Estimating the Uncertainty of Hydrological Predictions through Data-Driven Resampling Techniques
Publication: Journal of Hydrologic Engineering
Volume 20, Issue 1
Abstract
Estimating the uncertainty of hydrological models remains a relevant challenge in applied hydrology, mostly because it is not easy to parameterize the complex structure of hydrological model errors. A nonparametric technique is proposed as an alternative to parametric error models to estimate the uncertainty of hydrological predictions. Within this approach, the above uncertainty is assumed to depend on input data uncertainty, parameter uncertainty and model error, where the latter aggregates all sources of uncertainty that are not considered explicitly. Errors of hydrological models are simulated by resampling from their past realizations using a nearest neighbor approach, therefore avoiding a formal description of their statistical properties. The approach is tested using synthetic data which refer to the case study located in Italy. The results are compared with those obtained using a formal statistical technique (meta-Gaussian approach) from the same case study. Our findings prove that the nearest neighbor approach provides simplicity in application and a significant improvement in regard to the meta-Gaussian approach. Resampling techniques appear therefore to be an interesting option for uncertainty assessment in hydrology, provided that historical data are available to provide a consistent description of the model error.
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Acknowledgments
The work presented herein was carried out within the COST Action ES0901 titled “European Procedures for Flood Frequency Estimation (FloodFreq)” and the Panta Rhei Research Initiative of the International Association of Hydrological Sciences (IAHS). A financial support by EU for A.E.S. is gratefully acknowledged. A.E.S. would also like to acknowledge Prof. Kazimierz Banasik (WULS-SGGW, Poland) for his input in the overall execution of this project. The authors thank the eponymous reviewer Keith Beven and an anonymous reviewer, and the Guest Editor Sivakumar Bellie, for providing detailed and useful comments; although the authors disagree with a few of the comments, overall they helped to improve the paper substantially.
References
Ajami, N. K., Duan, Q., and Sorooshian, S. (2007). “An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction.” Water Resour. Res., 43(1), W01403.
Beven, K., Smith, P., Westerberg, I., and Freer, J. (2012). “Comment on ‘Pursuing the method of multiple working hypotheses for hydrological modeling’ by P. Clark et al.” Water Resour. Res., 48(11), W11801.
Beven, K. J. (2006). “A manifesto for the equifinality thesis.” J. Hydrol., 320(1–2), 18–36.
Beven, K. J. (2010). “Preferential flows and travel time distributions: Defining adequate hypothesis tests for hydrological process models.” Hydrol. Processes, 24(12), 1537–1547.
Beven, K. J. (2012). “Causal models as multiple working hypotheses about environmental processes.” Comptes Rendus Geosci., 344(2), 77–88.
Beven, K. J., and Binley, A. M. (1992). “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Processes, 6(3), 279–298.
Beven, K. J., and Smith, P. (2014). “Concepts of information content and likelihood in parameter calibration for hydrological simulation models.” J. Hydrol. Eng., (Feb. 26, 2014).
Beven, K. J., and Westerberg, I. K. (2011). “On red herrings and real herrings: Disinformation and information in hydrological inference.” Hydrol. Processes, 25(10), 1676–1680.
Beygelzimer, A., Kakade, S., and Langford, J. (2006). “Cover trees for nearest neighbor.” ACM Proc., 23rd Int. Conf. on Machine Learning, ACM, New York, 97–104.
Blöschl, G., Grayson, R. B., and Sivapalan, M. (1995). “On the representative elementary area (REA) concept and its utility for distributed rainfall-runoff modelling.” Hydrol. Processes, 9(3–4), 313–330.
Bogner, K., and Pappenberger, F. (2011). “Multiscale error analysis, correction, and predictive uncertainty estimation in a flood forecasting system.” Water Resour. Res., 47(7), W07524.
Boyle, D. P. (2000). “Multicriteria calibration of hydrological models.” Ph.D. thesis, Dept. of Hydrol. and Water Resour., Univ. of Arizona, Tucson, AZ.
Brath, A., Montanari, A., and Toth, E. (2002). “Neural networks and non-parametric methods for improving real-time flood forecasting through conceptual hydrological models.” Hydrol. Earth Syst. Sci. Discuss., 6(4), 627–639.
