normal leap frogging.

source
SpeedyWeather.flux_divergence!Method
flux_divergence!(
+

Performs the first two initial time steps (Euler forward, unfiltered leapfrog) to populate the prognostic variables with two time steps (t=0,Δt) that can then be used in the normal leap frogging.

source
SpeedyWeather.flux_divergence!Method
flux_divergence!(
     A_tend::LowerTriangularMatrix{Complex{NF}},
     A_grid::SpeedyWeather.RingGrids.AbstractGrid{NF},
     diagn::SpeedyWeather.DiagnosticVariablesLayer{NF, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF},
@@ -134,27 +134,27 @@
     add,
     flipsign
 )
-

Computes ∇⋅((u,v)*A) with the option to add/overwrite A_tend and to flip_sign of the flux divergence by doing so.

  • A_tend = ∇⋅((u,v)*A) for add=false, flip_sign=false
  • A_tend = -∇⋅((u,v)*A) for add=false, flip_sign=true
  • A_tend += ∇⋅((u,v)*A) for add=true, flip_sign=false
  • A_tend -= ∇⋅((u,v)*A) for add=true, flip_sign=true
source
SpeedyWeather.fluxes_to_tendencies!Method
fluxes_to_tendencies!(
+

Computes ∇⋅((u,v)*A) with the option to add/overwrite A_tend and to flip_sign of the flux divergence by doing so.

  • A_tend = ∇⋅((u,v)*A) for add=false, flip_sign=false
  • A_tend = -∇⋅((u,v)*A) for add=false, flip_sign=true
  • A_tend += ∇⋅((u,v)*A) for add=true, flip_sign=false
  • A_tend -= ∇⋅((u,v)*A) for add=true, flip_sign=true
source
SpeedyWeather.fluxes_to_tendencies!Method
fluxes_to_tendencies!(
     column::ColumnVariables,
     geometry::Geometry,
     constants::DynamicsConstants
 )
-

Convert the fluxes on half levels to tendencies on full levels.

source
SpeedyWeather.forcing!Method
forcing!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     forcing::JetStreamForcing
 )
-

Set for every latitude ring the tendency to the precomputed forcing in the momentum equations following the JetStreamForcing. The forcing is precomputed in initialize!(::JetStreamForcing,::ModelSetup).

source
SpeedyWeather.geopotential!Method
geopotential!(
+

Set for every latitude ring the tendency to the precomputed forcing in the momentum equations following the JetStreamForcing. The forcing is precomputed in initialize!(::JetStreamForcing,::ModelSetup).

source
SpeedyWeather.geopotential!Method
geopotential!(
     diagn::DiagnosticVariables,
     O::SpeedyWeather.AbstractOrography,
     C::DynamicsConstants
 )
-

Compute spectral geopotential geopot from spectral temperature temp and spectral surface geopotential geopot_surf (orography*gravity).

source
SpeedyWeather.geopotential!Method
geopotential!(
+

Compute spectral geopotential geopot from spectral temperature temp and spectral surface geopotential geopot_surf (orography*gravity).

source
SpeedyWeather.geopotential!Method
geopotential!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     pres::LowerTriangularMatrix,
     C::DynamicsConstants
 ) -> Any
-

calculates the geopotential in the ShallowWaterModel as g*η, i.e. gravity times the interface displacement (field pres)

source
SpeedyWeather.geopotential!Method
geopotential!(temp::Vector, C::DynamicsConstants) -> Vector
-

Calculate the geopotential based on temp in a single column. This exclues the surface geopotential that would need to be added to the returned vector. Function not used in the dynamical core but for post-processing and analysis.

source
SpeedyWeather.get_column!Method
get_column!(
+

calculates the geopotential in the ShallowWaterModel as g*η, i.e. gravity times the interface displacement (field pres)

source
SpeedyWeather.geopotential!Method
geopotential!(temp::Vector, C::DynamicsConstants) -> Vector
+

Calculate the geopotential based on temp in a single column. This exclues the surface geopotential that would need to be added to the returned vector. Function not used in the dynamical core but for post-processing and analysis.

source
SpeedyWeather.get_column!Method
get_column!(
     C::ColumnVariables,
     D::DiagnosticVariables,
     ij::Integer,
@@ -162,21 +162,21 @@
     G::Geometry,
     L::SpeedyWeather.AbstractLandSeaMask
 )
-

Update C::ColumnVariables by copying the prognostic variables from D::DiagnosticVariables at gridpoint index ij. Provide G::Geometry for coordinate information.

source
SpeedyWeather.get_run_idMethod
get_run_id(path::String, id::String) -> String
-

Checks existing run_???? folders in path to determine a 4-digit id number by counting up. E.g. if folder run_0001 exists it will return the string "0002". Does not create a folder for the returned run id.

source
SpeedyWeather.get_thermodynamics!Method
get_thermodynamics!(
+

Update C::ColumnVariables by copying the prognostic variables from D::DiagnosticVariables at gridpoint index ij. Provide G::Geometry for coordinate information.

source
SpeedyWeather.get_run_idMethod
get_run_id(path::String, id::String) -> String
+

Checks existing run_???? folders in path to determine a 4-digit id number by counting up. E.g. if folder run_0001 exists it will return the string "0002". Does not create a folder for the returned run id.

source
SpeedyWeather.get_thermodynamics!Method
get_thermodynamics!(
     column::ColumnVariables,
     model::PrimitiveWet
 )
-

Calculate thermodynamic quantities like saturation vapour pressure, saturation specific humidity, dry static energy, moist static energy and saturation moist static energy from the prognostic column variables.

source
SpeedyWeather.get_varMethod
get_var(progn::PrognosticVariables, var_name::Symbol; lf::Integer=1)

Returns the prognostic variable var_name at leapfrog index lf as a Vector{LowerTriangularMatrices}.

source
SpeedyWeather.hasMethod
has(
+

Calculate thermodynamic quantities like saturation vapour pressure, saturation specific humidity, dry static energy, moist static energy and saturation moist static energy from the prognostic column variables.

source
SpeedyWeather.get_varMethod
get_var(progn::PrognosticVariables, var_name::Symbol; lf::Integer=1)

Returns the prognostic variable var_name at leapfrog index lf as a Vector{LowerTriangularMatrices}.

source
SpeedyWeather.hasMethod
has(
     M::Type{<:SpeedyWeather.ModelSetup},
     var_name::Symbol
 ) -> Bool
-

Returns true if the model M has a prognostic variable var_name, false otherwise. The default fallback is that all variables are included.

source
SpeedyWeather.horizontal_diffusion!Function
horizontal_diffusion!(
+

Returns true if the model M has a prognostic variable var_name, false otherwise. The default fallback is that all variables are included.

source
SpeedyWeather.horizontal_diffusion!Function
horizontal_diffusion!(
     progn::SpeedyWeather.PrognosticLayerTimesteps,
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     model::ShallowWater
@@ -187,7 +187,7 @@
     model::ShallowWater,
     lf::Int64
 )
-

Apply horizontal diffusion to vorticity and diffusion in the ShallowWater models.

source
SpeedyWeather.horizontal_diffusion!Function
horizontal_diffusion!(
     progn::SpeedyWeather.PrognosticLayerTimesteps,
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     model::PrimitiveEquation
@@ -198,7 +198,7 @@
     model::PrimitiveEquation,
     lf::Int64
 ) -> Union{Nothing, Bool}
-

Apply horizontal diffusion applied to vorticity, diffusion and temperature in the PrimitiveEquation models. Uses the constant diffusion for temperature but possibly adaptive diffusion for vorticity and divergence.

source
SpeedyWeather.horizontal_diffusion!Function
horizontal_diffusion!(
+

Apply horizontal diffusion applied to vorticity, diffusion and temperature in the PrimitiveEquation models. Uses the constant diffusion for temperature but possibly adaptive diffusion for vorticity and divergence.

source
SpeedyWeather.horizontal_diffusion!Function
horizontal_diffusion!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     progn::SpeedyWeather.PrognosticLayerTimesteps,
     model::Barotropic
@@ -209,25 +209,25 @@
     model::Barotropic,
     lf::Int64
 )
-

Apply horizontal diffusion to vorticity in the Barotropic models.

source
SpeedyWeather.horizontal_diffusion!Method
horizontal_diffusion!(
     tendency::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
     A::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
     ∇²ⁿ_expl::AbstractArray{NF<:AbstractFloat, 1},
     ∇²ⁿ_impl::AbstractArray{NF<:AbstractFloat, 1}
 )
-

Apply horizontal diffusion to a 2D field A in spectral space by updating its tendency tendency with an implicitly calculated diffusion term. The implicit diffusion of the next time step is split into an explicit part ∇²ⁿ_expl and an implicit part ∇²ⁿ_impl, such that both can be calculated in a single forward step by using A as well as its tendency tendency.

source
SpeedyWeather.implicit_correction!Method
implicit_correction!(
+

Apply horizontal diffusion to a 2D field A in spectral space by updating its tendency tendency with an implicitly calculated diffusion term. The implicit diffusion of the next time step is split into an explicit part ∇²ⁿ_expl and an implicit part ∇²ⁿ_impl, such that both can be calculated in a single forward step by using A as well as its tendency tendency.

source
SpeedyWeather.implicit_correction!Method
implicit_correction!(
     diagn::DiagnosticVariables,
     implicit::ImplicitPrimitiveEq,
     progn::PrognosticVariables
 ) -> Any
-

Apply the implicit corrections to dampen gravity waves in the primitive equation models.

source
SpeedyWeather.implicit_correction!Method
implicit_correction!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer{NF, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF},
     progn::SpeedyWeather.PrognosticLayerTimesteps{NF},
     diagn_surface::SpeedyWeather.SurfaceVariables{NF, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF},
     progn_surface::SpeedyWeather.PrognosticSurfaceTimesteps{NF},
     implicit::ImplicitShallowWater
 )
-

Apply correction to the tendencies in diagn to prevent the gravity waves from amplifying. The correction is implicitly evaluated using the parameter implicit.α to switch between forward, centered implicit or backward evaluation of the gravity wave terms.

source
SpeedyWeather.initialize!Function
initialize!(
+

Apply correction to the tendencies in diagn to prevent the gravity waves from amplifying. The correction is implicitly evaluated using the parameter implicit.α to switch between forward, centered implicit or backward evaluation of the gravity wave terms.

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SpeedyWeather.initialize!Function
initialize!(
     scheme::HyperDiffusion,
     k::Int64,
     G::Geometry,
@@ -240,82 +240,82 @@
     L::SpeedyWeather.TimeStepper,
     vor_max::Real
 )
-

Precomputes the hyper diffusion terms in scheme for layer k based on the model time step in L, the vertical level sigma level in G, and the current (absolute) vorticity maximum level vor_max

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SpeedyWeather.initialize!Method
initialize!(model::Barotropic) -> SpeedyWeather.Simulation
-

Calls all initialize! functions for components of model, except for model.output and model.feedback which are always called at in time_stepping!.

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SpeedyWeather.initialize!Method
initialize!(
+

Precomputes the hyper diffusion terms in scheme for layer k based on the model time step in L, the vertical level sigma level in G, and the current (absolute) vorticity maximum level vor_max

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SpeedyWeather.initialize!Method
initialize!(model::Barotropic) -> SpeedyWeather.Simulation
+

Calls all initialize! functions for components of model, except for model.output and model.feedback which are always called at in time_stepping!.

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SpeedyWeather.initialize!Method
initialize!(
     orog::EarthOrography,
     P::SpeedyWeather.AbstractPlanet,
     S::SpectralTransform,
     G::Geometry
 ) -> LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat
-

Initialize the arrays orography,geopot_surf in orog by reading the orography field from file.

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SpeedyWeather.initialize!Method
initialize!(
     feedback::Feedback,
     clock::SpeedyWeather.Clock,
     model::SpeedyWeather.ModelSetup
 ) -> Union{Nothing, IOStream}
-

Initializes the a Feedback struct.

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SpeedyWeather.initialize!Method
initialize!(scheme::HeldSuarez, model::PrimitiveEquation)
-

initialize the HeldSuarez temperature relaxation by precomputing terms for the equilibrium temperature Teq.

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SpeedyWeather.initialize!Method
initialize!(scheme::HeldSuarez, model::PrimitiveEquation)
+

initialize the HeldSuarez temperature relaxation by precomputing terms for the equilibrium temperature Teq.

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SpeedyWeather.initialize!Method
initialize!(
     scheme::HyperDiffusion,
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     G::Geometry,
     L::SpeedyWeather.TimeStepper
 )
-

Pre-function to other initialize!(::HyperDiffusion) initialisors that calculates the (absolute) vorticity maximum for the layer of diagn.

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SpeedyWeather.initialize!Method
initialize!(
+

Pre-function to other initialize!(::HyperDiffusion) initialisors that calculates the (absolute) vorticity maximum for the layer of diagn.

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SpeedyWeather.initialize!Method
initialize!(
     scheme::HyperDiffusion,
     model::SpeedyWeather.ModelSetup
 )
-

Precomputes the hyper diffusion terms in scheme based on the model time step, and possibly with a changing strength/power in the vertical.

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SpeedyWeather.initialize!Method
initialize!(
+

Precomputes the hyper diffusion terms in scheme based on the model time step, and possibly with a changing strength/power in the vertical.

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SpeedyWeather.initialize!Method
initialize!(
     scheme::HyperDiffusion,
     L::SpeedyWeather.TimeStepper
 )
-

Precomputes the 2D hyper diffusion terms in scheme based on the model time step.

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SpeedyWeather.initialize!Method
initialize!(
     implicit::ImplicitPrimitiveEq,
     dt::Real,
     diagn::DiagnosticVariables,
     geometry::Geometry,
     constants::DynamicsConstants
 )
-

Initialize the implicit terms for the PrimitiveEquation models.

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SpeedyWeather.initialize!Method
initialize!(
     implicit::ImplicitShallowWater,
     dt::Real,
     constants::DynamicsConstants
 )
-

Update the implicit terms in implicit for the shallow water model as they depend on the time step dt.

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SpeedyWeather.initialize!Method
initialize!(
+

Update the implicit terms in implicit for the shallow water model as they depend on the time step dt.

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SpeedyWeather.initialize!Method
initialize!(
     scheme::JablonowskiRelaxation,
     model::PrimitiveEquation
 )
-

initialize the JablonowskiRelaxation temperature relaxation by precomputing terms for the equilibrium temperature Teq and the frequency (strength of relaxation).

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SpeedyWeather.initialize!Method
initialize!(scheme::LinearDrag, model::PrimitiveEquation)
-

Precomputes the drag coefficients for this BoundaryLayerDrag scheme.

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SpeedyWeather.initialize!Method
initialize!(
+

initialize the JablonowskiRelaxation temperature relaxation by precomputing terms for the equilibrium temperature Teq and the frequency (strength of relaxation).

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SpeedyWeather.initialize!Method
initialize!(scheme::LinearDrag, model::PrimitiveEquation)
+

Precomputes the drag coefficients for this BoundaryLayerDrag scheme.

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SpeedyWeather.initialize!Method
initialize!(
     scheme::NoTemperatureRelaxation,
     model::PrimitiveEquation
 )
-

just passes, does not need any initialization.

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SpeedyWeather.initialize!Method
initialize!(model::PrimitiveDry) -> SpeedyWeather.Simulation
-

Calls all initialize! functions for components of model, except for model.output and model.feedback which are always called at in time_stepping! and model.implicit which is done in first_timesteps!.

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SpeedyWeather.initialize!Method
initialize!(model::PrimitiveWet) -> SpeedyWeather.Simulation
-

Calls all initialize! functions for components of model, except for model.output and model.feedback which are always called at in time_stepping! and model.implicit which is done in first_timesteps!.

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SpeedyWeather.initialize!Method
initialize!(model::PrimitiveDry) -> SpeedyWeather.Simulation
+

Calls all initialize! functions for components of model, except for model.output and model.feedback which are always called at in time_stepping! and model.implicit which is done in first_timesteps!.

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SpeedyWeather.initialize!Method
initialize!(model::PrimitiveWet) -> SpeedyWeather.Simulation
+

Calls all initialize! functions for components of model, except for model.output and model.feedback which are always called at in time_stepping! and model.implicit which is done in first_timesteps!.

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SpeedyWeather.initialize!Method
initialize!(
     progn_new::PrognosticVariables,
     initial_conditions::StartFromFile,
     model::SpeedyWeather.ModelSetup
 ) -> PrognosticVariables
-

Restart from a previous SpeedyWeather.jl simulation via the restart file restart.jld2 Applies interpolation in the horizontal but not in the vertical.

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SpeedyWeather.initialize!Method
initialize!(
+

Restart from a previous SpeedyWeather.jl simulation via the restart file restart.jld2 Applies interpolation in the horizontal but not in the vertical.

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SpeedyWeather.initialize!Method
initialize!(
     progn::PrognosticVariables,
     initial_conditions::ZonalJet,
     model::ShallowWater
 ) -> LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat
-

Initial conditions from Galewsky, 2004, Tellus

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SpeedyWeather.initialize!Method
initialize!(model::ShallowWater) -> SpeedyWeather.Simulation
-

Calls all initialize! functions for components of model, except for model.output and model.feedback which are always called at in time_stepping! and model.implicit which is done in first_timesteps!.

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SpeedyWeather.initialize!Method
initialize!(model::ShallowWater) -> SpeedyWeather.Simulation
+

Calls all initialize! functions for components of model, except for model.output and model.feedback which are always called at in time_stepping! and model.implicit which is done in first_timesteps!.

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SpeedyWeather.initialize!Method
initialize!(
     clock::SpeedyWeather.Clock,
     time_stepping::SpeedyWeather.TimeStepper
 ) -> SpeedyWeather.Clock
-

Initialize the clock with the time step Δt in the time_stepping.

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SpeedyWeather.initialize!Method
initialize!(
     orog::ZonalRidge,
     P::SpeedyWeather.AbstractPlanet,
     S::SpectralTransform,
     G::Geometry
 ) -> LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat
-

Initialize the arrays orography,geopot_surf in orog following Jablonowski and Williamson, 2006.

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SpeedyWeather.initialize!Method
initialize!(
     output::OutputWriter{output_NF, Model},
     feedback::SpeedyWeather.AbstractFeedback,
     time_stepping::SpeedyWeather.TimeStepper,
@@ -323,37 +323,37 @@
     diagn::DiagnosticVariables,
     model
 )
-

Creates a netcdf file on disk and the corresponding netcdf_file object preallocated with output variables and dimensions. write_output! then writes consecuitive time steps into this file.

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SpeedyWeather.initialize!Method
initialize!(
+

Creates a netcdf file on disk and the corresponding netcdf_file object preallocated with output variables and dimensions. write_output! then writes consecuitive time steps into this file.

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SpeedyWeather.initialize!Method
initialize!(
     progn::PrognosticVariables{NF, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF},
     initial_conditions::SpeedyWeather.RandomWaves,
     model::ShallowWater
 )
-

Random initial conditions for the interface displacement η in the shallow water equations. The flow (u,v) is zero initially. This kicks off gravity waves that will interact with orography.

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SpeedyWeather.initialize!Method
initialize!(
+

Random initial conditions for the interface displacement η in the shallow water equations. The flow (u,v) is zero initially. This kicks off gravity waves that will interact with orography.

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SpeedyWeather.initialize!Method
initialize!(
     progn::PrognosticVariables{NF, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF},
     initial_conditions::StartWithRandomVorticity,
     model::SpeedyWeather.ModelSetup
 )
-

Start with random vorticity as initial conditions

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SpeedyWeather.initialize!Method
initialize!(
     progn::PrognosticVariables{NF, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF},
     initial_conditions::ZonalWind,
     model::PrimitiveEquation
 )
-

Initial conditions from Jablonowski and Williamson, 2006, QJR Meteorol. Soc

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SpeedyWeather.initialize!Method
initialize!(
     scheme::SpeedyWeather.StaticEnergyDiffusion{NF},
     model::PrimitiveEquation
 ) -> Any
-

Initialize dry static energy diffusion.

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SpeedyWeather.initialize_geopotentialMethod
initialize_geopotential(
     σ_levels_full::Vector,
     σ_levels_half::Vector,
     R_dry::Real
 ) -> Tuple{Vector{Float64}, Vector{Float64}}
-

Precomputes constants for the vertical integration of the geopotential, defined as

Φ_{k+1/2} = Φ_{k+1} + R*T_{k+1}*(ln(p_{k+1}) - ln(p_{k+1/2})) (half levels) Φ_k = Φ_{k+1/2} + R*T_k*(ln(p_{k+1/2}) - ln(p_k)) (full levels)

Same formula but k → k-1/2.

