Assessing the Uncertainty of the Xinanjiang Rainfall-Runoff Model: Effect of the Likelihood Function Choice on the GLUE Method
Publication: Journal of Hydrologic Engineering
Volume 20, Issue 10
Abstract
In this paper, the generalized likelihood uncertainty estimation (GLUE) methodology, which is widely applied in the field of hydrology, is used for testing and predictive uncertainty estimation in the application of the Xinanjiang rainfall-runoff (XAJ-RR) model for estimating monthly stream flow (Nangao reservoir) catchment in China. However, one of the drawbacks of using the GLUE method is the definition of the likelihood function, which reflects the behavior of the hydrological model. Although there are different formulations of likelihood functions in the literature, most previous research focused on the application of the GLUE method with the likelihood function of Nash-Sutcliffe (NS) efficiency. In this respect, to illustrate the impact of the selection of likelihood functions on the results of the GLUE method, the authors adopted four likelihood functions: NS, normalized absolute error (NAE), index of agreement (IoA), and Chiew and McMahon (CM). The main findings of the study are that (1) the parameter uncertainty is more sensitive to the choice of the likelihood functions than the uncertainty in the model prediction by the GLUE method; (2) the parameters of the XAJ-RR model with NS had less uncertainty compared to those of NAE, IoA, and CM; (3) the uncertainty bounds showed slight differences from various likelihood functions; and (4) the computational efficiency of the GLUE method based on likelihood function IoA was much better because the IoA likelihood function corresponded to narrower uncertainty bounds, higher bracketing of observations, and the best maximum value of likelihood functions. Thus, this study confirms the importance of the likelihood function selection in the application of GLUE to the uncertainty assessment of the XAJ-RR model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research is supported by the National Basic Research Program of China (2013CBA01806), the National Natural Science Foundation (NNSF) of China (51190091, 41371049), special funding from the State Key Laboratory of Desert and Oasis Ecology, and special funding from the State Key Laboratory of Hydrology–Water Resources and Hydraulic Engineering (Grant No. 20145027312).
References
Arabi, M., Govindaraju, R. S., and Hantush, M. M. (2007). “A probabilistic approach for analysis of uncertainty in the evaluation of watershed management practices.” J. Hydrol., 333(2–4), 459–471.
Bergström, S., and Forsman, A. (1973). “Development of a conceptual deterministic rainfall-runoff model.” Nordic Hydrol., 4(3), 147–170.
Beven, K. (2006). “A manifesto for the equifinality thesis.” J. Hydrol., 320(1–2), 18–36.
Beven, K., and Binley, A. (1992). “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Processes, 6(3), 279–298.
Beven, K., and Kirkby, M. (1979). “A physically based, variable contributing area model of basin hydrology.” Hydrol. Sci. Bull., 24(1), 43–69.
Beven, K., Smith, P. J., and Freer, J. E. (2008). “So just why would a modeler choose to be incoherent.” J. Hydrol., 354(1–4), 15–32.
Beven, K. J., and Freer, J. (2001). “Equifinality, data assimilation, and uncertainty estimation in mechanistic modeling of complex environmental systems using the GLUE methodology.” J. Hydrol., 249(1–4), 11–29.
Blasone, R. S., Madsen, H., and Robjerg, D. (2008a). “Uncertainty assessment of integrated distributed hydrological models using GLUE with Markov Chain Monte Carlo sampling.” J. Hydrol., 353(1–2), 18–32.
Blasone, R. S., Vrugt, J. A., Madsen, H., Rosbjerg, D., Robinson, B. A., and Zyvoloski, G. A. (2008b). “Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling.” Adv. Water Resour., 31(4), 630–648.
Burnash, R. J. C., Ferral, R. L., and McGuire, R. A. (1973). “A generalized streamflow simulation system: Conceptual modeling for digital computers.” Joint Federal-State River Forecast Center, Sacramento, CA.
Chiew, F., and McMahon, T. (1994). “Application of the daily rainfall-runoff model Modhydrolog to 28 Australian catchments.” J. Hydrol., 153(1–4), 383–416.
