Calibration of the semi-distributed PDM rainfall–runoff model in the Upper Lee catchment, UK

Abstract

Distributed hydrological models have the capability to incorporate spatially variable inputs, to represent spatial heterogeneity of catchments and to generate outputs at interior locations. However calibrating a distributed model is challenging so much so that a less powerful lumped model is often preferred. This paper describes a method of calibrating a semi-distributed model based on regionalisation of parameters, maintaining as far as possible their physical meaning, and applying spatial multipliers to optimise performance. A semi-distributed implementation of the Probability Distributed Moisture (PDM) model is employed using hourly data from the Upper Lee catchment, UK. Regression relationships between known catchment descriptors (land cover, soil type, climate and topography) and parameters of the PDM are developed using 10 gauged subcatchments and applied to give prior estimates of the parameters at smaller ungauged subcatchment scales. These prior estimates are adjusted using multipliers which are spatially uniform for each parameter. The analysis reveals that the semi-distributed PDM usually (but not always) performs better than a lumped version at gauged points in the catchment, without the introduction of additional degrees of freedom into the calibration. This result applies even when the rainfall input is assumed uniform over the catchment. However, predictions at ungauged points are poor, and the scope for using for additional sources of information, including using more physics based model components and the outputs of broader scale regionalisation studies, is discussed. Results also highlight the sensitivity of the model parameter estimates to the number of gauged catchments used in the regression analysis and to uncertainty associated with parameter equifinality.