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SpeedyWeather.large_scale_condensation!Method
large_scale_condensation!(
+

Precomputes constants for the vertical integration of the geopotential, defined as

Φ_{k+1/2} = Φ_{k+1} + R*T_{k+1}*(ln(p_{k+1}) - ln(p_{k+1/2})) (half levels) Φ_k = Φ_{k+1/2} + R*T_k*(ln(p_{k+1/2}) - ln(p_k)) (full levels)

Same formula but k → k-1/2.

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SpeedyWeather.large_scale_condensation!Method
large_scale_condensation!(
     column::ColumnVariables{NF},
     scheme::SpeedyCondensation,
     geometry::Geometry,
@@ -361,7 +361,7 @@
     atmosphere::SpeedyWeather.AbstractAtmosphere,
     time_stepping::SpeedyWeather.TimeStepper
 )
-

Large-scale condensation for a column by relaxation back to a reference relative humidity if larger than that. Calculates the tendencies for specific humidity and temperature and integrates the large-scale precipitation vertically for output.

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SpeedyWeather.launch_kernel!Method
launch_kernel!(device_setup::DeviceSetup, kernel!, ndrange, kernel_args...)

Launches the kernel! on the device_setup with ndrange computations over the kernel and arguments kernel_args

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SpeedyWeather.leapfrog!Method
leapfrog!(
+

Large-scale condensation for a column by relaxation back to a reference relative humidity if larger than that. Calculates the tendencies for specific humidity and temperature and integrates the large-scale precipitation vertically for output.

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SpeedyWeather.launch_kernel!Method
launch_kernel!(device_setup::DeviceSetup, kernel!, ndrange, kernel_args...)

Launches the kernel! on the device_setup with ndrange computations over the kernel and arguments kernel_args

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SpeedyWeather.leapfrog!Method
leapfrog!(
     A_old::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
     A_new::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
     tendency::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
@@ -369,140 +369,140 @@
     lf::Int64,
     L::Leapfrog{NF<:AbstractFloat}
 )
-

Performs one leapfrog time step with (lf=2) or without (lf=1) Robert+Williams filter (see Williams (2009), Montly Weather Review, Eq. 7-9).

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SpeedyWeather.linear_pressure_gradient!Method
linear_pressure_gradient!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     surface::SpeedyWeather.PrognosticSurfaceTimesteps,
     lf::Int64,
     C::DynamicsConstants,
     I::ImplicitPrimitiveEq
 ) -> LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat
-

Add the linear contribution of the pressure gradient to the geopotential. The pressure gradient in the divergence equation takes the form

-∇⋅(Rd*Tᵥ*∇lnpₛ) = -∇⋅(Rd*Tᵥ'*∇lnpₛ) - ∇²(Rd*Tₖ*lnpₛ)

So that the second term inside the Laplace operator can be added to the geopotential. Rd is the gas constant, Tᵥ the virtual temperature and Tᵥ' its anomaly wrt to the average or reference temperature Tₖ, lnpₛ is the logarithm of surface pressure.

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SpeedyWeather.linear_virtual_temperature!Method
linear_virtual_temperature!(
+

Add the linear contribution of the pressure gradient to the geopotential. The pressure gradient in the divergence equation takes the form

-∇⋅(Rd*Tᵥ*∇lnpₛ) = -∇⋅(Rd*Tᵥ'*∇lnpₛ) - ∇²(Rd*Tₖ*lnpₛ)

So that the second term inside the Laplace operator can be added to the geopotential. Rd is the gas constant, Tᵥ the virtual temperature and Tᵥ' its anomaly wrt to the average or reference temperature Tₖ, lnpₛ is the logarithm of surface pressure.

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SpeedyWeather.linear_virtual_temperature!Method
linear_virtual_temperature!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     progn::SpeedyWeather.PrognosticLayerTimesteps,
     constants::DynamicsConstants,
     lf::Int64
 ) -> Any
-

Calculates a linearised virtual temperature Tᵥ as

Tᵥ = T + Tₖμq

With absolute temperature T, layer-average temperarture Tₖ (computed in temperature_average!), specific humidity q and

μ = (1-ξ)/ξ, ξ = R_dry/R_vapour.

in spectral space.

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SpeedyWeather.linear_virtual_temperature!Method
linear_virtual_temperature!(
+

Calculates a linearised virtual temperature Tᵥ as

Tᵥ = T + Tₖμq

With absolute temperature T, layer-average temperarture Tₖ (computed in temperature_average!), specific humidity q and

μ = (1-ξ)/ξ, ξ = R_dry/R_vapour.

in spectral space.

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SpeedyWeather.linear_virtual_temperature!Method
linear_virtual_temperature!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     progn::SpeedyWeather.PrognosticLayerTimesteps,
     model::PrimitiveDry,
     lf::Integer
 ) -> LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat
-

Linear virtual temperature for model::PrimitiveDry: Just copy over arrays from temp to temp_virt at timestep lf in spectral space as humidity is zero in this model.

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SpeedyWeather.load_trajectoryMethod
load_trajectory(
+

Linear virtual temperature for model::PrimitiveDry: Just copy over arrays from temp to temp_virt at timestep lf in spectral space as humidity is zero in this model.

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SpeedyWeather.load_trajectoryMethod
load_trajectory(
     var_name::Union{String, Symbol},
     model::SpeedyWeather.ModelSetup
 ) -> Any
-

Loads a var_name trajectory of the model M that has been saved in a netCDF file during the time stepping.

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SpeedyWeather.moist_static_energy!Method
moist_static_energy!(
     column::ColumnVariables,
     thermodynamics::SpeedyWeather.Thermodynamics
 )
-

Compute the moist static energy

MSE = SE + Lc*Q = cₚT + Φ + Lc*Q

with the static energy SE, the latent heat of condensation Lc, the geopotential Φ. As well as the saturation moist static energy which replaces Q with Q_sat

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SpeedyWeather.nansMethod
A = nans(T,dims...)

Allocate array A with NaNs of type T. Similar to zeros(T,dims...).

source
SpeedyWeather.nar_detection!Method
nar_detection!(
+

Compute the moist static energy

MSE = SE + Lc*Q = cₚT + Φ + Lc*Q

with the static energy SE, the latent heat of condensation Lc, the geopotential Φ. As well as the saturation moist static energy which replaces Q with Q_sat

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SpeedyWeather.nansMethod
A = nans(T,dims...)

Allocate array A with NaNs of type T. Similar to zeros(T,dims...).

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SpeedyWeather.nar_detection!Method
nar_detection!(
     feedback::Feedback,
     progn::PrognosticVariables
 ) -> Union{Nothing, Bool}
-

Detect NaR (Not-a-Real) in the prognostic variables.

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SpeedyWeather.parameterization_tendencies!Method
parameterization_tendencies!(
     diagn::DiagnosticVariables,
     time::Dates.DateTime,
     model::PrimitiveEquation
 ) -> Any
-

Compute tendencies for u,v,temp,humid from physical parametrizations. Extract for each vertical atmospheric column the prognostic variables (stored in diagn as they are grid-point transformed), loop over all grid-points, compute all parametrizations on a single-column basis, then write the tendencies back into a horizontal field of tendencies.

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SpeedyWeather.pressure_on_orography!Method
pressure_on_orography!(
+

Compute tendencies for u,v,temp,humid from physical parametrizations. Extract for each vertical atmospheric column the prognostic variables (stored in diagn as they are grid-point transformed), loop over all grid-points, compute all parametrizations on a single-column basis, then write the tendencies back into a horizontal field of tendencies.

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SpeedyWeather.pressure_on_orography!Method
pressure_on_orography!(
     progn::PrognosticVariables,
     model::PrimitiveEquation
 )
-

Initialize surface pressure on orography by integrating the hydrostatic equation with the reference temperature lapse rate.

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SpeedyWeather.readable_secsMethod
readable_secs(secs::Real) -> Dates.CompoundPeriod
+

Initialize surface pressure on orography by integrating the hydrostatic equation with the reference temperature lapse rate.

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SpeedyWeather.readable_secsMethod
readable_secs(secs::Real) -> Dates.CompoundPeriod
 

Returns Dates.CompoundPeriod rounding to either (days, hours), (hours, minutes), (minutes, seconds), or seconds with 1 decimal place accuracy for >10s and two for less. E.g.

julia> readable_secs(12345)
-3 hours, 26 minutes
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SpeedyWeather.remaining_timeMethod
remaining_time(p::ProgressMeter.Progress) -> String
-

Estimates the remaining time from a ProgresssMeter.Progress. Adapted from ProgressMeter.jl

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SpeedyWeather.reset_column!Method
reset_column!(column::ColumnVariables{NF})
-

Set the accumulators (tendencies but also vertical sums and similar) back to zero for column to be reused at other grid points.

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SpeedyWeather.remaining_timeMethod
remaining_time(p::ProgressMeter.Progress) -> String
+

Estimates the remaining time from a ProgresssMeter.Progress. Adapted from ProgressMeter.jl

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SpeedyWeather.reset_column!Method
reset_column!(column::ColumnVariables{NF})
+

Set the accumulators (tendencies but also vertical sums and similar) back to zero for column to be reused at other grid points.

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SpeedyWeather.run!Method
run!(
     simulation::SpeedyWeather.Simulation;
     initialize,
     n_days,
     startdate,
     output
 ) -> PrognosticVariables
-

Run a SpeedyWeather.jl simulation. The simulation.model is assumed to be initialized, otherwise use initialize=true as keyword argument.

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SpeedyWeather.saturation_humidity!Method
saturation_humidity!(
+

Run a SpeedyWeather.jl simulation. The simulation.model is assumed to be initialized, otherwise use initialize=true as keyword argument.

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SpeedyWeather.saturation_humidity!Method
saturation_humidity!(
     column::ColumnVariables,
     thermodynamics::SpeedyWeather.Thermodynamics
 )
-

Compute (1) the saturation vapour pressure as a function of temperature using the August-Roche-Magnus formula,

eᵢ(T) = e₀ * exp(Cᵢ * (T - T₀) / (T - Tᵢ)),

where T is in Kelvin and i = 1,2 for saturation with respect to water and ice, respectively. And (2) the saturation specific humidity according to the formula,

0.622 * e / (p - (1 - 0.622) * e),

where e is the saturation vapour pressure, p is the pressure, and 0.622 is the ratio of the molecular weight of water to dry air.

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SpeedyWeather.scale!Method
scale!(progn::PrognosticVariables, scale::Real) -> Real
-

Scales the prognostic variables vorticity and divergence with the Earth's radius which is used in the dynamical core.

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SpeedyWeather.scale!Method
scale!(
+

Compute (1) the saturation vapour pressure as a function of temperature using the August-Roche-Magnus formula,

eᵢ(T) = e₀ * exp(Cᵢ * (T - T₀) / (T - Tᵢ)),

where T is in Kelvin and i = 1,2 for saturation with respect to water and ice, respectively. And (2) the saturation specific humidity according to the formula,

0.622 * e / (p - (1 - 0.622) * e),

where e is the saturation vapour pressure, p is the pressure, and 0.622 is the ratio of the molecular weight of water to dry air.

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SpeedyWeather.scale!Method
scale!(progn::PrognosticVariables, scale::Real) -> Real
+

Scales the prognostic variables vorticity and divergence with the Earth's radius which is used in the dynamical core.

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SpeedyWeather.scale!Method
scale!(
     progn::PrognosticVariables{NF, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF},
     var::Symbol,
     scale::Real
 )
-

Scale the variable var inside progn with scalar scale.

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SpeedyWeather.set_pressure!Method
set_pressure!(progn::PrognosticVariables{NF}, 
               pressure::AbstractMatrix, 
               Grid::Type{<:AbstractGrid}, 
-              lf::Integer=1) where NF

Sets the prognostic variable with the surface pressure in grid space at leapfrog index lf.

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SpeedyWeather.set_pressure!Method
set_pressure!(progn::PrognosticVariables{NF}, 
+              lf::Integer=1) where NF

Sets the prognostic variable with the surface pressure in grid space at leapfrog index lf.

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SpeedyWeather.set_pressure!Method
set_pressure!(progn::PrognosticVariables{NF}, 
               pressure::LowerTriangularMatrix;
-              lf::Integer=1) where NF

Sets the prognostic variable with the surface pressure in spectral space at leapfrog index lf.

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SpeedyWeather.set_pressure!Method
set_pressure!(progn::PrognosticVariables{NF}, 
+              lf::Integer=1) where NF

Sets the prognostic variable with the surface pressure in spectral space at leapfrog index lf.

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SpeedyWeather.set_pressure!Method
set_pressure!(progn::PrognosticVariables{NF}, 
               pressure::AbstractGrid, 
               M::ModelSetup;
-              lf::Integer=1) where NF

Sets the prognostic variable with the surface pressure in grid space at leapfrog index lf.

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SpeedyWeather.set_pressure!Method
set_pressure!(progn::PrognosticVariables{NF}, 
+              lf::Integer=1) where NF

Sets the prognostic variable with the surface pressure in grid space at leapfrog index lf.

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SpeedyWeather.set_pressure!Method
set_pressure!(progn::PrognosticVariables{NF}, 
               pressure::AbstractGrid, 
-              lf::Integer=1) where NF

Sets the prognostic variable with the surface pressure in grid space at leapfrog index lf.

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SpeedyWeather.set_var!Method
function set_var!(progn::PrognosticVariables{NF}, 
+              lf::Integer=1) where NF

Sets the prognostic variable with the surface pressure in grid space at leapfrog index lf.

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SpeedyWeather.set_var!Method
function set_var!(progn::PrognosticVariables{NF}, 
                   varname::Symbol, 
                   s::Number;
-                  lf::Integer=1) where NF

Sets all values of prognostic variable varname at leapfrog index lf to the scalar s.

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SpeedyWeather.set_var!Method
set_var!(progn::PrognosticVariables{NF}, 
+                  lf::Integer=1) where NF

Sets all values of prognostic variable varname at leapfrog index lf to the scalar s.

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SpeedyWeather.set_var!Method
set_var!(progn::PrognosticVariables{NF}, 
          varname::Symbol, 
          var::Vector{<:AbstractMatrix}, 
          Grid::Type{<:AbstractGrid}=FullGaussianGrid;
-         lf::Integer=1) where NF

Sets the prognostic variable with the name varname in all layers at leapfrog index lf with values given in var a vector with all information for all layers in grid space.

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SpeedyWeather.set_var!Method
set_var!(progn::PrognosticVariables{NF},        
+         lf::Integer=1) where NF

Sets the prognostic variable with the name varname in all layers at leapfrog index lf with values given in var a vector with all information for all layers in grid space.

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SpeedyWeather.set_var!Method
set_var!(progn::PrognosticVariables{NF},        
          varname::Symbol, 
          var::Vector{<:LowerTriangularMatrix};
-         lf::Integer=1) where NF

Sets the prognostic variable with the name varname in all layers at leapfrog index lf with values given in var a vector with all information for all layers in spectral space.

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SpeedyWeather.set_var!Method
set_var!(progn::PrognosticVariables{NF}, 
+         lf::Integer=1) where NF

Sets the prognostic variable with the name varname in all layers at leapfrog index lf with values given in var a vector with all information for all layers in spectral space.

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SpeedyWeather.set_var!Method
set_var!(progn::PrognosticVariables{NF}, 
          varname::Symbol, 
          var::Vector{<:AbstractGrid}, 
          M::ModelSetup;
-         lf::Integer=1) where NF

Sets the prognostic variable with the name varname in all layers at leapfrog index lf with values given in var a vector with all information for all layers in grid space.

source
SpeedyWeather.set_var!Method
set_var!(progn::PrognosticVariables{NF},        
+         lf::Integer=1) where NF

Sets the prognostic variable with the name varname in all layers at leapfrog index lf with values given in var a vector with all information for all layers in grid space.

source
SpeedyWeather.set_var!Method
set_var!(progn::PrognosticVariables{NF},        
          varname::Symbol, 
          var::Vector{<:AbstractGrid};
-         lf::Integer=1) where NF

Sets the prognostic variable with the name varname in all layers at leapfrog index lf with values given in var a vector with all information for all layers in grid space.

source
SpeedyWeather.speedstringMethod
speedstring(sec_per_iter, dt_in_sec) -> String
-

define a ProgressMeter.speedstring method that also takes a time step dt_in_sec to translate sec/iteration to days/days-like speeds.

source
SpeedyWeather.static_energy_diffusion!Method
static_energy_diffusion!(
+         lf::Integer=1) where NF

Sets the prognostic variable with the name varname in all layers at leapfrog index lf with values given in var a vector with all information for all layers in grid space.

source
SpeedyWeather.speedstringMethod
speedstring(sec_per_iter, dt_in_sec) -> String
+

define a ProgressMeter.speedstring method that also takes a time step dt_in_sec to translate sec/iteration to days/days-like speeds.

source
SpeedyWeather.surface_pressure_tendency!Method
surface_pressure_tendency!( Prog::PrognosticVariables,
                             Diag::DiagnosticVariables,
                             lf::Int,
-                            M::PrimitiveEquation)

Computes the tendency of the logarithm of surface pressure as

-(ū*px + v̄*py) - D̄

with ū,v̄ being the vertically averaged velocities; px, py the gradients of the logarithm of surface pressure ln(p_s) and D̄ the vertically averaged divergence.

  1. Calculate ∇ln(p_s) in spectral space, convert to grid.
  2. Multiply ū,v̄ with ∇ln(p_s) in grid-point space, convert to spectral.
  3. D̄ is subtracted in spectral space.
  4. Set tendency of the l=m=0 mode to 0 for better mass conservation.
source
SpeedyWeather.temperature_average!Method
temperature_average!(
+                            M::PrimitiveEquation)

Computes the tendency of the logarithm of surface pressure as

-(ū*px + v̄*py) - D̄

with ū,v̄ being the vertically averaged velocities; px, py the gradients of the logarithm of surface pressure ln(p_s) and D̄ the vertically averaged divergence.

