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Hillslope Width Function

Description

Fits each hillslope with a best-fit exponential hillslope width function of the form W = ce^ax, where W is the width of the hillslope and x is the distance from the hillslope divide. The resulting exponential hillslope conserves the area of the original hillslope by modifying the hillslope length. The following error metrics are calculated:

• ‘shape_err’: R2 value (ranges from 0 to 1) between observed hillslope widths and the widths predicted by the HWF (higher shape_err means a better fit)
• ‘pt_err’: percent error between the actual hillslope area and the polygon constrained by the hillslope points and outlet points. Larger pt_error implies a poor approximation of the hillslope by the points, and can be improved by increasing the number of points used.
• ‘Pt_trunc_err’. percent error between polygon constrained by the hillslope points and outlet points and hillslope defined by truncated points. Points are truncated where hillslope stops increasing or decreasing in width (to satisfy assumption that hillslopes are increasing or decreasing monotonically). Larger pt_trunc_err means that a large portion of the hillslope was truncated in this process.
• ‘strm_err- (for lateral hillslopes only): percent error between the Euclidean stream distance (measured as the linear distance between lateral hillslope outlet points) and the actual stream distance. Larger strm_err values mean that the approximation of linear stream channel may not be valid.

This tool modifies the input hillslopes feature with new fields: ‘a’, ‘c’, ‘xend’, ‘xtop’, ‘L’, ‘shape_err’, ‘pt_err’, ‘pt_trunc_err’, and ‘strm_err’.

Usage

Fits each hillslope with a best-fit exponential hillslope width function of the form W = ce^ax, where W is the width of the hillslope and x is the distance from the hillslope divide. The resulting exponential hillslope conserves the area of the original hillslope by modifying the hillslope length. This tool modifies the input hillslopes feature with new fields: ‘a’, ‘c’, ‘xend’, ‘xtop’, ‘L’, ‘shape_err’, ‘pt_err’, ‘pt_trunc_err’, and ‘strm_err’.

Parameters

Parameter Name	Type	Direction	Data Type	Dialog Reference
Input Partitioned Hillslopes	Required	Input	Feature Layer	Input partitioned hillslopes (use "Partition Hillslope" tool in Terrain Preprocessing).
Input Drainage Lines	Required	Input	Feature Layer	Drainage lines.
Input Number of Points	Required	Input	Double	Number of points to approximate the hillslope (must be an integer between 4 and 100).
Output Width Function Hillslopes	Required	Output	Feature Layer	Output hillslopes with width function applied.