Conceptually, stochastic parametric modeling offers a powerful tool to select a scale for expressing catchment variability for hydrologic simulation and relating model parameters to catchment characteristics. Practically, success depends on having an efficient method for model calibration. The calibration of a stochastic model is much more difficult than a deterministic one because simulation shifts from using fixed parameters to simulate of flows as deterministic values to taking multiple combinations of paramter values randomly from distributions to simulate flows as stochastic variables. The proposed method calibrates the first two moments of each parameter distribution to represent the average and the variability of catchment characteristics by using two objective functions. One minimizes relative errors between recorded and simulated flows, and the other bounds the range of simulated flows to cover the recorded flows. The method was successfully calibrated for four watersheds, and the results promise new understanding that will contribute to more reliable models.
Song, Zhida and James, L. Douglas, "Calibration of a Parametric-Stochastic Model" (1991). Reports. Paper 75.