  1. Calculate ∇ln(p_s) in spectral space, convert to grid.
  2. Multiply ū,v̄ with ∇ln(p_s) in grid-point space, convert to spectral.
  3. D̄ is subtracted in spectral space.
  4. Set tendency of the l=m=0 mode to 0 for better mass conservation.
source
SpeedyWeather.temperature_average!Method
temperature_average!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     temp::LowerTriangularMatrix,
     S::SpectralTransform
 ) -> Any
-

Calculates the average temperature of a layer from the l=m=0 harmonic and stores the result in diagn.temp_average

source
SpeedyWeather.temperature_relaxation!Method
temperature_relaxation!(
     column::ColumnVariables,
     scheme::JablonowskiRelaxation
 )
-

Apply HeldSuarez-like temperature relaxation to the Jablonowski and Williamson vertical profile.

source
SpeedyWeather.temperature_tendency!Method
temperature_tendency!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     C::DynamicsConstants,
     G::Geometry,
     S::SpectralTransform,
     I::ImplicitPrimitiveEq
 )
-

Compute the temperature tendency

∂T/∂t += -∇⋅((u,v)*T') + T'D + κTᵥ*Dlnp/Dt

+= because the tendencies already contain parameterizations and vertical advection. T' is the anomaly with respect to the reference/average temperature. Tᵥ is the virtual temperature used in the adiabatic term κTᵥ*Dlnp/Dt.

source
SpeedyWeather.temperature_tendency!Method
temperature_tendency!(
+

Compute the temperature tendency

∂T/∂t += -∇⋅((u,v)*T') + T'D + κTᵥ*Dlnp/Dt

+= because the tendencies already contain parameterizations and vertical advection. T' is the anomaly with respect to the reference/average temperature. Tᵥ is the virtual temperature used in the adiabatic term κTᵥ*Dlnp/Dt.

source
SpeedyWeather.time_stepping!Method
time_stepping!(
     progn::PrognosticVariables,
     diagn::DiagnosticVariables,
     model::SpeedyWeather.ModelSetup
 ) -> PrognosticVariables
-

Main time loop that that initializes output and feedback, loops over all time steps and calls the output and feedback functions.

source
SpeedyWeather.timestep!Function
timestep!(
+

Main time loop that that initializes output and feedback, loops over all time steps and calls the output and feedback functions.

source
SpeedyWeather.timestep!Function
timestep!(
     progn::PrognosticVariables,
     diagn::DiagnosticVariables,
     dt::Real,
@@ -523,7 +523,7 @@
     lf1::Int64,
     lf2::Int64
 )
-

Calculate a single time step for the model <: Barotropic.

source
SpeedyWeather.timestep!Method
timestep!(
     progn::PrognosticVariables{NF<:AbstractFloat, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF<:AbstractFloat},
     diagn::DiagnosticVariables{NF<:AbstractFloat, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF<:AbstractFloat},
     dt::Real,
@@ -544,7 +544,7 @@
     lf1::Int64,
     lf2::Int64
 ) -> Any
-

Calculate a single time step for the model<:PrimitiveEquation

source
SpeedyWeather.timestep!Method
timestep!(
     progn::PrognosticVariables{NF<:AbstractFloat, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF<:AbstractFloat},
     diagn::DiagnosticVariables{NF<:AbstractFloat, Grid} where Grid<:SpeedyWeather.RingGrids.AbstractGrid{NF<:AbstractFloat},
     dt::Real,
@@ -565,19 +565,19 @@
     lf1::Int64,
     lf2::Int64
 ) -> Union{Nothing, SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat}
-

Calculate a single time step for the model <: ShallowWater.

source
SpeedyWeather.unscale!Method
unscale!(variable::AbstractArray, scale::Real) -> Any
-

Undo the radius-scaling for any variable. Method used for netcdf output.

source
SpeedyWeather.unscale!Method
unscale!(progn::PrognosticVariables) -> Int64
-

Undo the radius-scaling of vorticity and divergence from scale!(progn,scale::Real).

source
SpeedyWeather.vertical_integration!Method
vertical_integration!(Diag::DiagnosticVariables,G::Geometry)

Calculates the vertically averaged (weighted by the thickness of the σ level) velocities (*coslat) and divergence. E.g.

u_mean = ∑_k=1^nlev Δσ_k * u_k

u,v are averaged in grid-point space, divergence in spectral space.

source
SpeedyWeather.unscale!Method
unscale!(variable::AbstractArray, scale::Real) -> Any
+

Undo the radius-scaling for any variable. Method used for netcdf output.

source
SpeedyWeather.unscale!Method
unscale!(progn::PrognosticVariables) -> Int64
+

Undo the radius-scaling of vorticity and divergence from scale!(progn,scale::Real).

source
SpeedyWeather.vertical_integration!Method
vertical_integration!(Diag::DiagnosticVariables,G::Geometry)

Calculates the vertically averaged (weighted by the thickness of the σ level) velocities (*coslat) and divergence. E.g.

u_mean = ∑_k=1^nlev Δσ_k * u_k

u,v are averaged in grid-point space, divergence in spectral space.

source
SpeedyWeather.virtual_temperature!Method
virtual_temperature!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     temp::LowerTriangularMatrix,
     constants::DynamicsConstants
 )
-

Calculates the virtual temperature Tᵥ as

Tᵥ = T(1+μq)

With absolute temperature T, specific humidity q and

μ = (1-ξ)/ξ, ξ = R_dry/R_vapour.

in grid-point space.

source
SpeedyWeather.virtual_temperature!Method
virtual_temperature!(
+

Calculates the virtual temperature Tᵥ as

Tᵥ = T(1+μq)

With absolute temperature T, specific humidity q and

μ = (1-ξ)/ξ, ξ = R_dry/R_vapour.

in grid-point space.

source
SpeedyWeather.virtual_temperature!Method
virtual_temperature!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     temp::LowerTriangularMatrix,
     model::PrimitiveDry
 ) -> SpeedyWeather.RingGrids.AbstractGrid{NF} where NF<:AbstractFloat
-

Virtual temperature in grid-point space: For the PrimitiveDry temperature and virtual temperature are the same (humidity=0). Just copy over the arrays.

source
SpeedyWeather.volume_flux_divergence!Method
volume_flux_divergence!(
+

Virtual temperature in grid-point space: For the PrimitiveDry temperature and virtual temperature are the same (humidity=0). Just copy over the arrays.

source
SpeedyWeather.volume_flux_divergence!Method
volume_flux_divergence!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     surface::SpeedyWeather.SurfaceVariables,
     orog::SpeedyWeather.AbstractOrography,
@@ -585,7 +585,7 @@
     G::Geometry,
     S::SpectralTransform
 )
-

Computes the (negative) divergence of the volume fluxes uh,vh for the continuity equation, -∇⋅(uh,vh).

source
SpeedyWeather.vordiv_tendencies!Method
vordiv_tendencies!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     surf::SpeedyWeather.SurfaceVariables,
     C::DynamicsConstants,
@@ -594,20 +594,20 @@
 )
 

Tendencies for vorticity and divergence. Excluding Bernoulli potential with geopotential and linear pressure gradient inside the Laplace operator, which are added later in spectral space.

u_tend +=  v*(f+ζ) - RTᵥ'*∇lnp_x
 v_tend += -u*(f+ζ) - RTᵥ'*∇lnp_y

+= because the tendencies already contain the parameterizations and vertical advection. f is coriolis, ζ relative vorticity, R the gas constant Tᵥ' the virtual temperature anomaly, ∇lnp the gradient of surface pressure and _x and _y its zonal/meridional components. The tendencies are then curled/dived to get the tendencies for vorticity/divergence in spectral space

∂ζ/∂t = ∇×(u_tend,v_tend)
-∂D/∂t = ∇⋅(u_tend,v_tend) + ...

+ ... because there's more terms added later for divergence.

source
SpeedyWeather.vordiv_tendencies!Method
vordiv_tendencies!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     surf::SpeedyWeather.SurfaceVariables,
     model::PrimitiveEquation
 )
-

Function barrier to unpack model.

source
SpeedyWeather.vorticity_flux!Method
vorticity_flux!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     model::Barotropic
 )
-

Vorticity flux tendency in the barotropic vorticity equation

∂ζ/∂t = ∇×(u_tend,v_tend)

with

u_tend = Fᵤ + v*(ζ+f) v_tend = Fᵥ - u*(ζ+f)

with Fᵤ,Fᵥ the forcing from forcing! already in u_tend_grid/v_tend_grid and vorticity ζ, coriolis f.

source
SpeedyWeather.vorticity_flux!Method
vorticity_flux!(
+

Vorticity flux tendency in the barotropic vorticity equation

∂ζ/∂t = ∇×(u_tend,v_tend)

with

u_tend = Fᵤ + v*(ζ+f) v_tend = Fᵥ - u*(ζ+f)

with Fᵤ,Fᵥ the forcing from forcing! already in u_tend_grid/v_tend_grid and vorticity ζ, coriolis f.

source
SpeedyWeather.vorticity_flux!Method
vorticity_flux!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     model::ShallowWater
 )
-

Vorticity flux tendency in the shallow water equations

∂ζ/∂t = ∇×(u_tend,v_tend) ∂D/∂t = ∇⋅(u_tend,v_tend)

with

u_tend = Fᵤ + v*(ζ+f) v_tend = Fᵥ - u*(ζ+f)

with Fᵤ,Fᵥ the forcing from forcing! already in u_tend_grid/v_tend_grid and vorticity ζ, coriolis f.

source
SpeedyWeather.vorticity_flux_curldiv!Method
vorticity_flux_curldiv!(
+

Vorticity flux tendency in the shallow water equations

∂ζ/∂t = ∇×(u_tend,v_tend) ∂D/∂t = ∇⋅(u_tend,v_tend)

with

u_tend = Fᵤ + v*(ζ+f) v_tend = Fᵥ - u*(ζ+f)

with Fᵤ,Fᵥ the forcing from forcing! already in u_tend_grid/v_tend_grid and vorticity ζ, coriolis f.

source
SpeedyWeather.vorticity_flux_curldiv!Method
vorticity_flux_curldiv!(
     diagn::SpeedyWeather.DiagnosticVariablesLayer,
     C::DynamicsConstants,
     G::Geometry,
@@ -615,38 +615,38 @@
     div,
     add
 )
-

Compute the vorticity advection as the curl/div of the vorticity fluxes

∂ζ/∂t = ∇×(u_tend,v_tend) ∂D/∂t = ∇⋅(u_tend,v_tend)

with

u_tend = Fᵤ + v*(ζ+f) v_tend = Fᵥ - u*(ζ+f)

with Fᵤ,Fᵥ from u_tend_grid/v_tend_grid that are assumed to be alread set in forcing!. Set div=false for the BarotropicModel which doesn't require the divergence tendency.

source
SpeedyWeather.workgroup_sizeMethod
workgroup_size(dev::AbstractDevice)

Returns a workgroup size depending on dev. WIP: Will be expanded in the future to also include grid information.

source
SpeedyWeather.write_column_tendencies!Method
write_column_tendencies!(
+

Compute the vorticity advection as the curl/div of the vorticity fluxes

∂ζ/∂t = ∇×(u_tend,v_tend) ∂D/∂t = ∇⋅(u_tend,v_tend)

with

u_tend = Fᵤ + v*(ζ+f) v_tend = Fᵥ - u*(ζ+f)

with Fᵤ,Fᵥ from u_tend_grid/v_tend_grid that are assumed to be alread set in forcing!. Set div=false for the BarotropicModel which doesn't require the divergence tendency.

source
SpeedyWeather.workgroup_sizeMethod
workgroup_size(dev::AbstractDevice)

Returns a workgroup size depending on dev. WIP: Will be expanded in the future to also include grid information.

source
SpeedyWeather.write_column_tendencies!Method
write_column_tendencies!(
     D::DiagnosticVariables,
     C::ColumnVariables,
     ij::Int64
 )
-

Write the parametrization tendencies from C::ColumnVariables into the horizontal fields of tendencies stored in D::DiagnosticVariables at gridpoint index ij.

source
SpeedyWeather.write_netcdf_time!Method
write_netcdf_time!(
+

Write the parametrization tendencies from C::ColumnVariables into the horizontal fields of tendencies stored in D::DiagnosticVariables at gridpoint index ij.

source
SpeedyWeather.write_netcdf_time!Method
write_netcdf_time!(
     output::OutputWriter,
     time::Dates.DateTime
 )
-

Write the current time time::DateTime to the netCDF file in output::OutputWriter.

source
SpeedyWeather.write_netcdf_variables!Method
write_netcdf_variables!(
     output::OutputWriter,
     diagn::DiagnosticVariables{NF, Grid, Model}
 )
-

Write diagnostic variables from diagn to the netCDF file in output::OutputWriter.

source
SpeedyWeather.write_output!Method
write_output!(
     outputter::OutputWriter,
     time::Dates.DateTime,
     diagn::DiagnosticVariables
 )
-

Writes the variables from diagn of time step i at time time into outputter.netcdf_file. Simply escapes for no netcdf output of if output shouldn't be written on this time step. Interpolates onto output grid and resolution as specified in outputter, converts to output number format, truncates the mantissa for higher compression and applies lossless compression.

source
SpeedyWeather.write_restart_fileMethod
write_restart_file(
+

Writes the variables from diagn of time step i at time time into outputter.netcdf_file. Simply escapes for no netcdf output of if output shouldn't be written on this time step. Interpolates onto output grid and resolution as specified in outputter, converts to output number format, truncates the mantissa for higher compression and applies lossless compression.

source
SpeedyWeather.write_restart_fileMethod
write_restart_file(
     progn::PrognosticVariables,
     output::OutputWriter
 ) -> Union{Nothing, String}
-

A restart file restart.jld2 with the prognostic variables is written to the output folder (or current path) that can be used to restart the model. restart.jld2 will then be used as initial conditions. The prognostic variables are bitrounded for compression and the 2nd leapfrog time step is discarded. Variables in restart file are unscaled.

source
SpeedyWeather.zero_tendencies!Method
zero_tendencies!(
+

A restart file restart.jld2 with the prognostic variables is written to the output folder (or current path) that can be used to restart the model. restart.jld2 will then be used as initial conditions. The prognostic variables are bitrounded for compression and the 2nd leapfrog time step is discarded. Variables in restart file are unscaled.

source
+

Set the tendencies in diagn to zero.

source
diff --git a/previews/PR387/installation/index.html b/previews/PR387/installation/index.html index 88bce8de6..8ec4d6a8f 100644 --- a/previews/PR387/installation/index.html +++ b/previews/PR387/installation/index.html @@ -1,3 +1,3 @@ Installation · SpeedyWeather.jl

Installation

SpeedyWeather.jl is registered in the Julia Registry. In most cases just open the Julia REPL and type

julia> using Pkg
-julia> Pkg.add("SpeedyWeather")

or, equivalently, (] opens the package manager)

julia>] add SpeedyWeather

which will automatically install the latest release and all necessary dependencies. If you run into any troubles please raise an issue.

However, you may want to make use of the latest features, then install directly from the main branch with

julia> Pkg.add(url="https://github.com/SpeedyWeather/SpeedyWeather.jl",rev="main")

other branches than main can be similarly installed. You can also type, equivalently,

julia>] add https://github.com/SpeedyWeather/SpeedyWeather.jl#main

Compatibility with Julia versions

SpeedyWeather.jl usually lives on the latest minor release and/or its predecessor. At the moment (June 2023) this means

  • Julia v1.8
  • Julia v1.9

are supported, but we dropped the support of earlier versions.

+julia> Pkg.add("SpeedyWeather")

or, equivalently, (] opens the package manager)

julia>] add SpeedyWeather

which will automatically install the latest release and all necessary dependencies. If you run into any troubles please raise an issue.

However, you may want to make use of the latest features, then install directly from the main branch with

julia> Pkg.add(url="https://github.com/SpeedyWeather/SpeedyWeather.jl",rev="main")

other branches than main can be similarly installed. You can also type, equivalently,

julia>] add https://github.com/SpeedyWeather/SpeedyWeather.jl#main

Compatibility with Julia versions

SpeedyWeather.jl usually lives on the latest minor release and/or its predecessor. At the moment (June 2023) this means

are supported, but we dropped the support of earlier versions.

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b/previews/PR387/lowertriangularmatrices/index.html @@ -55,6 +55,6 @@ 3×3 Matrix{Float32}: 0.332341 0.0 0.0 0.506243 0.766275 0.0 - 1.68542 1.59366 0.996616

Note, however, that the latter includes a conversion to Matrix, which is true for many operations, including inv or \. Hence when trying to do more sophisticated linear algebra with LowerTriangularMatrix we quickly leave lower triangular-land and go back to normal matrix-land.

Function and type index

SpeedyWeather.LowerTriangularMatrices.LowerTriangularMatrixType
L = LowerTriangularMatrix{T}(v::Vector{T},m::Int,n::Int)

A lower triangular matrix implementation that only stores the non-zero entries explicitly. L<:AbstractMatrix although in general we have L[i] != Matrix(L)[i], the former skips zero entries, tha latter includes them.

source
Base.fill!Method
fill!(L::LowerTriangularMatrix,x)

Fills the elements of L with x. Faster than fill!(::AbstractArray,x) as only the non-zero elements in L are assigned with x.

source
SpeedyWeather.LowerTriangularMatrices.eachharmonicMethod
unit_range = eachharmonic(Ls::LowerTriangularMatrix...)

creates unit_range::UnitRange to loop over all non-zeros in the LowerTriangularMatrices provided as arguments. Checks bounds first. All LowerTriangularMatrix's need to be of the same size. Like eachindex but skips the upper triangle with zeros in L.

source
SpeedyWeather.LowerTriangularMatrices.ij2kMethod
k = ij2k(   i::Integer,     # row index of matrix
+ 1.68542   1.59366   0.996616

Note, however, that the latter includes a conversion to Matrix, which is true for many operations, including inv or \. Hence when trying to do more sophisticated linear algebra with LowerTriangularMatrix we quickly leave lower triangular-land and go back to normal matrix-land.

Function and type index

SpeedyWeather.LowerTriangularMatrices.LowerTriangularMatrixType
L = LowerTriangularMatrix{T}(v::Vector{T},m::Int,n::Int)

A lower triangular matrix implementation that only stores the non-zero entries explicitly. L<:AbstractMatrix although in general we have L[i] != Matrix(L)[i], the former skips zero entries, tha latter includes them.

source
Base.fill!Method
fill!(L::LowerTriangularMatrix,x)

Fills the elements of L with x. Faster than fill!(::AbstractArray,x) as only the non-zero elements in L are assigned with x.

source
SpeedyWeather.LowerTriangularMatrices.eachharmonicMethod
unit_range = eachharmonic(Ls::LowerTriangularMatrix...)

creates unit_range::UnitRange to loop over all non-zeros in the LowerTriangularMatrices provided as arguments. Checks bounds first. All LowerTriangularMatrix's need to be of the same size. Like eachindex but skips the upper triangle with zeros in L.

source
SpeedyWeather.LowerTriangularMatrices.ij2kMethod
k = ij2k(   i::Integer,     # row index of matrix
             j::Integer,     # column index of matrix
-            m::Integer)     # number of rows in matrix

Converts the index pair i,j of an mxn LowerTriangularMatrix L to a single index k that indexes the same element in the corresponding vector that stores only the lower triangle (the non-zero entries) of L.

source
+ m::Integer) # number of rows in matrix

Converts the index pair i,j of an mxn LowerTriangularMatrix L to a single index k that indexes the same element in the corresponding vector that stores only the lower triangle (the non-zero entries) of L.

source diff --git a/previews/PR387/output/index.html b/previews/PR387/output/index.html index 42c216170..aa10f2dd4 100644 --- a/previews/PR387/output/index.html +++ b/previews/PR387/output/index.html @@ -63,4 +63,4 @@ • output_dt_sec::Int64: actual output time step [sec] • output_vars::Vector{Symbol}: [OPTION] which variables to output, - u, v, vor, div, pres, temp, humid + u, v, vor, div, pres, temp, humid diff --git a/previews/PR387/parameterizations/index.html b/previews/PR387/parameterizations/index.html index 3420c81f6..5e99d1c82 100644 --- a/previews/PR387/parameterizations/index.html +++ b/previews/PR387/parameterizations/index.html @@ -1,2 +1,2 @@ -Parameterizations · SpeedyWeather.jl
+Parameterizations · SpeedyWeather.jl
diff --git a/previews/PR387/ringgrids/index.html b/previews/PR387/ringgrids/index.html index 0913596b4..27e21434f 100644 --- a/previews/PR387/ringgrids/index.html +++ b/previews/PR387/ringgrids/index.html @@ -1,93 +1,93 @@ Submodule: RingGrids · SpeedyWeather.jl

RingGrids

RingGrids is a submodule that has been developed for SpeedyWeather.jl which is technically independent (SpeedyWeather.jl however imports it and so does SpeedyTransforms) and can also be used without running simulations. It is just not put into its own respective repository.

RingGrids defines several iso-latitude grids, which are mathematically described in the section on Grids. In brief, they include the regular latitude-longitude grids (here called FullClenshawGrid) as well as grids which latitudes are shifted to the Gaussian latitudes and reduced grids, meaning that they have a decreasing number of longitudinal points towards the poles to be more equal-area than full grids.

RingGrids defines and exports the following grids:

  • full grids: FullClenshawGrid, FullGaussianGrid, FullHEALPix, and FullOctaHEALPix
  • reduced grids: OctahedralGaussianGrid, OctahedralClenshawGrid, OctaHEALPixGrid and HEALPixGrid

The following explanation of how to use these can be mostly applied to any of them, however, there are certain functions that are not defined, e.g. the full grids can be trivially converted to a Matrix (i.e. they are rectangular grids) but not the OctahedralGaussianGrid.

What is a ring?

We use the term ring, short for iso-latitude ring, to refer to a sequence of grid points that all share the same latitude. A latitude-longitude grid is a ring grid, as it organises its grid-points into rings. However, other grids, like the cubed-sphere are not based on iso-latitude rings. SpeedyWeather.jl only works with ring grids because its a requirement for the Spherical Harmonic Transform to be efficient. See Grids.

Creating data on a RingGrid

Every grid in RingGrids has a grid.data field, which is a vector containing the data on the grid. The grid points are unravelled west to east then north to south, meaning that it starts at 90˚N and 0˚E then walks eastward for 360˚ before jumping on the next latitude ring further south, this way circling around the sphere till reaching the south pole. This may also be called ring order.

