Statistical Postprocessing of High-Resolution Regional Climate Model Output

Pablo A. Mendoza Department of Civil, Environmental, and Architectural Engineering and Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and Research Applications Laboratory, National Center for Atmospheric Research, Boulder, Colorado

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Balaji Rajagopalan Department of Civil, Environmental, and Architectural Engineering and Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, Colorado

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Martyn P. Clark Research Applications Laboratory, National Center for Atmospheric Research,* Boulder, Colorado

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Kyoko Ikeda Research Applications Laboratory, National Center for Atmospheric Research,* Boulder, Colorado

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Roy M. Rasmussen Research Applications Laboratory, National Center for Atmospheric Research,* Boulder, Colorado

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Abstract

Statistical postprocessing techniques have become essential tools for downscaling large-scale information to the point scale, and also for providing a better probabilistic characterization of hydrometeorological variables in simulation and forecasting applications at both short and long time scales. In this paper, the authors assess the utility of statistical postprocessing methods for generating probabilistic estimates of daily precipitation totals, using deterministic high-resolution outputs obtained with the Weather Research and Forecasting (WRF) Model. After a preliminary assessment of WRF simulations over a historical period, the performance of three postprocessing techniques is compared: multinomial logistic regression (MnLR), quantile regression (QR), and Bayesian model averaging (BMA)—all of which use WRF outputs as potential predictors. Results demonstrate that the WRF Model has skill in reproducing observed precipitation events, especially during fall/winter. Furthermore, it is shown that the spatial distribution of skill obtained from statistical postprocessing is closely linked with the quality of WRF precipitation outputs. A detailed comparison of statistical precipitation postprocessing approaches reveals that, although the poorest performance was obtained using MnLR, there is not an overall best technique. While QR should be preferred if skill (i.e., small probability forecast errors) and reliability (i.e., match between forecast probabilities and observed frequencies) are target properties, BMA is recommended in cases when discrimination (i.e., prediction of occurrence versus nonoccurrence) and statistical consistency (i.e., equiprobability of the observations within their ensemble distributions) are desired. Based on the results obtained here, the authors believe that future research should explore frameworks reconciling hierarchical Bayesian models with the use of the extreme value theory for high precipitation events.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Pablo A. Mendoza, National Center for Atmospheric Research, Research Applications Laboratory, P.O. Box 3000, Boulder, CO 80307-3000.E-mail: pmendoza@ucar.edu

Abstract

Statistical postprocessing techniques have become essential tools for downscaling large-scale information to the point scale, and also for providing a better probabilistic characterization of hydrometeorological variables in simulation and forecasting applications at both short and long time scales. In this paper, the authors assess the utility of statistical postprocessing methods for generating probabilistic estimates of daily precipitation totals, using deterministic high-resolution outputs obtained with the Weather Research and Forecasting (WRF) Model. After a preliminary assessment of WRF simulations over a historical period, the performance of three postprocessing techniques is compared: multinomial logistic regression (MnLR), quantile regression (QR), and Bayesian model averaging (BMA)—all of which use WRF outputs as potential predictors. Results demonstrate that the WRF Model has skill in reproducing observed precipitation events, especially during fall/winter. Furthermore, it is shown that the spatial distribution of skill obtained from statistical postprocessing is closely linked with the quality of WRF precipitation outputs. A detailed comparison of statistical precipitation postprocessing approaches reveals that, although the poorest performance was obtained using MnLR, there is not an overall best technique. While QR should be preferred if skill (i.e., small probability forecast errors) and reliability (i.e., match between forecast probabilities and observed frequencies) are target properties, BMA is recommended in cases when discrimination (i.e., prediction of occurrence versus nonoccurrence) and statistical consistency (i.e., equiprobability of the observations within their ensemble distributions) are desired. Based on the results obtained here, the authors believe that future research should explore frameworks reconciling hierarchical Bayesian models with the use of the extreme value theory for high precipitation events.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Pablo A. Mendoza, National Center for Atmospheric Research, Research Applications Laboratory, P.O. Box 3000, Boulder, CO 80307-3000.E-mail: pmendoza@ucar.edu
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  • Akaike, H., 1974: A new look at the statistical model identification. IEEE Trans. Autom. Control, 19, 716723, doi:10.1109/TAC.1974.1100705.

    • Search Google Scholar
    • Export Citation
  • Bannerjee, S., B. Carlin, and A. Gelfand, 2003: Hierarchical Modeling and Analysis for Spatial Data. Chapman and Hall, 472 pp.

