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changes after updating 2-moment distribution parameters #394

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May 10, 2024
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changes after updating 2-moment distribution parameters #394

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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -20,7 +20,7 @@ MLJ = "add582a8-e3ab-11e8-2d5e-e98b27df1bc7"
EmulatorModelsExt = ["DataFrames", "MLJ"]

[compat]
ClimaParams = "0.10.5"
ClimaParams = "0.10.6"
DataFrames = "1.6"
DocStringExtensions = "0.8, 0.9"
ForwardDiff = "0.10"
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3 changes: 2 additions & 1 deletion docs/src/API.md
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Expand Up @@ -176,7 +176,8 @@ Parameters.AccrTC1980
Parameters.LD2004
Parameters.VarTimescaleAcnv
Parameters.SB2006
Parameters.ParticlePDF_SB2006
Parameters.RainParticlePDF_SB2006
Parameters.CloudParticlePDF_SB2006
Parameters.AcnvSB2006
Parameters.AccrSB2006
Parameters.SelfColSB2006
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6 changes: 3 additions & 3 deletions docs/src/Microphysics2M.md
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Expand Up @@ -62,7 +62,7 @@ where ``D`` is the drop diameter which is proportional to ``x^{1/3}``.
Through this proportionality relation, we can express the raindrops exponential distribution as a gamma distribution function
```math
\begin{align}
f_r(x)=A_rx^\nu_r e^{-B_rx^{\mu_r}},
f_r(x)=A_rx^{-\nu_r}_r e^{-B_rx^{\mu_r}},
\end{align}
```
where ``\nu_r=-\frac{2}{3}``, and ``\mu_r=\frac{1}{3}``.
Expand Down Expand Up @@ -103,7 +103,7 @@ where:
The function ``\phi_{acnv}(\tau)`` is used to correct the autoconversion rate for the undeveloped cloud droplet spectrum and the early stage rain evolution assumptions. This is a universal function which is obtained by fitting to numerical results of the SCE:
```math
\begin{equation}
\phi_{acnv}(\tau) = A \tau^b(1-\tau^b)^c,
\phi_{acnv}(\tau) = A \tau^a(1-\tau^a)^b,
\end{equation}
```
where
Expand All @@ -116,7 +116,7 @@ The default free parameter values are:
|``\nu`` | ``2`` |
|``A`` | ``400`` |
|``a`` | ``0.7`` |
|``c`` | ``3`` |
|``b`` | ``3`` |
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Do we still need to define c that is used in autoconversion? (line 106?)

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There was an error in the documentation. Following the SB2006 paper and ClimaParams, c=4 is the accretion parameter, while in the autoconversion formula we have two parameters a and b, which are equal to 0.7 and 3. In the formula in line 106, b and c must be replaced with a and b respectively. I just change it in the last commit.

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Thank you!


The rate of change of raindrops number density is
``` math
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6 changes: 3 additions & 3 deletions docs/src/plots/RainEvapoartionSB2006.jl
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Expand Up @@ -26,11 +26,11 @@ function rain_evaporation_CPU(SB2006, aps, tps, q, q_rai, ρ, N_rai, T)

