  The objective of this three-part work is to formulate and rigorously analyse
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 surface and subsurface flows are considered. In this first part, we
identify and analyse the key physical parameters that appear in the governing
formulations used within hydrodynamic rainfall-runoff models. Such parameters
include those related to 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 estimates are needed 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 on 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.