Bulygina, N., and Gupta, H. (2009). “Estimating the uncertain mathematical structure of a water balance model via Bayesian data assimilation.” Water Resour. Res., 45(12), W00B13.
Bulygina, N., and Gupta, H. (2010). “How Bayesian data assimilation can be used to estimate the mathematical structure of a model.” Stochastic Env. Res. Risk Assessment, 24(6), 925–937.
Bulygina, N., and Gupta, H. (2011). “Correcting the mathematical structure of a hydrological model via Bayesian data assimilation.” Water Resour. Res., 47(5), W05514.
Clark, M. P., et al. (2008). “Framework for understanding structural errors (FUSE): A modular framework to diagnose differences between hydrological models.” Water Resour. Res., 44(12), W00B02.
Clark, M. P., Kavetski, D., and Fenicia, F. (2011). “Pursuing the method of multiple working hypotheses for hydrological modeling.” Water Resour. Res., 47(9), W09301.
Clark, M. P., and Slater, A. G. (2006). “Probabilistic quantitative precipitation estimation in complex terrain.” J. Hydrometeorol., 7(1), 3–22.
Cowpertwait, P. S. P. (1995). “A generalized spatial-temporal model of rainfall based on a clustered point process.” Proc. R. Soc. A, 450(1938), 163–175.
Cunha, L. K., Mandapaka, P. V., Krajewski, W. F., Mantilla, R., and Bradley, A. A. (2012). “Impact of radar-rainfall error structure on estimated flood magnitude across scales: An investigation based on a parsimonious distributed hydrological model.” Water Resour. Res., 48(10), W10515.
Di Baldassarre, G., and Montanari, A. (2009). “Uncertainty in river discharge observations: A quantitative analysis.” Hydrol. Earth Syst. Sci., 13(6), 913–921.
Doorenbos, J., et al. (1998). “Guidelines for predicting crop water requirements.” FAO Irrigation and Drainage Paper, Food and Agriculture Organization of the United Nations, Rome, Italy.
Ebtehaj, M., Moradkhani, H., and Gupta, H. V. (2010). “Improving robustness of hydrologic parameter estimation by the use of moving block bootstrap resampling.” Water Resour. Res., 46(7), W07515.
Franchini, M. (1996). “Use of a genetic algorithm combined with a local search method for the automatic calibration of conceptual rainfall-runoff models.” Hydrol. Sci. J., 41(1), 21–39.
Friedman, J. H., Bentley, J. L., and Finkel, R. A. (1977). “An algorithm for finding best matches in logarithmic expected time.” ACM Trans. Math. Software, 3(3), 209–226.
Gupta, H. V., Clark, M. P., Vrugt, J. A., Abramowitz, G., and Ye, M. (2012). “Towards a comprehensive assessment of model structural adequacy.” Water Resour. Res., 48(8), W08301.
Gupta, M. R., and Mortensen, W. H. (2009). “Weighted nearest neighbor classifiers and first-order error.”, Dept. of Electrical Engineering, Univ. of Washington, Seattle, WA.
Hajebi, K., Abbasi-Yadkori, Y., Shahbazi, H., and Zhang, H. (2011). “Fast approximate nearest-neighbor search with -nearest neighbor graph.” Proc., 22nd Int. Joint Conf. Artificial Intelligence-Vol. Two, AAAI Press, Palo Alto, CA, 1312–1317.
Hastie, T., Tibshirani, R., and Friedman, J. (2009). Elements of statistical learning: Data mining, inference, and prediction, Springer Science Business Media, LLC.
He, X., Refsgaard, J. C., Sonnenborg, T. O., Vejen, F., and Jensen, K. H. (2011). “Statistical analysis of the impact of radar rainfall uncertainties on water resources modeling.” Water Resour. Res., 47(9), W09526.
Karlsson, M., and Yakowitz, S. (1987a). “Nearest-neighbor methods for nonparametric rainfall-runoff forecasting.” Water Resour. Res., 23(7), 1300–1308.
Karlsson, M., and Yakowitz, S. (1987b). “Rainfall-runoff forecasting methods, old and new.” Stoch. Hydrol. Hydraul., 1(4), 303–318.
Koutsoyiannis, D. (2013). “Hydrology and change.” Hydrol. Sci. J., 58(6), 1177–1197.
