Sub-surface streamflow and storage with varying topography and precipitation.

The correlation between precipitation and streamflow is a fundamental element of the water cycle. Predicting this relation is complicated by the geometric and topological complexity of the flowpaths through the soil. This problem has been treated in the framework of peroclation theory, based on universal scaling arguments. However, addressing the dynamics of flow or the effects of finite boundaries introduces further complications to predictions on shorter time scales. This work aims to resolve the temporal distribution of fluxes by addressing three points: The finite-size effects brought in by the presence of topographic boundaries and pressure gradients, the frequency dependence of the conductivity, and the changing flow characteristics of the medium as its saturation varies. To the first point, some geometries can be handled by conformal transformation of slab crossing probabilities. Secondly, the dominant conductance has been found through critical path analysis. This already has a time-dependent formulation which needs to be extended to the hydraulic context. Lastly, while results for the saturation dependence of conductivity have already been obtained, they must be combined with a distribution of pressure drops throughout the medium to realize the flow characteristics.