A New Stochastic Approach to Model Heterogeneous Surface Runoff

Surface runoff in natural watersheds tends to exhibit spatiotemporally non-local flow patterns, due to the multi-scale heterogeneous nature of controlling factors. For example, the topography often generates preferential flow paths at all spatial scales and hence results in early arrivals of water packages, which is the typical behavior of superdiffusion. The concurrent ponding effect can also delay the motion of the other water bodies, generating the subdiffusion. Classical modeling techniques can not efficiently capture these impacts at realistic grid scales, motivating us to develop a space and time non-local flow model using the most recent fractional engine. This new physical model can characterize the influence of both the subgrid heterogeneity and the flow in upstream grids on the local flow. We expect that this approach, after combined properly with remote sensing data, may provide a useful way to understand the holistic runoff process in hierarchically structured natural watersheds.