diff --git a/R/lake.number.R b/R/lake.number.R index f2a5052..b8ca864 100644 --- a/R/lake.number.R +++ b/R/lake.number.R @@ -11,6 +11,21 @@ #' across the thermocline in a small lake (Robertson and Imberger, 1994), and #' to explain the magnitude of the vertical flux of ammonium in a lake (Romero #' et al., 1998). +#' In Imberger and Patterson (1990), Lake Number was defined as +#' Ln = (g * St * (zm - zT)) / (rho_0 * u*^2 * A0^3/2 * (zm - zg)) +#' with all values referenced from the lake bottom, e.g., +#' zm being the height of the water level, zT the height of metalimnion +#' and zg the height of center volume. +#' Our calculations assume that the reference is at the lake surface, therefore: +#' height of metalimnion becomes metalimnion depth (average of meta top and bot): +#' (zm - zT) --> (metaT + metaB)/2 +#' height of center of volume depth becomes center of volume depth Zcv: +#' (zm - zg) --> Zcv +#' Further, we note that in that original work St was defined as +#' St = int (z - zg) A(z) rho(z) dz +#' and rLakeAnalyzer defines St as +#' St = g/A0 int (z - zg) rho(z) dz +#' Therefore, we calculate St_uC = St * Ao / g #' #' @param bthA a numeric vector of cross sectional areas (m2) corresponding to #' bthD depths, hypsographic areas diff --git a/man/lake.number.Rd b/man/lake.number.Rd index a4469bd..115753d 100644 --- a/man/lake.number.Rd +++ b/man/lake.number.Rd @@ -43,6 +43,21 @@ Lake Number has been used, for example, to estimate the flux of oxygen across the thermocline in a small lake (Robertson and Imberger, 1994), and to explain the magnitude of the vertical flux of ammonium in a lake (Romero et al., 1998). +In Imberger and Patterson (1990), Lake Number was defined as +Ln = (g * St * (zm - zT)) / (rho_0 * u*^2 * A0^3/2 * (zm - zg)) +with all values referenced from the lake bottom, e.g., +zm being the height of the water level, zT the height of metalimnion +and zg the height of center volume. +Our calculations assume that the reference is at the lake surface, therefore: +height of metalimnion becomes metalimnion depth (average of meta top and bot): +(zm - zT) --> (metaT + metaB)/2 +height of center of volume depth becomes center of volume depth Zcv: +(zm - zg) --> Zcv +Further, we note that in that original work St was defined as +St = int (z - zg) A(z) rho(z) dz +and rLakeAnalyzer defines St as +St = g/A0 int (z - zg) rho(z) dz +Therefore, we calculate St_uC = St * Ao / g } \examples{