Sensitivity Analysis for Evaluating Importance of Variables Used in an Urban Water Supply Planning Model

The yield of an urban water supply system is defined as the average annual volume of water that can be supplied from the water supply system over a given planning period, subject to streamflow variability, operating rules and demand pattern, without violating the adopted level of service. Since yield plays a key role in the management of urban water supply systems, it is important for water authorities to accurately estimate it with minimal inherent uncertainty. Sensitivity analysis can identify key variables used in yield estimation, allowing water authorities to improve the knowledge of those variables (or input factors) and thus to improve the confidence and reliability of the system yield. The increase of computational power that has become available over the past decades has meant the variance based sensitivity analysis techniques, FAST (Fourier Amplitude Sensitivity Test) and Sobol', have become favourable. Additionally, the Morris method, a computationally inexpensive screening technique, is commonly used to economically identify non-influential input variables so they can be disregarded from the more computationally expensive variance based techniques. The case study considered in this study was a simple urban water supply system consisting of two storages and a single urban demand centre simulated using the REALM simulation package. Historic monthly data was used for streamflow, rainfall and evaporation. Twenty-eight input variables were identified within the model consisting of historic data, empirical values and model parameters. A screening experiment using the Morris method, the results were confirmed by the Extended FAST method (EFAST, a derivative of FAST), was used to identify non-influential input variables. These variables were then set at their nominal values and disregarded from the subsequent experiments using the FAST, EFAST and Sobol' techniques. The ranked results from the Morris and EFAST screening techniques showed close similarity with only some differences occurring in the lower influential variables. The sensitivity indices were dominated primarily by the streamflow, with the supply reliability, upper restriction rule curve and the maximum number of consecutive restriction months variables showing some significance. Detailed sensitivity analyses on the simple model were then performed using FAST, EFAST and Sobol' considering the ten highest ranked variables from the screening experiments. The remaining 18 variables were kept at their nominal value. Experiments of increasing model simulations, and hence accuracy, were performed until a convergence was met or the required number of simulation was impracticable. Comparison of the results of the detailed sensitivity analyses again indicated the dominance of the streamflow, and the minor significance of the supply reliability, upper restriction rule curve and the maximum number of consecutive restriction months variables. The results obtained from FAST and EFAST were reasonably similar, however the Sobol' experiments gave erroneous results, where the total-order sensitivity is less than the first-order effect. Nevertheless, these errors were found only for lower influential variables.