  • Barlage, M., and Coauthors, 2010: Noah land surface model modifications to improve snowpack prediction in the Colorado Rocky Mountains. J. Geophys. Res., 115, D22101, doi:10.1029/2009JD013470.

    • Search Google Scholar
    • Export Citation
  • Benestad, R. E., 2010: Downscaling precipitation extremes. Theor. Appl. Climatol., 100, 121, doi:10.1007/s00704-009-0158-1.

  • Bentzien, S., and P. Friederichs, 2012: Generating and calibrating probabilistic quantitative precipitation forecasts from the high-resolution NWP model COSMO-DE. Wea. Forecasting, 27, 9881002, doi:10.1175/WAF-D-11-00101.1.

    • Search Google Scholar
    • Export Citation
  • Bremnes, J. B., 2004: Probabilistic forecasts of precipitation in terms of quantiles using NWP model output. Mon. Wea. Rev., 132, 338347, doi:10.1175/1520-0493(2004)132<0338:PFOPIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Brier, G. W., 1950: The statistical theory of turbulence and the problem of diffusion in the atmosphere. J. Meteor., 7, 283290, doi:10.1175/1520-0469(1950)007<0283:TSTOTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Carpenter, T. M., and K. P. Georgakakos, 2004: Impacts of parametric and radar rainfall uncertainty on the ensemble streamflow simulations of a distributed hydrologic model. J. Hydrol., 298, 202221, doi:10.1016/j.jhydrol.2004.03.036.

    • Search Google Scholar
    • Export Citation
  • Carter, G. M., J. P. Dallavalle, and H. R. Glahn, 1989: Statistical forecasts based on the National Meteorological Center’s numerical weather prediction system. Wea. Forecasting, 4, 401412, doi:10.1175/1520-0434(1989)004<0401:SFBOTN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, F., and J. Dudhia, 2001: Coupling an advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569585, doi:10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, J., F. P. Brissette, A. Poulin, and R. Leconte, 2011: Overall uncertainty study of the hydrological impacts of climate change for a Canadian watershed. Water Resour. Res., 47, W12509, doi:10.1029/2011WR010602.

    • Search Google Scholar
    • Export Citation
  • Christensen, N. S., and D. P. Lettenmaier, 2007: A multimodel ensemble approach to assessment of climate change impacts on the hydrology and water resources of the Colorado River Basin. Hydrol. Earth Syst. Sci., 11, 14171434, doi:10.5194/hess-11-1417-2007.

    • Search Google Scholar
    • Export Citation
  • Clark, M. P., and L. E. Hay, 2004: Use of medium-range numerical weather prediction model output to produce forecasts of streamflow. J. Hydrometeor., 5, 1532, doi:10.1175/1525-7541(2004)005<0015:UOMNWP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Clark, M. P., and A. G. Slater, 2006: Probabilistic quantitative precipitation estimation in complex terrain. J. Hydrometeor., 7, 322, doi:10.1175/JHM474.1.

    • Search Google Scholar
    • Export Citation
  • Clark, M. P., S. Gangopadhyay, L. Hay, B. Rajagopalan, and R. Wilby, 2004: The Schaake Shuffle: A method for reconstructing space–time variability in forecasted precipitation and temperature fields. J. Hydrometeor., 5, 243262, doi:10.1175/1525-7541(2004)005<0243:TSSAMF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Clark, M. P., A. G. Slater, A. P. Barrett, L. E. Hay, G. J. McCabe, B. Rajagopalan, and G. H. Leavesley, 2006: Assimilation of snow covered area information into hydrologic and land-surface models. Adv. Water Resour., 29, 12091221, doi:10.1016/j.advwatres.2005.10.001.

    • Search Google Scholar
    • Export Citation
  • Cloke, H. L., and F. Pappenberger, 2008: Evaluating forecasts of extreme events for hydrological applications: An approach for screening unfamiliar performance measures. Meteor. Appl., 15, 181197, doi:10.1002/met.58.

    • Search Google Scholar
    • Export Citation
  • Colle, B. A., K. J. Westrick, and C. F. Mass, 1999: Evaluation of MM5 and Eta-10 precipitation forecasts over the Pacific Northwest during the cool season. Wea. Forecasting, 14, 137154, doi:10.1175/1520-0434(1999)014<0137:EOMAEP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Colle, B. A., C. F. Mass, and K. J. Westrick, 2000: MM5 precipitation verification over the Pacific Northwest during the 1997–99 cool seasons. Wea. Forecasting, 15, 730744, doi:10.1175/1520-0434(2000)015<0730:MPVOTP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Colle, B. A., J. B. Olson, and J. S. Tongue, 2003: Multiseason verification of the MM5. Part II: Evaluation of high-resolution precipitation forecasts over the northeastern United States. Wea. Forecasting, 18, 458480, doi:10.1175/1520-0434(2003)18<458:MVOTMP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Collins, W. D., and Coauthors, 2006: The Community Climate System Model version 3 (CCSM3). J. Climate, 19, 21222143, doi:10.1175/JCLI3761.1.

