Flow-length difference as a measure of topographic roughness/incision

A new surface roughness/incision measure is introduced based on the difference between the upstream flow length for each cell of a digital elevation model (DEM) along the topographic surface and its projection onto a horizontal plane. The upstream flow lengths along topographic surface can be calculated in ArcGIS software using the Flow Length tool with the inverse of cosine of local slope as weight. The projected horizontal flow length is derived using the same tool with the default weight of unity for each cell. The result of applying this index to the Oregon Cascade region, where big contrast in surface incision exists, shows that it not only reproduces the overall visual contrast in the spatial pattern of dissection, but also corresponds very well with the true degree of incision and reveals details. In contrast, the local relief and standard deviation of slopes, two other indices traditionally used to describe the degree to which the earth surface is incised by exogenic agents, do not always correspond to the true location of incision and lack the details. With more high resolution DEM data becoming available, this new roughness/incision measure can be used to quantify and reveal more detailed dissection pattern on Earth at various spatial scales.