A widely-used runoff generation model is the simple linear model (SLM), which is built on the concept of converting precipitation to storm runoff by a convolution integral with a response function involving a memory span. In this study, we propose a model incorporating potential evapotranspiration (PET) as an additional factor with a separate response function in addition to the main precipitation driver, which we call the two-variable linear model (TVLM). The TVLM was tested against the observed data from several catchments, and then used to assess the impact of climate variability on runoff. The results demonstrate that incorporating PET improves model performance with the same memory span in the precipitation response function. The precipitation response function is not affected by the addition of PET memory, which indicates that the PET term is a correction factor. The proposed TVLM better captures the runoff generation mechanisms.
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