Global Sensitivity Analysis of Hydraulic Models

Abstract

Mathematical models are based on physical relationships to approximate real phenomenon. Details increase complexity of models hence, increase the burden on modeller to incorporate numerous parameters. Sensitivity analysis is used as a useful tool to study which input influences the output most. Identification of most important factors helps decision makers to address uncertainty in the data available. Sensitivity analysis is categorized into local sensitivity analysis (LSA) and Global Sensitivity analysis (GSA).various methods are developed over the period of time for GSA of which Variance Based methods are widely being employed to assess models in water resources engineering. VBSA apportions variance of output into the variance of input. This work consists of application of VBSA to simple Equations for Resultant force on Pipe bend , Seepage loss in canals and a more complex case of numerical model of scaled down urban district flooding of CADAM Project. It is performed using SAFE toolbox, a MATLAB based utility developed by University of Bristol. Results are approximately reproduced for Pipe bend with slightly greater Sensitivity Indices. Diameter of Pipe 1 and Discharge in the bend cause drastic variations in Resultant force. However VBSA does not completely declare Pressure at Pipe 1 and Diameter of Pipe 2 as impotent. Hydraulic conductivity, depth and side slope are key factors which effect Seepage loss from canals. The main work of thesis is the urban district flood model. Variation of depth is checked against Manning‟s roughness(X1) and increased roughness for buildings (X2). MonteCarlo based Sobol indices, discussed by Saltelli et al., (2008) were estimated by employing simple random uniform (RSU) and Latin Hypercube (LH) experimental designs. A sample size of 4000 and 1500 was randomly selected for RSU and LHS respectively. At all eight locations X1 shows greater impact on water depths for both designs but X2 cannot be completely considered as unimportant. Its relative influence can be observed by increasing the number of input factors. In our case LHS has not outperformed with a smaller sample size. In RSU water depth decreases with increment in manning‟s roughness. In LH design, X2 does not affect water depth at first four gauges but as the flood wave moves through dense urban area, it increases with the increase in X2. Interaction indices from both designs indicate that X1 has strong interaction with other input factors for which detailed interaction analysis should be performed. VBSA is a computationally expensive method. Time constraint made it impossible to test various samples to reach sufficient size. Occurrence of negative indices is mainly due to the fore mentioned limitation