(; ν_air, D_vapor) = aps
(; av, bv, α, β, ρ0) = SB2006.evap
ρw = SB2006.pdf.ρw
x_star = SB2006.pdf.xr_min
ρw = SB2006.pdf_r.ρw
x_star = SB2006.pdf_r.xr_min
G = CO.G_func(aps, tps, T, TD.Liquid())

xr = CM2.raindrops_limited_vars(SB2006.pdf, q_rai, ρ, N_rai).xr
xr = CM2.raindrops_limited_vars(SB2006.pdf_r, q_rai, ρ, N_rai).xr
Dr = (FT(6) / FT(π) / ρw)^FT(1 / 3) * xr^FT(1 / 3)

t_star = (FT(6) * x_star / xr)^FT(1 / 3)
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97 changes: 43 additions & 54 deletions src/Microphysics2M.jl
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Expand Up @@ -46,9 +46,9 @@ end
# mean terminal velocity of raindrops, and rain evaporation rates from Seifert and Beheng 2001

"""
raindrops_limited_vars(pdf, q_rai, ρ, N_rai)
raindrops_limited_vars(pdf_r, q_rai, ρ, N_rai)

- `pdf` - a struct with SB2006 size distribution parameters
- `pdf_r` - a struct with SB2006 raindrops size distribution parameters
- `q_rai` - rain water specific humidity
- `ρ` - air density
- `N_rai` raindrops number density
Expand All @@ -57,12 +57,12 @@ Returns a named tupple containing the mean mass of raindrops, xr, and the rate p
size distribution of raindrops (based on drops diameter), λr, limited within prescribed ranges
"""
function raindrops_limited_vars(
pdf::CMP.ParticlePDF_SB2006{FT},
pdf_r::CMP.RainParticlePDF_SB2006{FT},
q_rai::FT,
ρ::FT,
N_rai::FT,
) where {FT}
(; xr_min, xr_max, N0_min, N0_max, λ_min, λ_max, ρw) = pdf
(; xr_min, xr_max, N0_min, N0_max, λ_min, λ_max, ρw) = pdf_r

L_rai = ρ * q_rai
xr_0 = L_rai / N_rai
Expand Down Expand Up @@ -231,7 +231,7 @@ Returns the raindrops number density tendency due to collisions of raindrops
that produce larger raindrops (self-collection) for `scheme == SB2006Type`
"""
function rain_self_collection(
pdf::CMP.ParticlePDF_SB2006{FT},
pdf::CMP.RainParticlePDF_SB2006{FT},
self::CMP.SelfColSB2006{FT},
q_rai::FT,
ρ::FT,
Expand Down Expand Up @@ -268,7 +268,7 @@ Returns the raindrops number density tendency due to breakup of raindrops
that produce smaller raindrops for `scheme == SB2006Type`
"""
function rain_breakup(
pdf::CMP.ParticlePDF_SB2006{FT},
pdf::CMP.RainParticlePDF_SB2006{FT},
brek::CMP.BreakupSB2006{FT},
q_rai::FT,
ρ::FT,
Expand All @@ -294,8 +294,8 @@ end
"""
rain_self_collection_and_breakup(SB2006, q_rai, ρ, N_rai)

- `SB2006` - a struct with SB2006 parameters for size distribution
self collection and breakup
- `SB2006` - a struct with SB2006 parameters for raindrops size
distribution, self collection, and breakup
- `q_rai` - rain water specific humidity
- `ρ` - air density
- `N_rai` - raindrops number density
Expand All @@ -304,14 +304,14 @@ Returns a named tupple containing the raindrops self-collection and breakup rate
for `scheme == SB2006Type`
"""
function rain_self_collection_and_breakup(
(; pdf, self, brek)::CMP.SB2006{FT},
(; pdf_r, self, brek)::CMP.SB2006{FT},
q_rai::FT,
ρ::FT,
N_rai::FT,
) where {FT}

sc = rain_self_collection(pdf, self, q_rai, ρ, N_rai)
br = rain_breakup(pdf, brek, q_rai, ρ, N_rai, sc)
sc = rain_self_collection(pdf_r, self, q_rai, ρ, N_rai)
br = rain_breakup(pdf_r, brek, q_rai, ρ, N_rai, sc)

return (; sc, br)
end