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 storm water quality modeling: The effect of acceptability threshold in the GLUE methodology.” Water Res., 42(8–9), 2061–2072.
Freni, G., Mannina, G., and Viviani, G. (2009). “Uncertainty in urban stormwater quality modelling: The influence of likelihood measure formulation in the GLUE methodology.” Sci. Total Environ., 408(1), 138–145.
Hankin, B. G., Hardy, R., Kettle, H., and Beven, K. J. (2001). “Using CFD in a GLUE framework to model the flow and dispersion characteristics of a natural fluvial dead zone.” Earth Surf. Processes Landforms, 26(6), 667–687.
Hassan, A. E., Bekhit, H. M., and Chapman, J. B. (2008). “Uncertainty assessment of a stochastic groundwater flow model using GLUE analysis.” J. Hydrol., 362(1–2), 89–109.
He, J., Dukes, M. D., Jones, J. W., Graham, W. D., and Judge, J. (2009). “Applying GLUE for estimating CERES-Maize genetic and soil parameters for sweet corn production.” Trans. Am. Soc. Agric. Bilo. Eng., 52, 1907–1921.
Jin, X. L., Xu, C. Y., Zhang, Q., and Singh, V. P. (2010). “Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model.” J. Hydrol., 383(3–4), 147–155.
Jung, Y., and Merwade, V. (2012). “Uncertainty quantification in flood inundation mapping using generalized likelihood uncertainty estimate and sensitivity analysis.” J. Hydrol. Eng., 507–520.
Kuczera, G., and Parent, E. (1998). “Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The Metropolis algorithm.” J. Hydrol., 211(1–4), 69–85.
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.
Li, L., Xia, J., Xu, C. Y., Chu, J., and Wang, R. (2009). “Analyze the sources of equifinality in hydrological model using GLUE methodology.” Hydro Informatics in Hydrology, Hydrogeology and Water Resources, Proc., Symp. JS.4 at the Joint IAHS & IAH Convention, Vol. 331, IAHS Publication, Wallingford, U.K., 130–138.
Li, L., Xia, J., Xu, C. Y., and Singh, V. (2010). “Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models.” J. Hydrol., 390(3–4), 210–221.
Mannina, G. (2011). “Uncertainty assessment of a water-quality model for ephemeral rivers using GLUE analysis.” J. Environ. Eng., 177–186.
Mantovan, P., and Todini, E. (2006). “Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology.” J. Hydrol., 330(1–2), 368–381.
Maskey, S., and Guinot, V. (2003). “Improved first-order second-moment method for uncertainty estimation in flood forecasting.” Hydrol. Sci. J., 48(2), 183–196.
Maskey, S., Guinot, V., and Price, R. K. (2004). “Treatment of precipitation uncertainty in rainfall-runoff modeling: A fuzzy set approach.” Adv. Water Resour., 27(9), 889–898.
McMichael, C. E., Hope, A. S., and Loaiciga, H. A. (2006). “Distributed hydrological modeling in California semi-arid shrublands: MIKE-SHE model calibration and uncertainty estimation.” J. Hydrol., 317(3–4), 307–324.
Melching, C. S. (1995). “Reliability estimation.” Computer models of watershed hydrology, V. P. Singh, ed., Water Resources Publications, Highlands Ranch, CO, 69–118.
Mitchell, S., Beven, K., and Freer, J. (2009). “Multiple sources of predictive uncertainty in modeled estimates of net ecosystem CO2 exchange.” Ecol. Modell., 220(23), 3259–3270.
Montanari, A. (2005). “Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall-runoff simulations.” Water Resour Res., 41(8), W08406.
Montanari, A. (2007). “What do we mean by uncertainty? The need for a consistent wording about uncertainty assessment in hydrology.” Hydrol. Processes, 21(6), 841–845.
Montanari, A., and Brath, A. (2004). “A stochastic approach for assessing the uncertainty of rainfall-runoff simulations.” Water Resour. Res., 40(1), W01106.
Nash, J. E., and Sutcliff, J. V. (1970). “River flow forecasting through the conceptual model. Part 1: A discussion of principles.” J. Hydrol., 10(3), 282–290.
