Identification of a Constrained Nonlinear Hydrological System Described by Volterra Functional Series

This paper addresses the problems of identification of a constrained nonlinear system (CNLS) described by Volterra functional series. A workable and practical method in terms of a penalty function principle and orthogonal expansion was developed, which involves an extension of the classical least squares solution to include a penalty function with arbitrarily defined weights which are adjusted to ensure that the constraints are satisfied. A total of nine basins across a range of climates and catchment areas in China were selected for examination of both daily and hourly rainfall‐runoff forecasting. It was found that the method described in this paper can provide a more reasonable and robust response function where hydrologic constraints are required. The nonlinear model yields a better streamflow forecasting than the linear model, particularly in peak flows.