Skip to main content

Advertisement

Log in

Toward more robust extreme flood prediction by Bayesian hierarchical and multimodeling

  • Original Paper
  • Published:
Natural Hazards Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

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

    Article  Google Scholar 

  • Banerjee S, Carlin BP, Gelfand AE (2014) Hierarchical modeling and analysis for spatial data. CRC Press, Boca Raton

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Cooley D, Nychka D, Naveau P (2007) Bayesian spatial modeling of extreme precipitation return levels. J Am Stat As 102:824–840

    Article  Google Scholar 

  • Cooper RM (2005) Estimation of peak discharges for rural, unregulated streams in Western Oregon. US Department of the Interior, US Geological Survey, Reston

    Google Scholar 

  • Dalrymple T (1960) Flood-frequency analyses, manual of hydrology: Part 3. USGPO, Washington

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Book  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7:1–26

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7:457–472

    Article  Google Scholar 

  • Gelman A, Carlin JB, Stern HS, Rubin DB (2014) Bayesian data analysis. Taylor & Francis, London

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Gupta VK, Mesa OJ, Dawdy DR (1994) Multiscaling theory of flood peaks: regional quantile analysis. Water Resour Res 30:3405

    Article  Google Scholar 

  • Hastings WK (1970) Monte carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109. doi:10.1093/biomet/57.1.97

    Article  Google Scholar 

  • Hazen A (1914) Discussion on “Flood flows” by WE Fuller. Trans ASCE 77:526–563

    Google Scholar 

  • 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

    Google Scholar 

  • Hosking JRM, Wallis JR (1988) The effect of intersite dependence on regional flood frequency analysis. Water Resour Res 24:588–600

    Article  Google Scholar 

  • Hosking JRM, Wallis JR (2005) Regional frequency analysis: an approach based on L-moments. Cambridge University Press, Cambridge

    Google Scholar 

  • Hsu KL, Moradkhani H, Sorooshian S (2009) A sequential Bayesian approach for hydrologic model selection and prediction. Water Resour Res. doi:10.1029/2008WR006824

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Kroll CN, Vogel RM (2002) Probability distribution of low streamflow series in the United States. J Hydrol Eng 7:137–146

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Madadgar S, Moradkhani H (2014) Improved Bayesian multimodeling: integration of copulas and Bayesian model averaging. Water Resour Res 50:9586–9603

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • McCuen RH (1979) Map skew. J Water Resour Plan Manag Div 105:269–277

    Google Scholar 

  • McCuen RH (2001) Generalized flood skew: map versus watershed skew. J Hydrol Eng 6:293–299

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Najafi MR, Moradkhani H (2014) A hierarchical Bayesian approach for the analysis of climate change impact on runoff extremes. Hydrol Process 28:6292–6308

    Article  Google Scholar 

  • Najafi MR, Moradkhani H (2015a) Ensemble combination of seasonal streamflow forecasts. J Hydrol Eng. doi:10.1061/(ASCE)HE.1943-5584.0001250

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Padoan SA, Ribatet M, Sisson SA (2010) Likelihood-based inference for max-stable processes. J Am Stat As 105:263–277

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Prudhomme C, Genevier M (2011) Can atmospheric circulation be linked to flooding in Europe? Hydrol Process 25:1180–1190. doi:10.1002/hyp.7879

    Article  Google Scholar 

  • Raftery AE, Gneiting T, Balabdaoui F, Polakowski M (2005) Using Bayesian model averaging to calibrate forecast ensembles. Mon Weather Rev 133:1155–1174

    Article  Google Scholar 

  • Reis DS, Stedinger JR (2005). Bayesian MCMC flood frequency analysis with historical information. J Hydrol 313:97–116

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Renard B (2011) A Bayesian hierarchical approach to regional frequency analysis. Water Resour Res. doi:10.1029/2010WR010089

    Google Scholar 

  • Renard B, Lall U (2014) Regional frequency analysis conditioned on large-scale atmospheric or oceanic fields. Water Resour Res 50:9536–9554

    Article  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • 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

    Article  Google Scholar 

  • Robinson JS, Sivapalan M (1997) An investigation into the physical causes of scaling and heterogeneity of regional flood frequency. Water Resour Res 33:1045

    Article  Google Scholar 

  • Schaefer MG (1990) Regional analyses of precipitation annual maxima in Washington State. Water Resour Res 26:119–131

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Stedinger JR, Griffis VW (2008) Flood frequency analysis in the United States: time to update. J Hydrol Eng 13:199–204

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Tasker GD, Stedinger JR (1986) Regional skew with weighted LS regression. J Water Resour Plan Manag 112:225–237

    Article  Google Scholar 

  • Tasker GD, Stedinger JR (1989) An operational GLS model for hydrologic regression. J Hydrol 111:361–375

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Vogel RM, Fennessey NM (1993) L moment diagrams should replace product moment diagrams. Water Resour Res 29:1745–1752

    Article  Google Scholar 

  • Vogel RM, Wilson I (1996) Probability distribution of annual maximum, mean, and minimum streamflows in the United States. J Hydrol Eng 1:69–76

    Article  Google Scholar 

  • Vogel RM, McMahon TA, Chiew FHS (1993) Floodflow frequency model selection in Australia. J Hydrol 146:421–449

    Article  Google Scholar 

  • Wang Z, Yan J, Zhang X (2014) Incorporating spatial dependence in regional frequency analysis. Water Resour Res 50:9570–9585

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Yan H (2012) Magnitude and frequency of floods for rural, unregulated streams of Tennessee by L-moments method. University of Arkansas, Fayetteville

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Yue S, Wang CY (2004) Possible regional probability distribution type of Canadian annual streamflow by L-moments. Water Resour Manag 18:425–438

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

Download references

Acknowledgments

Partial financial support for this project was provided by the National Science Foundation, Water Sustainability and Climate (WSC) program (Grant No. EAR-1038925).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hongxiang Yan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11069-015-2070-6

Keywords

Navigation