Data in a Matrix which follows this ring order can be put on a FullGaussianGrid like so

using SpeedyWeather.RingGrids
 map = randn(Float32,8,4)
8×4 Matrix{Float32}:
-  0.0323783   1.24392    1.11506    0.219666
- -1.48427    -1.58416    0.403698  -0.840577
- -0.399655   -0.171206  -0.536831  -0.878711
-  1.44365     0.416995   1.34314   -0.140653
- -0.722154    0.406199   0.138884  -0.905367
- -2.56936     1.35457    0.698576   0.719075
- -1.27974    -0.771802   1.4471     0.800861
-  0.125739    0.3444    -2.22072   -0.84624
grid = FullGaussianGrid(map)
32-element, 4-ring FullGaussianGrid{Float32}:
-  0.032378264
- -1.4842738
- -0.39965534
-  1.443653
- -0.7221541
- -2.5693562
- -1.2797434
-  0.1257392
-  1.2439239
- -1.5841565
+ -2.26633   -0.305644  -0.42068   -0.258864
+ -0.983142   0.865884  -0.29356   -0.413715
+  0.167005   1.72373   -0.922489   1.03346
+  0.603312   0.241117   1.20357   -0.621933
+  0.213815  -0.812776   0.185387  -1.81038
+  2.0115    -0.706547   2.15153   -0.276284
+ -1.99743   -2.05207   -0.174395   0.710069
+ -1.25383    1.18613    0.524713   0.402597
grid = FullGaussianGrid(map)
32-element, 4-ring FullGaussianGrid{Float32}:
+ -2.2663288
+ -0.983142
+  0.16700459
+  0.6033119
+  0.2138146
+  2.011503
+ -1.9974277
+ -1.2538292
+ -0.30564356
+  0.8658837
   ⋮
- -2.2207184
-  0.21966629
- -0.84057707
- -0.87871104
- -0.14065346
- -0.9053671
-  0.71907514
-  0.80086076
- -0.84623975

A full Gaussian grid has always $2N$ x $N$ grid points, but a FullClenshawGrid has $2N$ x $N-1$, if those dimensions don't match, the creation will throw an error. To reobtain the data from a grid, you can access its data field which returns a normal Vector

grid.data
32-element Vector{Float32}:
-  0.032378264
- -1.4842738
- -0.39965534
-  1.443653
- -0.7221541
- -2.5693562
- -1.2797434
-  0.1257392
-  1.2439239
- -1.5841565
+  0.5247126
+ -0.2588637
+ -0.41371524
+  1.0334626
+ -0.62193286
+ -1.8103814
+ -0.27628377
+  0.7100687
+  0.4025973

A full Gaussian grid has always $2N$ x $N$ grid points, but a FullClenshawGrid has $2N$ x $N-1$, if those dimensions don't match, the creation will throw an error. To reobtain the data from a grid, you can access its data field which returns a normal Vector

grid.data
32-element Vector{Float32}:
+ -2.2663288
+ -0.983142
+  0.16700459
+  0.6033119
+  0.2138146
+  2.011503
+ -1.9974277
+ -1.2538292
+ -0.30564356
+  0.8658837
   ⋮
- -2.2207184
-  0.21966629
- -0.84057707
- -0.87871104
- -0.14065346
- -0.9053671
-  0.71907514
-  0.80086076
- -0.84623975

Which can be reshaped to reobtain map from above. Alternatively you can Matrix(grid) to do this in one step

map == Matrix(FullGaussianGrid(map))
true

You can also use zeros,ones,rand,randn to create a grid, whereby nlat_half, i.e. the number of latitude rings on one hemisphere, Equator included, is used as a resolution parameter and here as a second argument.

nlat_half = 4
+  0.5247126
+ -0.2588637
+ -0.41371524
+  1.0334626
+ -0.62193286
+ -1.8103814
+ -0.27628377
+  0.7100687
+  0.4025973

Which can be reshaped to reobtain map from above. Alternatively you can Matrix(grid) to do this in one step

map == Matrix(FullGaussianGrid(map))
true

You can also use zeros,ones,rand,randn to create a grid, whereby nlat_half, i.e. the number of latitude rings on one hemisphere, Equator included, is used as a resolution parameter and here as a second argument.

nlat_half = 4
 grid = randn(OctahedralGaussianGrid{Float16},nlat_half)
208-element, 8-ring OctahedralGaussianGrid{Float16}:
-  0.3687
- -0.896
-  0.608
- -0.7554
- -0.7876
- -1.048
- -0.6865
- -1.214
- -0.586
- -0.822
+  1.301
+  1.135
+ -0.8794
+ -1.18
+ -0.7837
+ -0.852
+  0.2233
+ -0.9014
+  0.0797
+  0.765
   ⋮
-  1.637
-  0.8174
-  0.3098
-  0.515
-  1.309
-  0.719
-  1.849
-  0.3088
-  0.771

and any element type T can be used for OctahedralGaussianGrid{T} and similar for other grid types.

Visualising RingGrid data

As only the full grids can be reshaped into a matrix, the underlying data structure of any AbstractGrid is a vector. As shown in the examples above, one can therefore inspect the data as if it was a vector. But as that data has, through its <:AbstractGrid type, all the geometric information available to plot it on a map, RingGrids also exports plot function, based on UnicodePlots' heatmap.

nlat_half = 24
+  0.00484
+ -0.02615
+  1.025
+ -1.178
+ -1.298
+ -2.137
+ -1.457
+ -0.61
+ -0.3967

and any element type T can be used for OctahedralGaussianGrid{T} and similar for other grid types.

Visualising RingGrid data

As only the full grids can be reshaped into a matrix, the underlying data structure of any AbstractGrid is a vector. As shown in the examples above, one can therefore inspect the data as if it was a vector. But as that data has, through its <:AbstractGrid type, all the geometric information available to plot it on a map, RingGrids also exports plot function, based on UnicodePlots' heatmap.

nlat_half = 24
 grid = randn(OctahedralGaussianGrid,nlat_half)
 plot(grid)
                   48-ring OctahedralGaussianGrid{Float64}                
        ┌────────────────────────────────────────────────────────────┐  3  
-    90 ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ┌──┐
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄ ▄▄
-       ▄▄ ▄▄
-    ˚N ▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
-       ▄▄▄▄ ▄▄
-       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
-   -90 ▄▄▄▄▄▄▄▄▄▄▄▄▄ └──┘
+    90 ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ┌──┐
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄ ▄▄
+    ˚N ▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
+       ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄
+   -90 ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ └──┘
        └────────────────────────────────────────────────────────────┘ -3  
         0                           ˚E                           360      

Indexing RingGrids

All RingGrids have a single index ij which follows the ring order. While this is obviously not super exciting here are some examples how to make better use of the information that the data sits on a grid.

We obtain the latitudes of the rings of a grid by calling get_latd (get_lond is only defined for full grids, or use get_latdlonds for latitudes, longitudes per grid point not per ring)

grid = randn(OctahedralClenshawGrid,5)
 latd = get_latd(grid)
9-element Vector{Float64}:
@@ -111,161 +111,161 @@
 end

eachring creates a vector of UnitRange indices, such that we can loop over the ring index j (j=1 being closest to the North pole) pull the coriolis parameter at that latitude and then loop over all in-ring indices i (changing longitudes) to do something on the grid. Something similar can be done to scale/unscale with the cosine of latitude for example. We can always loop over all grid-points like so

for ij in eachgridpoint(grid)
     grid[ij]
 end

or use eachindex instead.

Interpolation on RingGrids

In most cases we will want to use RingGrids so that our data directly comes with the geometric information of where the grid-point is one the sphere. We have seen how to use get_latd, get_lond, ... for that above. This information generally can also be used to interpolate our data from grid to another or to request an interpolated value on some coordinates. Using our data on grid which is an OctahedralGaussianGrid from above we can use the interpolate function to get it onto a FullGaussianGrid (or any other grid for purpose)

grid = randn(OctahedralGaussianGrid{Float32},4)
208-element, 8-ring OctahedralGaussianGrid{Float32}:
-  1.4255751
- -1.309481
-  0.6231467
- -1.7938612
-  0.07164579
-  0.24647328
- -0.90753895
-  0.8543748
- -0.6990326
-  0.58978236
+ -0.24358216
+  1.9246707
+  0.48408505
+  1.2275171
+ -1.6430018
+  0.43321857
+ -0.9144202
+ -0.2961518
+ -0.6149102
+ -0.219993
   ⋮
- -1.6980417
-  1.5007036
- -1.8604438
-  0.28537956
-  0.5705362
- -1.3501593
- -0.06627656
-  0.81239814
- -0.4265069
interpolate(FullGaussianGrid,grid)
128-element, 8-ring FullGaussianGrid{Float64}:
-  1.4255751371383667
- -0.8263241052627563
- -0.5853572487831116
- -0.39473098516464233
-  0.2464732825756073
- -0.46706050634384155
-  0.0776711106300354
-  0.267578661441803
- -1.0115002393722534
- -0.16445070505142212
+  0.12671563
+  0.3333629
+ -0.8086505
+  0.55352676
+  0.2698654
+  1.4028726
+ -0.47198698
+  0.118484855
+ -1.241099
interpolate(FullGaussianGrid,grid)
128-element, 8-ring FullGaussianGrid{Float64}:
+ -0.24358215928077698
+  1.5645242929458618
+  0.8558010756969452
+ -0.9253720641136169
+  0.4332185685634613
+ -0.7598530948162079
+ -0.4555309861898422
+ -0.31872229278087616
+ -0.18993614614009857
+  0.7200056314468384
   ⋮
-  0.35125666856765747
- -0.6507344245910645
- -0.8983553647994995
- -0.1798701286315918
- -0.25107622146606823
-  0.570536196231842
- -1.0291886031627655
-  0.37306078523397446
- -0.11678066849708557

By default this will linearly interpolate (it's an Anvil interpolator, see below) onto a grid with the same nlat_half, but we can also coarse-grain or fine-grain by specifying nlat_half directly as 2nd argument

interpolate(FullGaussianGrid,6,grid)
288-element, 12-ring FullGaussianGrid{Float64}:
-  0.9876192403267864
- -0.562728559682099
-  0.0035992605104878256
- -0.38024061305323653
- -0.7792992702468243
-  0.08648053012714597
-  0.18558029501273607
- -0.4685635962081578
-  0.19959058342871142
-  0.07075907288502434
+ -0.7010833024978638
+  0.5267024636268616
+  0.1783774495124817
+ -0.23764380812644958
+  0.21298244595527405
+  0.26986539363861084
+  0.93415766954422
+ -0.176751047372818
+ -0.9012030363082886

By default this will linearly interpolate (it's an Anvil interpolator, see below) onto a grid with the same nlat_half, but we can also coarse-grain or fine-grain by specifying nlat_half directly as 2nd argument

interpolate(FullGaussianGrid,6,grid)
288-element, 12-ring FullGaussianGrid{Float64}:
+ -0.1558803784178822
+  1.0731789110809589
+  0.6657218598377481
+  0.5919330245255432
+  0.1939250796678761
+ -0.8724038284238359
+  0.3044874344622578
+ -0.4594123214344641
+ -0.33182334936544283
+ -0.3000504625686988
   ⋮
- -0.14636683744693166
- -0.8029747093368653
-  0.20242928660925114
-  0.36406836797782877
- -0.7246647087052893
- -0.36020319438703347
-  0.22974327150775223
-  0.24767977060844396
- -0.4368863285367758

So we got from an 8-ring OctahedralGaussianGrid{Float16} to a 12-ring FullGaussianGrid{Float64}, so it did a conversion from Float16 to Float64 on the fly too, because the default precision is Float64 unless specified. interpolate(FullGaussianGrid{Float16},6,grid) would have interpolated onto a grid with element type Float16.

One can also interpolate onto a given coordinate ˚N, ˚E like so

interpolate(30.0,10.0,grid)
-0.15453684f0

we interpolated the data from grid onto 30˚N, 10˚E. To do this simultaneously for many coordinates they can be packed into a vector too

interpolate([30.0,40.0,50.0],[10.0,10.0,10.0],grid)
3-element Vector{Float32}:
- -0.15453684
- -0.23148234
- -0.19469064

which returns the data on grid at 30˚N, 40˚N, 50˚N, and 10˚E respectively. Note how the interpolation here retains the element type of grid.

Performance for RingGrid interpolation

Every time an interpolation like interpolate(30.0,10.0,grid) is called, several things happen, which are important to understand to know how to get the fastest interpolation out of this module in a given situation. Under the hood an interpolation takes three arguments

  • output vector
  • input grid
  • interpolator

The output vector is just an array into which the interpolated data is written, providing this prevents unnecessary allocation of memory in case the destination array of the interpolation already exists. The input grid contains the data which is subject to interpolation, it must come on a ring grid, however, its coordinate information is actually already in the interpolator. The interpolator knows about the geometry of the grid the data is coming on and the coordinates it is supposed to interpolate onto. It has therefore precalculated the indices that are needed to access the right data on the input grid and the weights it needs to apply in the actual interpolation operation. The only thing it does not know is the actual data values of that grid. So in the case you want to interpolate from grid A to grid B many times, you can just reuse the same interpolator. If you want to change the coordinates of the output grid but its total number of points remain constants then you can update the locator inside the interpolator and only else you will need to create a new interpolator. Let's look at this in practice. Say we have two grids an want to interpolate between them

grid_in = rand(HEALPixGrid,4)
+ -0.21639183999182812
+ -0.29594097342053427
+  0.2896133830752481
+  0.1288218863251114
+  0.7710592180400461
+  0.049305667688641044
+ -0.17497186815214977
+ -0.28241724415350733
+ -0.876854486115074

So we got from an 8-ring OctahedralGaussianGrid{Float16} to a 12-ring FullGaussianGrid{Float64}, so it did a conversion from Float16 to Float64 on the fly too, because the default precision is Float64 unless specified. interpolate(FullGaussianGrid{Float16},6,grid) would have interpolated onto a grid with element type Float16.

One can also interpolate onto a given coordinate ˚N, ˚E like so

interpolate(30.0,10.0,grid)
1.0182791f0

we interpolated the data from grid onto 30˚N, 10˚E. To do this simultaneously for many coordinates they can be packed into a vector too

interpolate([30.0,40.0,50.0],[10.0,10.0,10.0],grid)
3-element Vector{Float32}:
+  1.0182791
+  0.45855322
+ -0.15471964

which returns the data on grid at 30˚N, 40˚N, 50˚N, and 10˚E respectively. Note how the interpolation here retains the element type of grid.

Performance for RingGrid interpolation

Every time an interpolation like interpolate(30.0,10.0,grid) is called, several things happen, which are important to understand to know how to get the fastest interpolation out of this module in a given situation. Under the hood an interpolation takes three arguments

  • output vector
  • input grid
  • interpolator

The output vector is just an array into which the interpolated data is written, providing this prevents unnecessary allocation of memory in case the destination array of the interpolation already exists. The input grid contains the data which is subject to interpolation, it must come on a ring grid, however, its coordinate information is actually already in the interpolator. The interpolator knows about the geometry of the grid the data is coming on and the coordinates it is supposed to interpolate onto. It has therefore precalculated the indices that are needed to access the right data on the input grid and the weights it needs to apply in the actual interpolation operation. The only thing it does not know is the actual data values of that grid. So in the case you want to interpolate from grid A to grid B many times, you can just reuse the same interpolator. If you want to change the coordinates of the output grid but its total number of points remain constants then you can update the locator inside the interpolator and only else you will need to create a new interpolator. Let's look at this in practice. Say we have two grids an want to interpolate between them

grid_in = rand(HEALPixGrid,4)
 grid_out = zeros(FullClenshawGrid,6)
 interp = RingGrids.interpolator(grid_out,grid_in)
SpeedyWeather.RingGrids.AnvilInterpolator{Float64, HEALPixGrid{Float64}}(SpeedyWeather.RingGrids.GridGeometry{HEALPixGrid{Float64}}(4, 7, 48, [90.0, 66.44353569089876, 41.8103148957786, 19.471220634490685, 0.0, -19.47122063449071, -41.81031489577862, -66.44353569089876, -90.00000000000001], [45.0, 135.0, 225.0, 315.0, 22.5, 67.5, 112.5, 157.5, 202.5, 247.49999999999997  …  112.5, 157.5, 202.5, 247.49999999999997, 292.5, 337.5, 45.0, 135.0, 225.0, 315.0], UnitRange{Int64}[1:4, 5:12, 13:20, 21:28, 29:36, 37:44, 45:48], [4, 8, 8, 8, 8, 8, 4], [45.0, 22.5, 0.0, 22.5, 0.0, 22.5, 45.0]), SpeedyWeather.RingGrids.AnvilLocator{Float64}(264, [0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  46, 46, 47, 47, 47, 47, 47, 48, 48, 48], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  47, 47, 48, 48, 48, 48, 48, 45, 45, 45], [4, 4, 4, 1, 1, 1, 1, 1, 1, 2  …  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1, 1, 1, 2, 2, 2, 2, 2, 2, 3  …  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0.6367678868600251, 0.6367678868600251, 0.6367678868600251, 0.6367678868600251, 0.6367678868600251, 0.6367678868600251, 0.6367678868600251, 0.6367678868600251, 0.6367678868600251, 0.6367678868600251  …  0.3632321131399741, 0.3632321131399741, 0.3632321131399741, 0.3632321131399741, 0.3632321131399741, 0.3632321131399741, 0.3632321131399741, 0.3632321131399741, 0.3632321131399741, 0.3632321131399741], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.8333333333333333, 0.9999999999999998, 0.16666666666666652, 0.33333333333333304, 0.5, 0.6666666666666665, 0.8333333333333326, 0.0, 0.16666666666666652, 0.3333333333333326], [0.5, 0.6666666666666667, 0.8333333333333333, 0.0, 0.16666666666666657, 0.33333333333333315, 0.5, 0.6666666666666666, 0.8333333333333331, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]))

Now we have created an interpolator interp which knows about the geometry where to interpolate from and the coordinates there to interpolate to. It is also initialized, meaning it has precomputed the indices to of grid_in that are supposed to be used. It just does not know about the data of grid_in (and neither of grid_out which will be overwritten anyway). We can now do

interpolate!(grid_out,grid_in,interp)
 grid_out
264-element, 11-ring FullClenshawGrid{Float64}:
- 0.6654969470097967
- 0.6931246696185578
- 0.7207523922273189
- 0.7483801148360801
- 0.7509249476597815
- 0.7534697804834828
- 0.7560146133071842
- 0.7585594461308856
- 0.7611042789545869
- 0.7636491117782882
+ 0.32029472056477953
+ 0.35042436348673184
+ 0.3805540064086841
+ 0.4106836493306364
+ 0.3625733676326187
+ 0.314463085934601
+ 0.2663528042365832
+ 0.21824252253856546
+ 0.17013224084054776
+ 0.12202195914252997
  ⋮
- 0.7116468020222301
- 0.6820951340028104
- 0.6525434659833907
- 0.6229917979639711
- 0.5934401299445514
- 0.5638884619251319
- 0.534336793905712
- 0.5073764005689011
- 0.4804160072320902

which is identical to interpolate(grid_out,grid_in) but you can reuse interp for other data. The interpolation can also handle various element types (the interpolator interp does not have to be updated for this either)

grid_out = zeros(FullClenshawGrid{Float16},6);
+ 0.4129701421886367
+ 0.4863418202424242
+ 0.5597134982962119
+ 0.6330851763499996
+ 0.7064568544037874
+ 0.7798285324575747
+ 0.8532002105113627
+ 0.8578166657966629
+ 0.862433121081963

which is identical to interpolate(grid_out,grid_in) but you can reuse interp for other data. The interpolation can also handle various element types (the interpolator interp does not have to be updated for this either)

grid_out = zeros(FullClenshawGrid{Float16},6);
 interpolate!(grid_out,grid_in,interp)
 grid_out
264-element, 11-ring FullClenshawGrid{Float16}:
- 0.6655
- 0.6934
- 0.7207
- 0.7485
- 0.751
- 0.7534
- 0.756
- 0.759
- 0.761
- 0.7637
+ 0.3203
+ 0.3503
+ 0.3806
+ 0.4106
+ 0.3625
+ 0.3145
+ 0.2664
+ 0.2183
+ 0.1702
+ 0.122
  ⋮
- 0.7114
- 0.682
- 0.6523
- 0.623
- 0.5933
- 0.564
- 0.534
- 0.5073
- 0.4805

and we have converted data from a HEALPixGrid{Float64} (Float64 is always default if not specified) to a FullClenshawGrid{Float16} including the type conversion Float64-Float16 on the fly. Technically there are three data types and their combinations possible: The input data will come with a type, the output array has an element type and the interpolator has precomputed weights with a given type. Say we want to go from Float16 data on an OctahedralGaussianGrid to Float16 on a FullClenshawGrid but using Float32 precision for the interpolation itself, we would do this by

grid_in = randn(OctahedralGaussianGrid{Float16},24)
+ 0.413
+ 0.4863
+ 0.5596
+ 0.6333
+ 0.7065
+ 0.78
+ 0.853
+ 0.858
+ 0.8623

and we have converted data from a HEALPixGrid{Float64} (Float64 is always default if not specified) to a FullClenshawGrid{Float16} including the type conversion Float64-Float16 on the fly. Technically there are three data types and their combinations possible: The input data will come with a type, the output array has an element type and the interpolator has precomputed weights with a given type. Say we want to go from Float16 data on an OctahedralGaussianGrid to Float16 on a FullClenshawGrid but using Float32 precision for the interpolation itself, we would do this by

grid_in = randn(OctahedralGaussianGrid{Float16},24)
 grid_out = zeros(FullClenshawGrid{Float16},24)
 interp = RingGrids.interpolator(Float32,grid_out,grid_in)
 interpolate!(grid_out,grid_in,interp)
 grid_out
4512-element, 47-ring FullClenshawGrid{Float16}:
-  0.09125
-  0.1506
-  0.21
-  0.2693
-  0.3286
-  0.538
-  0.8696
-  1.201
-  1.532
-  1.582
+ -0.315
+ -0.5283
+ -0.7417
+ -0.9556
+ -1.169
+ -1.023
+ -0.582
+ -0.1407
+  0.3003
+  0.485
   ⋮
-  1.0205
-  1.049
-  0.8564
-  0.665
-  0.4731
-  0.1084
-  0.05106
- -0.006535
- -0.06415

