Multidimensional Governing Equations of Matrix Flow Component of Subsurface Stormflow as Function of Bedrock Surface Geometry

Abstract

Subsurface flow is a critical component in the hydrological cycle, since it controls the quantity and timing of surface runoff and groundwater flow. Field studies have shown the fundamental influence of the bedrock surface geometry on subsurface stormflow (SSSF) and that the SSSF process consists of at least two major components: the matrix flow component and the macropore flow component that are in dynamical interaction toward forming the SSSF. Furthermore, field studies have shown that the bedrock surface that underlies the SSSF has essentially a two‐dimensional (2D) geometry, where not only the longitudinal profile along the hillslope but also the profile in the transverse direction influence the subsurface stormflow over the bedrock. The macropore flow itself being a multidimensional flow process, requires a multidimensional matrix flow component in order to quantify realistic dynamical interactions between these components within the subsurface stormflow module of a watershed hydrology model. Within this framework, the critical research question is how to extend the existing 2D Boussinesq model for the matrix flow over an inclined flat 2D surface in the longitudinal hillslope direction by developing the governing equations of matrix flow at hillslope scale over various 2D bedrock surface geometries that are reported in the field studies of SSSF. Then, numerical experiments are performed by applying the developed governing equations to various bedrock surface geometries. The results of the numerical simulations show (a) the proposed governing equations can simulate various two‐dimensional bedrock surface geometries, and are capable of incorporating the upward or downward concavity of bedrock surface in longitudinal and transverse directions into SSSF by modulating the timing and magnitude of the flows and (b) the proposed governing equations for matrix flow provide an appropriate setting for the dynamical interaction of the matrix flows with the macropore flows, creating a promising modeling framework for SSSF.