Abstract
Flood information, especially extreme flood, is necessary for any large hydraulic structure design and flood risk management. Flood mitigation also requires a comprehensive assessment of flood risk and an explicit quantification of the flood uncertainty. In the present study, we use a multimodel ensemble approach based on Bayesian model averaging (BMA) method to account for model structure and distribution uncertainties. The usefulness of this approach is assessed by a case study over the Willamette River Basin (WRB) in Pacific Northwest, USA. Besides the standard log-Pearson Type III distribution, we also identified that the generalized extreme value and three-parameter lognormal distributions were both potential distributions in WRB. Three different statistical models, including the Bulletin-17B quantile model, index-flood model, and spatial Bayesian hierarchical model, were considered in the study. The BMA method is then used to assign weights to different models, where better performing model receives higher weights. It was found that the major uncertainty in extreme flood prediction is contributed by model structure, while the choice of distribution plays a lesser important role in quantification of flood uncertainty. The BMA approach provides a more robust extreme flood prediction than any single model.
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References
Baker JP, Hulse DW, Gregory SV et al (2004) Alternative futures for the Willamette River Basin, Oregon. Ecol Appl 14:313–324. doi:10.1890/02-5011
Banerjee S, Carlin BP, Gelfand AE (2014) Hierarchical modeling and analysis for spatial data. CRC Press, Boca Raton
Cheng L, AghaKouchak A (2014) Nonstationary precipitation intensity–duration–frequency curves for infrastructure design in a changing climate. Sci Rep 4:7093. doi:10.1038/srep07093
Cheng L, AghaKouchak A, Gilleland E, Katz RW (2014) Non-stationary extreme value analysis in a changing climate. Clim Change 127:353–369. doi:10.1007/s10584-014-1254-5
Cohn TA, England JF, Berenbrock CE et al (2013) A generalized Grubbs-Beck test statistic for detecting multiple potentially influential low outliers in flood series. Water Resour Res 49:5047–5058
Coles S, Pericchi L (2003) Anticipating catastrophes through extreme value modelling. J R Stat Soc Ser C Appl Stat 52:405–416. doi:10.1111/1467-9876.00413
Cooley D, Sain SR (2010) Spatial hierarchical modeling of precipitation extremes from a regional climate model. J Agric Biol Environ Stat 15:381–402. doi:10.1007/s13253-010-0023-9
Cooley D, Nychka D, Naveau P (2007) Bayesian spatial modeling of extreme precipitation return levels. J Am Stat As 102:824–840
Cooper RM (2005) Estimation of peak discharges for rural, unregulated streams in Western Oregon. US Department of the Interior, US Geological Survey, Reston
Dalrymple T (1960) Flood-frequency analyses, manual of hydrology: Part 3. USGPO, Washington
Dawdy DR, Griffis VW, Gupta VK (2012) Regional flood-frequency analysis: how we got here and where we are going. J Hydrol Eng 17:953–959
DeChant CM, Moradkhani H (2014a) Hydrologic prediction and uncertainty quantification, handbook of engineering hydrology, modeling, climate change and variability. CRC Press, Taylor and Francis Group, Boca Raton, pp 387–414
DeChant CM, Moradkhani H (2014b) Toward a reliable prediction of seasonal forecast uncertainty: addressing model and initial condition uncertainty with ensemble data assimilation and Sequential Bayesian Combination. J Hydrol 519:2967–2977
Duan Q, Ajami N, Gao X, Sorooshian S (2007) Multi-model ensemble hydrologic prediction using Bayesian model averaging. Adv Water Resour 30:1371–1386. doi:10.1016/j.advwatres.2006.11.014
Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7:1–26
Fawcett L, Walshaw D (2006) A hierarchical model for extreme wind speeds. J R Stat Soc Ser C Appl Stat 55:631–646. doi:10.1111/j.1467-9876.2006.00557.x
Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Am Stat As 85:398–409. doi:10.1080/01621459.1990.10476213
Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7:457–472
Gelman A, Carlin JB, Stern HS, Rubin DB (2014) Bayesian data analysis. Taylor & Francis, London
Gilroy KL, McCuen RH (2012) A nonstationary flood frequency analysis method to adjust for future climate change and urbanization. J Hydrol 414–415:40–48. doi:10.1016/j.jhydrol.2011.10.009
Griffis VW, Stedinger JR (2007) The use of GLS regression in regional hydrologic analyses. J Hydrol 344:82–95. doi:10.1016/j.jhydrol.2007.06.023
Griffis VW, Stedinger JR (2009) Log-Pearson Type 3 distribution and its application in flood frequency analysis. III: Sample skew and weighted skew estimators. J Hydrol Eng 14:121–130
Griffis VW, Stedinger JR, Cohn TA (2004) Log Pearson type 3 quantile estimators with regional skew information and low outlier adjustments. Water Resour Res 40. doi:10.1029/2003WR002697
Gruber AM, Reis DS Jr, Stedinger JR (2007) Models of regional skew based on Bayesian GLS regression. World Environ Water Resour Congr 2007:1–10
Gupta VK, Mesa OJ, Dawdy DR (1994) Multiscaling theory of flood peaks: regional quantile analysis. Water Resour Res 30:3405
Hastings WK (1970) Monte carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109. doi:10.1093/biomet/57.1.97
Hazen A (1914) Discussion on “Flood flows” by WE Fuller. Trans ASCE 77:526–563
Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser C Appl Stat 52:105–124. doi:10.2307/2345653
Hosking JRM, Wallis JR (1988) The effect of intersite dependence on regional flood frequency analysis. Water Resour Res 24:588–600
Hosking JRM, Wallis JR (2005) Regional frequency analysis: an approach based on L-moments. Cambridge University Press, Cambridge
Hsu KL, Moradkhani H, Sorooshian S (2009) A sequential Bayesian approach for hydrologic model selection and prediction. Water Resour Res. doi:10.1029/2008WR006824
Katz RW, Parlange MB, Naveau P (2002) Statistics of extremes in hydrology. Adv Water Resour 25:1287–1304. doi:10.1016/S0309-1708(02)00056-8
Kroll CN, Vogel RM (2002) Probability distribution of low streamflow series in the United States. J Hydrol Eng 7:137–146
Kwon H-H, Brown C, Lall U (2008) Climate informed flood frequency analysis and prediction in Montana using hierarchical Bayesian modeling. Geophys Res Lett 35. doi:10.1029/2007GL032220
Lavers DA, Villarini G, Allan RP, Wood EF, Wade AJ (2012) The detection of atmospheric rivers in atmospheric reanalyses and their links to British winter floods and the large-scale climatic circulation. J Geophys Res: Atmos (1984–2012) 117. doi:10.1029/2012JD018027
Lettenmaier DP, Wallis JR, Wood EF (1987) Effect of regional heterogeneity on flood frequency estimation. Water Resour Res 23:313–323
Lima CHR, Lall U (2010) Spatial scaling in a changing climate: a hierarchical bayesian model for non-stationary multi-site annual maximum and monthly streamflow. J Hydrol 383:307–318. doi:10.1016/j.jhydrol.2009.12.045
Madadgar S, Moradkhani H (2014) Improved Bayesian multimodeling: integration of copulas and Bayesian model averaging. Water Resour Res 50:9586–9603
Martins ES, Stedinger JR (2000) Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resour Res 36:737–744. doi:10.1029/1999WR900330
McCuen RH (1979) Map skew. J Water Resour Plan Manag Div 105:269–277
