terra (version 1.9-46)

pitfiller: Pit Filler

Description

Fills pits (depressions with no outlet) in a elevation raster using the PEM4PIT terrain erosion model.

Usage

# S4 method for SpatRaster
pitfiller(x, pit, flowdir, niter = 10, lambda = 0,
                 deviation_type = "lad", max_iters=10^6, U = 1, D = 300, beta = 0.9,
                 theta_exp = 0.5, filename = "", ...)

Value

A SpatRaster with pits filled.

Arguments

x

SpatRaster with elevation values

pit

SpatRaster with pits identified with values > 0. See pitfinder

flowdir

SpatRaster with flow direction. See flowDir

niter

Number of iterations

lambda

Deviation parameter

deviation_type

Type of deviation. See flowDir

max_iters

Maximum iterations for drainage path starting points detection. See flowDir

U

Uplift rate. See Details

D

Diffusion coefficient. See Details

beta

Erosion coefficient. See Details

theta_exp

Exponent for contributing area. See Details

filename

Character. Output filename

...

Additional arguments for writing files, as in writeRaster

Author

Emanuele Cordano

Details

The PEM4PIT (Physical Erosion Model for PIT and flat areas correction) equation [Grimaldi at al, 2007] corrects DEMs by simulating erosion processes. It improves hydrologic modeling by enhancing flow direction and contributing area representation. Function is still experimental.

The model is based on the steady-state sediment balance equation:

$$0 = U - \beta A^{\theta} \left( \frac{z - z_d}{\Delta l} \right) + \frac{4D}{\Delta x^2} \left( \bar{z} - z \right)$$

Rearranging terms to isolate \(z\):

$$\beta A^{\theta} \left( \frac{z - z_d}{\Delta l} \right) = U + \frac{4D}{\Delta x^2} \left( \bar{z} - z \right)$$

Distributing terms:

$$\beta A^{\theta} \frac{z}{\Delta l} - \beta A^{\theta} \frac{z_d}{\Delta l} = U + \frac{4D \bar{z}}{\Delta x^2} - \frac{4D z}{\Delta x^2}$$

Combining like terms:

$$\beta A^{\theta} \frac{z}{\Delta l} + \frac{4D z}{\Delta x^2} = U + \frac{4D \bar{z}}{\Delta x^2} + \beta A^{\theta} \frac{z_d}{\Delta l}$$

Factoring out \(z\):

$$z \left( \beta A^{\theta} \frac{1}{\Delta l} + \frac{4D}{\Delta x^2} \right) = U + \frac{4D \bar{z}}{\Delta x^2} + \beta A^{\theta} \frac{z_d}{\Delta l}$$

Solving for \(z\):

$$z = \frac{U \Delta l \Delta x^2 + 4D \Delta l \bar{z} + \beta A^{\theta} \Delta x^2 z_d}{\beta A^{\theta} \Delta x^2 + 4D \Delta l}$$

References

Grimaldi, S., Nardi, F., Di Benedetto, F., Istanbulluoglu, E., & Bras, R. L. (2007). A physically-based method for removing pits in digital elevation models. Advances in Water Resources, 30(10), 2151--2158. tools:::Rd_expr_doi("10.1016/j.advwatres.2006.11.016")

Tucker, G. E., & Bras, R. L. (1998). Hillslope processes, drainage density, and landscape morphology. Water Resources Research, 34(10), 2751--2764. tools:::Rd_expr_doi("10.1029/98WR01474")

Niemann, J. D., Bras, R. L., & Veneziano, D. (2003). A physically based interpolation method for fluvially eroded topography. Water Resources Research, 39, 1017. tools:::Rd_expr_doi("10.1029/2001WR001050")

Niemann, J. D., Bras, R. L., Veneziano, D., & Rinaldo, A. (2001). Impacts of surface elevation on the growth and scaling properties of simulated river networks. Geomorphology, 40(1--2), 37--55. tools:::Rd_expr_doi("10.1016/S0169-555X(01)00036-8")

See Also

terrain, watershed, flowDir, pitfinder

Examples

elev <- rast(system.file("ex/elev.tif", package = "terra"))
elev <- project(elev, "epsg:32632")

lambda <- 0.5 ## try also 0 (default)
flowdir <- flowDir(elev, lambda = lambda)
pits <- pitfinder(flowdir, pits_on_boundary = FALSE)
fill <- pitfiller(elev, pits, flowdir, lambda=lambda)

elev2 <- pitfiller(x = elev, pit = pits, flowdir = flowdir, lambda = lambda)
flowdir2 <- terrain(elev2, "flowdir")
flowdir2 <- flowDir(elev2, lambda = lambda)
pits2 <- pitfinder(flowdir2, pits_on_boundary = FALSE)
fill2 <- pitfiller(elev, pits2, flowdir2, lambda=lambda)