Bayesian estimation of parameters in a regional hydrological model

Engeland, Kolbjørn; Gottschalk, Lars

doi:10.5194/hess-6-883-2002

Cited by 75 publications

(60 citation statements)

References 20 publications

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“…For climate change scenarios, this uncertainty further assumes significance in terms of determining planning and policy measures. A variety of methods have been developed to quantify parameter and model structure uncertainty of conceptual hydrological models [Kuczera and Parent, 1998;Bates and Campbell, 2001;Engeland and Gottschalk, 2002;Jin et al, 2010]. Kuczera and Parent [1998] considered two approaches for parameter uncertainty modeling, the importance sampling, or generalized likelihood uncertainty estimation (GLUE) framework of Beven and Binley [1992]; and a Bayesian approach using Markov Chain Monte Carlo (MCMC) methods.…”

Section: Introductionmentioning

confidence: 99%

Bayesian parameter uncertainty modeling in a macroscale hydrologic model and its impact on Indian river basin hydrology under climate change

Raje

Krishnan

2012

Water Resources Research

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[1] Macroscale hydrologic models (MHMs) were developed to study changes in land surface hydrology due to changing climate over large domains, such as continents or large river basins. However, there are many sources of uncertainty introduced in MHM hydrological simulation, such as model structure error, ineffective model parameters, and low-accuracy model input or validation data. It is hence important to model the uncertainty arising in projection results from an MHM. The objective of this study is to present a Bayesian statistical inference framework for parameter uncertainty modeling of a macroscale hydrologic model. The Bayesian approach implemented using Markov Chain Monte Carlo (MCMC) methods is used in this study to model uncertainty arising from calibration parameters of the Variable Infiltration Capacity (VIC) MHM. The study examines large-scale hydrologic impacts for Indian river basins and changes in discharges for three major river basins with distinct climatic and geographic characteristics, under climate change. Observed/reanalysis meteorological variables such as precipitation, temperature and wind speed are used to drive the VIC macroscale hydrologic model. An objective function describing the fit between observed and simulated discharges at four stations is used to compute the likelihood of the parameters. An MCMC approach using the Metropolis-Hastings algorithm is used to update probability distributions of the parameters. For future hydrologic simulations, bias-corrected GCM projections of climatic variables are used. The posterior distributions of VIC parameters are used for projection of 5th and 95th percentile discharge statistics at four stations, namely, Farakka, Jamtara, Garudeshwar, and Vijayawada for an ensemble of three GCMs and three scenarios, for two time slices. Spatial differences in uncertainty projections of runoff and evapotranspiration for years 2056-2065 for the a1b scenario at the 5th and 95th percentile levels are also projected. Results from the study show increased mean monthly discharges for Farakka and Vijayawada stations, and increased low, mid and high duration flows at Farakka, Jamtara and Vijayawada for the future. However, it is seen that uncertainty introduced due to choice of GCM, is larger than that due to parameter uncertainty for the VIC MHM. The largest effects of runoff predictive uncertainty due to uncertainty in VIC parameters are seen in the Himalayan foothills belt, and the high-precipitation Northeast region of the country. It is demonstrated through the study that it is relevant and feasible to provide Bayesian uncertainty estimates for macroscale models in projection of large-scale and regional hydrologic impacts.Citation: Raje, D., and R. Krishnan (2012), Bayesian parameter uncertainty modeling in a macroscale hydrologic model and its impact on Indian river basin hydrology under climate change, Water Resour. Res., 48, W08522,

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Section: Introductionmentioning

confidence: 99%

Bayesian parameter uncertainty modeling in a macroscale hydrologic model and its impact on Indian river basin hydrology under climate change

Raje

Krishnan

2012

Water Resources Research

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“…Uncertainties related to model structure, parameter calibration and input data affect the performance of the regionalization of precipitation-runoff models for continuous simulation of streamflow (see Wagener and Wheater, 2006;Oudin et al, 2008;Oudin et al, 2010;Kim and Kaluarachchi, 2008;Gupta et al, 2008). Engeland and Gottschalk (2002) noted that structural errors in the model are more important than parameter uncertainties. Oudin et al (2010) noted that the physical meaning of calibrated model parameters suffers from problems in model identification, model structural errors, and difficulties in finding an appropriate calibration strategy.…”

Section: Factors That Influence Regionalization Performancementioning

confidence: 99%

Evaluation of Regionalization Methods for Hourly Continuous Streamflow Simulation Using Distributed Models in Boreal Catchments

