Analytical estimation of annual runoff distribution in ungauged seasonally dry basins based on a first order Taylor expansion of the Fu's equation

The assessment of the mean annual runoff and its interannual variability in a basin is the first and fundamental task for several activities related to water resources management and water quality analysis. The scarcity of observed runoff data is a common problem worldwide so that the runoff estimation in ungauged basins is still an open question. In this context, the main aim of this work is to propose and test a simple tool able to estimate the probability distribution of the annual surface runoff in ungauged river basins in arid and semi-arid areas using a simplified Fu's parameterization of the Budyko's curve at regional scale. Starting from a method recently developed to derive the distribution of annual runoff, under the assumption of negligible inter-annual change in basin water storage, we here generalize the application to any catchment where the parameter of the Fu's curve is known. Specifically, we provide a closed-form expression of the annual runoff distribution as a function of the mean and standard deviation of annual rainfall and potential evapotranspiration, and the Fu's parameter. The proposed method is based on a first order Taylor expansion of the Fu's equation and allows calculating the probability density function of annual runoff in seasonally dry arid and semi-arid geographic context around the world by taking advantage of simple easy-to-find climatic data and the many studies with estimates of the Fu's parameter worldwide. The computational simplicity of the proposed tool makes it a valuable supporting tool in the field of water resources assessment for practitioners, regional agencies and authorities.