Advertisement

Application to Post-processing of Meteorological Seasonal Forecasting

  • Andrew Schepen
  • Q. J. WangEmail author
  • David E. Robertson
Reference work entry

Abstract

Seasonal hydrological forecasting relies on accurate and reliable ensemble climate forecasts. A calibration, bridging, and merging (CBaM) method has been developed to statistically postprocess seasonal climate forecasts from general circulation models (GCMs). Postprocessing corrects conditional biases in raw GCM outputs and produces forecasts that are reliable in ensemble spread. The CBaM method is designed to extract as much skill as possible from the GCM. This is achieved by firstly producing multiple forecasts using different GCM output fields, such as rainfall, temperature, and sea surface temperatures, as predictors. These forecasts are then combined based on evidence of skill in hindcasts. Calibration refers to direct postprocessing of the target variable – rainfall for example. Bridging refers to indirect forecasting of the target variable – forecasting rainfall with the GCM’s Nino3.4 forecast for example. Merging is designed to optimally combine calibration and bridging forecasts. Merging includes connecting forecast ensemble members across forecast time periods by using the “Schaake Shuffle,” which creates time series forecasts with appropriate temporal correlation structure. CBaM incorporates parameter and model uncertainty, leading to reliable forecasts in most applications. Here, CBaM is applied to produce monthly catchment rainfall forecasts out to 12 months for a catchment in northeastern Australia. Bridging is shown to improve forecast skill in several seasons, and the ensemble time series forecasts are shown to be reliable for both monthly and seasonal totals.

Keywords

Seasonal forecasting Post-processing Bayesian joint probability Bayesian model averaging Precipitation Temperature Forecast verification 

