Hydrologic Connectivity and Patch‐To‐Hillslope Scale Relations in Dryland Ecosystems

In drylands, runoff during storms redistributes water and nutrients from bare soil areas to vegetated patches, subsidizing vegetation with additional resources. The extent of this redistribution depends on the interplay between surface roughness and permeability; greater permeability in vegetated patches promotes run‐on to vegetation, but greater surface roughness diverts runoff, producing tortuous flow paths that bypass vegetation. Here, this interplay is examined in virtual experiments using the 2D Saint Venant Equations to measure runoff connectivity. Flowpaths are delineated using tracers advected by the flow. Distances between tracer sources and sinks along flowpaths measure hydrologic connectivity at two lengthscales: connectivity to the hillslope outlet and within‐slope source‐sink connectivity. Differences between these connectivity lengthscales indicate how flow may “by‐pass” vegetated patches within hillslopes. At the hillslope scale, a derived power‐law relation between the runoff coefficient and outlet connectivity describes hillslope water losses, providing a foundation for identifying landscapes likely to shed water. Plain Language Summary In drylands—semiarid and arid regions that comprise 40% of the earth's land surface—runoff redistributes rainfall from bare soil to vegetated areas, providing plants with extra water beyond that falling locally as rain. Runoff flowpaths that bypass vegetation and route water off a hillslope, however, disrupt this redistribution. Such flowpaths are usually formed by continuously‐connected areas of bare soil. To determine whether runoff redistributes water to vegetation patches or bypasses them, we use measures of runoff connectivity within the hillslope (i.e., from where rainfall lands to where it infiltrates) and to the outlet (i.e., from where rainfall lands to the downslope edge of the hill). Where vegetated patches are rougher, bypassing becomes more likely. The connectivity of runoff to the outlet is shown to predict runoff losses from hillslopes and, therefore, whether landscapes are likely to conserve or shed water. Key Points Methods are needed to bridge differences between patch and hillslope scales for interpreting runoff observations in dryland ecosystems Virtual experiments with particle tracing relate the hillslope runoff coefficient to source‐sink and outlet connectivity length scales A derived power‐law relation between runoff coefficient and outlet connectivity is robust to variations in rain