Subsurface flow and transport modelling at the hillslope scale

Abstract

In hilly and humid forest areas with highly conductive soils, subsurface flow consider as the main mechanism of stream flow generation and responsible for the transport of solutes into the surface water bodies which is transported through the subsurface soil. However, the contribution of the subsurface flow is poorly represented in current generation of land surface hydrological models (LSMs). The lack of physical basis of their common parameterizations precludes a priori estimation, which is a major drawback for prediction in ungauged basins. This thesis is organized in to three sections which analyse the subsurface flow and transport through numerical modelling starting from a simple analysis of homogenous system to complex hillslope with variable soil and topographic properties. First, the relation Q(S) (where Q is the discharge and S is the saturated storage in the hillslope), as a function of some simple structural parameters is evaluated through two-dimensional numerical simulations and makes use of dimensionless quantities. The method lies in between simple analytical approaches, like those based on the Boussinesq formulation, and more complex distributed models. The results confirm the validity of the widely used power law assumption forQ(S) . Similar relations can be obtained by performing a standard recession curve analysis. Second, physically based parameterization of the storage-discharge relationship relating to subsurface flow is developed using the Richards’ equation. These parameterizations are derived through a two-step up-scaling procedure: firstly, through simulations with a physically based subsurface flow model for idealized three dimensional rectangular hillslopes, accounting for within-hillslope random heterogeneity of soil hydraulic properties, and then through subsequent up-scaling to the catchment scale by accounting for between-hillslope and within-catchment heterogeneity of topographic features. These theoretical simulation results produced parameterizations of the storage-discharge relationship in terms of soil hydraulic properties, topographic slope and their heterogeneities that were consistent with results of previous studies. The resulted parameterization is regionalized across 50 actual catchments in eastern United States, and compared with the equivalent empirical results obtained on the basis of analysis of observed streamflow recession curves, revealed a systematic inconsistency. It was found that the difference between the theoretical and empirically derived results could be explained, to first order, by climate in the form of climatic aridity index. Third, the performances of four different models of solute transport in catchments were analysed. The models employ the concept of travel time distribution. A recapitulation and critical analysis of the models and their basic assumptions is performed first, emphasizing their limitations and potential problems arising in their application. Then, detailed numerical experiments are used as a benchmark for the calibration and the assessment of the models’ capabilities to simulate transport. The scope of the exercise is to test the performance of the models and their limitations in the ideal case in which the catchment system and all the hydrological variables (flow, concentration, storage, etc.) are perfectly known at any level of detail. The performance of the models and their limitations is presented and discussed. The results suggest that a time invariant formulation of the travel time distribution is usually inappropriate and not much effective in predicting transport.