Bayesian estimation of parameters in a regional hydrological model

By K. Engeland, L. Gottschalk. 2002

88 citations recorded by the source corpus.

Abstract. This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1) process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis

Subfields: Environmental Chemistry, Environmental Engineering, Water Science and Technology

View Paper: https://www.semanticscholar.org/paper/e2eb54186fef3ebf684515bd8aa0b1d50c27354d

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In Environmental Chemistry

In Environmental Engineering

In Water Science and Technology

Citations in the corpus

Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models (2010, unknown): “The Box-Cox transformation has been used by Engeland and Gottschalk (2002) and Yang et al. (2007) and it can be expressed as: hðy; kÞ ¼ yk 1 k k–0 lnðyÞ k ¼ 0 ( ð2Þ The square-root transformation is a special case of the Box-Cox transformation. k-parameter is used in the residual test for choosing…”
Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model (2010, methodology): “Engeland et al. (2005) showed that the effect of the model structural uncertainty on the total simulation uncertainty of a conceptual water balance model was larger than parameter uncertainty. Marshall et al. (2007) stated that the uncertainty in model structure requires developing alternatives, whe”
Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? (2009, methodology): “…is admirably suited for systematically addressing and quantifying the various error sources within a single cohesive, integrated, and hierarchical manner (Kuczera and Parent 1998; Bates and Campbell 2001; Engeland and Gottschalk 2002; Vrugt et al. 2003; Marshall et al. 2004; Liu and Gupta 2007).”
Uncertainty estimates by Bayesian method with likelihood of AR (1) plus Normal model and AR (1) plus Multi-Normal model in different time-scales hydrological models (2011, methodology): “Some methods use a statistical model of the residuals to address all the uncertainty sources (Engeland and Gottschalk, 2002; Jin et al., 2010; Krzysztofowicz, 2002; Montanari and Grossi, 2008).”
Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation (2008, background): “…statistics have increasingly found use in the field of hydrology for statistical inference of parameters, state variables, and model output prediction [Kuczera and Parent, 1998; Bates and Campbell, 2001; Engeland and Gottschalk, 2002; Vrugt et al., 2003; Marshall et al., 2004; Liu and Gupta, 2007].”