Everything You Wanted to Know About Slope-Area Analysis * But Were Afraid to Ask

In the 1990's, the widespread availability of geographic information systems (GIS) and digital elevation models (DEMs) produced a flood of data describing landscapes, and slope-area analysis was used to reduce this torrent to a trickle of information about the processes shaping the landscape. At its most extreme, slope-area analysis reduces the landscape to a single line in a log-log plot of drainage area and local slope. Slope-area analysis has been used to display the landscape, divide it into process domains, and predict the location and movement of channel heads. However, slope-area analysis rests upon certain key assumptions (e.g. drainage area is linearly related to discharge) which may not be accurate in small, steep mountain basins, and some of the hypotheses generated within the context of slope-area plots may not apply outside of these graphs in the observed landscape. Some of the questions that should be asked about slope-area analysis: --Are drainage area and discharge really interchangeable across the entire landscape? --Are process and form uniquely related in slope-area plots? Can different landscape forms result from the same process? Or can one process occur in a variety of landscape forms? Can climatic changes lead to legacy landscapes that were carved by historic processes different than the modern processes? --Can an entire landscape be accurately decomposed to a single line and mechanistically interpreted? -- How do theoretical predictions (e.g. channel head locations or sediment transport laws) in slope-area plots transfer to an observed landscape that only occupies a limited portion of the slope-area space diagram? We answered some of these questions through analysis of surveys of steep, mountain channels and hillslopes that produced debris flows in the semi-arid mountains of southwest Idaho. We found two distinct slope-area trends in the debris flow initiation zone. These trends were associated with differently shaped basins that may control the concentration or dissipation of the peak discharge and leads to two different relationships between drainage area and discharge. These two distinct trends are obscured when the entire basin is decomposed into a single line in a slope-area plot through log-bin averaging, and the resulting line is a blend of the two trends. In addition to multiple forms resulting from a single process, we also observed a single process occurring in areas with multiple forms. In particular, we observed debris-flow erosion in the diffusive, fluvial, and debris flow process domains (as predicted by their trends in slope-area plots). We also found that the observed trends of the location of channel heads in slope-area plots is determined by the slope-area trend of the underlying landscape rather than by trends predicted by theoretical threshold relationships of sediment transport. Slope-area analysis provides a specific view of the landscape. This perspective may help to elucidate fundamental aspects of landscapes, but certain questions should be asked to ensure the applicability of slope-area analysis to a particular landscape and the accuracy of its predictions.