Koutsoyiannis, D., Yao, H., and Georgakakos, A. (2008). “Medium-range flow prediction for the Nile: A comparison of stochastic and deterministic methods.” Hydrol. Sci. J., 53(1), 142–164.
Krueger, T., et al. (2010). “Ensemble evaluation of hydrological model hypotheses.” Water Resour. Res., 46(7), W07516.
Krzysztofowicz, R. (2002). “Bayesian system for probabilistic river stage forecasting.” J. Hydrol., 268(1–4), 16–40.
Laio, F., and Tamea, S. (2007). “Verification tools for probabilistic forecasts of continuous hydrological variables.” Hydrol. Earth Syst. Sci. Disc., 11(4), 1267–1277.
Legleiter, C. J., Kyriakidis, P. C., McDonald, R. R., and Nelson, J. M. (2011). “Effects of uncertain topographic input data on two-dimensional flow modeling in a gravel-bed river.” Water Resour. Res., 47(3), W03518.
Liu, T., Moore, A. W., Gray, A., and Yang, K. (2004). “An investigation of practical approximate nearest neighbor algorithms.” Adv. Neural Inf. Process. Syst., 17, 825–832.
Liu, Y., Freer, J., Beven, K., and Matgen, P. (2009). “Towards a limits of acceptability approach to the calibration of hydrological models: Extending observation error.” J. Hydrol., 367(1–2), 93–103.
Mantovan, P., and Todini, E. (2006). “Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology.” J. Hydrol., 330(1–2), 368–381.
McMillan, H., Freer, J., Pappenberger, F., Krueger, T., and Clark, M. (2010). “Impacts of uncertain river flow data on rainfall-runoff model calibration and discharge predictions.” Hydrol. Processes, 24(10), 1270–1284.
McMillan, H., Jackson, B., Clark M., Kavetski, D., and Woods, R. (2011). “Rainfall uncertainty in hydrological modelling: An evaluation of multiplicative error models Mendeley.” J. Hydrol., 400(1–2), 83–94.
Mendoza, P. A., McPhee, J., and Vargas, X. (2012). “Uncertainty in flood forecasting: A distributed modeling approach in a sparse data catchment.” Water Resour. Res., 48(9), W09532.
Mitchell, T. M. (1998). Machine learning, McGraw-Hill, New York.
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. (2011). “Uncertainty of hydrological predictions.” Treatise on water science, Peter Wilderer, ed., Oxford Academic Press, Oxford, U.K., 459–478.
Montanari, A., et al. (2013). “‘Panta Rhei—Everything flows’: Change in hydrology and society—The IAHS scientific decade 2013–2022.” Hydrol. Sciences J., 58(6), 1256–1275.
Montanari, A., and Brath, A. (2004). “A stochastic approach for assessing the uncertainty of rainfall-runoff simulations.” Water Resour. Res., 40(1), W01106.
Montanari, A., and Di Baldassarre, G. (2013). “Data errors and hydrological modelling: The role of model structure to propagate observation uncertainty.” Adv. Water Resour., 51, 498–505.
Montanari, A., and Grossi, G. (2008). “Estimating the uncertainty of hydrological forecasts: A statistical approach.” Water Resour. Res., 44(12), W00B08.
Montanari, A., and Koutsoyiannis, D. (2012). “A blueprint for process-based modeling of uncertain hydrological systems.” Water Resour. Res., 48(9), W09555.
Montanari, A., Rosso, R., and Taqqu, M. S. (1997). “Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation.” Water Resour. Res., 33(5), 1035–1044.
Moretti, G., and Montanari, A. (2008). “Inferring the flood frequency distribution for an ungauged basin using a spatially distributed rainfall-runoff model.” Hydrol. Earth Syst. Sci., 12(4), 1141–1152.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models. Part-I: A discussion of principles.” J. Hydrol., 10(3), 282–290.
Neuman, S. P. (2003). “Maximum likelihood Bayesian averaging of uncertain model predictions.” Stochastic Env. Res. Risk Assessment, 17(5), 291–305.
Pianosi, F., and Raso, L. (2012). “Dynamic modeling of predictive uncertainty by regression on absolute errors.” Water Resour. Res., 48(3), W03516.
Renard, B., Kavetski, D., Leblois, M., Thyer, M., Kuczera, G., and Franks, S. W. (2011). “Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation.” Water Resour. Res., 47(11), W11516.
