Abstract
Various hydrologic models with different complexities have been developed to represent the characteristics of river basins, improve streamflow forecasts such as seasonal volumetric flow predictions, and meet other demands from different stakeholders. Because no single hydrologic model is able to perfectly simulate the observed flow, multimodel combination techniques are developed to combine forecasts obtained from different models and to quantify the uncertainties with the goal of improving upon single-model performance. In this study, a comprehensive set of multimodel ensemble averaging techniques with varying complexities are investigated for operational forecasting over four river basins in the Western United States. Ensemble merging models are divided into three categories of simple, intermediate, and complex, and comparison is made between each class by using a bootstrap approach. Analysis suggests that model combination effectively improves most of the individual seasonal forecasts and can outperform the best forecast model. Simple average, median, Bates-Granger, constrained linear regression, and Bayesian model averaging optimized by expectation maximization showed better results compared with other methods over three basins. For the Rogue River basin, the intermediate and complex models outperformed most of the individual forecasts and the simple methods. Multimodeling techniques based on information criteria showed similar performances.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Partial financial support for this work was provided by NOAA-CSTAR Grant No. NA11NWS4680002. The authors would also like to thank Andrew Wood from the NWRFC, David Garen from USDA-NRCS, and Randal Wortman from USACE for providing the data sets and individual model results used in this study.
References
Ajami, N. K., Duan, Q., Gao, X., and Sorooshian, S. (2006). “Multimodel combination techniques for analysis of hydrological simulations: Application to distributed model intercomparison project results.” J. Hydrometeorol., 7(4), 755–768.
Bates, J. M., and Granger, C. W. J. (1969). “The combination of forecasts.” OR, 20(4), 451–468.
Beyene, T., Lettenmaier, D. P., and Kabat, P. (2010). “Hydrologic impacts of climate change on the Nile River basin: Implications of the 2007 IPCC scenarios.” Clim. Change, 100(3–4), 433–461.
Bohn, T. J., Sonessa, M. Y., and Lettenmaier, D. P. (2010). “Seasonal hydrologic forecasting: Do multimodel ensemble averages always yield improvements in forecast skill?” J. Hydrometeorol., 11(6), 1358–1372.
Burnham, K. P., and Anderson, D. R. (2002). Model selection and multi-model inference: A practical information—Theoretic approach, Springer.
Buser, C., Künsch, H., and Schär, C. (2010). “Bayesian multi-model projections of climate: Generalization and application to ENSEMBLES results.” Clim. Res., 44(2–3), 227–241.
Butts, M. B., Payne, J. T., Kristensen, M., and Madsen, H. (2004). “An evaluation of the impact of model structure on hydrological modelling uncertainty for streamflow simulation.” J. Hydrol., 298(1), 242–266.
Cayan, D. R., Kammerdiener, S. A., Dettinger, M. D., Caprio, J. M., and Peterson, D. H. (2001). “Changes in the onset of spring in the western United States.” Bull. Am. Meteorol. Soc., 82(3), 399–415.
Day, G. N. (1985). “Extended streamflow forecasting using NWSRFS.” J. Water Resour. Plann. Manage., 157–170.
Dechant, C., and Moradkhani, H. (2011). “Radiance data assimilation for operational snow and streamflow forecasting.” Adv. Water Resour., 34(3), 351–364.
DeChant, C. M., and Moradkhani, H. (2014a). Hydrologic prediction and uncertainty quantification, handbook of engineering hydrology, modeling, climate change and variability, CRC Press, Taylor & Francis Group, 387–414.
DeChant, C. M., and 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.
Dickinson, J. (1973). “Some statistical results in the combination of forecasts.” J. Oper. Res. Soc., 24(2), 253–260.
Dickinson, J. (1975). “Some comments on the combination of forecasts.” Oper. Res. Q., 26(1), 205–210.
