Merge pull request #114 from robertladwig/master

Added calculation of lake number

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