Method for Probabilistic Flood Forecasting Considering Rainfall and Model Parameter Uncertainties
Publication: Journal of Hydrologic Engineering
Volume 24, Issue 12
Abstract
Hydrologic basin models are generalizations of natural hydrologic processes and inevitably contain multiple uncertainties in the simulation of rainfall-runoff events. These uncertainties typically include input uncertainty, model structure uncertainty, and model parameter uncertainty. The input uncertainty is divided into rainfall calculation uncertainty (RCU) and precipitation forecasting uncertainty. For model parameter uncertainty, there are only a few parameters in a hydrologic basin model that make significant contributions to flood forecasting so that only the probability distribution functions of those sensitive parameters need to be evaluated. In this study, a new method of RCU assessment is derived using an inverse sampling gauge (ISG) approach, in which the influencing factors of the RCU are addressed in the calculated area precipitation and standard deviation. Additionally, the coefficient of variation-Nash-Sutcliffe efficiency measure (CV-NS) method is introduced to identify the sensitive parameters of a hydrologic model. The methods of ISG and CV-NS are tested in Huangnizhuang Basin, China, in the evaluation of the RCU and the parameters uncertainty of the Xinanjiang model. It is indicated that the ISG method is useful in RCU estimation by deriving the conditional probabilistic distribution of areal precipitation, and the CV-NS method is effective and simply in the operation of sensitive parameters’ identification. In addition, the continuous ranked probability skill score (CRPSS) is employed as an indicator to show the relative performance of predictions. Three probabilistic predictions considering different sources of uncertainties are conducted and compared with the deterministic prediction. The results of the comparisons suggest that predictions considering one or more uncertainties have higher predictive performance than the deterministic one. Moreover, main source of uncertainty can be identified by the results of CRPSS among different probabilistic predictions. In this study area, the model parameters’ uncertainty is the main uncertainty.
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Acknowledgments
This study was supported by the National Key Research and Development Program of China (Grant Nos. 2016YFC0402709 and 2016YFC0402706), the Special Fund for Public Welfare Industry of the Ministry of Water Resources of China (Grant No. 201301066), and the National Natural Science Foundation of China (Grant No. 51179046).
References
Ajami, N. K., Q. Duan, and S. Sorooshian. 2007. “An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction.” Water Resour. Res. 43 (1): W1403. https://doi.org/10.1029/2005WR004745.
Alfieri, L., F. Pappenberger, F. Wetterhall, T. Haiden, D. Richardson, and P. Salamon. 2014. “Evaluation of ensemble streamflow predictions in Europe.” J. Hydrol. 517 (19): 913–922. https://doi.org/10.1016/j.jhydrol.2014.06.035.
Beven, K., and A. Binley. 1992. “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Process. 6 (3): 279–298. https://doi.org/10.1002/hyp.3360060305.
Clark, M. P., A. G. Slater, D. E. Rupp, R. A. Woods, J. A. Vrugt, H. V. Gupta, T. Wagener, and L. E. Hay. 2008. “Framework for understanding structural errors (FUSE): A modular framework to diagnose differences between hydrological models.” Water Resour. Res. 44 (12): W00B02. https://doi.org/10.1029/2007WR006735.
Coccia, G., and E. Todini. 2011. “Recent developments in predictive uncertainty assessment based on the model conditional processor approach.” Hydrol. Earth Syst. Sci. 15 (10): 3253–3274. https://doi.org/10.5194/hess-15-3253-2011.
Duan, Q., S. Sorooshian, and V. Gupta. 1992. “Effective and efficient global optimization for conceptual rainfall-runoff models.” Water Resour. Res. 28 (4): 1015–1031. https://doi.org/10.1029/91WR02985.
Duan, Q., S. Sorooshian, and V. K. Gupta. 1994. “Optimal use of the SCE-UA global optimization method for calibrating watershed models.” J. Hydrol. 158 (3–4): 265–284. https://doi.org/10.1016/0022-1694(94)90057-4.
Franz, K. J., T. S. Hogue, M. Barik, and M. He. 2014. “Assessment of SWE data assimilation for ensemble streamflow predictions.” J. Hydrol. 519 (27): 2737–2746. https://doi.org/10.1016/j.jhydrol.2014.07.008.
Gneiting, T., A. E. Raftery, A. H. Westveld III, and T. Goldman. 2005. “Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation.” Mon. Weather Rev. 133 (5): 1098–1118. https://doi.org/10.1175/MWR2904.1.
