Modified Generalized Likelihood Uncertainty Estimation (GLUE) Methodology for Considering the Subjectivity of Likelihood Measure Selection
Publication: Journal of Hydrologic Engineering
Volume 16, Issue 6
Abstract
The generalized likelihood uncertainty estimation (GLUE) methodology has been widely used in many areas as an effective and general strategy for model calibration and uncertainty estimation associated with complex models. The application of GLUE requires a formal definition of a likelihood measure. However, it has been recognized that the choice of a likelihood measure is inherently subjective. This, in turn, introduces a new kind of uncertainty—the uncertainty owing to the lack of knowledge in choosing the true likelihood measure in the GLUE methodology. This study proposes a practical framework to address this uncertainty by using multiple likelihood measures, analogous to considering multiple expert opinions. The final uncertainty probability estimates are then obtained by combining the estimates from individual likelihood measures based on probability theory.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
We are indebted to Stefan Finsterle and Boris Faybishenko at Lawrence Berkeley National Laboratory for their critical and careful review of a preliminary version of this manuscript. This work was supported by the U.S. Department of Energy (DOE), under DOE Contract No. DOEDE-AC02-05CH11231.
References
Ambroise, B., Beven, K., and Freer, J. (1996). “Toward a generalization of the TOPMODEL concepts: Topographic indices of hydrological similarity.” Water Resour. Res., 32(7), 2135–2145.
Beven, K. (2006). “A manifesto for the equifinality thesis.” J. Hydrol. (Amsterdam), 320(1-2), 18–36.
Beven, K., and Binley, A. (1992). “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Processes, 6, 279–298.
Beven, K., and Freer, J. (2001). “Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology.” J. Hydrol. (Amsterdam), 249(1-4), 11–29.
Beven, K., Freer, J., Hankin, B., and Schulz, K. (2000). “The use of generalised likelihood measures for uncertainty estimation in high-order models of environmental systems.” Nonlinear and nonstationary signal processing, W. J. Fitzgerald et al., eds., Cambridge University Press, Cambridge, UK, 115–151.
Beven, K., Smith, P. J., and Freer, J. (2008). “So just why would a modeler choose to be incoherent?” J. Hydrol. (Amsterdam), 354(1-4), 15–32.
Beven, K., and Young, P. (2003). “Comment on ‘Bayesian recursive parameter estimation for hydrologic models’ by M. Thiemann, M. Trosset, H. Gupta, and S. Sorooshian.” Water Resour. Res., 39(5), 1116.
Finsterle, S., and Najita, J. (1998). “Robust estimation of hydrogeologic model parameters.” Water Resour. Res., 34(11), 2939–2947.
Franks, S. W., and Beven, K. (1997). “Estimation of evapotranspiration at the landscape scale: A fuzzy disaggregation approach.” Water Resour. Res., 33(12), 2929–2938.
Franks, S. W., and Beven, K. (1999). “Conditioning a multiple-patch SVAT model using uncertain time-space estimates of latent heat fluxes as inferred from remotely sensed data.” Water Resour. Res., 35(9), 2751–2761.
Franks, S. W., Gineste, P., Beven, K., and Merot, P. (1998). “On constraining the predictions of a distributed moder: The incorporation of fuzzy estimates of saturated areas into the calibration process.” Water Resour. Res., 34(4), 787–797.
Freer, J., Beven, K., and Ambroise, B. (1996). “Bayesian estimation of uncertainty in runoff prediction and the value of data: An application of the GLUE approach.” Water Resour. Res., 32(7), 2161–2173.
Freni, G., Mannina, G., and Viviani, G. (2008). “Uncertainty in urban stormwater quality modelling: The effect of acceptability threshold in the GLUE methodology.” Water Res., 42(8-9), 2061–2072.
Freni, G., Mannina, G., and Viviani, G. (2009a). “Urban runoff modelling uncertainty: Comparison among Bayesian and pseudo-Bayesian methods.” Environ. Model. Software, 24(9), 1100–1111.
Freni, G., Mannina, G., and Viviani, G. (2009b). “Uncertainty in urban stormwater quality modelling: The influence of likelihood measure formulation in the GLUE methodology.” Sci. Total Environ., 408(1), 138–45.
Lamb, R., Beven, K., and Myrabø, S. (1998). “Use of spatially distributed water table observations to constrain uncertainty in a rainfall-runoff model.” Adv. Water Resour., 22(4), 305–317.
Liu, Y., and Gupta, H. V. (2007). “Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework.” Water Resour. Res., 43, W07401.
Makowski, D., Wallach, D., and Tremblay, M. (2002). “Using a Bayesian approach to parameter estimation; Comparison of the GLUE and MCMC methods.” Agronomie, 22(2), 191–203.
Mantovan, P., and Todini, E. (2006). “Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology.” J. Hydrol. (Amsterdam), 330(1-2), 368–381.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models, Part I—A discussion of principles.” J. Hydrol. (Amsterdam), 10(3), 282–290.
Page, T., Beven, K., Freer, J., and Jenkins, A. (2003). “Investigating the uncertainty in predicting responses to atmospheric deposition using the model of acidification of groundwater in catchments (MAGIC) within a generalised likelihood uncertainty estimation (GLUE) framework.” Water Air Soil Pollut., 142(1/4), 71–94.
Ratto, M., Young, P., Romanowicz, R., Pappenberger, F., Saltelli, A., and Pagano, A. (2007). “Uncertainty, sensitivity analysis and the role of data based mechanistic modeling in hydrology.” Hydrol. Earth Syst. Sci., 11(4), 1249–1266.
Romanowicz, R., and Beven, K. (2006). “Comments on generalised likelihood uncertainty estimation.” Reliab. Eng. Syst. Saf., 91(10-11), 1315–1321.
Smith, P. J., Tawn, J., and Beven, K. (2008). “Informal likelihood measures in model assessment: Theoretic development and investigation.” Adv. Water Resour., 31(8), 1087–1100.
Thorndahl, S., Beven, K., Jensen, J., and Schaarup-Jensen, K. (2008). “Event based uncertainty assessment in urban drainage modelling, applying the GLUE methodology.” J. Hydrol. (Amsterdam), 357(3-4), 421–437.
Zak, S. K., Beven, K., and Reynolds, B. (1997). “Uncertainty in the estimation of critical loads: A practical methodology.” Water Air Soil Pollut., 98(3-4), 297–316.
Zhang, Y. (2010). “Using the Choquet integral for screening geological storage sites.” Greenhouse Gases: Science and Technology, in press.
Zio, E., and Apostolakis, G. E. (1997). “Accounting for expert-to-expert variability: A potential source of bias in performance assessment of high-level radioactive waste repositories.” Ann. Nucl. Energy, 24(10), 751–762.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 16 • Issue 6 • June 2011
Pages: 558 - 561
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Mar 26, 2010
Accepted: Sep 25, 2010
Published online: Oct 19, 2010
Published in print: Jun 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.