As a last example we want to illustrate a situation where we would always want to interpolate onto 10 coordinates, but their locations may change. In order to avoid recreating an interpolator object we would do (AnvilInterpolator is described in Anvil interpolator)

npoints = 10    # number of coordinates to interpolate onto
+ -0.5938
+ -0.665
+ -0.8896
+ -1.114
+ -1.339
+ -1.292
+ -1.1
+ -0.9062
+ -0.7134

As a last example we want to illustrate a situation where we would always want to interpolate onto 10 coordinates, but their locations may change. In order to avoid recreating an interpolator object we would do (AnvilInterpolator is described in Anvil interpolator)

npoints = 10    # number of coordinates to interpolate onto
 interp = AnvilInterpolator(Float32,HEALPixGrid,24,npoints)
SpeedyWeather.RingGrids.AnvilInterpolator{Float32, HEALPixGrid}(SpeedyWeather.RingGrids.GridGeometry{HEALPixGrid}(24, 47, 1728, [90.0, 86.10076357950555, 82.19700324028634, 78.28414760510762, 74.35752898700072, 70.41233167174659, 66.44353569089876, 62.445854167002665, 58.41366190347208, 54.34091230386124  …  -54.340912303861266, -58.41366190347208, -62.445854167002665, -66.44353569089876, -70.41233167174661, -74.35752898700072, -78.28414760510763, -82.19700324028634, -86.10076357950557, -90.00000000000001], [45.0, 135.0, 225.0, 315.0, 22.5, 67.5, 112.5, 157.5, 202.5, 247.49999999999997  …  112.5, 157.5, 202.5, 247.49999999999997, 292.5, 337.5, 45.0, 135.0, 225.0, 315.0], UnitRange{Int64}[1:4, 5:12, 13:24, 25:40, 41:60, 61:84, 85:112, 113:144, 145:180, 181:220  …  1509:1548, 1549:1584, 1585:1616, 1617:1644, 1645:1668, 1669:1688, 1689:1704, 1705:1716, 1717:1724, 1725:1728], [4, 8, 12, 16, 20, 24, 28, 32, 36, 40  …  40, 36, 32, 28, 24, 20, 16, 12, 8, 4], [45.0, 22.5, 14.999999999999998, 11.25, 9.0, 7.499999999999999, 6.428571428571429, 5.625, 5.0, 4.5  …  4.5, 5.0, 5.625, 6.428571428571429, 7.499999999999999, 9.0, 11.25, 14.999999999999998, 22.5, 45.0]), SpeedyWeather.RingGrids.AnvilLocator{Float32}(10, [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]))

with the first argument being the number format used during interpolation, then the input grid type, its resolution in terms of nlat_half and then the number of points to interpolate onto. However, interp is not yet initialized as it does not know about the destination coordinates yet. Let's define them, but note that we already decided there's only 10 of them above.

latds = collect(0.0:5.0:45.0)
 londs = collect(-10.0:2.0:8.0)

now we can update the locator inside our interpolator as follows

RingGrids.update_locator!(interp,latds,londs)

With data matching the input from above, a nlat_half=24 HEALPixGrid, and allocate 10-element output vector

output_vec = zeros(10)
 grid_input = rand(HEALPixGrid,24)

we can use the interpolator as follows

interpolate!(output_vec,grid_input,interp)
10-element Vector{Float64}:
- 0.588230785316095
- 0.8642179847856983
- 0.7622365191567455
- 0.36272690191511137
- 0.6500977513224726
- 0.5387626538104123
- 0.5349327817054701
- 0.2688604447917838
- 0.31697114719702313
- 0.5178650673443685

which is the approximately the same as doing it directly without creating an interpolator first and updating its locator

interpolate(latds,londs,grid_input)
10-element Vector{Float64}:
- 0.5882307855597485
- 0.8642179844229808
- 0.7622365265119007
- 0.36272689778751194
- 0.6500977516887622
- 0.5387626559331357
- 0.5349327893548189
- 0.26886044495477024
- 0.31697114944356103
- 0.5178650678077409

but allows for a reuse of the interpolator. Note that the two output arrays are not exactly identical because we manually set our interpolator interp to use Float32 for the interpolation whereas the default is Float64.

Anvil interpolator

Currently the only interpolator implemented is a 4-point bilinear interpolator, which schematically works as follows. Anvil interpolation is the bilinear average of a,b,c,d which are values at grid points in an anvil-shaped configuration at location x, which is denoted by Δab,Δcd,Δy, the fraction of distances between a-b,c-d, and ab-cd, respectively. Note that a,c and b,d do not necessarily share the same longitude/x-coordinate.

        0..............1    # fraction of distance Δab between a,b
+ 0.2244148047994153
+ 0.8580780134258924
+ 0.6922997966761509
+ 0.7277266122431129
+ 0.46313343505697335
+ 0.5849641285849124
+ 0.18175390369548128
+ 0.45246715719948843
+ 0.2666881475859376
+ 0.3937135457271472

which is the approximately the same as doing it directly without creating an interpolator first and updating its locator

interpolate(latds,londs,grid_input)
10-element Vector{Float64}:
+ 0.22441480329069233
+ 0.8580780127000087
+ 0.6922997982595649
+ 0.7277266204152792
+ 0.4631334344165774
+ 0.5849641285411729
+ 0.18175390419597942
+ 0.4524671509034788
+ 0.26668814919567135
+ 0.39371354639827566

but allows for a reuse of the interpolator. Note that the two output arrays are not exactly identical because we manually set our interpolator interp to use Float32 for the interpolation whereas the default is Float64.

Anvil interpolator

Currently the only interpolator implemented is a 4-point bilinear interpolator, which schematically works as follows. Anvil interpolation is the bilinear average of a,b,c,d which are values at grid points in an anvil-shaped configuration at location x, which is denoted by Δab,Δcd,Δy, the fraction of distances between a-b,c-d, and ab-cd, respectively. Note that a,c and b,d do not necessarily share the same longitude/x-coordinate.

        0..............1    # fraction of distance Δab between a,b
         |<  Δab   >|
 
 0^      a -------- o - b    # anvil-shaped average of a,b,c,d at location x
@@ -278,26 +278,26 @@
           |<  Δcd >|
           0...............1 # fraction of distance Δcd between c,d
 
-^ fraction of distance Δy between a-b and c-d.

This interpolation is chosen as by definition of the ring grids, a and b share the same latitude, so do c and d, but the longitudes can be different for all four, a,b,c,d.

Function index

SpeedyWeather.RingGrids.AbstractFullGridType
abstract type AbstractFullGrid{T} <: AbstractGrid{T} end

An AbstractFullGrid is a horizontal grid with a constant number of longitude points across latitude rings. Different latitudes can be used, Gaussian latitudes, equi-angle latitdes, or others.

source
SpeedyWeather.RingGrids.AbstractGridType
abstract type AbstractGrid{T} <: AbstractVector{T} end

The abstract supertype for all spatial grids on the sphere supported by SpeedyWeather.jl. Every new grid has to be of the form

abstract type AbstractGridClass{T} <: AbstractGrid{T} end
+^ fraction of distance Δy between a-b and c-d.

This interpolation is chosen as by definition of the ring grids, a and b share the same latitude, so do c and d, but the longitudes can be different for all four, a,b,c,d.

Function index

SpeedyWeather.RingGrids.AbstractFullGridType
abstract type AbstractFullGrid{T} <: AbstractGrid{T} end

An AbstractFullGrid is a horizontal grid with a constant number of longitude points across latitude rings. Different latitudes can be used, Gaussian latitudes, equi-angle latitdes, or others.

source
SpeedyWeather.RingGrids.AbstractGridType
abstract type AbstractGrid{T} <: AbstractVector{T} end

The abstract supertype for all spatial grids on the sphere supported by SpeedyWeather.jl. Every new grid has to be of the form

abstract type AbstractGridClass{T} <: AbstractGrid{T} end
 struct MyNewGrid{T} <: AbstractGridClass{T}
     data::Vector{T}     # all grid points unravelled into a vector
     nlat_half::Int      # resolution: latitude rings on one hemisphere (Equator incl)
-end

MyNewGrid should belong to a grid class like AbstractFullGrid, AbstractOctahedralGrid or AbstractHEALPixGrid (that already exist but you may introduce a new class of grids) that share certain features such as the number of longitude points per latitude ring and indexing, but may have different latitudes or offset rotations. Each new grid Grid (or grid class) then has to implement the following methods (as an example, see octahedral.jl)

Fundamental grid properties getnpoints # total number of grid points nlatodd # does the grid have an odd number of latitude rings? getnlat # total number of latitude rings getnlat_half # number of latitude rings on one hemisphere incl Equator

Indexing getnlonmax # maximum number of longitudes points (at the Equator) getnlonperring # number of longitudes on ring j eachindexinring # a unit range that indexes all longitude points on a ring

Coordinates getcolat # vector of colatitudes (radians) getcolatlon # vectors of colatitudes, longitudes (both radians)

Spectral truncation truncationorder # linear, quadratic, cubic = 1,2,3 for grid gettruncation # spectral truncation given a grid resolution get_resolution # grid resolution given a spectral truncation

Quadrature weights and solid angles getquadratureweights # = sinθ Δθ for grid points on ring j for meridional integration getsolidangle # = sinθ Δθ Δϕ, solid angle of grid points on ring j

source
SpeedyWeather.RingGrids.AbstractHEALPixGridType
abstract type AbstractHEALPixGrid{T} <: AbstractGrid{T} end

An AbstractHEALPixGrid is a horizontal grid similar to the standard HEALPixGrid, but different latitudes can be used, the default HEALPix latitudes or others.

source
SpeedyWeather.RingGrids.AbstractInterpolatorType
abstract type AbstractInterpolator{NF,G} end

Supertype for Interpolators. Every Interpolator <: AbstractInterpolator is expected to have two fields,

  • geometry, which describes the grid G to interpolate from
  • locator, which locates the indices on G and their weights to interpolate onto a new grid.

NF is the number format used to calculate the interpolation, which can be different from the input data and/or the interpolated data on the new grid.

source
SpeedyWeather.RingGrids.AbstractLocatorType
AbstractLocator{NF}

Supertype of every Locator, which locates the indices on a grid to be used to perform an interpolation. E.g. AnvilLocator uses a 4-point stencil for every new coordinate to interpolate onto. Higher order stencils can be implemented by defining OtherLocator <: AbstractLocactor.

source
SpeedyWeather.RingGrids.AbstractOctaHEALPixGridType
abstract type AbstractOctaHEALPixGrid{T} <: AbstractGrid{T} end

An AbstractOctaHEALPixGrid is a horizontal grid similar to the standard OctahedralGrid, but the number of points in the ring closest to the Poles starts from 4 instead of 20, and the longitude of the first point in each ring is shifted as in HEALPixGrid. Also, different latitudes can be used.

source
SpeedyWeather.RingGrids.AbstractOctahedralGridType
abstract type AbstractOctahedralGrid{T} <: AbstractGrid{T} end

An AbstractOctahedralGrid is a horizontal grid with 16+4i longitude points on the latitude ring i starting with i=1 around the pole. Different latitudes can be used, Gaussian latitudes, equi-angle latitdes, or others.

source
SpeedyWeather.RingGrids.AnvilLocatorType
AnvilLocator{NF<:AbstractFloat} <: AbtractLocator

Contains arrays that locates grid points of a given field to be uses in an interpolation and their weights. This Locator is a 4-point average in an anvil-shaped grid-point arrangement between two latitude rings.

source
SpeedyWeather.RingGrids.AnvilLocatorMethod
L = AnvilLocator(   ::Type{NF},         # number format used for the interpolation
+end

MyNewGrid should belong to a grid class like AbstractFullGrid, AbstractOctahedralGrid or AbstractHEALPixGrid (that already exist but you may introduce a new class of grids) that share certain features such as the number of longitude points per latitude ring and indexing, but may have different latitudes or offset rotations. Each new grid Grid (or grid class) then has to implement the following methods (as an example, see octahedral.jl)

Fundamental grid properties getnpoints # total number of grid points nlatodd # does the grid have an odd number of latitude rings? getnlat # total number of latitude rings getnlat_half # number of latitude rings on one hemisphere incl Equator

Indexing getnlonmax # maximum number of longitudes points (at the Equator) getnlonperring # number of longitudes on ring j eachindexinring # a unit range that indexes all longitude points on a ring

Coordinates getcolat # vector of colatitudes (radians) getcolatlon # vectors of colatitudes, longitudes (both radians)

Spectral truncation truncationorder # linear, quadratic, cubic = 1,2,3 for grid gettruncation # spectral truncation given a grid resolution get_resolution # grid resolution given a spectral truncation

Quadrature weights and solid angles getquadratureweights # = sinθ Δθ for grid points on ring j for meridional integration getsolidangle # = sinθ Δθ Δϕ, solid angle of grid points on ring j

source
SpeedyWeather.RingGrids.AbstractHEALPixGridType
abstract type AbstractHEALPixGrid{T} <: AbstractGrid{T} end

An AbstractHEALPixGrid is a horizontal grid similar to the standard HEALPixGrid, but different latitudes can be used, the default HEALPix latitudes or others.

source
SpeedyWeather.RingGrids.AbstractInterpolatorType
abstract type AbstractInterpolator{NF,G} end

Supertype for Interpolators. Every Interpolator <: AbstractInterpolator is expected to have two fields,

  • geometry, which describes the grid G to interpolate from
  • locator, which locates the indices on G and their weights to interpolate onto a new grid.

NF is the number format used to calculate the interpolation, which can be different from the input data and/or the interpolated data on the new grid.

source
SpeedyWeather.RingGrids.AbstractLocatorType
AbstractLocator{NF}

Supertype of every Locator, which locates the indices on a grid to be used to perform an interpolation. E.g. AnvilLocator uses a 4-point stencil for every new coordinate to interpolate onto. Higher order stencils can be implemented by defining OtherLocator <: AbstractLocactor.

source
SpeedyWeather.RingGrids.AbstractOctaHEALPixGridType
abstract type AbstractOctaHEALPixGrid{T} <: AbstractGrid{T} end

An AbstractOctaHEALPixGrid is a horizontal grid similar to the standard OctahedralGrid, but the number of points in the ring closest to the Poles starts from 4 instead of 20, and the longitude of the first point in each ring is shifted as in HEALPixGrid. Also, different latitudes can be used.

source
SpeedyWeather.RingGrids.AbstractOctahedralGridType
abstract type AbstractOctahedralGrid{T} <: AbstractGrid{T} end

An AbstractOctahedralGrid is a horizontal grid with 16+4i longitude points on the latitude ring i starting with i=1 around the pole. Different latitudes can be used, Gaussian latitudes, equi-angle latitdes, or others.

source
SpeedyWeather.RingGrids.AnvilLocatorType
AnvilLocator{NF<:AbstractFloat} <: AbtractLocator

Contains arrays that locates grid points of a given field to be uses in an interpolation and their weights. This Locator is a 4-point average in an anvil-shaped grid-point arrangement between two latitude rings.

source
SpeedyWeather.RingGrids.AnvilLocatorMethod
L = AnvilLocator(   ::Type{NF},         # number format used for the interpolation
                     npoints::Integer    # number of points to interpolate onto
-                    ) where {NF<:AbstractFloat}

Zero generator function for the 4-point average AnvilLocator. Use update_locator! to update the grid indices used for interpolation and their weights. The number format NF is the format used for the calculations within the interpolation, the input data and/or output data formats may differ.

source
SpeedyWeather.RingGrids.FullClenshawGridType
G = FullClenshawGrid{T}

A FullClenshawGrid is a regular latitude-longitude grid with an odd number of nlat equi-spaced latitudes, the central latitude ring is on the Equator. The same nlon longitudes for every latitude ring. The grid points are closer in zonal direction around the poles. The values of all grid points are stored in a vector field data that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.FullGaussianGridType
G = FullGaussianGrid{T}

A full Gaussian grid is a regular latitude-longitude grid that uses nlat Gaussian latitudes, and the same nlon longitudes for every latitude ring. The grid points are closer in zonal direction around the poles. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.FullHEALPixGridType
G = FullHEALPixGrid{T}

A full HEALPix grid is a regular latitude-longitude grid that uses nlat latitudes from the HEALPix grid, and the same nlon longitudes for every latitude ring. The grid points are closer in zonal direction around the poles. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.FullOctaHEALPixGridType
G = FullOctaHEALPixGrid{T}

A full OctaHEALPix grid is a regular latitude-longitude grid that uses nlat OctaHEALPix latitudes, and the same nlon longitudes for every latitude ring. The grid points are closer in zonal direction around the poles. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.GridGeometryMethod
G = GridGeometry(   Grid::Type{<:AbstractGrid},
-                    nlat_half::Integer)

Precomputed arrays describing the geometry of the Grid with resolution nlat_half. Contains latitudes and longitudes of grid points, their ring index j and their unravelled indices ij.

source
SpeedyWeather.RingGrids.HEALPixGridType
H = HEALPixGrid{T}

A HEALPix grid with 12 faces, each nsidexnside grid points, each covering the same area. The number of latitude rings on one hemisphere (incl Equator) nlat_half is used as resolution parameter. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.OctaHEALPixGridType
H = OctaHEALPixGrid{T}

A OctaHEALPix grid with 4 base faces, each nlat_halfxnlat_half grid points, each covering the same area. The values of all grid points are stored in a vector field data that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.OctahedralClenshawGridType
G = OctahedralClenshawGrid{T}

An Octahedral Clenshaw grid that uses nlat equi-spaced latitudes. Like FullClenshawGrid, the central latitude ring is on the Equator. Like OctahedralGaussianGrid, the number of longitude points per latitude ring decreases towards the poles. Starting with 20 equi-spaced longitude points (starting at 0˚E) on the rings around the poles, each latitude ring towards the equator has consecuitively 4 more points, one for each face of the octahedron. E.g. 20,24,28,32,...nlon-4,nlon,nlon,nlon-4,...,32,28,24,20. The maximum number of longitue points is nlon. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.OctahedralGaussianGridType
G = OctahedralGaussianGrid{T}

An Octahedral Gaussian grid that uses nlat Gaussian latitudes, but a decreasing number of longitude points per latitude ring towards the poles. Starting with 20 equi-spaced longitude points (starting at 0˚E) on the rings around the poles, each latitude ring towards the equator has consecuitively 4 more points, one for each face of the octahedron. E.g. 20,24,28,32,...nlon-4,nlon,nlon,nlon-4,...,32,28,24,20. The maximum number of longitue points is nlon. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.Matrix!Method
Matrix!(M::AbstractMatrix,
+                    ) where {NF<:AbstractFloat}

