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The objective of this three-part work is to formulate and rigorously analysea number of reduced mathematical models that are nevertheless capable ofdescribing the hydrology at the scale of a river basin (i.e. catchment).Coupled surface and subsurface flows are considered. In this first part, weidentify and analyse the key physical parameters that appear in the governingformulations used within hydrodynamic rainfall-runoff models. Such parametersinclude those related to catchment dimensions, topography, soil and rockproperties, rainfall intensities, Manning's coefficients, and river channeldimensions. Despite the abundance of research that has produced data setsdescribing properties of specific river basins, there have been few studiesthat have investigated the ensemble of typical scaling of key physicalproperties; these estimates are needed to perform a proper dimensional analysisof rainfall-runoff models. Therefore, in this work, we perform an extensiveanalysis of the parameters; our results form a benchmark and provide guidanceto practitioners on the typical parameter sizes and interdependencies.Crucially, the analysis is presented in a fashion that can be reproduced andextended by other researchers, and wherever possible, uses publicly availabledata sets for catchments in the United Kingdom.

On the development and analysis of coupled surface-subsurface models of catchments. Part 1. Analysis of dimensions and parameters for UK catchments