McCuen RH (2001) Generalized flood skew: map versus watershed skew. J Hydrol Eng 6:293–299
Milly PCD, Betancourt J, Falkenmark M et al (2008) Climate change. Stationarity is dead: whither water management? Science 319:573–574. doi:10.1126/science.1151915
Moradkhani H, Hsu K-L, Gupta H, Sorooshian S (2005) Uncertainty assessment of hydrologic model states and parameters: sequential data assimilation using the particle filter. Water Resour Res 41:W05012. doi:10.1029/2004WR003604
Moradkhani H, Dechant CM, Sorooshian S (2012) Evolution of ensemble data assimilation for uncertainty quantification using the particle filter-Markov chain Monte Carlo method. Water Resour Res 48:W12520. doi:10.1029/2012WR012144
Najafi MR, Moradkhani H (2013) Analysis of runoff extremes using spatial hierarchical Bayesian modeling. Water Resour Res 49:6656–6670. doi:10.1002/wrcr.20381
Najafi MR, Moradkhani H (2014) A hierarchical Bayesian approach for the analysis of climate change impact on runoff extremes. Hydrol Process 28:6292–6308
Najafi MR, Moradkhani H (2015a) Ensemble combination of seasonal streamflow forecasts. J Hydrol Eng. doi:10.1061/(ASCE)HE.1943-5584.0001250
Najafi MR, Moradkhani H (2015b) Multi-model ensemble analysis of runoff extremes for climate change impact assessments. J Hydrol 525:352–361. doi:10.1016/j.jhydrol.2015.03.045
Najafi MR, Moradkhani H, Jung IW (2011) Assessing the uncertainties of hydrologic model selection in climate change impact studies. Hydrol Process 25:2814–2826. doi:10.1002/hyp.8043
Nakamura J, Lall U, Kushnir Y, Robertson AW, Seager R (2013) Dynamical structure of extreme floods in the US Midwest and the United Kingdom. J Hydrometeorol 14:485–504
Padoan SA, Ribatet M, Sisson SA (2010) Likelihood-based inference for max-stable processes. J Am Stat As 105:263–277
Parrish MA, Moradkhani H, Dechant CM (2012) Toward reduction of model uncertainty: integration of Bayesian model averaging and data assimilation. Water Resour Res. doi:10.1029/2011WR011116
Prudhomme C, Genevier M (2011) Can atmospheric circulation be linked to flooding in Europe? Hydrol Process 25:1180–1190. doi:10.1002/hyp.7879
Raftery AE, Gneiting T, Balabdaoui F, Polakowski M (2005) Using Bayesian model averaging to calibrate forecast ensembles. Mon Weather Rev 133:1155–1174
Reis DS, Stedinger JR (2005). Bayesian MCMC flood frequency analysis with historical information. J Hydrol 313:97–116
Reis DS, Stedinger JR, Martins ES (2005) Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation. Water Resour Res. doi:10.1029/2004WR003445
Renard B (2011) A Bayesian hierarchical approach to regional frequency analysis. Water Resour Res. doi:10.1029/2010WR010089
Renard B, Lall U (2014) Regional frequency analysis conditioned on large-scale atmospheric or oceanic fields. Water Resour Res 50:9536–9554
Renard B, Sun X, Lang M (2013) Bayesian methods for non-stationary extreme value analysis. In: AghaKouchak A, Easterling D, Hsu K, Schubert S, Sorooshian S (eds) Extremes in a changing climate, water science and technology library, vol 65. Springer, Netherlands, pp 39–95
Ribatet M, Sauquet E, Grésillon JM, Ouarda TBMJ (2007) A regional Bayesian POT model for flood frequency analysis. Stoch Environ Res Risk Assess 21:327–339. doi:10.1007/s00477-006-0068-z
Robinson JS, Sivapalan M (1997) An investigation into the physical causes of scaling and heterogeneity of regional flood frequency. Water Resour Res 33:1045
Schaefer MG (1990) Regional analyses of precipitation annual maxima in Washington State. Water Resour Res 26:119–131
Schoups G, Vrugt JA (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. doi:10.1029/2009WR008933