Diks, C. G., and Vrugt, J. A. (2010). “Comparison of point forecast accuracy of model averaging methods in hydrologic applications.” Stochastic Environ. Res. Risk Assess., 24(6), 809–820.
Duan, Q., Ajami, N. K., Gao, X., and Sorooshian, S. (2007). “Multi-model ensemble hydrologic prediction using Bayesian model averaging.” Adv. Water Resour., 30(5), 1371–1386.
Georgakakos, K. P., Seo, D.-J., Gupta, H., Schaake, J., and Butts, M. B. (2004). “Towards the characterization of streamflow simulation uncertainty through multimodel ensembles.” J. Hydrol., 298(1), 222–241.
Gupta, H. V., Kling, H., Yilmaz, K. K., and Martinez, G. F. (2009). “Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling.” J. Hydrol., 377(1), 80–91.
Hagedorn, R., Doblas-Reyes, F. J., and Palmer, T. (2005). “The rationale behind the success of multi-model ensembles in seasonal forecasting—I. Basic concept.” Tellus A, 57(3), 219–233.
Halmstad, A., Najafi, M. R., and Moradkhani, H. (2013). “Analysis of precipitation extremes with the assessment of regional climate models over the Willamette River basin, USA.” Hydrol. Process., 27(18), 2579–2590.
Hamlet, A. F., Mote, P. W., Clark, M. P., and Lettenmaier, D. P. (2005). “Effects of temperature and precipitation variability on snowpack trends in the western United States.” J. Clim., 18(21), 4545–4561.
Hurvich, C. M., and Tsai, C.-L. (1989). “Regression and time series model selection in small samples.” Biometrika, 76(2), 297–307.
Jiang, W., and Simon, R. (2007). “A comparison of bootstrap methods and an adjusted bootstrap approach for estimating the prediction error in microarray classification.” Stat. Med., 26(29), 5320–5334.
Li, H., Luo, L., Wood, E. F., and Schaake, J. (2009). “The role of initial conditions and forcing uncertainties in seasonal hydrologic forecasting.” J. Geophys. Res. Atmos., 114(D4), 1984–2012.
MacCullagh, P., and Nelder, J. A. (1989). Generalized linear models, CRC.
Madadgar, S., and Moradkhani, H. (2014). “Improved Bayesian multimodeling: Integration of copulas and Bayesian model averaging.” Water Resour. Res., 50(12), 9586–9603.
Mallows, C. L. (1995). “More comments on .” Technometrics, 37(4), 362–372.
Moradkhani, H., and Meier, M. (2010). “Long-lead water supply forecast using large-scale climate predictors and independent component analysis.” J. Hydrol. Eng., 744–762.
Mote, P. W., and Salathe, E. P., Jr. (2010). “Future climate in the Pacific Northwest.” Clim. Change, 102(1–2), 29–50.
Najafi, M., Moradkhani, H., and Jung, I. (2011a). “Assessing the uncertainties of hydrologic model selection in climate change impact studies.” Hydrol. Processes, 25(18), 2814–2826.
Najafi, M. R., Kavianpour, Z., Najafi, B., Kavianpour, M. R., and Moradkhani, H. (2011b). “Air demand in gated tunnels—A Bayesian approach to merge various predictions.” J. Hydroinf., 14(1), 152–166.
Najafi, M. R., and Moradkhani, H. (2013). “Analysis of runoff extremes using spatial hierarchical Bayesian modeling.” Water Resour. Res., 49(10), 6656–6670.
Najafi, M. R., and Moradkhani, H. (2014). “A hierarchical Bayesian approach for the analysis of climate change impact on runoff extremes.” Hydrol. Processes, 28(26), 6292-6308.
Najafi, M. R., and Moradkhani, H. (2015). “Multi-model ensemble analysis of runoff extremes for climate change impact assessments.” J. Hydrol., 525, 352–361.
Najafi, M. R., Moradkhani, H., and Piechota, T. C. (2012). “Ensemble streamflow prediction: Climate signal weighting methods vs. climate forecast system reanalysis.” J. Hydrol., 442, 105–116.
