Recession analysis across scales: The impact of both random and nonrandom spatial variability on aggregated hydrologic response

Recession analysis across scales can provide insight into the spatial aggregation of hydrologic processes. Accordingly, we analyzed individual late-time recession curves from 25 nested USGS stream gauges over a period of ∼150days with negligible precipitation during the 2012–2013 North American drought. These gauges are located in the Iowa and Cedar River basins and drain areas ranging from ∼70 to 17,000km2. Our data analyses show that these late-time recession processes can be represented by a linear reservoir model with a constant recession time scale of about 34days, indicating linear and homogeneous recession behaviors at the large scales investigated. However, others have shown that the early-time recession process becomes more nonlinear as spatial scale and, thus, spatial variability increases. We developed a distributed drainage model as a diagnostic tool to understand these seemingly contradictory recession characteristics at multiple spatial scales and different stages. With a hierarchical description of the recession variability at the hillslope scale, our model can simultaneously produce the increasing nonlinear early-time and the linear and homogenous late-time recession behaviors at larger scales. The hierarchical representation classifies hillslopes according to the Strahler orders of the stream links into which they drain. We postulate that a larger difference in recession behaviors will occur between hillslopes from different orders than between those from the same order. Overall, this study shows how the spatial randomness and nonrandomness of small-scale process variability control the hydrologic responses at larger scales and suggests a combined (nonrandom–random) representation of watersheds for aggregating hydrologic processes.