Stedinger JR (1983) Estimating a regional flood frequency distribution. Water Resour Res 19:503–510
Stedinger JR, Griffis VW (2008) Flood frequency analysis in the United States: time to update. J Hydrol Eng 13:199–204
Stedinger JR, Tasker GD (1985) Regional hydrologic analysis. 1. Ordinary, weighted, and generalized least-squares compared. Water Resour Res 21:1421–1432. doi:10.1029/WR022i005p00844
Stedinger JR, Tasker GD (1986) Regional hydrologic analysis, 2, model-error estimators, estimation of sigma and log-Pearson Type 3 distributions. Water Resour Res 22:1487–1499. doi:10.1029/WR022i010p01487
Tasker GD, Stedinger JR (1986) Regional skew with weighted LS regression. J Water Resour Plan Manag 112:225–237
Tasker GD, Stedinger JR (1989) An operational GLS model for hydrologic regression. J Hydrol 111:361–375
Towler E, Rajagopalan B, Gilleland E et al (2010) Modeling hydrologic and water quality extremes in a changing climate: a statistical approach based on extreme value theory. Water Resour Res. doi:10.1029/2009WR008876
U.S. Water Resources Council (1982) Guidelines for determining flood flow frequency. Bulletin 17B, Hydrology Subcommittee, Office of Water Data Coordination, US Geological Survey, Reston, Virginia
Viglione A, Merz R, Salinas JL, Blöschl G (2013) Flood frequency hydrology: 3. A Bayesian analysis. Water Resour Res 49:675–692
Vogel RM, Fennessey NM (1993) L moment diagrams should replace product moment diagrams. Water Resour Res 29:1745–1752
Vogel RM, Wilson I (1996) Probability distribution of annual maximum, mean, and minimum streamflows in the United States. J Hydrol Eng 1:69–76
Vogel RM, McMahon TA, Chiew FHS (1993) Floodflow frequency model selection in Australia. J Hydrol 146:421–449
Wang Z, Yan J, Zhang X (2014) Incorporating spatial dependence in regional frequency analysis. Water Resour Res 50:9570–9585
Weigel AP, Liniger MA, Appenzeller C (2008) Can multi-model combination really enhance the prediction skill of probabilistic ensemble forecasts? Q J R Meteorol Soc 134:241–260
Yan H (2012) Magnitude and frequency of floods for rural, unregulated streams of Tennessee by L-moments method. University of Arkansas, Fayetteville
Yan H, Edwards FG (2013) Effects of land use change on hydrologic response at a watershed scale, Arkansas. J Hydrol Eng 18:1779–1785. doi:10.1061/(ASCE)HE.1943-5584.0000743
Yan H, Moradkhani H (2015) A regional Bayesian hierarchical model for flood frequency analysis. Stoch Environ Res Risk Assess 29:1019–1036. doi:10.1007/s00477-014-0975-3
Yan H, DeChant CM, Moradkhani H (2015) Improving soil moisture profile prediction with the particle filter-Markov chain Monte Carlo method. IEEE Trans Geosci Remote Sens 53:6134–6147. doi:10.1109/TGRS.2015.2432067
Yue S, Wang CY (2004) Possible regional probability distribution type of Canadian annual streamflow by L-moments. Water Resour Manag 18:425–438
Zhang Q, Gu X, Singh VP et al (2015) Evaluation of flood frequency under non-stationarity resulting from climate indices and reservoir indices in the East River basin, China. J Hydrol 527:565–575. doi:10.1016/j.jhydrol.2015.05.029
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Partial financial support for this project was provided by the National Science Foundation, Water Sustainability and Climate (WSC) program (Grant No. EAR-1038925).
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Yan, H., Moradkhani, H. Toward more robust extreme flood prediction by Bayesian hierarchical and multimodeling. Nat Hazards 81, 203–225 (2016). https://doi.org/10.1007/s11069-015-2070-6
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DOI: https://doi.org/10.1007/s11069-015-2070-6