Hypsographic Table of a Conic Lake — hypso

Hypsographic Table of a Lake with Conical Morphometry

Source

Generated data, see example below.

References

Sachse, R., Petzoldt, T., Blumstock, M., Moreira, S., Pätzig, M., Rücker, J., Janse, J. H., Mooij, W. M., Hilt, S. (2014). Extending one-dimensional models for deep lakes to simulate the impact of submerged macrophytes on water quality. Environmental Modelling and Software, 61, 410-423

Hrbácek, J. (1966). A morphometrical study of some backwaters and fish ponds in relation to the representative plankton samples (with an appendix by C. 0. Junge on depth distribution for quadric surfaces and other configurations). Hydrobiological Studies, 1, 221–257.

Examples


zmax   <- 20                            # maximum depth (m)
area   <- function(Amax, zmax, z){Amax * (1 - (z)/zmax)^2}
volume <- function(Amax, zmax, z){Amax * zmax/3 * (1 - z/zmax)^3}
Amax   <- 12.07 * 1000 * 1000           # total Area (m^2)
depth  <- seq(zmax, 0, -.1)             # depth (m)

hypso_cone <- data.frame(depth = depth,
  volume = volume(Amax, zmax, depth),
  area=area(Amax, zmax, depth)
)

## inverted  depth order
hypso_cone$level <- zmax - hypso_cone$depth