Expand All @@ -332,7 +332,7 @@ Fall velocity of individual rain drops is parameterized:
- following Chen et. al 2022, DOI: 10.1016/j.atmosres.2022.106171 for `velo_scheme == Chen2022Type`
"""
function rain_terminal_velocity(
(; pdf)::CMP.SB2006{FT},
(; pdf_r)::CMP.SB2006{FT},
(; ρ0, aR, bR, cR)::CMP.SB2006VelType{FT},
q_rai::FT,
ρ::FT,
Expand All @@ -342,13 +342,13 @@ function rain_terminal_velocity(
if q_rai < eps(FT)
return (FT(0), FT(0))
end
λr = raindrops_limited_vars(pdf, q_rai, ρ, N_rai).λr
λr = raindrops_limited_vars(pdf_r, q_rai, ρ, N_rai).λr
vt0 = max(FT(0), sqrt(ρ0 / ρ) * (aR - bR / (1 + cR / λr)))
vt1 = max(FT(0), sqrt(ρ0 / ρ) * (aR - bR / (1 + cR / λr)^FT(4)))
return (vt0, vt1)
end
function rain_terminal_velocity(
(; pdf)::CMP.SB2006{FT},
(; pdf_r)::CMP.SB2006{FT},
vel::CMP.Chen2022VelTypeRain{FT},
q_rai::FT,
ρ::FT,
Expand All @@ -360,7 +360,7 @@ function rain_terminal_velocity(
# coefficients from Table B1 from Chen et. al. 2022
aiu, bi, ciu = CO.Chen2022_vel_coeffs_small(vel, ρ)
# size distribution parameter
λ = raindrops_limited_vars(pdf, q_rai, ρ, N_rai).λr
λ = raindrops_limited_vars(pdf_r, q_rai, ρ, N_rai).λr

# eq 20 from Chen et al 2022
vt0 = sum(CO.Chen2022_vel_add.(aiu, bi, ciu, λ, 0))
Expand Down Expand Up @@ -401,7 +401,7 @@ specific humidity due to rain rain_evaporation, assuming a power law velocity re
fall velocity of individual drops and an exponential size distribution, for `scheme == SB2006Type`
"""
function rain_evaporation(
(; pdf, evap)::CMP.SB2006{FT},
(; pdf_r, evap)::CMP.SB2006{FT},
aps::CMP.AirProperties{FT},
tps::TDP.ThermodynamicsParameters{FT},
q::TD.PhasePartition{FT},
Expand All @@ -419,11 +419,11 @@ function rain_evaporation(

(; ν_air, D_vapor) = aps
(; av, bv, α, β, ρ0) = evap
x_star = pdf.xr_min
ρw = pdf.ρw
x_star = pdf_r.xr_min
ρw = pdf_r.ρw
G = CO.G_func(aps, tps, T, TD.Liquid())

xr = raindrops_limited_vars(pdf, q_rai, ρ, N_rai).xr
xr = raindrops_limited_vars(pdf_r, q_rai, ρ, N_rai).xr
Dr = (FT(6) / FT(π) / ρw)^FT(1 / 3) * xr^FT(1 / 3)

t_star = (FT(6) * x_star / xr)^FT(1 / 3)
Expand All @@ -447,11 +447,12 @@ function rain_evaporation(
return (; evap_rate_0, evap_rate_1)
end

"""
radar_reflectivity(struct, q_liq, q_rai, N_liq, N_rai, ρ_air, ρ_w, τ_q, τ_N)
"""
radar_reflectivity(structs, q_liq, q_rai, N_liq, N_rai, ρ_air, ρ_w, τ_q, τ_N)

- `struct` - type for 2-moment rain autoconversion parameterization
- `q_liq` - cloud water specific humidity
- `structs` - structs with SB2006 cloud droplets and raindrops
size distributions parameters
- `q_liq` - cloud water specific humidity
- `q_rai` - rain water specific humidity
- `N_liq` - cloud droplet number density
- `N_rai` - rain droplet number density
Expand All @@ -465,7 +466,7 @@ size distribuions normalized by the reflectivty of 1 millimiter drop in a volume
one meter cube
"""
function radar_reflectivity(
acnv::CMP.AcnvSB2006{FT},
(; pdf_c, pdf_r)::CMP.SB2006{FT},
q_liq::FT,
q_rai::FT,
N_liq::FT,
Expand All @@ -476,15 +477,8 @@ function radar_reflectivity(
τ_N::FT,
) where {FT}

# we assume a cloud droplets gamma distribution,
# where the parameters are νc=2 and μc=1
(; νc) = acnv

