Development of neuro-fuzzy models to account for temporal and spatial variations in a lumped rainfall–runoff model

For many good and practical reasons, lumped rainfall–runoff models are widely used to represent a catchment’s response to rainfall. However, they have some acknowledged limitation, some of which are addressed here using a neuro-fuzzy model to combine, in an optimal way, a number of lumped-sub-models. For instance, to address temporal variation, one of the sub-models in the combination may perform well under flood conditions and another under drier conditions and the neuro-fuzzy system would combine their outputs for each time-step in a manner depending on the prevailing conditions. Similarly to address spatial variation, one of the sub-models may perform well for the upland parts of the catchment and another for the lowland parts and again the neuro-fuzzy system is expected to combine the different outputs appropriately. The proposed combination method can use any lumped catchment model, but has been tested here with the simple linear model (SLM) and the soil moisture and accounting routing (SMAR) models. Eleven catchments with different hydrological and meteorological conditions have been used to assess the models with respect to temporal variations in response while one catchment is used to address the effect of spatial variation. The neuro-fuzzy combined-sub-models of SLM and SMAR modelled the temporal and spatial variation in catchment response better than the lumped version of each model. Also the SMAR model significantly outperformed the SLM either as a lumped model or as a sub-model in any of the combinations.