Determination of optimal kernels for second‐order stationary surface runoff systems

Abstract

Adopting a discretization scheme for input, output, and kernel functions of second‐order Volterra series representation of the surface runoff system leads to a set of linear equations for the unknown ordinates of the two‐kernel functions. The equations are solved by an iterative descent optimization procedure taking into account also additional constraining equations derived from the properties of the kernel functions and the definition of the system adopted. The objective function for the optimization procedure is the sum of squared deviations between observed and predicted output ordinates for all storms included in the record. The inclusion of the constraining equations is done by an iterative scheme based on the penalty function method. The algorithm adopted for the solution converges to the optimal solution in a finite number of iterations, and its rate of convergence is independent of initial values adopted for the unknowns. A numerical example based on an eight‐storm record is included.