Schoups, G., and Vrugt, J. A. (2010). “A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and nonGaussian errors.” Water Resour. Res., 46(10), W10531.
Shrestha, D. L., Kayastha, N., and Solomatine, D. P. (2009). “A novel approach to parameter uncertainty analysis of hydrological models using neural networks.” Hydrol. Earth Syst. Sci., 13(7), 1235.
Shrestha, D. L., and Solomatine, D. P. (2006). “Machine learning approaches for estimation of prediction interval for the model output.” Neural Networks, 19(2), 225–235.
Sikorska, A. E. (2012). “Interactive comment on ‘Bayesian uncertainty assessment of flood predictions in ungauged urban basins for conceptual rainfall-runoff models’ by A.E. Sikorska et al.” Hydrol. Earth Syst. Sci. Discuss., 8, C6284–C6310.
Sikorska, A. E., Scheidegger, A., Banasik, K., and Rieckermann, J. (2012). “Bayesian uncertainty assessment of flood predictions in ungauged urban basins for conceptual rainfall-runoff models.” Hydrol. Earth Syst. Sci., 16(4), 1221–1236.
Sikorska, A. E., Scheidegger, A., Banasik, K., and Rieckermann, J. (2013). “Considering rating curve uncertainty in water level predictions.” Hydrol. Earth Syst. Sci., 17, 4415–4427.
Skøien, J. O., Blöschl, G., and Western, A. W. (2003). “Characteristic space scales and timescales in hydrology.” Water Resour. Res., 39(10), 1304.
Srikanthan, R., Kuczera, G., and Thyer, M. (2009). “‘Calibrate it twice’: A simple resampling method for incorporating parameter uncertainty in stochastic data generation.” Proc., H2O 09: 32nd Hydrology and Water Resources Symp., A.C.T. Engineers, Newcastle, NSW, Australia, 1028–1039.
Sun, S., and Bertrand-Krajewski, J-L. (2013). “Separately accounting for uncertainties in rainfall and runoff: Calibration of event based conceptual hydrological models in small urban catchments using Bayesian method.” Water Resour. Res., 49(9), 5381–5394.
Tada, T., and Beven, K. J. (2012). “Hydrological model calibration using a short period of observations.” Hydrol. Processes, 26(6), 883–892.
Toth, E., Montanari, A., and Brath, A. (1999). “Real-time flood forecasting via combined use of conceptual and stochastic models.” Physics Chemistry Earth, 24(7), 793–798.
Vrugt, J. A., and Robinson, B. A. (2007). “Improved evolutionary optimization from genetically adaptive multimethod search.” Proc. National Acad. Sci., 104(3), 708–711.
Vrugt, J. A., and Ter Braak, C. J. F. (2011). “DREAM(D): An adaptive markov chain monte carlo simulation algorithm to solve discrete, noncontinuous, and combinatorial posterior parameter estimation problems.” Hydrol. Earth Syst. Sci., 15, 3701–3713.
Winsemius, H. C., Savenije, H. H. G., and Bastiaanssen, W. G. M. (2008). “Constraining model parameters on remotely sensed evaporation: Justification for distribution in ungauged basins?” Hydrol. Earth Syst. Sci., 12(6), 1403–1413.
Winsemius, H. C., Savenije, H. H. G., Gerrits, A. M. J., Zapreeva, E. A., and Klees, R. (2006). “Comparison of two model approaches in the Zambezi River basin with regard to model reliability and identifiability.” Hydrol. Earth Syst. Sci., 10(3), 339–352.
Winsemius, H. C., Schaefli, B., Montanari, A., and Savenije, H. H. G. (2009). “On the calibration of hydrological models in ungauged basins: A framework for integrating hard and soft hydrological information.” Water Resour. Res., 45(12), W12422.
Yang, J., Reichert, P., Abbaspour, K. C., and Yang, H. (2007). “Hydrological modelling of the Chaohe basin in China: Statistical model formulation and Bayesian inference.” J. Hydrol., 340(3–4), 167–182.
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Journal of Hydrologic Engineering
Volume 20 • Issue 1 • January 2015
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© 2014 American Society of Civil Engineers.
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Received: Dec 20, 2012
Accepted: Oct 22, 2013
Published online: Jun 30, 2014
Discussion open until: Nov 30, 2014
Published in print: Jan 1, 2015
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