License Information

Use of this function requires a license for Whitebox Workflows for Python Professional (WbW-Pro). Please visit www.whiteboxgeo.com to purchase a license.

Description

This tool calculates the spatial pattern of unsphericity curvature, which describes the degree to which the shape of the topographic surface is nonspherical at a given point (Shary, 1995), from a digital elevation model (DEM). It is calculated as half the difference between the maximal_curvature and the minimal_curvature. Unsphericity has values equal to or greater than zero and is measured in units of m-1. Larger values indicate locations that are less spherical in form.

The user must specify the name of the input DEM (dem) and the output raster (output). The The Z conversion factor (zfactor) 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. Curvature values are often very small and as such the user may opt to log-transform the output raster (log). Transforming the values applies the equation by Shary et al. (2002):

Θ' = sign(Θ) ln(1 + 10n|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

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 PA (1995) Land surface in gravity points classification by a complete system of curvatures. Mathematical Geology 27: 373–390.

Shary P. A., Sharaya L. S. and Mitusov A. V. (2002) Fundamental quantitative methods of land surface analysis. Geoderma 107: 1–32.

See Also

minimal_curvature, maximal_curvature, mean_curvature, gaussian_curvature, profile_curvature, tangential_curvature

Function Signature

def unsphericity(self, dem: Raster, log_transform: bool = False, z_factor: float = 1.0) -> Raster: ...

Project Links

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