Profile Curvature

This tool calculates the profile curvature from a digital elevation model (\(dem\)), or the rate of change in slope along a flow line.

Curvature is the second derivative of the topographic surface defined by a DEM. Profile curvature characterizes the degree of downslope acceleration or deceleration within the landscape (Gallant and Wilson, 2000).

WhiteboxTools reports curvature in radians multiplied by 100 for easier interpretation because curvature values are typically very small.

Usage

wbw_profile_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.

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#profile_curvature

Gallant, J. C., and J. P. Wilson, 2000, Primary topographic attributes, in Terrain Analysis: Principles and Applications, edited by J. P. Wilson and J. C. Gallant pp. 51-86, John Wiley, Hoboken, N.J.
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.

See also

wbw_gaussian_curvature(), wbw_mean_curvature()

Examples

f <- system.file("extdata/dem.tif", package = "wbw")
wbw_read_raster(f) |>
  wbw_profile_curvature()
#> +-----------------------------------------------+ 
#> | WhiteboxRaster                                |
#> | Profile 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   : -0.170079                       |
#> | max value   : 0.172405                        |
#> +-----------------------------------------------+