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

Various field studies have shown the fundamental influence of the bedrock surface geometry on subsurface stormflow (SSSF). Various field studies have also shown that the SSSF process consist of at least two major components: the matrix flow component and the macropore flow component that are in dynamic interaction toward forming the SSSF. This study focuses on the matrix flow component of 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 transverse profile perpendicular to the main hillslope direction influence the subsurface stormflow over the bedrock. The macropore flow itself being a multidimensional flow process, the general setting for the dynamic interaction of the matri x flow and macropore flow components of SSSF is the treatment of both of these processes as multidimensional flow processes. Within this framework, this study attempts 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 This is a non-peer reviewed preprint submitted to EarthArXiv . 2 geometries that are reported in the field studies of SSSF. Then a numeric al experiment is performed by applying the developed governing equations to two different bedrock surface geometries. The results of the numerical simulations of the matrix flow component of SSSF show the impact of the 2D bedrock surface geometry on the characteristics of the matrix flow in both longitudinal and transvers directions over a hillslope.