Shape similarity in surface runoff process across neighboring hillslopes in Iowa

Understanding the link between the organization of rainfall-runoff processes at the small scale and catchment scale is essential to distributed hydrologic modeling. To explore the spatial structure of hillslope scale runoff process, we used the lagged regression analysis to quantify the relationship between the event scale surface runoff processes (represented by hydrographs averaged over their areas) from 12 closely located hillslopes in central Iowa, USA. These agricultural experimental hillslopes receiving various prairie filter stripes treatments drain areas ranging from 0.48 to3.19 hectares, and the distances between them vary from tens of meters to about 3 kilometers. We compared the hydrographs from the rest 11 hillslopes to the hydrograph at the benchmark hillslope (i.e., hillslope B6 with no treatment). Our analysis showed that, for any individual event when noticeable overland runoff occurred, the hydrologic responses from these hillslopes have similar shape but different magnitudes. Our analysis also showed that, for any paired hillslopes, the shape similarity persisted but the scaling factor (the regression slope between two flow series) changed over time. Our further analysis revealed that for any runoff event, the spatial variation of the scaling factor did not depend on the slope, slope length, area, and prairie stripe width at the footslope of the hillslopes. Interestingly, we found that for 9 out of the 11 paired hillslopes, 40-70% of the temporal variation in the scaling factors can be explained by the antecedent wetness condition and the maximum hourly rain accumulation. These results suggest that except for nonlinearity and heterogeneity, shape similarity (or proportionality) in space is another feature of small scale runoff process.