Hypsographic Functions for Conical Lake Geometry

The functions calculate area resp. volume of a lake with a conical depth profile.

Usage

areaFunction(level, zmax, amax)

volumeFunction(level, zmax, amax)

vol2level(vol, zmax, amax)

Arguments

level

vector of water level above ground

zmax

maximum lake depth

amax

surface area of the lake surface for level = zmax

vol

vector of given volume(s)

Examples

level <- seq(0, 50, 1)
amax  <- 9e6
zmax  <- 50
area <- areaFunction(level, zmax, amax)
vol  <- volumeFunction(level, zmax, amax)
plot(vol, cumsum(area), type="l")

(vol - cumsum(area)) / vol
#>  [1]         NaN -2.00000000 -0.87500000 -0.55555556 -0.40625000 -0.32000000
#>  [7] -0.26388889 -0.22448980 -0.19531250 -0.17283951 -0.15500000 -0.14049587
#> [13] -0.12847222 -0.11834320 -0.10969388 -0.10222222 -0.09570312 -0.08996540
#> [19] -0.08487654 -0.08033241 -0.07625000 -0.07256236 -0.06921488 -0.06616257
#> [25] -0.06336806 -0.06080000 -0.05843195 -0.05624143 -0.05420918 -0.05231867
#> [31] -0.05055556 -0.04890739 -0.04736328 -0.04591368 -0.04455017 -0.04326531
#> [37] -0.04205247 -0.04090577 -0.03981994 -0.03879027 -0.03781250 -0.03688281
#> [43] -0.03599773 -0.03515414 -0.03434917 -0.03358025 -0.03284499 -0.03214124
#> [49] -0.03146701 -0.03082049 -0.03020000