On the development and analysis of coupled surface-subsurface models of catchments. Part 3. Analytical solutions and scaling laws

The objective of this three-part work is the formulation and rigorous analysis of a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled effects of surface and subsurface flows are considered. In this third part, we focus on the development of analytical solutions and scaling laws for a benchmark catchment model that models the river flow (runoff) generated during a single rainfall. We demonstrate that for catchments characterised by a shallow impenetrable bedrock, the shallow-water approximation allows a reduction of the governing formulation to a coupled system of one-dimensional time-dependent equations for the surface and subsurface flows. Asymptotic analysis is used to derive semi-analytical solutions of the model. We provide simple asymptotic scaling laws describing the peak flow formation. These scaling laws can be used as an analytical benchmark for assessing the validity of other physical, conceptual, or statistical models of catchments

On the development and analysis of coupled surface-subsurface models of catchments. Part 2. A three-dimensional benchmark model and its properties

The objective of this three-part work is the formulation and rigorous analysis of a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled effects of surface and subsurface flows are considered. In this second part, we construct a benchmark catchment scenario and investigate the effects of parameters within their typical ranges. Previous research on coupled surface-subsurface models have focused on numerical simulations of site-specific catchments; here our focus is broader and emphasises the study of general solutions to the mathematical models, and their dependencies on dimensionless parameters. This study provides a foundation based on the examination of a geometrically simple three-dimensional benchmark scenario. We develop a nondimensional coupled surface-subsurface model, and extract the key dimensionless parameters. We then apply asymptotic methods in order to discuss some potential simplifications, including the reduction of the geometry to a two-dimensional form, where the principal groundwater and overland flows occur in the hillslope direction. Numerical solutions demonstrate the effects of model parameters and provide guidance on the validity of the dimensional reductions

On the development and analysis of coupled surface-subsurface models of catchments. Part 1. Parameter estimation and sensitivity analysis of catchment properties

The objective of this three-part work is the formulation and rigorous analysis of a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled effects of surface and subsurface flows are considered. In this first part, we identify and analyse the key physical parameters that appear in governing formulations used within hydrodynamic rainfall-runoff models. Such parameters include those related to the catchment dimensions, topography, soil and rock properties, rainfall intensities, Manning's coefficients, and river channel dimensions. Despite the abundance of research that has produced data sets describing properties of specific river basins, there have been few studies that have investigated the ensemble of typical scaling of key physical properties; these are needed in order to perform a proper dimensional analysis of rainfall-runoff models. Therefore, in this work, we perform an extensive analysis of the parameters; our results form a benchmark and provide guidance to practitioners of the typical parameter sizes and interdependencies. Crucially, the analysis is presented in a fashion that can be reproduced and extended by other researchers, and wherever possible, uses publicly available data sets for catchments in the United Kingdom