Cited by 387Hydrology and Watershed Management StudiesMeteorological Phenomena and SimulationsGroundwater flow and contamination studies

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Appraisal of the generalized likelihood uncertainty estimation (GLUE) method

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Stedinger, Jery R., Vogel, Richard M., Lee, Seung Uk, Batchelder, Rebecca·2008·Water Resources Research

DOI 10.1029/2008wr006822

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Abstract

Recent research documents that the widely accepted generalized likelihood uncertainty estimation (GLUE) method for describing forecasting precision and the impact of parameter uncertainty in rainfall/runoff watershed models fails to achieve the intended purpose when used with an informal likelihood measure. In particular, GLUE generally fails to produce intervals that capture the precision of estimated parameters, and the difference between predictions and future observations. This paper illustrates these problems with GLUE using a simple linear rainfall/runoff model so that model calibration is a linear regression problem for which exact expressions for prediction precision and parameter uncertainty are well known and understood. The simple regression example enables us to clearly and simply illustrate GLUE deficiencies. Beven and others have suggested that the choice of the likelihood measure used in a GLUE computation is subjective and may be selected to reflect the goals of the modeler. If an arbitrary likelihood is adopted that does not reasonably reflect the sampling distribution of the model errors, then GLUE generates arbitrary results without statistical validity that should not be used in scientific work. The traditional subjective likelihood measures that have been used with GLUE also fail to reflect the nonnormality, heteroscedasticity, and serial correlation among the residual errors generally found in real problems, and hence are poor metrics for even simple sensitivity analyses and model calibration. Most previous applications of GLUE only produce uncertainty intervals for the average model prediction, which by construction should not be expected to include future observations with the prescribed probability. We show how the GLUE methodology when properly implemented with a statistically valid likelihood function can provide prediction intervals for future observations which will agree with widely accepted and statistically valid analyses.

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Self-citation

Authors: Stedinger, J. R., Vogel, R. M., Lee, S. U., & Batchelder, R.
Affiliations: Cornell University (US)
Tufts University (US)
ORCID: Stedinger, Jery R.
Vogel, Richard M.
Venue: Water Resources Research
Publisher: American Geophysical Union (AGU)
Published: 2008-11
Volume: 44
Issue: 12
ISSN: 0043-1397 (ISSN-L)
1944-7973
DOI: 10.1029/2008wr006822
OpenAlex: W2155633525
Cited by: 386
References: 69
Citations by year: 2026: 6 · 2025: 11 · 2024: 10 · 2023: 8 · 2022: 21 · 2021: 21 · 2020: 29 · 2019: 29 · 2018: 28 · 2017: 15 · 2016: 29 · 2015: 29 · 2014: 31 · 2013: 33 · 2012: 34
FWCI: 18.29
Type: journal article
Language: en
Open access: bronze
doi.org
Licence: onlinelibrary.wiley.com/termsAndConditions#vor (vor)
Locations: Water Resources Research (publishedVersion)
Topics: Physical Sciences › Environmental Science › Water Science and Technology › Hydrology and Watershed Management Studies
Physical Sciences › Earth and Planetary Sciences › Atmospheric Science › Meteorological Phenomena and Simulations
Physical Sciences › Environmental Science › Environmental Engineering › Groundwater flow and contamination studies
Keywords: generalized likelihood uncertainty estimation, adhesives, rainfall-runoff modeling, parameter uncertainty, prediction intervals, likelihood function, model calibration, linear regression, forecast uncertainty, heteroscedasticity, serial correlation, uncertainty intervals

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Appraisal of the generalized likelihood uncertainty estimation (GLUE) method

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