    • Search Google Scholar
    • Export Citation
  • De Lannoy, G. J. M., P. R. Houser, V. R. N. Pauwels, and N. E. C. Verhoest, 2006: Assessment of model uncertainty for soil moisture through ensemble verification. J. Geophys. Res., 111, D10101, doi:10.1029/2005JD006367.

    • Search Google Scholar
    • Export Citation
  • Delle Monache, L., J. P. Hacker, Y. Zhou, X. Deng, and R. B. Stull, 2006: Probabilistic aspects of meteorological and ozone regional ensemble forecasts. J. Geophys. Res., 111, D24307, doi:10.1029/2005JD006917.

    • Search Google Scholar
    • Export Citation
  • Delle Monache, L., F. A. Eckel, D. L. Rife, B. Nagarajan, and K. Searight, 2013: Probabilistic weather prediction with an analog ensemble. Mon. Wea. Rev., 141, 34983516, doi:10.1175/MWR-D-12-00281.1.

    • Search Google Scholar
    • Export Citation
  • Fraley, C., A. E. Raftery, and T. Gneiting, 2010: Calibrating multimodel forecast ensembles with exchangeable and missing members using Bayesian model averaging. Mon. Wea. Rev., 138, 190202, doi:10.1175/2009MWR3046.1.

    • Search Google Scholar
    • Export Citation
  • Fraley, C., A. E. Raftery, T. Gneiting, and J. M. Sloughter, 2013: ensembleBMA: An R package for probabilistic forecasting using ensembles and Bayesian model averaging. Tech. Rep. 516, Department of Statistics, University of Washington, 19 pp. [Available online at http://www.stat.washington.edu/research/reports/2008/tr516.pdf.]

  • Friederichs, P., and A. Hense, 2007: Statistical downscaling of extreme precipitation events using censored quantile regression. Mon. Wea. Rev., 135, 23652378, doi:10.1175/MWR3403.1.

    • Search Google Scholar
    • Export Citation
  • Furrer, E. M., and R. W. Katz, 2008: Improving the simulation of extreme precipitation events by stochastic weather generators. Water Resour. Res.,44, W12439, doi:10.1029/2008WR007316.

  • Gangopadhyay, S., M. Clark, K. Werner, D. Brandon, and B. Rajagopalan, 2004: Effects of spatial and temporal aggregation on the accuracy of statistically downscaled precipitation estimates in the upper Colorado River basin. J. Hydrometeor., 5, 11921206, doi:10.1175/JHM-391.1.

    • Search Google Scholar
    • Export Citation
  • Glahn, H. R., and D. A. Lowry, 1972: The use of Model Output Statistics (MOS) in objective weather forecasting. J. Appl. Meteor., 11, 12031211, doi:10.1175/1520-0450(1972)011<1203:TUOMOS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Grimit, E. P., and C. F. Mass, 2007: Measuring the ensemble spread–error relationship with a probabilistic approach: Stochastic ensemble results. Mon. Wea. Rev., 135, 203221, doi:10.1175/MWR3262.1.

    • Search Google Scholar
    • Export Citation
  • Gutiérrez, J. M., D. San-Martín, S. Brands, R. Manzanas, and S. Herrera, 2013: Reassessing statistical downscaling techniques for their robust application under climate change conditions. J. Climate, 26, 171188, doi:10.1175/JCLI-D-11-00687.1.

