Scaling of surface soil moisture over heterogeneous fields subjected to a single rainfall event

Determining surface soil moisture evolution over a range of scales remains a challenge because of multi-scale heterogeneity exhibited by soils. Measurement techniques are not in accordance with the scales at which information on soil moisture is needed. In situ point measurements are expensive and provide information only at a few select points. On the other hand, the spatial resolution of remote sensing data is too coarse for hydrologic applications. Currently, surface soil moisture evolution for heterogeneous fields subjected to rainfall conditions is achieved by a computationally intensive numerical solution of the Richards equation. To describe surface soil moisture evolution at local- and field-scale in an efficient manner, reference scaling curves are developed in this study based on a sharp front approximation and by adopting a log-normally distributed spatial hydraulic conductivity field. These scaling curves facilitate the determination of temporal evolution of surface soil moisture at any unmeasured location in the field, and can be used to obtain the field-scale surface soil moisture evolution for a single rainfall event. The scaling curves are computationally straight forward, and reduce the need for extensive soil moisture measurements at numerous locations in the field. Comparisons with experimental and numerical simulation results show that the proposed scaling curves hold promise for describing mean surface soil moisture evolution at the field-scale.