Nielsen, S. A., and Hansen, E. (1973). “Numerical simulation of the rainfall runoff processes on a daily basis.” Nordic Hydrol., 4(3), 171–190.
Schoups, G., and Vrugt, J. A. (2010). “A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non Gaussian errors.” Water Resour. Res., 46, W10531.
Shrestha, D. L., and Solomatine, D. (2008). “Data-driven approaches for estimating uncertainty in rainfall-runoff modeling.” Int. J. River Basin Manage., 6(2), 109–122.
SIMLAB 2.2 [Computer software]. Joint Research Centre—European Commission, 〈http://www.hec.usace.army.mil/software/hec-ras/hec-georas.html〉 (Mar. 28, 2014).
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.
Spina, S., Lombardo, F., Ridolfi, E., Russo, F., and Napolitano, F. (2012). “Uncertainty in rainfall-runoff modeling: An application of GLUE approach to the Rome’s urban area.” EGU Publication, Vienna, Austria, 10433.
Stedinger, J. R., Vogel, R. M., Lee, S. U., and Batchelder, R. (2008). “Appraisal of the generalized likelihood uncertainty estimation (GLUE) method.” Water Resour. Res., 44(12), W00B06.
Sugawara, M. (1967). “The flood forecasting by a series storage type model.” Proc., Int. Symp. on Floods and Their Computation, Vol. 85, IAHS Publication, Wallingford, U.K., 1–6.
Sugawara, M. (1995). “Tank model.” Computer models of watershed hydrology, V. P. Singh, ed., Water Resources Publications, Highlands Ranch, CO, 165–214.
Tadesse, A., and Anagnostou, E. N. (2005). “A statistical approach to ground radar-rainfall estimation.” J. Atmos. Oceanic Technol., 22(11), 1720–1732.
Thorndahl, S., Beven, K. J., Jensen, J. B., and Jensen, K. S. (2008). “Event based uncertainty assessment in urban drainage modeling, applying the GLUE methodology.” J. Hydrol., 357(3–4), 421–437.
Tung, Y. K. (1996). “Uncertainty and reliability analysis.” Water resources handbook, L. W. Mays, ed., McGraw-Hill, New York, 7.1–7.65.
Vachaud, G., and Chen, T. (2002). “Sensitivity of a large-scale hydrologic model to quality of input data obtained at different scales; distributed versus stochastic non-distributed modeling.” J. Hydrol., 264(1–4), 101–112.
Viola, F., Noto, L. V., Cannarozzo, M., and La, L. G. (2009). “Daily streamflow prediction with uncertainty in ephemeral catchments using the GLUE methodology.” Phys. Chem. Earth, 34(10–12), 701–706.
Willmott, C. J., et al. (1985). “Statistics for the evaluation and comparison of models.” J. Geophys. Res. Oceans., 90(NC5), 8995–9005.
Yang, J., Reichert, P., Abbaspour, K. C., Xia, J., and Yang, H. (2008). “Comparing uncertainty analysis techniques for a SWAT application to the Chaohe basin in China.” J. Hydrol., 358(1–2), 1–23.
Zhao, R. J, and Wang, P. L. (1988). “The Xinanjiang model parameter discussing.” Hydrology, 6, 2–9 (in Chinese).
Zhao, R. J. (1992). “The Xinanjiang model applied in China.” J. Hydrol., 135(1–4), 371–381.
Zhao, R. J., Wang, P. L., and Hu, F. B. (1992). “Relations between parameter values and corresponding natural conditions of Xinanjiang model.” J. HOHAI Univ., 20, 52–59 (in Chinese).
Zhao, R. J., Zhang, Y. L., Fang, L. R., Liu, X. R., and Zhang, Q. S. (1980). “The Xinanjiang model.” Hydrological Forecasting Proc., Oxford Symp., Vol. 129, IAHS Publication, Wallingford, U.K., 351–356.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 20 • Issue 10 • October 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jun 16, 2014
Accepted: Dec 16, 2014
Published online: Feb 9, 2015
Discussion open until: Jul 9, 2015
Published in print: Oct 1, 2015
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.