    • Search Google Scholar
    • Export Citation
  • Gutmann, E., T. Pruitt, M. P. Clark, L. Brekke, J. R. Arnold, D. A. Raff, and R. M. Rasmussen, 2014: An intercomparison of statistical downscaling methods used for water resource assessments in the United States. Water Resour. Res., 50, 7167–7186, doi:10.1002/2014WR015559.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., 1997: Reliability diagrams for multicategory probabilistic forecasts. Wea. Forecasting, 12, 736741, doi:10.1175/1520-0434(1997)012<0736:RDFMPF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., 2001: Interpretation of rank histograms for verifying ensemble forecasts. Mon. Wea. Rev., 129, 550560, doi:10.1175/1520-0493(2001)129<0550:IORHFV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., and J. S. Whitaker, 2006: Probabilistic quantitative precipitation forecasts based on reforecast analogs: Theory and application. Mon. Wea. Rev., 134, 32093229, doi:10.1175/MWR3237.1.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., J. S. Whitaker, and X. Wei, 2004: Ensemble reforecasting: Improving medium-range forecast skill using retrospective forecasts. Mon. Wea. Rev., 132, 14341447, doi:10.1175/1520-0493(2004)132<1434:ERIMFS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hastie, T., R. Tibshirani, and J. Friedman, 2009: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. Springer, 745 pp.

  • Hoerling, M., and J. Eischeid, 2007: Past peak water in the Southwest. Southwest Hydrol.,6, 18–19.

  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, doi:10.1175/MWR3199.1.

    • Search Google Scholar
    • Export Citation
  • Ikeda, K., and Coauthors, 2010: Simulation of seasonal snowfall over Colorado. Atmos. Res., 97, 462477, doi:10.1016/j.atmosres.2010.04.010.

    • Search Google Scholar
    • Export Citation
  • Jolliffe, I., and D. Stephenson, 2003: Forecast Verification: A Practitioner’s Guide in Atmospheric Science. John Wiley and Sons, 240 pp.

  • Jones, M. S., B. A. Colle, and J. S. Tongue, 2007: Evaluation of a mesoscale short-range ensemble forecast system over the northeast United States. Wea. Forecasting, 22, 3655, doi:10.1175/WAF973.1.

    • Search Google Scholar
    • Export Citation
  • Juban, J., N. Siebert, and G. N. Kariniotakis, 2007: Probabilistic short-term wind power forecasting for the optimal management of wind generation. 2007 IEEE Lausanne Power Tech, IEEE, 683–688, doi:10.1109/PCT.2007.4538398.

  • Koenker, R., 2012: Quantile regression in R: A vignette. [Available online at http://cran.r-project.org/web/packages/quantreg/vignettes/rq.pdf.]

  • Koenker, R., and G. Bassett Jr., 1978: Regression quantiles. Econometrica, 46, 3350, doi:10.2307/1913643.

  • Koenker, R., and V. D’Orey, 1987: Computing regression quantiles. J. Roy. Stat. Soc., 36A, 383393.

  • Koenker, R., and K. F. Hallock, 2001: Quantile regression. J. Econ. Perspect., 15, 143156, doi:10.1257/jep.15.4.143.

  • Laio, F., and S. Tamea, 2007: Verification tools for probabilistic forecasts of continuous hydrological variables. Hydrol. Earth Syst. Sci., 11, 12671277, doi:10.5194/hess-11-1267-2007.

    • Search Google Scholar
    • Export Citation
  • Mascaro, G., R. Deidda, and E. R. Vivoni, 2008: A new verification method to ensure consistent ensemble forecasts through calibrated precipitation downscaling models. Mon. Wea. Rev., 136, 33743391, doi:10.1175/2008MWR2339.1.

    • Search Google Scholar
    • Export Citation
  • McCullagh, J., and P. Nelder, 1989: Generalized Linear Models. 2nd ed. Chapman and Hall/CRC, 532 pp.

  • Mendoza, P. A., J. McPhee, and X. Vargas, 2012: Uncertainty in flood forecasting: A distributed modeling approach in a sparse data catchment. Water Resour. Res., 48, W09532, doi:10.1029/2011WR011089.

    • Search Google Scholar
    • Export Citation
  • Mendoza, P. A., B. Rajagopalan, M. P. Clark, G. Cortés, and J. McPhee, 2014: A robust multimodel framework for ensemble seasonal hydroclimatic forecasts. Water Resour. Res., 50, 6030–6052, doi:10.1002/2014WR015426.

    • Search Google Scholar
    • Export Citation
  • Mesinger, F., and Coauthors, 2006: North American Regional Reanalysis. Bull. Amer. Meteor. Soc., 87, 343360, doi:10.1175/BAMS-87-3-343.

    • Search Google Scholar
    • Export Citation
  • Milly, P. C. D., K. A. Dunne, and A. V. Vecchia, 2005: Global pattern of trends in streamflow and water availability in a changing climate. Nature, 438, 347350, doi:10.1038/nature04312.

