Analytical solution for nonlinear hydrologic routing with general power-law storage function

Abstract A new analytical solution for nonlinear storage routing with a general power-law storage function is presented. The resulting implicit solution, expressed in terms of the incomplete beta function, is valid for inflow hydrographs that may be represented by a series of pulses of arbitrary widths. The new solution thus extends the existing analytical solutions reported in the literature which are valid only for specific exponents in the power-law storage function. An explicit solution expressed in terms of the Lambert-W function is also presented for reservoirs for reservoirs with linear storage-elevation relationship and a single orifice or submerged sluice gate outlet. To support practical design applications and to demonstrate the utility of the new solution, we provide approximate explicit solutions and four simple applications. The results show that, being exact, the new solution is not subject to numerical errors or instabilities and may hence be used in a variety of modeling, design, optimization, forecasting, and control applications involving nonlinear routing with power-law storage functions.