Ecohydrological model of flow duration curves and annual minima

To address streamflow variability in river basins, Botter et al. (2007a) recently provided an analytical solution for the seasonal probability distribution function of daily streamflows on the basis of a stochastic description of soil moisture dynamics at basin scales. In this paper the above model is extended to the annual timescale to derive analytical expressions for the long-term flow duration curve on the basis of a few climatic, ecohydrologic, and geomorphic parameters of the basin. A novel analytical expression for the cumulative probability distribution of the annual minima is also derived from the "troughs under threshold" theory. The expressions derived provide a physically based linkage between flow duration curves and the distribution of annual minima through geomorphic, climatic, and ecological features of the basin. Our theoretical results prove in good agreement with observational streamflow data in a 50 km² vegetated basin located in North Carolina (USA), suggesting that the model developed may represent a valid tool for estimating low-flow statistics in gauged and ungauged basins.