Application of Non‐Linear Automatic Optimization Techniques for Calibration of HSPF

Abstract

Development of TMDLs (total maximum daily loads) is often facilitated by using the software system BASINS (Better Assessment Science Integrating point and Nonpoint Sources). One of the key elements of BASINS is the watershed model HSPF (Hydrological Simulation Program Fortran) developed by USEPA. Calibration of HSPF is a very tedious and time consuming task, more than 100 parameters are involved in the calibration process. In the current research, three non-linear automatic optimization techniques are applied and compared, as well an efficient way to calibrate HSPF is suggested. Parameter optimization using local and global optimization techniques for the watershed model is discussed. Approaches to automatic calibration of HSPF using the nonlinear parameter estimator PEST (Parameter Estimation Tool) with its Gauss-Marquardt-Levenberg (GML) method, Random multiple Search Method (RSM), and Shuffled Complex Evolution method developed at the University of Arizona (SCE-UA) are presented. Sensitivity analysis was conducted and the most and the least sensitive parameters were identified. It was noted that sensitivity depends on number of adjustable parameters. As more parameters were optimized simultaneously--a wider range of parameter values can maintain the model in the calibrated state. Impact of GML, RSM, and SCE-UA variables on ability to find the global minimum of the objective function (OF) was studied and the best variables are suggested. All three methods proved to be more efficient than manual HSPF calibration. Optimization results obtained by these methods are very similar, although in most cases RSM outperforms GML and SCE-UA outperforms RSM. GML is a very fast method, it can perform as well as SCE-UA when the variables are properly adjusted, initial guess is good and insensitive parameters are eliminated from the optimization process. SCE-UA is very robust and convenient to use. Logical definition of key variables in most cases leads to the global minimum.