Quantifying Uncertainty
Hossain, F. and Anagnostou, E.N.. "Assessment of a stochastic interpolation based parameter sampling scheme for efficient uncertainty analyses of hydrologic models" Computers & Geosciences. 31
(4).
MAY 2005.
pp. 497--512.
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. (c) 2004 Elsevier Ltd. All rights reserved.
Hossain, F., Anagnostou, E.N., and Lee, K.H.. "A non-linear and stochastic response surface method for Bayesian estimation of uncertainty in soil moisture simulation from a land surface model" Nonlinear processes in Geophysics. 11
(4).
2004.
pp. 427--440.
This study presents a simple and efficient scheme for Bayesian estimation of uncertainty in soil moisture simulation by a Land Surface Model (LSM). The scheme is assessed within a Monte Carlo (MC) simulation framework based on the Generalized Likelihood Uncertainty Estimation (GLUE) methodology. A primary limitation of using the GLUE method 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 non-linear deterministic behavior between soil moisture and land surface parameters. Uncertainty in soil moisture simulation (model output) is approximated through a Hermite polynomial chaos expansion of normal random variables that represent the model's parameter (model input) uncertainty. The unknown coefficients of the polynomial are calculated using limited number of model simulation runs. The calibrated polynomial is then used as a fast-running proxy to the slower-running LSM to predict the degree of representativeness of a randomly sampled model parameter set. An evaluation of the scheme's efficiency in sampling is made through comparison with the fully random MC sampling (the norm for GLUE) and the nearest-neighborhood sampling technique. The scheme was able to reduce computational burden of random MC sampling for GLUE in the ranges of 10\%-70\%. The scheme was also found to be about 10\% more efficient than the nearest-neighborhood sampling method in predicting a sampled parameter set's degree of representativeness. The GLUE based on the proposed sampling scheme did not alter the essential features of the uncertainty structure in soil moisture simulation. The scheme can potentially make GLUE uncertainty estimation for any LSM more efficient as it does not impose any additional structural or distributional assumptions.