Gaussian Curvature

This tool calculates the Gaussian curvature from a digital elevation model ($dem$). Gaussian curvature is the product of maximal and minimal curvatures, and retains values in each point of the topographic surface after its bending without breaking, stretching, and compressing (Florinsky, 2017).

Gaussian curvature is measured in units of $m^{-2}$.

Usage

wbw_gaussian_curvature(dem, log_transform = FALSE, z_factor = 1)

Arguments

dem: Raster object of class WhiteboxRaster. See wbw_read_raster() for more details.
log_transform: logical, default FALSE. Wheter log-transform the output raster or not. See details.
z_factor: double, Z conversion factor is only important when the vertical and horizontal units are not the same in the DEM. When this is the case, the algorithm will multiply each elevation in the DEM by the Z conversion factor

Value

WhiteboxRaster object in units of $m^{-2}$.

Details

Curvature values are often very small and as such the user may opt to log-transform the output raster ($log_transform$). Transforming the values applies the equation by Shary et al. (2002):

$$Θ' = sign(Θ) ln(1 + 10^n|Θ|)$$

where $Θ$ is the parameter value and $n$ is dependent on the grid cell size.

For DEMs in projected coordinate systems, the tool uses the 3rd-order bivariate Taylor polynomial method described by Florinsky (2016). Based on a polynomial fit of the elevations within the 5x5 neighbourhood surrounding each cell, this method is considered more robust against outlier elevations (noise) than other methods.

For DEMs in geographic coordinate systems (i.e. angular units), the tool uses the 3x3 polynomial fitting method for equal angle grids also described by Florinsky (2016).

References

For more information, see https://www.whiteboxgeo.com/manual/wbw-user-manual/book/tool_help.html#gaussian_curvature

Florinsky, I. (2016). Digital terrain analysis in soil science and geology. Academic Press.
Florinsky, I. V. (2017). An illustrated introduction to general geomorphometry. Progress in Physical Geography, 41(6), 723-752.
Shary P. A., Sharaya L. S. and Mitusov A. V. (2002) Fundamental quantitative methods of land surface analysis. Geoderma 107: 1–32.

Examples

f <- system.file("extdata/dem.tif", package = "wbw")
wbw_read_raster(f) |>
  wbw_gaussian_curvature()
#> +-----------------------------------------------+ 
#> | WhiteboxRaster                                |
#> | Gaussian Curvature                            |
#> |...............................................| 
#> | bands       : 1                               |
#> | dimensions  : 726, 800  (nrow, ncol)          |
#> | resolution  : 5.002392, 5.000243  (x, y)      |
#> | EPSG        : 2193  (Linear_Meter)            |
#> | extent      : 1925449 1929446 5582091 5585717 |
#> | min value   : -0.009157                       |
#> | max value   : 0.009663                        |
#> +-----------------------------------------------+