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

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