Najafi, M. R., Moradkhani, H., and Wherry, S. A. (2010). “Statistical downscaling of precipitation using machine learning with optimal predictor selection.” J. Hydrol. Eng., 650–664.
Najafi, M. R., Zwiers, F. P., and Gillett, N. P. (2015). “Attribution of Arctic temperature change to greenhouse-gas and aerosol influences.” Nat. Clim. Change, 5, 246–249.
Newbold, P., and Granger, C. W. (1974). “Experience with forecasting univariate time series and the combination of forecasts.” J. R. Stat. Soc. Ser. A (General), 137(2), 131–165.
Parrish, M. A., Moradkhani, H., and DeChant, C. M. (2012). “Toward reduction of model uncertainty: Integration of Bayesian model averaging and data assimilation.” Water Resour. Res., 48(3), W03519.
Raftery, A. E. (1995). “Bayesian model selection in social research.” Sociological Method., 25, 111–164.
Raftery, A. E., Gneiting, T., Balabdaoui, F., and Polakowski, M. (2005). “Using Bayesian model averaging to calibrate forecast ensembles.” Mon. Weather Rev., 133(5), 1155–1174.
Raftery, A. E., Madigan, D., and Hoeting, J. A. (1997). “Bayesian model averaging for linear regression models.” J. Am. Stat. Assoc., 92(437), 179–191.
Reid, D. J. (1968). “Combining three estimates of gross domestic product.” Economica, 35(140), 431–444.
Shamseldin, A. Y., O’Connor, K. M., and Liang, G. (1997). “Methods for combining the outputs of different rainfall-runoff models.” J. Hydrol., 197(1–4), 203–229.
Tebaldi, C., and Knutti, R. (2007). “The use of the multi-model ensemble in probabilistic climate projections.” Philos. Trans. R. Soc. London, Ser. A, 365(1857), 2053–2075.
Twedt, T. M., Shaake, J. C., and Peck, E. L. (1977). “National weather service extended streamflow prediction.”, Hydrologic Research Laboratory, Silver Spring, MD.
Vicuña, S., Garreaud, R. D., and McPhee, J. (2011). “Climate change impacts on the hydrology of a snowmelt driven basin in semiarid Chile.” Clim. Change, 105(3–4), 469–488.
Viney, N. R., et al. (2009). “Assessing the impact of land use change on hydrology by ensemble modelling (LUCHEM) II: Ensemble combinations and predictions.” Adv. Water Resour., 32(2), 147–158.
Vrugt, J. A., Ter Braak, C., Diks, C., Robinson, B. A., Hyman, J. M., and Higdon, D. (2009). “Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling.” Int. J. Nonlinear Sci. Numer. Simul., 10(3), 273–290.
Weigel, A., Liniger, M., and Appenzeller, C. (2008). “Can multi-model combination really enhance the prediction skill of probabilistic ensemble forecasts?” Q. J. R. Meteorolog. Soc., 134(630), 241–260.
Wood, A. W., and Lettenmaier, D. P. (2006). “A test bed for new seasonal hydrologic forecasting approaches in the western United States.” Bull. Am. Meteorolog. Soc., 87(12), 1699–1712.
Wood, A. W., and Schaake, J. C. (2008). “Correcting errors in streamflow forecast ensemble mean and spread.” J. Hydrometeorol., 9(1), 132–148.
Xiong, L., Shamseldin, A. Y., and O’connor, K. M. (2001). “A non-linear combination of the forecasts of rainfall-runoff models by the first-order Takagi-Sugeno fuzzy system.” J. Hydrol., 245(1), 196–217.
Information & Authors
Information
Published In
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jul 29, 2014
Accepted: Apr 10, 2015
Published online: Jun 5, 2015
Discussion open until: Nov 5, 2015
Published in print: Jan 1, 2016
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.