pitfiller: Pit Filler

In terra: Spatial Data Analysis

Pit Filler

Description

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

Usage

## S4 method for signature '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 = "", ...)

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

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}

Value

A SpatRaster with pits filled.

Author(s)

Emanuele Cordano

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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)

terra documentation built on Aug. 22, 2026, 5:07 p.m.