References

  1. K. Ashok, S. Behera, S. Rao, H. Weng, T. Yamagata, El Niño Modoki and its possible teleconnection. J. Geophys. Res. 112, C11007 (2007)CrossRefGoogle Scholar
  2. J. Barnard, R. McCulloch, X.-L. Meng, Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Stat. Sin. 10, 1281–1312 (2000)Google Scholar
  3. J. Cheng, J. Yang, Y. Zhou, Y. Cui, Flexible background mixture models for foreground segmentation. Image Vis. Comput. 24, 473–482 (2006)CrossRefGoogle Scholar
  4. M. Clark, S. Gangopadhyay, L. Hay, B. Rajagopalan, R. Wilby, The Schaake shuffle: a method for reconstructing space–time variability in forecasted precipitation and temperature fields. J. Hydrometeorol. 5, 243–262 (2004)CrossRefGoogle Scholar
  5. J. Eklund, S. Karlsson, Forecast combination and model averaging using predictive measures. Econ. Rev. 26, 329–363 (2007)CrossRefGoogle Scholar
  6. A. Gelman, J.B. Carlin, H.S. Stern, D.B. Rubin, Bayesian data analysis (Chapman and Hall, New York, 1995). 526 ppGoogle Scholar
  7. J. Geweke, C. Whiteman, Chapter 1, Bayesian forecasting, in Handbook of Economic Forecasting, ed. by G. Elliott, C.W.J. Granger, A. Timmermann, vol. 1 (Elsevier B.V., Amsterdam, 2006), pp. 3–80. ISSN 1574-0706, ISBN 9780444513953,  https://doi.org/10.1016/S1574-0706(05)01001-3CrossRefGoogle Scholar
  8. S. Hawthorne, Q.J. Wang, A. Schepen, D. Robertson, Effective use of general circulation model outputs for forecasting monthly rainfalls to long lead times. Water Resour. Res. 49(9), 5427–5436 (2013)CrossRefGoogle Scholar
  9. W.-R. Hsu, A.H. Murphy, The attributes diagram. A geometrical framework for assessing the quality of probability forecasts. Int. J. Forecast. 2, 285–293 (1986)CrossRefGoogle Scholar
  10. C.H. Jackson, S.G. Thompson, L.D. Sharples, Accounting for uncertainty in health economic decision models by using model averaging. J. R. Stat. Soc. A. Stat. Soc. 172, 383–404 (2009)CrossRefGoogle Scholar
  11. D.A. Jones, W. Wang, R. Fawcett, High-quality spatial climate data-sets for Australia. Aust. Meteorol. Oceanogr. J. 58, 233–248 (2009)CrossRefGoogle Scholar
  12. F. Laio, S. Tamea, Verification tools for probabilistic forecasts of continuous hydrological variables. Hydrol. Earth Syst. Sci. 11, 1267–1277 (2007)CrossRefGoogle Scholar
  13. E.-P. Lim, H.H. Hendon, D.L.T. Anderson, A. Charles, O. Alves, Dynamical, statistical-dynamical, and multimodel ensemble forecasts of Australian spring season rainfall. Mon. Weather Rev. 139, 958–975 (2011)CrossRefGoogle Scholar
  14. L. Luo, E.F. Wood, M. Pan, Bayesian merging of multiple climate model forecasts for seasonal hydrological predictions. J. Geophys. Res. 112, D10102 (2007)CrossRefGoogle Scholar
  15. A.G. Marshall, D. Hudson, M.C. Wheeler, H.H. Hendon, O. Alves, Evaluating key drivers of Australian intra-seasonal climate variability in POAMA-2: a progress report. CAWCR Res. Lett. 7, 10–16 (2012)Google Scholar
  16. J.E. Matheson, R.L. Winkler, Scoring rules for continuous probability distributions. Manag. Sci. 22, 1087–1096 (1976)CrossRefGoogle Scholar
  17. J.S. Risbey, M.J. Pook, P.C. McIntosh, M.C. Wheeler, H.H. Hendon, On the remote drivers of rainfall variability in Australia. Mon. Weather Rev. 137, 3233–3253 (2009)CrossRefGoogle Scholar
  18. D. Robertson, D. Shrestha, Q. Wang, Post processing rainfall forecasts from numerical weather prediction models for short term streamflow forecasting. Hydrol. Earth Syst. Sci. Discuss. 10, 6765–6806 (2013)CrossRefGoogle Scholar
  19. R.T. Rust, D.C. Schmittlein, A Bayesian cross-validated likelihood method for comparing alternative specifications of quantitative models. Market. Sci. 4(1), 20–40 (1985)CrossRefGoogle Scholar
  20. N.H. Saji, B.N. Goswami, P.N. Vinayachandran, T. Yamagata, A dipole mode in the tropical Indian Ocean. Nature 401, 360–363 (1999)Google Scholar
  21. A. Schepen, Q.J. Wang, Ensemble forecasts of monthly catchment rainfall out to long lead times by post-processing coupled general circulation model output. J. Hydrol. 519, 2920–2931 (2014)CrossRefGoogle Scholar
