Practical Considerations for the Application of a Recursive Analytical Solution of the Nonlinear Storage Equation for Flood Control Reservoir Sizing

Abstract

In the practice of flood control reservoir sizing the smooth theoretical stage-storage power function relationship necessary for an analytical solution of the nonlinear storage equation is often replaced by a complex series of piece-wise linear functions. A recursive analytical solution can still be employed provided the straight line sections are segmented into a series of intervals over which the straight lines are approximated to a prescribed accuracy by individual power functions. During the application of the recursive analytical solution one must keep track of the outflow stage in order to employ the relevant parameters of the piecewise power functions.