Zero generator function for the 4-point average AnvilLocator. Use update_locator! to update the grid indices used for interpolation and their weights. The number format NF is the format used for the calculations within the interpolation, the input data and/or output data formats may differ.

source
SpeedyWeather.RingGrids.FullClenshawGridType
G = FullClenshawGrid{T}

A FullClenshawGrid is a regular latitude-longitude grid with an odd number of nlat equi-spaced latitudes, the central latitude ring is on the Equator. The same nlon longitudes for every latitude ring. The grid points are closer in zonal direction around the poles. The values of all grid points are stored in a vector field data that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.FullGaussianGridType
G = FullGaussianGrid{T}

A full Gaussian grid is a regular latitude-longitude grid that uses nlat Gaussian latitudes, and the same nlon longitudes for every latitude ring. The grid points are closer in zonal direction around the poles. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.FullHEALPixGridType
G = FullHEALPixGrid{T}

A full HEALPix grid is a regular latitude-longitude grid that uses nlat latitudes from the HEALPix grid, and the same nlon longitudes for every latitude ring. The grid points are closer in zonal direction around the poles. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.FullOctaHEALPixGridType
G = FullOctaHEALPixGrid{T}

A full OctaHEALPix grid is a regular latitude-longitude grid that uses nlat OctaHEALPix latitudes, and the same nlon longitudes for every latitude ring. The grid points are closer in zonal direction around the poles. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.GridGeometryMethod
G = GridGeometry(   Grid::Type{<:AbstractGrid},
+                    nlat_half::Integer)

Precomputed arrays describing the geometry of the Grid with resolution nlat_half. Contains latitudes and longitudes of grid points, their ring index j and their unravelled indices ij.

source
SpeedyWeather.RingGrids.HEALPixGridType
H = HEALPixGrid{T}

A HEALPix grid with 12 faces, each nsidexnside grid points, each covering the same area. The number of latitude rings on one hemisphere (incl Equator) nlat_half is used as resolution parameter. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.OctaHEALPixGridType
H = OctaHEALPixGrid{T}

A OctaHEALPix grid with 4 base faces, each nlat_halfxnlat_half grid points, each covering the same area. The values of all grid points are stored in a vector field data that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.OctahedralClenshawGridType
G = OctahedralClenshawGrid{T}

An Octahedral Clenshaw grid that uses nlat equi-spaced latitudes. Like FullClenshawGrid, the central latitude ring is on the Equator. Like OctahedralGaussianGrid, the number of longitude points per latitude ring decreases towards the poles. Starting with 20 equi-spaced longitude points (starting at 0˚E) on the rings around the poles, each latitude ring towards the equator has consecuitively 4 more points, one for each face of the octahedron. E.g. 20,24,28,32,...nlon-4,nlon,nlon,nlon-4,...,32,28,24,20. The maximum number of longitue points is nlon. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.OctahedralGaussianGridType
G = OctahedralGaussianGrid{T}

An Octahedral Gaussian grid that uses nlat Gaussian latitudes, but a decreasing number of longitude points per latitude ring towards the poles. Starting with 20 equi-spaced longitude points (starting at 0˚E) on the rings around the poles, each latitude ring towards the equator has consecuitively 4 more points, one for each face of the octahedron. E.g. 20,24,28,32,...nlon-4,nlon,nlon,nlon-4,...,32,28,24,20. The maximum number of longitue points is nlon. The values of all grid points are stored in a vector field v that unravels the data 0 to 360˚, then ring by ring, which are sorted north to south.

source
SpeedyWeather.RingGrids.Matrix!Method
Matrix!(M::AbstractMatrix,
         G::OctaHEALPixGrid;
         quadrant_rotation=(0,1,2,3),
         matrix_quadrant=((2,2),(1,2),(1,1),(2,1)),
-        )

Sorts the gridpoints in G into the matrix M without interpolation. Every quadrant of the grid G is rotated as specified in quadrant_rotation, 0 is no rotation, 1 is 90˚ clockwise, 2 is 180˚ etc. Grid quadrants are counted eastward starting from 0˚E. The grid quadrants are moved into the matrix quadrant (i,j) as specified. Defaults are equivalent to centered at 0˚E and a rotation such that the North Pole is at M's midpoint.

source
SpeedyWeather.RingGrids.Matrix!Method
Matrix!(M::AbstractMatrix,
+        )

Sorts the gridpoints in G into the matrix M without interpolation. Every quadrant of the grid G is rotated as specified in quadrant_rotation, 0 is no rotation, 1 is 90˚ clockwise, 2 is 180˚ etc. Grid quadrants are counted eastward starting from 0˚E. The grid quadrants are moved into the matrix quadrant (i,j) as specified. Defaults are equivalent to centered at 0˚E and a rotation such that the North Pole is at M's midpoint.

source
SpeedyWeather.RingGrids.Matrix!Method
Matrix!(M::AbstractMatrix,
         G::OctahedralClenshawGrid;
         quadrant_rotation=(0,1,2,3),
         matrix_quadrant=((2,2),(1,2),(1,1),(2,1)),
-        )

Sorts the gridpoints in G into the matrix M without interpolation. Every quadrant of the grid G is rotated as specified in quadrant_rotation, 0 is no rotation, 1 is 90˚ clockwise, 2 is 180˚ etc. Grid quadrants are counted eastward starting from 0˚E. The grid quadrants are moved into the matrix quadrant (i,j) as specified. Defaults are equivalent to centered at 0˚E and a rotation such that the North Pole is at M's midpoint.

source
SpeedyWeather.RingGrids.Matrix!Method
Matrix!(MGs::Tuple{AbstractMatrix{T},OctaHEALPixGrid}...;kwargs...)

Like Matrix!(::AbstractMatrix,::OctaHEALPixGrid) but for simultaneous processing of tuples ((M1,G1),(M2,G2),...) with matrices Mi and grids Gi. All matrices and grids have to be of the same size respectively.

source
SpeedyWeather.RingGrids.Matrix!Method
Matrix!(MGs::Tuple{AbstractMatrix{T},OctahedralClenshawGrid}...;kwargs...)

Like Matrix!(::AbstractMatrix,::OctahedralClenshawGrid) but for simultaneous processing of tuples ((M1,G1),(M2,G2),...) with matrices Mi and grids Gi. All matrices and grids have to be of the same size respectively.

source
SpeedyWeather.RingGrids._scale_lat!Method
_scale_lat!(
+        )

Sorts the gridpoints in G into the matrix M without interpolation. Every quadrant of the grid G is rotated as specified in quadrant_rotation, 0 is no rotation, 1 is 90˚ clockwise, 2 is 180˚ etc. Grid quadrants are counted eastward starting from 0˚E. The grid quadrants are moved into the matrix quadrant (i,j) as specified. Defaults are equivalent to centered at 0˚E and a rotation such that the North Pole is at M's midpoint.

source
SpeedyWeather.RingGrids.Matrix!Method
Matrix!(MGs::Tuple{AbstractMatrix{T},OctaHEALPixGrid}...;kwargs...)

Like Matrix!(::AbstractMatrix,::OctaHEALPixGrid) but for simultaneous processing of tuples ((M1,G1),(M2,G2),...) with matrices Mi and grids Gi. All matrices and grids have to be of the same size respectively.

source
SpeedyWeather.RingGrids.Matrix!Method
Matrix!(MGs::Tuple{AbstractMatrix{T},OctahedralClenshawGrid}...;kwargs...)

Like Matrix!(::AbstractMatrix,::OctahedralClenshawGrid) but for simultaneous processing of tuples ((M1,G1),(M2,G2),...) with matrices Mi and grids Gi. All matrices and grids have to be of the same size respectively.

source
SpeedyWeather.RingGrids._scale_lat!Method
_scale_lat!(
     A::SpeedyWeather.RingGrids.AbstractGrid{NF},
     v::AbstractVector
 ) -> SpeedyWeather.RingGrids.AbstractGrid
-

Generic latitude scaling applied to A in-place with latitude-like vector v.

source
SpeedyWeather.RingGrids.anvil_averageMethod
anvil_average(a, b, c, d, Δab, Δcd, Δy) -> Any
 

The bilinear average of a,b,c,d which are values at grid points in an anvil-shaped configuration at location x, which is denoted by Δab,Δcd,Δy, the fraction of distances between a-b,c-d, and ab-cd, respectively. Note that a,c and b,d do not necessarily share the same longitude/x-coordinate. See schematic:

            0..............1    # fraction of distance Δab between a,b
             |<  Δab   >|
 
@@ -309,38 +309,38 @@
     1         c ------ o ---- d
 
               |<  Δcd >|
-              0...............1 # fraction of distance Δcd between c,d

^ fraction of distance Δy between a-b and c-d.

source
SpeedyWeather.RingGrids.average_on_polesMethod
average_on_poles(
     A::SpeedyWeather.RingGrids.AbstractGrid{NF<:AbstractFloat},
     rings::Vector{<:UnitRange{<:Integer}}
 ) -> Tuple{Any, Any}
-

Computes the average at the North and South pole from a given grid A and it's precomputed ring indices rings. The North pole average is an equally weighted average of all grid points on the northern-most ring. Similar for the South pole.

source
SpeedyWeather.RingGrids.average_on_polesMethod
average_on_poles(
+

Computes the average at the North and South pole from a given grid A and it's precomputed ring indices rings. The North pole average is an equally weighted average of all grid points on the northern-most ring. Similar for the South pole.

source
SpeedyWeather.RingGrids.average_on_polesMethod
average_on_poles(
     A::SpeedyWeather.RingGrids.AbstractGrid{NF<:Integer},
     rings::Vector{<:UnitRange{<:Integer}}
 ) -> Tuple{Any, Any}
-

Method for A::Abstract{T<:Integer} which rounds the averaged values to return the same number format NF.

source
SpeedyWeather.RingGrids.eachringMethod
eachring(grid::SpeedyWeather.RingGrids.AbstractGrid) -> Any
+

Method for A::Abstract{T<:Integer} which rounds the averaged values to return the same number format NF.

source
SpeedyWeather.RingGrids.eachringMethod
eachring(grid::SpeedyWeather.RingGrids.AbstractGrid) -> Any
 

Vector{UnitRange} rings to loop over every ring of grid grid and then each grid point per ring. To be used like

rings = eachring(grid)
 for ring in rings
     for ij in ring
-        grid[ij]
source
SpeedyWeather.RingGrids.eachringMethod
eachring(
     grid1::SpeedyWeather.RingGrids.AbstractGrid,
     grids::Grid<:SpeedyWeather.RingGrids.AbstractGrid...
 ) -> Any
-

Same as eachring(grid) but performs a bounds check to assess that all grids in grids are of same size.

source
SpeedyWeather.RingGrids.get_nlonsMethod
get_nlons(
     Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid},
     nlat_half::Integer;
     both_hemispheres
 ) -> Any
-

Returns a vector nlons for the number of longitude points per latitude ring, north to south. Provide grid Grid and its resolution parameter nlat_half. For both_hemisphere==false only the northern hemisphere (incl Equator) is returned.

source
SpeedyWeather.RingGrids.grid_cell_average!Method
grid_cell_average!(
+

Returns a vector nlons for the number of longitude points per latitude ring, north to south. Provide grid Grid and its resolution parameter nlat_half. For both_hemisphere==false only the northern hemisphere (incl Equator) is returned.

source
SpeedyWeather.RingGrids.grid_cell_average!Method
grid_cell_average!(
     output::SpeedyWeather.RingGrids.AbstractGrid,
     input::SpeedyWeather.RingGrids.AbstractFullGrid
 ) -> SpeedyWeather.RingGrids.AbstractGrid
-

Averages all grid points in input that are within one grid cell of output with coslat-weighting. The output grid cell boundaries are assumed to be rectangles spanning half way to adjacent longitude and latitude points.

source
SpeedyWeather.RingGrids.grid_cell_averageMethod
grid_cell_average(
+

Averages all grid points in input that are within one grid cell of output with coslat-weighting. The output grid cell boundaries are assumed to be rectangles spanning half way to adjacent longitude and latitude points.

source
SpeedyWeather.RingGrids.grid_cell_averageMethod
grid_cell_average(
     Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid},
     nlat_half::Integer,
     input::SpeedyWeather.RingGrids.AbstractFullGrid
 ) -> Any
-

Averages all grid points in input that are within one grid cell of output with coslat-weighting. The output grid cell boundaries are assumed to be rectangles spanning half way to adjacent longitude and latitude points.

source
SpeedyWeather.RingGrids.whichringMethod
whichring(
+

Averages all grid points in input that are within one grid cell of output with coslat-weighting. The output grid cell boundaries are assumed to be rectangles spanning half way to adjacent longitude and latitude points.

source
SpeedyWeather.RingGrids.whichringMethod
whichring(
     ij::Integer,
     rings::Vector{UnitRange{Int64}}
 ) -> Int64
-

Obtain ring index j from gridpoint ij and Vector{UnitRange} describing rind indices as obtained from eachring(::Grid)

source
+

Obtain ring index j from gridpoint ij and Vector{UnitRange} describing rind indices as obtained from eachring(::Grid)

