Proposal of a lumped hydrological model based on general equations of growth – application to five watersheds in the UK

Abstract. This paper explores a new approach to lumped hydrological modelling based on general laws of growth, in particular using the classic logistic equation proposed by Verhulst. By identifying homologies between the growth of a generic system and the evolution of the flow at the outlet of a river basin, and adopting some complementary hypotheses, a compact model with 3 parameters, extensible to 4 or 5, is obtained. The model assumes that a hydrological system, under persistent conditions of precipitation, potential evapotranspiration and land uses, tends to reach an equilibrium discharge that can be expressed as a function of a dynamic aridity index, including a free parameter reflecting the basin properties. The rate at which the system approaches such equilibrium discharge, which is constantly changing and generally not attainable, is another parameter of the model; finally, a time lag is introduced to reflect a characteristic delay between the input (precipitation) and output (discharge) in the system behaviour. To test the suitability of the proposed model, 5 previously studied river basins in the UK, with different characteristics, have been analysed at a daily scale, and the results compared with those of the model IHACRES (Identification of unit Hydrographs and Component flows from Rainfall, Evaporation and Streamflow data). It is found that the logistic equilibrium model with 3 parameters properly reproduces the hydrological behaviour of such basins, improving the IHACRES in four of them; moreover, the model parameters are relatively stable over different periods of calibration and evaluation. Adding more parameters to the basic structure, the fits only improve slightly in some of the analysed series, but potentially increasing equifinality effects. The results obtained indicate that growth equations, with possible variations, can be useful and parsimonious tools for hydrological modelling, at least in certain types of watersheds.