    • Search Google Scholar
    • Export Citation
  • Nasonova, O. N., Y. M. Gusev, and Y. E. Kovalev, 2011: Impact of uncertainties in meteorological forcing data and land surface parameters on global estimates of terrestrial water balance components. Hydrol. Processes,25, 1074–1090, doi:10.1002/hyp.7651.

  • Nielsen, H. A., H. Madsen, and T. S. Nielsen, 2006: Using quantile regression to extend an existing wind power forecasting system with probabilistic forecasts. Wind Energy, 9, 95108, doi:10.1002/we.180.

    • Search Google Scholar
    • Export Citation
  • Pappenberger, F., A. Ghelli, R. Buizza, and K. Bódis, 2009: The skill of probabilistic precipitation forecasts under observational uncertainties within the generalized likelihood uncertainty estimation framework for hydrological applications. J. Hydrometeor., 10, 807819, doi:10.1175/2008JHM956.1.

    • Search Google Scholar
    • Export Citation
  • Pappenberger, F., J. Thielen, and M. Del Medico, 2011: The impact of weather forecast improvements on large scale hydrology: Analysing a decade of forecasts of the European Flood Alert System. Hydrol. Processes, 25, 10911113, doi:10.1002/hyp.7772.

    • Search Google Scholar
    • Export Citation
  • Prein, A. F., G. J. Holland, R. M. Rasmussen, J. Done, K. Ikeda, M. P. Clark, and C. H. Liu, 2013: Importance of regional climate model grid spacing for the simulation of heavy precipitation in the Colorado headwaters. J. Climate, 26, 48484857, doi:10.1175/JCLI-D-12-00727.1.

    • Search Google Scholar
    • Export Citation
  • R Development Core Team, 2011: R: A language and environment for statistical computing. R Foundation for Statistical Computing. [Available online at http://www.r-project.org/.]

  • Raftery, A. E., T. Gneiting, F. Balabdaoui, and M. Polakowski, 2005: Using Bayesian model averaging to calibrate forecast ensembles. Mon. Wea. Rev., 133, 11551174, doi:10.1175/MWR2906.1.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, R., and Coauthors, 2011: High-resolution coupled climate runoff simulations of seasonal snowfall over Colorado: A process study of current and warmer climate. J. Climate, 24, 30153048, doi:10.1175/2010JCLI3985.1.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, R., and Coauthors, 2012: How well are we measuring snow: The NOAA/FAA/NCAR Winter Precipitation Test Bed. Bull. Amer. Meteor. Soc., 93, 811829, doi:10.1175/BAMS-D-11-00052.1.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, R., and Coauthors, 2014: Climate change impacts on the water balance of the Colorado headwaters: High-resolution regional climate model simulations. J. Hydrometeor., 15, 10911116, doi:10.1175/JHM-D-13-0118.1.

    • Search Google Scholar
    • Export Citation
  • Ray, A., J. Barsugli, K. Averyt, K. Wolter, M. Hoerling, N. Doesken, B. Udall, and R. Webb, 2008: Climate change in Colorado: A synthesis to support water resources management and adaptation. Intermountain West Climate Summary, University of Colorado at Boulder, Boulder, CO, 3 pp. [Available online at http://wwa.colorado.edu/climate/iwcs/archive/IWCS_2008_Nov_feature.pdf.]

  • Renner, M., M. G. F. Werner, S. Rademacher, and E. Sprokkereef, 2009: Verification of ensemble flow forecasts for the River Rhine. J. Hydrol., 376, 463475, doi:10.1016/j.jhydrol.2009.07.059.

    • Search Google Scholar
    • Export Citation
  • Rodríguez, G., cited 2007: Lecture notes on generalized linear models. [Available online at http://data.princeton.edu/wws509/notes/.]

  • Roulin, E., and S. Vannitsem, 2012: Postprocessing of ensemble precipitation predictions with extended logistic regression based on hindcasts. Mon. Wea. Rev., 140, 874888, doi:10.1175/MWR-D-11-00062.1.

    • Search Google Scholar
    • Export Citation
  • Ruiz, J., C. Saulo, and E. Kalnay, 2009: Comparison of methods used to generate probabilistic quantitative precipitation forecasts over South America. Wea. Forecasting, 24, 319336, doi:10.1175/2008WAF2007098.1.

    • Search Google Scholar
    • Export Citation
  • Scheuerer, M., 2014: Probabilistic quantitative precipitation forecasting using ensemble Model Output Statistics. Quart. J. Roy. Meteor. Soc., 140, 10861096, doi:10.1002/qj.2183.