Götzinger, J., and A. Bárdossy. 2008. “Generic error model for calibration and uncertainty estimation of hydrological models.” Water Resour. Res. 44 (12): W00B07. https://doi.org/10.1029/2007WR006691.
Haario, H., E. Saksman, and J. Tamminem. 2001. “An adaptive metropolis algorithm.” Bernoulli 7 (2): 223–242. https://doi.org/10.2307/3318737.
Hersbach, H. 2000. “Decomposition of the continuous ranked probability score for ensemble prediction systems.” Weather Forecast. 15 (5): 559–570. https://doi.org/10.1175/1520-0434(2000)015%3C0559:DOTCRP%3E2.0.CO;2.
Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky. 1999. “Bayesian model averaging: A tutorial.” Stat. Sci. 14 (4): 382–417. https://doi.org/10.1214/ss/1009212519.
Hu, Y., M. J. Schmeits, S. Jan van Andel, J. S. Verkade, M. Xu, D. P. Solomatine, and Z. Liang. 2016. “A stratified sampling approach for improved sampling from a calibrated ensemble forecast distribution.” J. Hydrometeorol. 17 (9): 2405–2417. https://doi.org/10.1175/JHM-D-15-0205.1.
Huang, S., Q. Huang, J. Chang, G. Leng, and Y. Chen. 2017. “Variations in precipitation and runoff from a multivariate perspective in the Wei River Basin, China.” Quat. Int. 440: 30–39. https://doi.org/10.1016/j.quaint.2016.05.020.
Huard, D., and A. Mailhot. 2008. “Calibration of hydrological model GR2M using Bayesian uncertainty analysis.” Water Resour. Res. 44 (2): W02424. https://doi.org/10.1029/2007WR005949.
Kavetski, D., G. Kuczera, and S. W. Franks. 2006a. “Bayesian analysis of input uncertainty in hydrological modeling. 1: Theory.” Water Resour. Res. 42 (3): W3407. https://doi.org/10.1029/2005WR004368.
Kavetski, D., G. Kuczera, and S. W. Franks. 2006b. “Bayesian analysis of input uncertainty in hydrological modeling. 2: Application.” Water Resour. Res. 42 (3): W3408. https://doi.org/10.1029/2005WR004376.
Kelly, K. S., and R. Krzysztofowicz. 2000. “Precipitation uncertainty processor for probabilistic river stage forecasting.” Water Resour. Res. 36 (9): 2643–2653. https://doi.org/10.1029/2000WR900061.
Kobold, M., and K. Sugelj. 2005. “Precipitation forecasts and their uncertainty as input into hydrological models.” Hydrol. Earth Syst. Sci. 9 (4): 322–332. https://doi.org/10.5194/hess-9-322-2005.
Krzysztofowicz, R. 1999. “Bayesian theory of probabilistic forecasting via deterministic hydrologic model.” Water Resour. Res. 35 (9): 2739–2750. https://doi.org/10.1029/1999WR900099.
Krzysztofowicz, R. 2002. “Bayesian system for probabilistic river stage forecasting.” J. Hydrol. 268 (1–4): 16–40. https://doi.org/10.1016/S0022-1694(02)00106-3.
Krzysztofowicz, R., and H. D. Herr. 2001. “Hydrologic uncertainty processor for probabilistic river stage forecasting: Precipitation-dependent model.” J. Hydrol. 249 (1–4): 46–68. https://doi.org/10.1016/S0022-1694(01)00412-7.
Krzysztofowicz, R., and C. J. Maranzano. 2004. “Hydrologic uncertainty processor for probabilistic stage transition forecasting.” J. Hydrol. 293 (1–4): 57–73. https://doi.org/10.1016/j.jhydrol.2004.01.003.
Kuczera, G., D. Kavetski, S. Franks, and M. Thyer. 2006. “Towards a Bayesian total error analysis of conceptual rainfall-runoff models: Characterising model error using storm-dependent parameters.” J. Hydrol. 331 (1–2): 161–177. https://doi.org/10.1016/j.jhydrol.2006.05.010.
Leoncini, G., R. S. Plant, S. L. Gray, and P. A. Clark. 2013. “Ensemble forecasts of a flood-producing storm: Comparison of the influence of model-state perturbations and parameter modifications.” Q. J. R. Meteorol. Soc. 139 (670): 198–211. https://doi.org/10.1002/qj.1951.