et al. 2015

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Regionalization for prediction in ungauged basins at hourly resolution is important for water resources management (e.g. floods and hydropeaking). In this paper, calibration of 26 catchments (39-3090 km 2 ) in mid-Norway was performed using hourly records and three spatially distributed (1x1 km 2 ) precipitation-runoff models: a first-order nonlinear system model (hereafter Kirchmod), the HBV model and the Basic-Grid-Model (BGM). Four regionalization methods for each model namely parameter set yielding maximum regional weighted average (MRWA) performance measures (PM), regional median of optimal parameters (RMedP), nearest neighbor (NN) and physical similarity (PS) were evaluated and compared with three benchmarks. Parameter transfer from best regional donor (BRD) and from an ideal best arbitrary single-donor (BASD), and local calibration (LC) were as benchmarks. The physical similarity attributes include hypsometric curves (PSH), land use (PSL), drainage density (PSD), catchment area (PSA), terrain slope (PSS), bedrock geology (PSR), soil type (PSSO) and combination of all (PSC).Comprehensive evaluation of single-and multi-donors, simple benchmarks and more advanced regionalization methods using multi-models, two PM and their statistical evaluation indicate that the identification of regionalization methods is dependent on the models, the PM and their statistical evaluation. In general, the PSH, PSC and BRD methods performed better for the Nash-Sutcliffe efficiency (NSE) based on boxplots and regional median values of both the NSE and relative deterioration or improvement of the NSE from the local calibration due to the regionalization. The methods also performed better for the individual catchments. The PSS, RMedP, MRWA and BRD methods performed better for the log-transformed streamflow 2 (NSEln) based on the same evaluation criteria. Similar performance to the more advanced regionalization methods of transfer of homogeneous parameter sets across the whole region from the BRD for both NSE and NSEln indicate the potential of the simple regionalization approach for predicting runoff response in the region.

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“…Many solutions have been presented to solve the former two factors, such as the generalized likelihood uncertainty estimation (GLUE) (Beven andBinley 1992, Montanari 2005), Bayesian (Krzysztofowicz 1999, Engeland and Gottschalk 2002, Mantovan and Todini 2006, Ajami et al 2007, Jin et al 2010 and Markov Chain Monte Carlo (MCMC) (Vrugt et al 2003, Benke et al 2008. As modern weather radars are able to provide estimated rainfall with high spatial and temporal resolutions covering a large area, they have been widely used in hydrological applications.…”

Section: Introductionmentioning

confidence: 99%

Modelling radar-rainfall estimation uncertainties using elliptical and Archimedean copulas with different marginal distributions

Dai

Han

Rico‐Ramirez

et al. 2014

Hydrological Sciences Journal

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Given that radar-based rainfall has been broadly applied in hydrological studies, quantitative modelling of its uncertainty is critically important, as the error of input rainfall is the main source of error in hydrological modelling. Using an ensemble of rainfall estimates is an elegant solution to characterize the uncertainty of radarbased rainfall and its spatial and temporal variability. This paper has fully formulated an ensemble generator for radar precipitation estimation based on the copula method. Each ensemble member is a probable realization that represents the unknown true rainfall field based on the distribution of radar rainfall (RR) error and its spatial error structure. An uncertainty model consisting of a deterministic component and a random error factor is presented based on the distribution of gauge rainfall conditioned on the radar rainfall (GR|RR). Two kinds of copulas (elliptical and Archimedean copulas) are introduced to generate random errors, which are imposed by the deterministic component. The elliptical copulas (e.g. Gaussian and t-copula) generate the random errors based on the multivariate distribution, typically of decomposition of the error correlation matrix using the LU decomposition algorithm. The Archimedean copulas (e.g. Clayton and Gumbel) utilize the conditional dependence between different radar pixels to obtain random errors. Based on those, a case application is carried out in the Brue catchment located in southwest England. The results show that the simulated uncertainty bands of rainfall encompass most of the reference raingauge measurements with good agreement between the simulated and observed spatial dependences. This indicates that the proposed scheme is a statistically reliable method in ensemble radar rainfall generation and is a useful tool for describing radar rainfall uncertainty.Key words radar-rainfall estimates; rainfall uncertainties; copula; ensemble generation Modélisation des incertitudes d'estimation des précipitations par radar en utilisant les copules elliptiques et d'Archimède avec différentes distributions marginales Résumé Étant donné que les précipitations par radar sont couramment utilisées dans les études hydrologiques, la modélisation quantitative de leur incertitude est très importante, car l'erreur sur les précipitations est la principale source d'erreur dans la modélisation hydrologique. L'utilisation d'un ensemble d'estimations des précipitations est une solution élégante pour caractériser l'incertitude des précipitations par radar et sa variabilité spatiale et temporelle. Cet article propose un générateur d'ensembles pour l'estimation de la précipitation par radar basé sur la méthode des copules. Chaque membre de l'ensemble est une réalisation possible du vrai champ de pluie inconnu, basée sur la distribution des erreurs des précipitations radar (PR) et leur structure spatiale. Nous proposons un modèle d'incertitude constitué d'une composante déterministe et d'un facteur d'erreur aléatoire reposant sur la répartition des précipit...

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Bayesian estimation of parameters in a regional hydrological model

Cited by 75 publications

References 20 publications

Bayesian parameter uncertainty modeling in a macroscale hydrologic model and its impact on Indian river basin hydrology under climate change

Bayesian parameter uncertainty modeling in a macroscale hydrologic model and its impact on Indian river basin hydrology under climate change

Evaluation of Regionalization Methods for Hourly Continuous Streamflow Simulation Using Distributed Models in Boreal Catchments

Modelling radar-rainfall estimation uncertainties using elliptical and Archimedean copulas with different marginal distributions

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