# we assume a raindrops exponential distribution
# which can be seen as a gamma distribution with
# parameters νr=-2/3 and μr=1/3
νr = FT(-2 / 3)
μr = FT(1 / 3)
(; νc, μc) = pdf_c
(; νr, μr) = pdf_r

# change of units for N_liq and N_rai
# from m^-3 to mm^-3
Expand All @@ -501,12 +495,12 @@ function radar_reflectivity(

Bc =
(xc == 0) ? FT(0) :
(SF.gamma(FT(νc + 1)) * xc / SF.gamma(FT(νc + 2)))^FT(-1)
(SF.gamma(FT(νc + 1) / μc) * xc / SF.gamma(FT(νc + 2) / μc))^(-μc)
Br =
(xr == 0) ? FT(0) :
(SF.gamma(FT(νr + 1) / μr) * xr / SF.gamma(FT(νr + 2) / μr))^(-μr)
Ac = (N_liq * Bc^(FT(νc + 1))) / SF.gamma(FT(νc + 1))
Ar = (μr * N_rai * Br^(FT(νr + 1) / μr)) / SF.gamma(FT(νr + 1) / μr)
Ac = μc * N_liq * Bc^(FT(νc + 1) / μc) / SF.gamma(FT(νc + 1) / μc)
Ar = μr * N_rai * Br^(FT(νr + 1) / μr) / SF.gamma(FT(νr + 1) / μr)

Zc = (Bc == 0) ? FT(0) : (FT(24) * Ac / (Bc^FT(5) * C^FT(2)))
Zr = (Br == 0) ? FT(0) : (FT(2160) * Ar / (Br^FT(7) * C^FT(2)))
Expand All @@ -515,11 +509,12 @@ function radar_reflectivity(
FT(10) * (log10((Zc + Zr) / Z₀) + log10(FT(1e-9)))
end

"""
effective_radius(struct, q_liq, q_rai, N_liq, N_rai, ρ_air, ρ_w, τ_q, τ_N)
"""
effective_radius(structs, q_liq, q_rai, N_liq, N_rai, ρ_air, ρ_w, τ_q, τ_N)

- `struct` - type for 2-moment rain autoconversion parameterization
- `q_liq` - cloud water specific humidity
- `structs` - structs with SB2006 cloud droplets and raindrops
size distribution parameters
- `q_liq` - cloud water specific humidity
- `q_rai` - rain water specific humidity
- `N_liq` - cloud droplet number density
- `N_rai` - rain droplet number density
Expand All @@ -532,7 +527,7 @@ Returns effective radius using the 2-moment scheme
cloud and rain particle size distributions
"""
function effective_radius(
acnv::CMP.AcnvSB2006{FT},
(; pdf_c, pdf_r)::CMP.SB2006{FT},
q_liq::FT,
q_rai::FT,
N_liq::FT,
Expand All @@ -543,15 +538,8 @@ function effective_radius(
τ_N::FT,
) where {FT}

# we assume a cloud droplets gamma distribution,
# where the parameters are νc=2 and μc=1
(; νc) = acnv

# we assume a raindrops exponential distribution
# which can be seen as a gamma distribution with
# parameters νr=-2/3 and μr=1/3
νr = FT(-2 / 3)
μr = FT(1 / 3)
(; νc, μc) = pdf_c
(; νr, μr) = pdf_r

# change of units for N_liq and N_rai
# from m^-3 to mm^-3
Expand All @@ -563,16 +551,17 @@ function effective_radius(

xc = (N_liq < τ_N) ? FT(0) : ((q_liq * ρ_air) / N_liq)
xr = (N_rai < τ_N) ? FT(0) : ((q_rai * ρ_air) / N_rai)

C = FT((4 / 3) * π * ρ_w)

Bc =
(xc == 0) ? FT(0) :
(SF.gamma(FT(νc + 1)) * xc / SF.gamma(FT(νc + 2)))^(-1)
(SF.gamma(FT(νc + 1) / μc) * xc / SF.gamma(FT(νc + 2) / μc))^(-μc)
Br =
(xr == 0) ? FT(0) :
((SF.gamma(FT(νr + 1) / μr) * xr / SF.gamma(FT(νr + 2) / μr))^(-μr))
Ac = (N_liq * Bc^(FT(νc + 1))) / SF.gamma(FT(νc + 1))
Ar = (μr * N_rai * Br^(FT(νr + 1) / μr)) / SF.gamma(FT(νr + 1) / μr)
(SF.gamma(FT(νr + 1) / μr) * xr / SF.gamma(FT(νr + 2) / μr))^(-μr)
Ac = μc * N_liq * Bc^(FT(νc + 1) / μc) / SF.gamma(FT(νc + 1) / μc)
Ar = μr * N_rai * Br^(FT(νr + 1) / μr) / SF.gamma(FT(νr + 1) / μr)

cloud_3moment = (Bc == 0) ? FT(0) : (FT(6) * Ac * C^3 / (Bc * C)^FT(4))
cloud_2moment =
Expand Down
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