Gully-erosion estimation and terrain reconstruction using analyses of microtopographic roughness and LiDAR

Gully mapping techniques successfully identify gullies over a large range of breadths and depths in complex landscapes but practices for estimating gully volumes need further development. Gully gap-interpolation for estimation of gully volume does not often factor in landscape microtopography in the generation of the new surface. These approaches can thus overestimate large classical gully volumes, averaging over depressions, or underestimate volumes by creating overly-smooth highly curved surfaces. Microtopographic methodology was developed to estimate the pre-gully surface and gully volume across the Calhoun Critical Zone Observatory (CCZO) in South Carolina, USA. The CCZO is a Southern Piedmont landscape severely gullied by historic agriculture with upland Ultisols many meters deep. Our gully-mapping and gully-filling approaches used 1 m(2) LiDAR elevation data and is based on the premise that gullies are local depressions on uplands which are deeply incised with high microtopographic roughness. Our smoothing-via-filling-rough-depressions (SvFRD) algorithm iteratively fills gullies until landscape microtopographic roughness is reduced and unchanging after a subsequent iteration. Results were evaluated in the context of prior landscape bulk erosion estimates ranging from 1483 to 3708 m(3)/ha as well as field surveys of gullies. Minimally eroded reference and highly-eroded post-agricultural terrain were compared to test gully-mapping and volume accuracy. Comparing gully-volume estimation techniques, inverse-distance-weighting (IDW) yielded the highest volume (1072 m(3)/ha) followed by ANUDEM (638 m(3)/ha) while spline-interpolation yielded the lowest estimate (555 m(3)/ha). SvFRD landscape gully volume estimates (615.5 m(3)/ha) were most similar to ANUDEM interpolation with roughness and gully extent results most similar to spline interpolation. Spline interpolation is effective and easily implemented but if microtopographic accuracy and mapping of fine-scale erosions features is desired to hindcast pre-gully terrain conditions, our depression-filling approach, implemented using free GIS and statistical software, is an effective method to estimate reasonable erosion volumes.