Li, B., Z. Liang, Y. He, L. Hu, W. Zhao, and K. Acharya. 2016. “Comparison of parameter uncertainty analysis techniques for a TOPMODEL application.” Stochastic Environ. Res. Risk Assess. 31 (5): 1045–1059. https://doi.org/10.1007/s00477-016-1319-2.
Liang, Z., D. Wang, Y. Guo, Y. Zhang, and R. Dai. 2013. “Application of bayesian model averaging approach to multimodel ensemble hydrologic forecasting.” J. Hydrol. Eng. 18 (11): 1426–1436. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000493.
Si, W., W. Bao, and H. V. Gupta. 2015. “Updating real-time flood forecasts via the dynamic system response curve method.” Water Resour. Res. 51 (7): 5128–5144. https://doi.org/10.1002/2015WR017234.
Singh, V. P. 1995. Computer models of watershed hydrology. Highlands Ranch, CO: Water Resources.
Smith, P. J., K. J. Beven, A. H. Weerts, and D. Leedal. 2012. “Adaptive correction of deterministic models to produce probabilistic forecasts.” Hydrol. Earth Syst. Sci. 16 (8): 2783–2799. https://doi.org/10.5194/hess-16-2783-2012.
Thyer, M., B. Renard, D. Kavetski, G. Kuczera, S. W. Franks, and S. Srikanthan. 2009. “Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis.” Water Resour. Res. 45 (12): 1–22. https://doi.org/10.1029/2008WR006825.
Todini, E. 2008. “A model conditional processor to assess predictive uncertainty in flood forecasting.” Int. J. River Basin Manage. 6 (2): 123–137. https://doi.org/10.1080/15715124.2008.9635342.
Van Steenbergen, N., J. Ronsyn, and P. Willems. 2012. “A non-parametric data-based approach for probabilistic flood forecasting in support of uncertainty communication.” Environ. Modell. Software 33: 92–105. https://doi.org/10.1016/j.envsoft.2012.01.013.
Vrugt, J. A., H. V. Gupta, W. Bouten, and S. Sorooshian. 2003. “A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters.” Water Resour. Res. 39 (8): 1201. https://doi.org/10.1029/2002WR001642.
Vrugt, J. A., C. J. F. Ter Braak, M. P. Clark, J. M. Hyman, and B. A. Robinson. 2008. “Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation.” Water Resour. Res. 44 (12): W00B09. https://doi.org/10.1029/2007WR006720.
Wang, J., Z. Liang, X. Jiang, B. Li, and L. Chen. 2016. “Bayesian theory based self-adapting real-time correction model for flood forecasting.” Water 8 (3): 75. https://doi.org/10.3390/w8030075.
Woldemeskel, F., D. McInerney, J. Lerat, M. Thyer, D. Kavetski, D. Shin, N. Tuteja, and G. Kuczera. 2018. “Evaluating post-processing approaches for monthly and seasonal streamflow forecasts.” Hydrol. Earth Syst. Sci. 22 (12): 6257–6278. https://doi.org/10.5194/hess-22-6257-2018.
Xing, Z., X. Rui, Q. Fu, Y. Ji, and S. Zhu. 2011. “Nash model parameter uncertainty analysis by AM-MCMC based on BFS and probabilistic flood forecasting.” Chin. Geog. Sci. 21 (1): 74–83. https://doi.org/10.1007/s11769-010-0433-1.
Zeng, X., D. Wang, J. Wu, X. Zhu, L. Wang, and A. X. Zou. 2015. “Uncertainty evaluation of a groundwater conceptual model by using a multimodel averaging method.” Hum. Ecol. Risk Assess. 21 (5): 1246–1258. https://doi.org/10.1080/10807039.2014.957945.
Zhao, R. J., Y. L. Zhang, L. R. Fang, X. R. Liu, and Q. S. Zhang. 1980. “The Xinangjiang model.” In Proc., Oxford Symp., 1980351–1980356. Wallingford, UK: International Association of Hydrological Sciences.
Zhijia, L., X. Penglei, and T. Jiahui. 2013. “Study of the xinanjiang model parameter calibration.” J. Hydrol. Eng. 18 (11): 1513–1521. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000527.
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Journal of Hydrologic Engineering
Volume 24 • Issue 12 • December 2019
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©2019 American Society of Civil Engineers.
History
Received: Jan 16, 2018
Accepted: Jul 31, 2019
Published online: Sep 30, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 29, 2020
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