## Description

This tool calculates the curvedness (Koenderink and van Doorn, 1992) from a digital elevation model (DEM). Curvedness is the root mean square of maximal and minimal curvatures, and measures the magnitude of surface bending, regardless of shape (Florinsky, 2017). Curvedness is characteristically low-values for flat areas and higher for areas of sharp bending (Florinsky, 2017). The index is also inversely proportional with the size of the object (Koenderink and van Doorn, 1992). Curvedness has values equal to or greater than zero and is measured in units of m-1.

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. Raw curvedness values are often challenging to visualize given their range and magnitude, 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.

Koenderink, J. J., and Van Doorn, A. J. (1992). Surface shape and curvature scales. Image and vision computing, 10(8), 557-564.

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

## See Also

shape_index, minimal_curvature, maximal_curvature, tangential_curvature, profile_curvature, mean_curvature, gaussian_curvature

## Function Signature

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

## Project Links

WbW Homepage User Manual Support WbW