Hydrologic model calibration using fuzzy TSK surrogate model

In order to find the best parameter set of a hydrologic model, error minimization is often used. In this case, optimization is performed using fuzzy TSK surrogate model, a fuzzy Tagaki Sugeno Kang based method chosen for its efficiency and robustness. Parameter space exploration is performed using the surrogate model, thus avoiding the use of the computationally expensive full model. The dimensionality of the problem is not very high (requires the calibration of 15-150 parameters), however the computational cost for the evaluation of the cost function is significant. In order to evaluate the cost function for a single set of parameters, 2hrs (for watersheds smaller than 100 km²) to 24 hrs (for watersheds larger than 100,000 km²) of computer time is required. To avoid this cost, the surrogate model is constructed to approximate the actual model, which maps the known data points. Since the surrogate model is inexpensive to evaluate, we can explore the model space and find the optimum value cheaply. In each iteration, the surrogate model is used to predict the minimizer of the actual model, then the actual model is evaluated at the predicted minimizer and the surrogate is updated to include the new data. This process continues until sufficient cost function (error) reduction is achieved.