source diff --git a/previews/PR387/run_0001/progress.txt b/previews/PR387/run_0001/progress.txt index 00dee32a3..b51d70d6f 100644 --- a/previews/PR387/run_0001/progress.txt +++ b/previews/PR387/run_0001/progress.txt @@ -1,4 +1,4 @@ -Starting SpeedyWeather.jl run 0001 on Mon, 16 Oct 2023 21:37:14 +Starting SpeedyWeather.jl run 0001 on Mon, 16 Oct 2023 21:36:43 Integrating: SpectralGrid: ├ Spectral: T63 LowerTriangularMatrix{Complex{Float32}}, radius = 6.371e6 m @@ -9,25 +9,25 @@ Time: 6.0 days at Δt = 900s All data will be stored in /home/runner/work/SpeedyWeather.jl/SpeedyWeather.jl/docs/build/run_0001 - 5%, ETA: 0:00:01, Inf millenia/day - 10%, ETA: 0:00:01, 1376.56 years/day - 15%, ETA: 0:00:01, 1041.39 years/day - 20%, ETA: 0:00:01, 1380.45 years/day - 25%, ETA: 0:00:01, 1143.69 years/day - 30%, ETA: 0:00:01, 1036.52 years/day - 35%, ETA: 0:00:01, 1211.28 years/day - 40%, ETA: 0:00:01, 1088.68 years/day - 45%, ETA: 0:00:01, 1026.59 years/day - 50%, ETA: 0:00:01, 982.43 years/day - 55%, ETA: 0:00:01, 1081.70 years/day - 60%, ETA: 0:00:01, 1026.92 years/day - 65%, ETA: 0:00:01, 990.54 years/day - 70%, ETA: 0:00:00, 1067.55 years/day - 75%, ETA: 0:00:00, 988.26 years/day - 80%, ETA: 0:00:00, 962.52 years/day - 85%, ETA: 0:00:00, 1023.34 years/day - 90%, ETA: 0:00:00, 995.12 years/day - 95%, ETA: 0:00:00, 973.60 years/day -100%, ETA: 0:00:00, 1023.53 years/day + 5%, ETA: 0:00:02, 663.01 years/day + 10%, ETA: 0:00:02, 677.07 years/day + 15%, ETA: 0:00:02, 688.23 years/day + 20%, ETA: 0:00:02, 685.65 years/day + 25%, ETA: 0:00:02, 689.46 years/day + 30%, ETA: 0:00:01, 693.00 years/day + 35%, ETA: 0:00:01, 690.79 years/day + 40%, ETA: 0:00:01, 688.20 years/day + 45%, ETA: 0:00:01, 690.40 years/day + 50%, ETA: 0:00:01, 673.26 years/day + 55%, ETA: 0:00:01, 674.97 years/day + 60%, ETA: 0:00:01, 672.08 years/day + 65%, ETA: 0:00:01, 674.59 years/day + 70%, ETA: 0:00:01, 673.47 years/day + 75%, ETA: 0:00:01, 674.81 years/day + 80%, ETA: 0:00:00, 675.12 years/day + 85%, ETA: 0:00:00, 676.71 years/day + 90%, ETA: 0:00:00, 677.14 years/day + 95%, ETA: 0:00:00, 656.49 years/day +100%, ETA: 0:00:00, 656.26 years/day -Integration done in 1 second, 380 milliseconds. +Integration done in 2 seconds, 160 milliseconds. diff --git a/previews/PR387/run_0002/progress.txt b/previews/PR387/run_0002/progress.txt index 132014fdd..9f3cd3682 100644 --- a/previews/PR387/run_0002/progress.txt +++ b/previews/PR387/run_0002/progress.txt @@ -1,4 +1,4 @@ -Starting SpeedyWeather.jl run 0002 on Mon, 16 Oct 2023 21:37:42 +Starting SpeedyWeather.jl run 0002 on Mon, 16 Oct 2023 21:37:23 Integrating: SpectralGrid: ├ Spectral: T63 LowerTriangularMatrix{Complex{Float32}}, radius = 6.371e6 m @@ -9,25 +9,25 @@ Time: 12.0 days at Δt = 900s All data will be stored in /home/runner/work/SpeedyWeather.jl/SpeedyWeather.jl/docs/build/run_0002 - 5%, ETA: 0:00:03, 1386.89 years/day - 10%, ETA: 0:00:02, 1404.86 years/day - 15%, ETA: 0:00:02, 1398.98 years/day - 20%, ETA: 0:00:02, 1119.48 years/day - 25%, ETA: 0:00:02, 1158.51 years/day - 30%, ETA: 0:00:02, 1193.55 years/day - 35%, ETA: 0:00:02, 1083.90 years/day - 40%, ETA: 0:00:02, 1114.29 years/day - 45%, ETA: 0:00:01, 1137.58 years/day - 50%, ETA: 0:00:01, 1071.27 years/day - 55%, ETA: 0:00:01, 1091.28 years/day - 60%, ETA: 0:00:01, 1110.71 years/day - 65%, ETA: 0:00:01, 1060.63 years/day - 70%, ETA: 0:00:01, 1078.29 years/day - 75%, ETA: 0:00:01, 1095.53 years/day - 80%, ETA: 0:00:01, 1057.65 years/day - 85%, ETA: 0:00:00, 1073.52 years/day - 90%, ETA: 0:00:00, 1086.73 years/day - 95%, ETA: 0:00:00, 1036.39 years/day -100%, ETA: 0:00:00, 1049.65 years/day + 5%, ETA: 0:00:04, 1319.82 years/day + 10%, ETA: 0:00:04, 899.62 years/day + 15%, ETA: 0:00:03, 811.49 years/day + 20%, ETA: 0:00:03, 783.05 years/day + 25%, ETA: 0:00:03, 755.74 years/day + 30%, ETA: 0:00:03, 739.79 years/day + 35%, ETA: 0:00:03, 729.06 years/day + 40%, ETA: 0:00:02, 724.84 years/day + 45%, ETA: 0:00:02, 719.87 years/day + 50%, ETA: 0:00:02, 717.45 years/day + 55%, ETA: 0:00:02, 715.06 years/day + 60%, ETA: 0:00:02, 711.76 years/day + 65%, ETA: 0:00:01, 738.36 years/day + 70%, ETA: 0:00:01, 734.97 years/day + 75%, ETA: 0:00:01, 729.31 years/day + 80%, ETA: 0:00:01, 726.19 years/day + 85%, ETA: 0:00:01, 723.65 years/day + 90%, ETA: 0:00:00, 721.18 years/day + 95%, ETA: 0:00:00, 703.95 years/day +100%, ETA: 0:00:00, 703.43 years/day -Integration done in 2 seconds, 700 milliseconds. +Integration done in 4 seconds, 30 milliseconds. diff --git a/previews/PR387/run_0003/progress.txt b/previews/PR387/run_0003/progress.txt index 319dc2129..a3ec5bde1 100644 --- a/previews/PR387/run_0003/progress.txt +++ b/previews/PR387/run_0003/progress.txt @@ -1,4 +1,4 @@ -Starting SpeedyWeather.jl run 0003 on Mon, 16 Oct 2023 21:37:55 +Starting SpeedyWeather.jl run 0003 on Mon, 16 Oct 2023 21:37:41 Integrating: SpectralGrid: ├ Spectral: T63 LowerTriangularMatrix{Complex{Float32}}, radius = 6.371e6 m @@ -9,24 +9,24 @@ Time: 20.0 days at Δt = 900s All data will be stored in /home/runner/work/SpeedyWeather.jl/SpeedyWeather.jl/docs/build/run_0003 - 5%, ETA: 0:00:04, Inf millenia/day - 10%, ETA: 0:00:04, Inf millenia/day - 15%, ETA: 0:00:04, Inf millenia/day - 20%, ETA: 0:00:04, Inf millenia/day - 25%, ETA: 0:00:03, Inf millenia/day - 30%, ETA: 0:00:03, Inf millenia/day - 35%, ETA: 0:00:03, Inf millenia/day - 40%, ETA: 0:00:03, Inf millenia/day - 45%, ETA: 0:00:03, Inf millenia/day - 50%, ETA: 0:00:02, Inf millenia/day - 55%, ETA: 0:00:02, Inf millenia/day - 60%, ETA: 0:00:02, Inf millenia/day + 5%, ETA: 0:00:06, Inf millenia/day + 10%, ETA: 0:00:06, Inf millenia/day + 15%, ETA: 0:00:06, Inf millenia/day + 20%, ETA: 0:00:05, Inf millenia/day + 25%, ETA: 0:00:05, Inf millenia/day + 30%, ETA: 0:00:05, Inf millenia/day + 35%, ETA: 0:00:04, Inf millenia/day + 40%, ETA: 0:00:04, Inf millenia/day + 45%, ETA: 0:00:04, Inf millenia/day + 50%, ETA: 0:00:03, Inf millenia/day + 55%, ETA: 0:00:03, Inf millenia/day + 60%, ETA: 0:00:03, Inf millenia/day 65%, ETA: 0:00:02, Inf millenia/day - 70%, ETA: 0:00:01, Inf millenia/day - 75%, ETA: 0:00:01, Inf millenia/day + 70%, ETA: 0:00:02, Inf millenia/day + 75%, ETA: 0:00:02, Inf millenia/day 80%, ETA: 0:00:01, Inf millenia/day 85%, ETA: 0:00:01, Inf millenia/day - 90%, ETA: 0:00:00, Inf millenia/day + 90%, ETA: 0:00:01, Inf millenia/day 95%, ETA: 0:00:00, Inf millenia/day 100%, ETA: 0:00:00, Inf millenia/day diff --git a/previews/PR387/run_0004/progress.txt b/previews/PR387/run_0004/progress.txt index fbea7e60f..bb5eb9c42 100644 --- a/previews/PR387/run_0004/progress.txt +++ b/previews/PR387/run_0004/progress.txt @@ -1,4 +1,4 @@ -Starting SpeedyWeather.jl run 0004 on Mon, 16 Oct 2023 21:38:02 +Starting SpeedyWeather.jl run 0004 on Mon, 16 Oct 2023 21:37:51 Integrating: SpectralGrid: ├ Spectral: T127 LowerTriangularMatrix{Complex{Float32}}, radius = 6.371e6 m @@ -9,24 +9,24 @@ Time: 2.0 days at Δt = 450s All data will be stored in /home/runner/work/SpeedyWeather.jl/SpeedyWeather.jl/docs/build/run_0004 - 5%, ETA: 0:00:05, Inf millenia/day - 10%, ETA: 0:00:04, Inf millenia/day - 15%, ETA: 0:00:04, Inf millenia/day - 20%, ETA: 0:00:04, Inf millenia/day - 25%, ETA: 0:00:03, Inf millenia/day - 30%, ETA: 0:00:03, Inf millenia/day - 35%, ETA: 0:00:03, Inf millenia/day - 40%, ETA: 0:00:03, Inf millenia/day - 45%, ETA: 0:00:03, Inf millenia/day - 50%, ETA: 0:00:02, Inf millenia/day - 55%, ETA: 0:00:02, Inf millenia/day - 60%, ETA: 0:00:02, Inf millenia/day + 5%, ETA: 0:00:07, Inf millenia/day + 10%, ETA: 0:00:07, Inf millenia/day + 15%, ETA: 0:00:06, Inf millenia/day + 20%, ETA: 0:00:06, Inf millenia/day + 25%, ETA: 0:00:05, Inf millenia/day + 30%, ETA: 0:00:05, Inf millenia/day + 35%, ETA: 0:00:05, Inf millenia/day + 40%, ETA: 0:00:04, Inf millenia/day + 45%, ETA: 0:00:04, Inf millenia/day + 50%, ETA: 0:00:04, Inf millenia/day + 55%, ETA: 0:00:03, Inf millenia/day + 60%, ETA: 0:00:03, Inf millenia/day 65%, ETA: 0:00:02, 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0:00:21, Inf millenia/day - 35%, ETA: 0:00:17, Inf millenia/day - 40%, ETA: 0:00:14, Inf millenia/day - 45%, ETA: 0:00:12, Inf millenia/day - 50%, ETA: 0:00:10, Inf millenia/day - 55%, ETA: 0:00:08, Inf millenia/day - 60%, ETA: 0:00:07, Inf millenia/day - 65%, ETA: 0:00:06, Inf millenia/day - 70%, ETA: 0:00:05, Inf millenia/day - 75%, ETA: 0:00:04, Inf millenia/day - 80%, ETA: 0:00:03, Inf millenia/day - 85%, ETA: 0:00:02, Inf millenia/day - 90%, ETA: 0:00:01, Inf millenia/day + 5%, ETA: 0:03:07, Inf millenia/day + 10%, ETA: 0:01:30, Inf millenia/day + 15%, ETA: 0:00:59, Inf millenia/day + 20%, ETA: 0:00:43, Inf millenia/day + 25%, ETA: 0:00:34, Inf millenia/day + 30%, ETA: 0:00:27, Inf millenia/day + 35%, ETA: 0:00:22, Inf millenia/day + 40%, ETA: 0:00:18, Inf millenia/day + 45%, ETA: 0:00:16, Inf millenia/day + 50%, ETA: 0:00:13, Inf millenia/day + 55%, ETA: 0:00:11, Inf millenia/day + 60%, ETA: 0:00:09, Inf millenia/day + 65%, ETA: 0:00:08, Inf millenia/day + 70%, ETA: 0:00:06, Inf 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z@9&o#&J`!G5tJ3?N!Pk&seT^NG>YM)C{LWs8k-p`!%-jzEv+Mi(vJp5&Enx^M_3-M z_YXWEzM~rk{Suw+6VDdz&qi=xsB6xax=#;C#gH7T(JP^C#P)_psTxnc*EWfV!(6Lx zr#W-2%!RP&DDgFuaD#l}8cRvm(A0?2nm~kKalg|i?Gs4P|MsuG$2jb*J0RB9Ea^Ib zP@->VOK69e&q1Y(|EUZ0}r}Ra(F*G!Zy>k`wn`4{B`(>_pYMP~sLxS6PHcP@$ zfL8$KL-Kj2zgarU`b%Q{o1IQH#Ai)X^B@gl()aLGx&}5#_pnTHGS%cv&Jt583?9!C8_TY) zXS2mQo8QU((@HhF8pL$5Ub=6}60@sbOan;o&ywiyY^hLFRIz~Yn)~ZzX4mOVskpjd z+IMGhs7XWYHhW<*#pQ1hS6r5)h5P4$(mu$L=)?7~bSHkDxkBI8q~!&VAJdx0{XclJ B68-=H diff --git a/previews/PR387/run_test/progress.txt b/previews/PR387/run_test/progress.txt index 8d355b357..4daa60d02 100644 --- a/previews/PR387/run_test/progress.txt +++ b/previews/PR387/run_test/progress.txt @@ -1,4 +1,4 @@ -Starting SpeedyWeather.jl run test on Mon, 16 Oct 2023 21:36:53 +Starting SpeedyWeather.jl run test on Mon, 16 Oct 2023 21:36:12 Integrating: SpectralGrid: ├ Spectral: T63 LowerTriangularMatrix{Complex{Float32}}, radius = 6.371e6 m @@ -9,25 +9,25 @@ Time: 5.0 days at Δt = 450s All data will be stored in /home/runner/work/SpeedyWeather.jl/SpeedyWeather.jl/docs/build/run_test - 5%, ETA: 0:00:03, 569.11 years/day - 10%, ETA: 0:00:03, 570.14 years/day - 15%, ETA: 0:00:02, 428.50 years/day - 20%, ETA: 0:00:02, 460.18 years/day - 25%, ETA: 0:00:02, 476.82 years/day - 30%, ETA: 0:00:02, 428.93 years/day - 35%, ETA: 0:00:02, 424.24 years/day - 40%, ETA: 0:00:02, 439.00 years/day - 45%, ETA: 0:00:02, 414.16 years/day - 50%, ETA: 0:00:01, 425.75 years/day - 55%, ETA: 0:00:01, 436.25 years/day - 60%, ETA: 0:00:01, 418.20 years/day - 65%, ETA: 0:00:01, 427.01 years/day - 70%, ETA: 0:00:01, 435.17 years/day - 75%, ETA: 0:00:01, 421.17 years/day - 80%, ETA: 0:00:01, 428.20 years/day - 85%, ETA: 0:00:00, 434.98 years/day - 90%, ETA: 0:00:00, 422.67 years/day - 95%, ETA: 0:00:00, 428.96 years/day -100%, ETA: 0:00:00, 433.68 years/day + 5%, ETA: 0:00:06, 270.79 years/day + 10%, ETA: 0:00:04, 275.59 years/day + 15%, ETA: 0:00:04, 280.10 years/day + 20%, ETA: 0:00:03, 282.42 years/day + 25%, ETA: 0:00:03, 282.62 years/day + 30%, ETA: 0:00:03, 283.78 years/day + 35%, ETA: 0:00:03, 304.74 years/day + 40%, ETA: 0:00:02, 302.16 years/day + 45%, ETA: 0:00:02, 300.54 years/day + 50%, ETA: 0:00:02, 298.47 years/day + 55%, ETA: 0:00:02, 296.70 years/day + 60%, ETA: 0:00:02, 296.07 years/day + 65%, ETA: 0:00:01, 295.52 years/day + 70%, ETA: 0:00:01, 294.25 years/day + 75%, ETA: 0:00:01, 293.62 years/day + 80%, ETA: 0:00:01, 293.28 years/day + 85%, ETA: 0:00:01, 302.21 years/day + 90%, ETA: 0:00:00, 295.02 years/day + 95%, ETA: 0:00:00, 294.63 years/day +100%, ETA: 0:00:00, 293.11 years/day -Integration done in 2 seconds, 720 milliseconds. +Integration done in 4 seconds, 30 milliseconds. diff --git a/previews/PR387/speedytransforms/index.html b/previews/PR387/speedytransforms/index.html index 59c448d8e..6c2938bf4 100644 --- a/previews/PR387/speedytransforms/index.html +++ b/previews/PR387/speedytransforms/index.html @@ -263,9 +263,9 @@ ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ ▄▄ -90 ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄ └──┘ └────────────────────────────────────────────────────────────┘ -600 - 0 ˚E 360

    Strikingly similar! The remaining differences are the ageostrophic motions but also note that the mean is off. This is because geostrophy only use/defines the gradient of $\eta$ not the absolute values itself. Our geostrophic $\eta_g$ has by construction a mean of zero (that is how we define the inverse Laplace operator) but the actual $\eta$ is some 1400m higher.

    Functions and type index

    SpeedyWeather.SpeedyTransforms.SpectralTransformMethod
    S = SpectralTransform(  alms::AbstractMatrix{Complex{NF}};
    +        0                           ˚E                           360       

    Strikingly similar! The remaining differences are the ageostrophic motions but also note that the mean is off. This is because geostrophy only use/defines the gradient of $\eta$ not the absolute values itself. Our geostrophic $\eta_g$ has by construction a mean of zero (that is how we define the inverse Laplace operator) but the actual $\eta$ is some 1400m higher.

    Functions and type index

    SpeedyWeather.SpeedyTransforms.SpectralTransformMethod
    S = SpectralTransform(  alms::AbstractMatrix{Complex{NF}};
                             recompute_legendre::Bool=true,
    -                        Grid::Type{<:AbstractGrid}=DEFAULT_GRID)

    Generator function for a SpectralTransform struct based on the size of the spectral coefficients alms and the grid Grid. Recomputes the Legendre polynomials by default.

    source
    SpeedyWeather.SpeedyTransforms.SpectralTransformMethod
    SpectralTransform(
    +                        Grid::Type{<:AbstractGrid}=DEFAULT_GRID)

    Generator function for a SpectralTransform struct based on the size of the spectral coefficients alms and the grid Grid. Recomputes the Legendre polynomials by default.

    source
    SpeedyWeather.SpeedyTransforms.SpectralTransformMethod
    SpectralTransform(
         ::Type{NF},
         Grid::Type{<:SpeedyWeather.RingGrids.AbstractGrid},
         lmax::Int64,
    @@ -274,30 +274,30 @@
         legendre_shortcut,
         dealiasing
     ) -> SpectralTransform
    -

    Generator function for a SpectralTransform struct. With NF the number format, Grid the grid type <:AbstractGrid and spectral truncation lmax,mmax this function sets up necessary constants for the spetral transform. Also plans the Fourier transforms, retrieves the colatitudes, and preallocates the Legendre polynomials (if recompute_legendre == false) and quadrature weights.

    source
    SpeedyWeather.SpeedyTransforms.SpectralTransformMethod
    S = SpectralTransform(  map::AbstractGrid;
    -                        recompute_legendre::Bool=true)

    Generator function for a SpectralTransform struct based on the size and grid type of gridded field map. Recomputes the Legendre polynomials by default.

    source
    SpeedyWeather.RingGrids.get_nlat_halfFunction
    get_nlat_half(trunc::Integer) -> Any
    +

    Generator function for a SpectralTransform struct. With NF the number format, Grid the grid type <:AbstractGrid and spectral truncation lmax,mmax this function sets up necessary constants for the spetral transform. Also plans the Fourier transforms, retrieves the colatitudes, and preallocates the Legendre polynomials (if recompute_legendre == false) and quadrature weights.

    source
    SpeedyWeather.SpeedyTransforms.SpectralTransformMethod
    S = SpectralTransform(  map::AbstractGrid;
    +                        recompute_legendre::Bool=true)

    Generator function for a SpectralTransform struct based on the size and grid type of gridded field map. Recomputes the Legendre polynomials by default.

    source
    SpeedyWeather.RingGrids.get_nlat_halfFunction
    get_nlat_half(trunc::Integer) -> Any
     get_nlat_half(trunc::Integer, dealiasing::Real) -> Any
    -

    For the spectral truncation trunc (e.g. 31 for T31) return the grid resolution parameter nlat_half (number of latitude rings on one hemisphere including the Equator) following a dealiasing parameter (default 2) to match spectral and grid resolution.

    source
    SpeedyWeather.SpeedyTransforms.UV_from_vor!Method
    UV_from_vor!(
    +

    For the spectral truncation trunc (e.g. 31 for T31) return the grid resolution parameter nlat_half (number of latitude rings on one hemisphere including the Equator) following a dealiasing parameter (default 2) to match spectral and grid resolution.

    source
    SpeedyWeather.SpeedyTransforms.UV_from_vor!Method
    UV_from_vor!(
         U::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         V::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         vor::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         S::SpectralTransform{NF<:AbstractFloat}
     )
    -

    Get U,V (=(u,v)*coslat) from vorticity ζ spectral space (divergence D=0) Two operations are combined into a single linear operation. First, invert the spherical Laplace ∇² operator to get stream function from vorticity. Then compute zonal and meridional gradients to get U,V.

    source
    SpeedyWeather.SpeedyTransforms.UV_from_vordiv!Method
    UV_from_vordiv!(
    +

    Get U,V (=(u,v)*coslat) from vorticity ζ spectral space (divergence D=0) Two operations are combined into a single linear operation. First, invert the spherical Laplace ∇² operator to get stream function from vorticity. Then compute zonal and meridional gradients to get U,V.

    source
    SpeedyWeather.SpeedyTransforms.UV_from_vordiv!Method
    UV_from_vordiv!(
         U::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         V::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         vor::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         div::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         S::SpectralTransform{NF<:AbstractFloat}
     ) -> Any
    -

    Get U,V (=(u,v)*coslat) from vorticity ζ and divergence D in spectral space. Two operations are combined into a single linear operation. First, invert the spherical Laplace ∇² operator to get stream function from vorticity and velocity potential from divergence. Then compute zonal and meridional gradients to get U,V.

    source
    SpeedyWeather.SpeedyTransforms._divergence!Method
    _divergence!(
    +

    Get U,V (=(u,v)*coslat) from vorticity ζ and divergence D in spectral space. Two operations are combined into a single linear operation. First, invert the spherical Laplace ∇² operator to get stream function from vorticity and velocity potential from divergence. Then compute zonal and meridional gradients to get U,V.

    source
    SpeedyWeather.SpeedyTransforms._divergence!Method
    _divergence!(
         kernel,
         div::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         u::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         v::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         S::SpectralTransform{NF<:AbstractFloat}
     )
    -

    Generic divergence function of vector u,v that writes into the output into div. Generic as it uses the kernel kernel such that curl, div, add or flipsign options are provided through kernel, but otherwise a single function is used.

    source
    SpeedyWeather.SpeedyTransforms.curl!Method
    curl!(
    +

    Generic divergence function of vector u,v that writes into the output into div. Generic as it uses the kernel kernel such that curl, div, add or flipsign options are provided through kernel, but otherwise a single function is used.

    source
    SpeedyWeather.SpeedyTransforms.curl!Method
    curl!(
         curl::LowerTriangularMatrix,
         u::LowerTriangularMatrix,
         v::LowerTriangularMatrix,
    @@ -305,7 +305,7 @@
         flipsign,
         add
     )
    -

    Curl of a vector u,v written into curl, curl = ∇×(u,v). u,v are expected to have a 1/coslat-scaling included, then curl is not scaled. flipsign option calculates -∇×(u,v) instead. add option calculates curl += ∇×(u,v) instead. flipsign and add can be combined. This functions only creates the kernel and calls the generic divergence function _divergence! subsequently with flipped u,v -> v,u for the curl.

    source
    SpeedyWeather.SpeedyTransforms.curlMethod
    curl(
    +

    Curl of a vector u,v written into curl, curl = ∇×(u,v). u,v are expected to have a 1/coslat-scaling included, then curl is not scaled. flipsign option calculates -∇×(u,v) instead. add option calculates curl += ∇×(u,v) instead. flipsign and add can be combined. This functions only creates the kernel and calls the generic divergence function _divergence! subsequently with flipped u,v -> v,u for the curl.

    source
    SpeedyWeather.SpeedyTransforms.curlMethod
    curl(
         u::LowerTriangularMatrix,
         v::LowerTriangularMatrix
     ) -> Any
    @@ -314,11 +314,11 @@
     u = spectral(u_grid)
     v = spectral(v_grid)
     vor = curl(u,v)
    -vor_grid = gridded(div)
    source
    SpeedyWeather.SpeedyTransforms.curlMethod
    curl(
         u::SpeedyWeather.RingGrids.AbstractGrid,
         v::SpeedyWeather.RingGrids.AbstractGrid
     ) -> Any
    -

    Curl (∇×) of two vector components u,v on a grid. Applies 1/coslat scaling, transforms to spectral space and returns the spectral curl, which is scaled with the radius of the sphere. Divide by radius for unscaling.

    source
    SpeedyWeather.SpeedyTransforms.divergence!Method
    divergence!(
    +

    Curl (∇×) of two vector components u,v on a grid. Applies 1/coslat scaling, transforms to spectral space and returns the spectral curl, which is scaled with the radius of the sphere. Divide by radius for unscaling.

    source
    SpeedyWeather.SpeedyTransforms.divergence!Method
    divergence!(
         div::LowerTriangularMatrix,
         u::LowerTriangularMatrix,
         v::LowerTriangularMatrix,
    @@ -326,7 +326,7 @@
         flipsign,
         add
     )
    -

    Divergence of a vector u,v written into div, div = ∇⋅(u,v). u,v are expected to have a 1/coslat-scaling included, then div is not scaled. flipsign option calculates -∇⋅(u,v) instead. add option calculates div += ∇⋅(u,v) instead. flipsign and add can be combined. This functions only creates the kernel and calls the generic divergence function _divergence! subsequently.

