approx.bathy: Estimate hypsography curve
In rLakeAnalyzer: Lake Physics Tools

Description Usage Arguments Value References Examples

Estimates a depth-area curve for a lake using lake surface area, maximum depth and mean depth. Two methods for estimating the curve are available; 'cone' assumes the lake is shaped as a cone and requires only surface area and maximum depth; "voldev" uses the volume development (Vd) parameter from Hakanson (1981) and Johansson et al. (2007). Vd is a dimensionless parameter that describes lake basin shape in relation to the volume of cone whose base area and height equal the surface area and maximum lake depth, it is estimated as Vd = Zmean/Zmax (Hakanson et al. 2000). Method "voldev' requires lake surface area, mean and maximum depth. Depths at which the area is estimated can be set by as a numeric vector or as a regularly spaced sequence.

1 2	approx.bathy(Zmax, lkeArea, Zmean = NULL, method = "cone", zinterval = 1, depths = seq(0, Zmax, by = zinterval))

`Zmax`	a single value of the maxiumum depth of the lake (in m)
`lkeArea`	a sinlge value of the surface area of the lake (in m^2)
`Zmean`	a single value of the mean depth of the lake (in m)
`method`	specifies the method used to estimate depth-area relationship, can be "cone"(default) or "voldev". Method "voldev" requires Zmean. See notes for details.
`zinterval`	a sinlge value defining the depth interval at which volumes should be calculated, default is 1 m.
`depths`	a numeric vector of depths (in m) at which areas are estimated. If not specified depths is regularly spaced sequence of values with the interval set by zinterval.

a dataframe which defines the lake area for each depth. Columns are depths (m) and Area.at.z (m^2). Area at 0 m should equal the user entered lkeArea.

Hakanson, L. (1981). On lake bottom dynamics - the energy- topography factor. Canadian Journal of Earth Sciences, 18, 899-909. Johansson, H., A. A. Brolin, and L. Hakanson. 2007. New approaches to the modelling of lake basin morphometry. Environ. Model. Assess. 12: 213-228.

 
Voldev.ex = approx.bathy(Zmax = 25, Zmean = 12, lkeArea = 39400000, method = "voldev")
Voldevshallow.ex = approx.bathy(Zmax = 25, Zmean = 6, lkeArea = 39400000, method = "voldev")
Cone.ex = approx.bathy(Zmax = 25, lkeArea = 39400000, method = "cone")

# plot depth-area curves
  plot(Cone.ex$depths ~ Cone.ex$Area.at.z, xlab = "Area (m^3)", ylab = "Depth (m)")
  points(Voldev.ex$depths ~ Voldev.ex$Area.at.z, col = "red")
  points(Voldevshallow.ex$depths ~ Voldevshallow.ex$Area.at.z, col = "blue")