  22. A. Schepen, Q.J. Wang, Model averaging methods to merge operational statistical and dynamic seasonal streamflow forecasts in Australia. Water Resour. Res. 51(3), 1797–1812 (2015)CrossRefGoogle Scholar
  23. A. Schepen, Q.J. Wang, D. Robertson, Evidence for using lagged climate indices to forecast Australian seasonal rainfall. J. Climate 25, 1230–1246 (2012)CrossRefGoogle Scholar
  24. Q. Shao, M. Li, An improved statistical analogue downscaling procedure for seasonal precipitation forecast. Stoch. Env. Res. Risk Assess. 27(4), 819–830 (2013)CrossRefGoogle Scholar
  25. T. Shinozaki, S. Furui, T. Kawahara, Gaussian mixture optimization based on efficient cross-validation. IEEE J. Sel. Top. Sign. Process 4, 540–547 (2010)CrossRefGoogle Scholar
  26. P. Smyth, Clustering using Monte Carlo cross-validation. KDD, 126–133 (1996). http://www.aaai.org/Papers/KDD/1996/KDD96-021.pdf
  27. P. Smyth, Model selection for probabilistic clustering using cross-validated likelihood. Stat. Comput. 10(1), 63–72 (2000)CrossRefGoogle Scholar
  28. M. Stone, An asymptotic equivalence of choice of model by cross-validation and Akaike’s criterion. J. R. Stat. Soc. Ser. B Methodol. 44–47 (1977)Google Scholar
  29. M. Thyer, G. Kuczera, Q.J. Wang, Quantifying parameter uncertainty in stochastic models using the Box-Cox transformation. J. Hydrol. 265, 246–257 (2002)CrossRefGoogle Scholar
  30. M. Thyer, B. Renard, D. Kavetski, G. Kuczera, S.W. Franks, S. Srikanthan, Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: a case study using Bayesian total error analysis. Water Resour. Res. 45, W00B14 (2009)CrossRefGoogle Scholar
  31. B. Timbal, D. Jones, Future projections of winter rainfall in southeast Australia using a statistical downscaling technique. Clim. Change 86, 165–187 (2008)CrossRefGoogle Scholar
  32. N.K. Tuteja, D. Shin, R. Laugesen, U. Khan, Q. Shao, E. Wang, M. Li et al., Experimental evaluation of the dynamic seasonal streamflow forecasting approach (2012). Report published by the Bureau of Meteorology, Melbourne. Available online http://www.bom.gov.au/water/about/publications/document/dynamic_seasonal_streamflow_forecasting.pdf
  33. D.C. Verdon, S.W. Franks, Indian Ocean sea surface temperature variability and winter rainfall: Eastern Australia. Water Resour. Res. 41 W09413 (2005). doi:10.1029/2004WR003845.Google Scholar
  34. Q.J. Wang, D.E. Robertson, Multisite probabilistic forecasting of seasonal flows for streams with zero value occurrences. Water Resour. Res. 47, W02546 (2011)Google Scholar
  35. Q.J. Wang, D.E. Robertson, F.H.S. Chiew, A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites. Water Resour. Res. 45 W05407 (2009),  https://doi.org/10.1029/2008WR007355
  36. G. Wang et al., POAMA-2 SST skill assessment and beyond. CAWCR Res. Lett. 6, 40–46 (2011a)Google Scholar
  37. Q. Wang, T. Pagano, S. Zhou, H. Hapuarachchi, L. Zhang, D. Robertson, Monthly versus daily water balance models in simulating monthly runoff. J. Hydrol. 404, 166–175 (2011b)CrossRefGoogle Scholar
  38. Q. Wang, D. Shrestha, D. Robertson, P. Pokhrel, A log-sinh transformation for data normalization and variance stabilization. Water Resour. Res. 48, W05514 (2012a)Google Scholar
  39. Q.J. Wang, A. Schepen, D.E. Robertson, Merging seasonal rainfall forecasts from multiple statistical models through Bayesian model averaging. J. Climate 25, 5524–5537 (2012b)CrossRefGoogle Scholar
  40. I.K. Yeo, R.A. Johnson, A new family of power transformations to improve normality or symmetry. Biometrika 87, 954–959 (2000)CrossRefGoogle Scholar
  41. D. Zhu, A.O. Hero, Bayesian hierarchical model for large-scale covariance matrix estimation. J. Comput. Biol. 14, 1311–1326 (2007)CrossRefGoogle Scholar
  42. Z. Zivkovic, F. van der Heijden, Recursive unsupervised learning of finite mixture models. IEEE Trans. Pattern Anal. Mach. Intell. 26, 651–656 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Andrew Schepen
    • 1
  • Q. J. Wang
    • 2
    Email author
  • David E. Robertson
    • 2
  1. 1.CSIRO Land and WaterDutton ParkAustralia
  2. 2.CSIRO Land and WaterClaytonAustralia

Personalised recommendations