    source
    SpeedyWeather.SpeedyTransforms.divergenceMethod
    divergence(
    +

    Divergence of a vector u,v written into div, div = ∇⋅(u,v). u,v are expected to have a 1/coslat-scaling included, then div is not scaled. flipsign option calculates -∇⋅(u,v) instead. add option calculates div += ∇⋅(u,v) instead. flipsign and add can be combined. This functions only creates the kernel and calls the generic divergence function _divergence! subsequently.

    source
    SpeedyWeather.SpeedyTransforms.divergenceMethod
    divergence(
         u::LowerTriangularMatrix,
         v::LowerTriangularMatrix
     ) -> Any
    @@ -335,69 +335,69 @@
     u = spectral(u_grid,one_more_degree=true)
     v = spectral(v_grid,one_more_degree=true)
     div = divergence(u,v)
    -div_grid = gridded(div)

    Both div and div_grid are scaled with the radius.

    source
    SpeedyWeather.SpeedyTransforms.divergenceMethod
    divergence(
         u::SpeedyWeather.RingGrids.AbstractGrid,
         v::SpeedyWeather.RingGrids.AbstractGrid
     ) -> Any
    -

    Divergence (∇⋅) of two vector components u,v on a grid. Applies 1/coslat scaling, transforms to spectral space and returns the spectral divergence, which is scaled with the radius of the sphere. Divide by radius for unscaling.

    source
    SpeedyWeather.SpeedyTransforms.get_recursion_factorsMethod
    get_recursion_factors(  ::Type{NF}, # number format NF
    +

    Divergence (∇⋅) of two vector components u,v on a grid. Applies 1/coslat scaling, transforms to spectral space and returns the spectral divergence, which is scaled with the radius of the sphere. Divide by radius for unscaling.

    source
    SpeedyWeather.SpeedyTransforms.get_recursion_factorsMethod
    get_recursion_factors(  ::Type{NF}, # number format NF
                             lmax::Int,  # max degree l of spherical harmonics (0-based here)
                             mmax::Int   # max order m of spherical harmonics
    -                        ) where {NF<:AbstractFloat}

    Returns a matrix of recursion factors ϵ up to degree lmax and order mmax of number format NF.

    source
    SpeedyWeather.SpeedyTransforms.get_truncationFunction
    get_truncation(nlat_half::Integer) -> Any
     get_truncation(nlat_half::Integer, dealiasing::Real) -> Any
    -

    For the grid resolution parameter nlat_half (e.g. 24 for a 48-ring FullGaussianGrid) return the spectral truncation trunc (max degree of spherical harmonics) following a dealiasing parameter (default 2) to match spectral and grid resolution.

    source
    SpeedyWeather.SpeedyTransforms.gridded!Method
    gridded!(   map::AbstractGrid,
    +

    For the grid resolution parameter nlat_half (e.g. 24 for a 48-ring FullGaussianGrid) return the spectral truncation trunc (max degree of spherical harmonics) following a dealiasing parameter (default 2) to match spectral and grid resolution.

    source
    SpeedyWeather.SpeedyTransforms.gridded!Method
    gridded!(   map::AbstractGrid,
                 alms::LowerTriangularMatrix,
    -            S::SpectralTransform)

    Spectral transform (spectral to grid) of the spherical harmonic coefficients alms to a gridded field map. The spectral transform is number format-flexible as long as the parametric types of map, alms, S are identical. The spectral transform is grid-flexible as long as the typeof(map)<:AbstractGrid. Uses the precalculated arrays, FFT plans and other constants in the SpectralTransform struct S.

    source
    SpeedyWeather.SpeedyTransforms.griddedMethod
    gridded(
    +            S::SpectralTransform)

    Spectral transform (spectral to grid) of the spherical harmonic coefficients alms to a gridded field map. The spectral transform is number format-flexible as long as the parametric types of map, alms, S are identical. The spectral transform is grid-flexible as long as the typeof(map)<:AbstractGrid. Uses the precalculated arrays, FFT plans and other constants in the SpectralTransform struct S.

    source
    SpeedyWeather.SpeedyTransforms.griddedMethod
    gridded(
         alms::AbstractArray{T<:Complex{NF}, 2};
         recompute_legendre,
         Grid,
         kwargs...
     ) -> Any
    -

    Spectral transform (spectral to grid space) from spherical coefficients alms to a newly allocated gridded field map. Based on the size of alms the grid type grid, the spatial resolution is retrieved based on the truncation defined for grid. SpectralTransform struct S is allocated to execute gridded(alms,S).

    source
    SpeedyWeather.SpeedyTransforms.griddedMethod
    gridded(
    +

    Spectral transform (spectral to grid space) from spherical coefficients alms to a newly allocated gridded field map. Based on the size of alms the grid type grid, the spatial resolution is retrieved based on the truncation defined for grid. SpectralTransform struct S is allocated to execute gridded(alms,S).

    source
    SpeedyWeather.SpeedyTransforms.griddedMethod
    gridded(
         alms::AbstractMatrix,
         S::SpectralTransform{NF};
         kwargs...
     ) -> Any
    -

    Spectral transform (spectral to grid space) from spherical coefficients alms to a newly allocated gridded field map with precalculated properties based on the SpectralTransform struct S. alms is converted to a LowerTriangularMatrix to execute the in-place gridded!.

    source
    SpeedyWeather.SpeedyTransforms.roundup_fftMethod
    m = roundup_fft(n::Int;
    -                small_primes::Vector{Int}=[2,3,5])

    Returns an integer m >= n with only small prime factors 2, 3 (default, others can be specified with the keyword argument small_primes) to obtain an efficiently fourier-transformable number of longitudes, m = 2^i * 3^j * 5^k >= n, with i,j,k >=0.

    source
    SpeedyWeather.SpeedyTransforms.spectral!Method
    spectral!(  alms::LowerTriangularMatrix,
    +

    Spectral transform (spectral to grid space) from spherical coefficients alms to a newly allocated gridded field map with precalculated properties based on the SpectralTransform struct S. alms is converted to a LowerTriangularMatrix to execute the in-place gridded!.

    source
    SpeedyWeather.SpeedyTransforms.roundup_fftMethod
    m = roundup_fft(n::Int;
    +                small_primes::Vector{Int}=[2,3,5])

    Returns an integer m >= n with only small prime factors 2, 3 (default, others can be specified with the keyword argument small_primes) to obtain an efficiently fourier-transformable number of longitudes, m = 2^i * 3^j * 5^k >= n, with i,j,k >=0.

    source
    SpeedyWeather.SpeedyTransforms.spectral!Method
    spectral!(  alms::LowerTriangularMatrix,
                 map::AbstractGrid,
    -            S::SpectralTransform)

    Spectral transform (grid to spectral space) from the gridded field map on a grid<:AbstractGrid to a LowerTriangularMatrix of spherical harmonic coefficients alms. Uses FFT in the zonal direction, and a Legendre Transform in the meridional direction exploiting symmetries. The spectral transform is number format-flexible as long as the parametric types of map, alms, S are identical. The spectral transform is grid-flexible as long as the typeof(map)<:AbstractGrid. Uses the precalculated arrays, FFT plans and other constants in the SpectralTransform struct S.

    source
    SpeedyWeather.SpeedyTransforms.spectralMethod
    spectral(
    +            S::SpectralTransform)

    Spectral transform (grid to spectral space) from the gridded field map on a grid<:AbstractGrid to a LowerTriangularMatrix of spherical harmonic coefficients alms. Uses FFT in the zonal direction, and a Legendre Transform in the meridional direction exploiting symmetries. The spectral transform is number format-flexible as long as the parametric types of map, alms, S are identical. The spectral transform is grid-flexible as long as the typeof(map)<:AbstractGrid. Uses the precalculated arrays, FFT plans and other constants in the SpectralTransform struct S.

    source
    SpeedyWeather.SpeedyTransforms.spectralMethod
    spectral(
         map::AbstractMatrix;
         Grid,
         kwargs...
     ) -> LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat
    -

    Converts map to grid(map) to execute spectral(map::AbstractGrid;kwargs...).

    source
    SpeedyWeather.SpeedyTransforms.spectralMethod
    spectral(
         map::SpeedyWeather.RingGrids.AbstractGrid,
         S::SpectralTransform{NF}
     ) -> LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat
    -

    Spectral transform (grid to spectral) map to grid(map) to execute spectral(map::AbstractGrid;kwargs...).

    source
    SpeedyWeather.SpeedyTransforms.spectralMethod
    spectral(
         map::SpeedyWeather.RingGrids.AbstractGrid{NF};
         recompute_legendre,
         one_more_degree
     ) -> LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat
    -

    Converts map to Grid(map) to execute spectral(map::AbstractGrid;kwargs...).

    source
    SpeedyWeather.SpeedyTransforms.spectral_interpolationMethod
    alms_interp = spectral_interpolation(   ::Type{NF},
                                             alms::LowerTriangularMatrix,
                                             ltrunc::Integer,
                                             mtrunc::Integer
    -                                        ) where NF

    Returns a spectral coefficient matrix alms_interp that is alms padded with zeros to interpolate in spectral space. If trunc is smaller or equal to the implicit truncation in alms obtained from its size than spectral_truncation is automatically called instead, returning alms_trunc, a coefficient matrix that is smaller than alms, implicitly setting higher degrees and orders to zero.

    source
    SpeedyWeather.SpeedyTransforms.spectral_smoothing!Method
    spectral_smoothing!(A::LowerTriangularMatrix,c;power=1)

    Smooth the spectral field A following A = (1-(1-c)∇²ⁿ) with power n of a normalised Laplacian so that the highest degree lmax is dampened by multiplication with c. Anti-diffusion for c>1.

    source
    SpeedyWeather.SpeedyTransforms.spectral_smoothingMethod
    A_smooth = spectral_smoothing(A::LowerTriangularMatrix,c;power=1)

    Smooth the spectral field A following A_smooth = (1-c*∇²ⁿ)A with power n of a normalised Laplacian so that the highest degree lmax is dampened by multiplication with c. Anti-diffusion for c<0.

    source
    SpeedyWeather.SpeedyTransforms.spectral_truncation!Method
    spectral_truncation!(alms::AbstractMatrix,ltrunc::Integer,mtrunc::Integer)

    Truncate spectral coefficients alms in-place by setting (a) the upper right triangle to zero and (b) all coefficients for which the degree l is larger than the truncation ltrunc or order m larger than the truncaction mtrunc.

    source
    SpeedyWeather.SpeedyTransforms.spectral_truncation!Method
    spectral_truncation!(alms::LowerTriangularMatrix,ltrunc::Integer,mtrunc::Integer)

    Truncate spectral coefficients alms in-place by setting all coefficients for which the degree l is larger than the truncation ltrunc or order m larger than the truncaction mtrunc. Similar to spectral_truncation!(::AbstractMatrix, ...) but skips the upper triangle which is zero by design for LowerTriangularMatrix.

    source
    SpeedyWeather.SpeedyTransforms.spectral_truncationMethod
    alms_trunc = spectral_truncation(alms,trunc)

    Returns a spectral coefficient matrix alms_trunc that is truncated from alms to the size (trunc+1)². alms_trunc only contains those coefficient of alms for which m,l ≤ trunc, and l ≥ m are zero anyway. If trunc is larger than the implicit truncation in alms obtained from its size than spectral_interpolation is automatically called instead, returning alms_interp, a coefficient matrix that is larger than alms with padded zero coefficients.

    source
    SpeedyWeather.SpeedyTransforms.ϵlmMethod
    ϵ = ϵ(l,m)

    Recursion factors ϵ as a function of degree l and order m (0-based) of the spherical harmonics. ϵ(l,m) = sqrt((l^2-m^2)/(4*l^2-1)) with default number format Float64.

    source
    SpeedyWeather.SpeedyTransforms.ϵlmMethod
    ϵ = ϵ(NF,l,m)

    Recursion factors ϵ as a function of degree l and order m (0-based) of the spherical harmonics. ϵ(l,m) = sqrt((l^2-m^2)/(4*l^2-1)) and then converted to number format NF.

    source
    SpeedyWeather.SpeedyTransforms.∇!Method
    ∇!(
    +                                        ) where NF

    Returns a spectral coefficient matrix alms_interp that is alms padded with zeros to interpolate in spectral space. If trunc is smaller or equal to the implicit truncation in alms obtained from its size than spectral_truncation is automatically called instead, returning alms_trunc, a coefficient matrix that is smaller than alms, implicitly setting higher degrees and orders to zero.

    source
    SpeedyWeather.SpeedyTransforms.spectral_smoothing!Method
    spectral_smoothing!(A::LowerTriangularMatrix,c;power=1)

    Smooth the spectral field A following A = (1-(1-c)∇²ⁿ) with power n of a normalised Laplacian so that the highest degree lmax is dampened by multiplication with c. Anti-diffusion for c>1.

    source
    SpeedyWeather.SpeedyTransforms.spectral_smoothingMethod
    A_smooth = spectral_smoothing(A::LowerTriangularMatrix,c;power=1)

    Smooth the spectral field A following A_smooth = (1-c*∇²ⁿ)A with power n of a normalised Laplacian so that the highest degree lmax is dampened by multiplication with c. Anti-diffusion for c<0.

    source
    SpeedyWeather.SpeedyTransforms.spectral_truncation!Method
    spectral_truncation!(alms::AbstractMatrix,ltrunc::Integer,mtrunc::Integer)

    Truncate spectral coefficients alms in-place by setting (a) the upper right triangle to zero and (b) all coefficients for which the degree l is larger than the truncation ltrunc or order m larger than the truncaction mtrunc.

    source
    SpeedyWeather.SpeedyTransforms.spectral_truncation!Method
    spectral_truncation!(alms::LowerTriangularMatrix,ltrunc::Integer,mtrunc::Integer)

    Truncate spectral coefficients alms in-place by setting all coefficients for which the degree l is larger than the truncation ltrunc or order m larger than the truncaction mtrunc. Similar to spectral_truncation!(::AbstractMatrix, ...) but skips the upper triangle which is zero by design for LowerTriangularMatrix.

    source
    SpeedyWeather.SpeedyTransforms.spectral_truncationMethod
    alms_trunc = spectral_truncation(alms,trunc)

    Returns a spectral coefficient matrix alms_trunc that is truncated from alms to the size (trunc+1)². alms_trunc only contains those coefficient of alms for which m,l ≤ trunc, and l ≥ m are zero anyway. If trunc is larger than the implicit truncation in alms obtained from its size than spectral_interpolation is automatically called instead, returning alms_interp, a coefficient matrix that is larger than alms with padded zero coefficients.

    source
    SpeedyWeather.SpeedyTransforms.ϵlmMethod
    ϵ = ϵ(l,m)

    Recursion factors ϵ as a function of degree l and order m (0-based) of the spherical harmonics. ϵ(l,m) = sqrt((l^2-m^2)/(4*l^2-1)) with default number format Float64.

    source
    SpeedyWeather.SpeedyTransforms.ϵlmMethod
    ϵ = ϵ(NF,l,m)

    Recursion factors ϵ as a function of degree l and order m (0-based) of the spherical harmonics. ϵ(l,m) = sqrt((l^2-m^2)/(4*l^2-1)) and then converted to number format NF.

    source
    SpeedyWeather.SpeedyTransforms.∇!Method
    ∇!(
         dpdx::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         dpdy::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         p::LowerTriangularMatrix{Complex{NF<:AbstractFloat}},
         S::SpectralTransform{NF<:AbstractFloat}
     ) -> Tuple{LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat, LowerTriangularMatrix{Complex{NF}} where NF<:AbstractFloat}
    -

    Applies the gradient operator ∇ applied to input p and stores the result in dpdx (zonal derivative) and dpdy (meridional derivative). The gradient operator acts on the unit sphere and therefore omits the radius scaling

    source
    SpeedyWeather.SpeedyTransforms.∇²!Method
    ∇²!(    ∇²alms::LowerTriangularMatrix,
    +

    Applies the gradient operator ∇ applied to input p and stores the result in dpdx (zonal derivative) and dpdy (meridional derivative). The gradient operator acts on the unit sphere and therefore omits the radius scaling

    source
    SpeedyWeather.SpeedyTransforms.∇²!Method
    ∇²!(    ∇²alms::LowerTriangularMatrix,
             alms::LowerTriangularMatrix,
             S::SpectralTransform;
             add::Bool=false,
             flipsign::Bool=false,
    -        inverse::Bool=false)

    Laplace operator ∇² applied to the spectral coefficients alms in spherical coordinates. The radius R is omitted in the eigenvalues which are precomputed in S. ∇²! is the in-place version which directly stores the output in the first argument ∇²alms.

    Keyword arguments

    • add=true adds the ∇²(alms) to the output
    • flipsign=true computes -∇²(alms) instead
    • inverse=true computes ∇⁻²(alms) instead

    Default is add=false, flipsign=false, inverse=false. These options can be combined.

    source
    SpeedyWeather.SpeedyTransforms.∇²Method
    ∇²(alms::LowerTriangularMatrix, S::SpectralTransform) -> Any
    -

    Laplace operator ∇² applied to input alms, using precomputed eigenvalues from S. The Laplace operator acts on the unit sphere and therefore omits the 1/radius^2 scaling

    source
    SpeedyWeather.SpeedyTransforms.∇²Method
    ∇²(alms::LowerTriangularMatrix) -> Any
    -

    Returns the Laplace operator ∇² applied to input alms. The Laplace operator acts on the unit sphere and therefore omits the 1/radius^2 scaling

    source
    SpeedyWeather.SpeedyTransforms.∇⁻²!Method
    ∇⁻²!(   ∇⁻²alms::LowerTriangularMatrix,
    +        inverse::Bool=false)

    Laplace operator ∇² applied to the spectral coefficients alms in spherical coordinates. The radius R is omitted in the eigenvalues which are precomputed in S. ∇²! is the in-place version which directly stores the output in the first argument ∇²alms.

    Keyword arguments

    • add=true adds the ∇²(alms) to the output
    • flipsign=true computes -∇²(alms) instead
    • inverse=true computes ∇⁻²(alms) instead

    Default is add=false, flipsign=false, inverse=false. These options can be combined.

    source
    SpeedyWeather.SpeedyTransforms.∇²Method
    ∇²(alms::LowerTriangularMatrix, S::SpectralTransform) -> Any
    +

    Laplace operator ∇² applied to input alms, using precomputed eigenvalues from S. The Laplace operator acts on the unit sphere and therefore omits the 1/radius^2 scaling

    source
    SpeedyWeather.SpeedyTransforms.∇²Method
    ∇²(alms::LowerTriangularMatrix) -> Any
    +

    Returns the Laplace operator ∇² applied to input alms. The Laplace operator acts on the unit sphere and therefore omits the 1/radius^2 scaling

    source
    SpeedyWeather.SpeedyTransforms.∇⁻²!Method
    ∇⁻²!(   ∇⁻²alms::LowerTriangularMatrix,
             alms::LowerTriangularMatrix,
             S::SpectralTransform;
             add::Bool=false,
    -        flipsign::Bool=false)

    Calls ∇²!(∇⁻²alms, alms, S; add, flipsign, inverse=true).

    source
    SpeedyWeather.SpeedyTransforms.∇⁻²Method
    ∇⁻²(
         ∇²alms::LowerTriangularMatrix,
         S::SpectralTransform
     ) -> Any
    -

    InverseLaplace operator ∇⁻² applied to input alms, using precomputed eigenvalues from S. The Laplace operator acts on the unit sphere and therefore omits the radius^2 scaling

    source
    SpeedyWeather.SpeedyTransforms.∇⁻²Method
    ∇⁻²(∇²alms::LowerTriangularMatrix) -> Any
    -

    Returns the inverse Laplace operator ∇⁻² applied to input alms. The Laplace operator acts on the unit sphere and therefore omits the radius^2 scaling

    source
    +

    InverseLaplace operator ∇⁻² applied to input alms, using precomputed eigenvalues from S. The Laplace operator acts on the unit sphere and therefore omits the radius^2 scaling

    source
    SpeedyWeather.SpeedyTransforms.∇⁻²Method
    ∇⁻²(∇²alms::LowerTriangularMatrix) -> Any
    +

    Returns the inverse Laplace operator ∇⁻² applied to input alms. The Laplace operator acts on the unit sphere and therefore omits the radius^2 scaling

    source

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