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Figure 4: Plots of best fit lines, in log – log space, of valley-bottom gradient as a function of catchment area in Pancho Rico Valley low order drainages (after Stock and Dietrich, 2003; Stock and Dietrich, 2006). The plots having the greatest n magnitude use all catchment area and valley-bottom gradient values for a given low-order drainage. The plots having successively lower n magnitudes are based data sets from which catchment area to valley-bottom gradient values from the upper parts of the drainage are excluded. By excluding values from the upper part of the low order drainage, each plot having a successively smaller n magnitude represents the catchment area to valley-bottom gradient relationship of a segment of the low order drainage that is smaller and farther down valley than the segment(s) represented by the plot or plots having greater n magnitudes. The different slopes of best-fit lines for different segments within a given drainage reflect the step-like, downvalley gradient decrease that accompanies downvalley catchment area increase typical of drainage bottoms eroded by debris flows. If an analysis such this is performed on a drainage eroded by a stream, all the best fit lines would have the same slope, because valley bottoms eroded by streams are characterized by a gradual and steady decrease of valley-bottom gradient as catchment area increases (Stock and Dietrich, 2003). Details regarding how these plots were generated are described in Stock and Dietrich (2003), Stock and Dietrich (2006), and Garcia and Mahan (2009).

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Antonio Garcia
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