    • Search Google Scholar
    • Export Citation
  • Schmeits, M. J., and K. J. Kok, 2010: A comparison between raw ensemble output, (modified) Bayesian model averaging, and extended logistic regression using ECMWF ensemble precipitation reforecasts. Mon. Wea. Rev., 138, 41994211, doi:10.1175/2010MWR3285.1.

    • Search Google Scholar
    • Export Citation
  • Schmith, T., 2008: Stationarity of regression relationships: Application to empirical downscaling. J. Climate, 21, 45294537, doi:10.1175/2008JCLI1910.1.

    • Search Google Scholar
    • Export Citation
  • Serreze, M. C., M. P. Clark, R. L. Armstrong, D. A. McGinnis, and R. S. Pulwarty, 1999: Characteristics of the western United States snowpack from snowpack telemetry (SNOTEL) data. Water Resour. Res., 35, 21452160, doi:10.1029/1999WR900090.

    • Search Google Scholar
    • Export Citation
  • Sloughter, J. M. L., A. E. Raftery, T. Gneiting, and C. Fraley, 2007: Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Mon. Wea. Rev., 135, 32093220, doi:10.1175/MWR3441.1.

    • Search Google Scholar
    • Export Citation
  • Sokol, Z., 2003: MOS-based precipitation forecasts for river basins. Wea. Forecasting, 18, 769781, doi:10.1175/1520-0434(2003)018<0769:MPFFRB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Stensrud, D. J., and N. Yussouf, 2007: Reliable probabilistic quantitative precipitation forecasts from a short-range ensemble forecasting system. Wea. Forecasting, 22, 317, doi:10.1175/WAF968.1.

    • Search Google Scholar
    • Export Citation
  • Sweeney, C. P., P. Lynch, and P. Nolan, 2013: Reducing errors of wind speed forecasts by an optimal combination of post-processing methods. Meteor. Appl., 20, 3240, doi:10.1002/met.294.

    • Search Google Scholar
    • Export Citation
  • Tareghian, R., and P. F. Rasmussen, 2013: Statistical downscaling of precipitation using quantile regression. J. Hydrol., 487, 122135, doi:10.1016/j.jhydrol.2013.02.029.

    • Search Google Scholar
    • Export Citation
  • Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 50955115, doi:10.1175/2008MWR2387.1.

    • Search Google Scholar
    • Export Citation
  • Vannitsem, S., 2011: Bias correction and post-processing under climate change. Nonlinear Processes Geophys., 18, 911924, doi:10.5194/npg-18-911-2011.

    • Search Google Scholar
    • Export Citation
  • Vano, J. A., T. Das, and D. P. Lettenmaier, 2012: Hydrologic sensitivities of Colorado River runoff to changes in precipitation and temperature. J. Hydrometeor., 13, 932949, doi:10.1175/JHM-D-11-069.1.

    • Search Google Scholar
    • Export Citation
  • Vano, J. A., and Coauthors, 2014: Understanding uncertainties in future Colorado River streamflow. Bull. Amer. Meteor. Soc., 95, 5978, doi:10.1175/BAMS-D-12-00228.1.

    • Search Google Scholar
    • Export Citation
  • Weerts, A. H., H. C. Winsemius, and J. S. Verkade, 2011: Estimation of predictive hydrological uncertainty using quantile regression: Examples from the National Flood Forecasting System (England and Wales). Hydrol. Earth Syst. Sci., 15, 255265, doi:10.5194/hess-15-255-2011.

    • Search Google Scholar
    • Export Citation
  • Wilby, R. L., and I. Harris, 2006: A framework for assessing uncertainties in climate change impacts: Low-flow scenarios for the River Thames, UK. Water Resour. Res., 42, W02419, doi:10.1029/2005WR004065.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 2006: Comparison of ensemble-MOS methods in the Lorenz ’96 setting. Meteor. Appl., 13, 243256, doi:10.1017/S1350482706002192.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 2009: Extending logistic regression to provide full-probability-distribution MOS forecasts. Meteor. Appl., 16, 361368, doi:10.1002/met.134.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 2011: Statistical Methods in the Atmospheric Sciences. 3rd ed. Academic Press, 704 pp.

  • Wilks, D. S., and T. M. Hamill, 2007: Comparison of ensemble-MOS methods using GFS reforecasts. Mon. Wea. Rev., 135, 23792390, doi:10.1175/MWR3402.1.

    • Search Google Scholar
    • Export Citation
  • Yee, T. W., 2010: The VGAM package for categorical data analysis. J. Stat. Software, 32, 134.

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