Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Journal of Computational Physics
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This study assesses a stochastic interpolation based parameter sampling scheme for efficient uncertainty analyses of stream flow prediction by hydrologic models. The sampling scheme is evaluated within the generalised likelihood uncertainty estimation (GLUE; Beven and Binley, 1992) methodology. A primary limitation in using the GLUE method as an uncertainty tool is the prohibitive computational burden imposed by uniform random sampling of the model's parameter distributions. Sampling is improved in the proposed scheme by stochastic modeling of the parameters' response surface that recognizes the inherent non-linear parameter interactions. Uncertainty in discharge prediction (model output) is approximated through a Hermite polynomial chaos approximation of normal random variables that represent the model's parameter (model input) uncertainty. The unknown coefficients of the approximated polynomial are calculated using limited number of model simulation runs. The calibrated Hermite polynomial is then used as a fast-running proxy to the slower-running hydrologic model to predict the degree of representativeness of a randomly sampled model parameter set. An evaluation of the scheme's improvement in sampling is made over a medium-sized watershed in Italy using the TOPMODEL (Beven and Kirkby, 1979). Even for a very high (8) dimensional parameter uncertainty domain the scheme was consistently able to reduce computational burden of uniform sampling for GLUE by at least 15-25%. It was also found to have significantly higher degree of consistency in sampling accuracy than the nearest neighborhood sampling method. The GLUE based on the proposed sampling scheme preserved the essential features of the uncertainty structure in discharge simulation. The scheme demonstrates the potential for increasing efficiency of GLUE uncertainty estimation for rainfall-runoff models as it does not impose any additional structural or distributional assumptions.