Improving the North American multi-model ensemble (NMME) precipitation forecasts at local areas using wavelet and machine learning

  • Lei Xu
  • Nengcheng ChenEmail author
  • Xiang Zhang
  • Zeqiang ChenEmail author
  • Chuli Hu
  • Chao Wang


Seasonal precipitation forecasts at regional or local areas can help guide agricultural practice and urban water resource management. The North American multi-model ensemble (NMME) is a seasonal forecasting system providing precipitation forecasts globally. Bias correction and downscaling of the NMME is a critical step before applied at local scales. Here, the machine learning methods coupling with wavelet are used to correct the precipitation forecasts in NMME for 518 meteorological stations in China for eight models at 0.5–8.5 months leads. Compared with the traditional quantile mapping (QM) approach, the wavelet support vector machine (WSVM) and wavelet random forest (WRF) methods exhibit obvious advantage in downscaling, with an overall average improvement of Pearson’s correlation coefficient increasing by 0.05–0.3 and root mean square error (RMSE) reducing by 18–40 mm (21–33%) for individual models. Both the spatial and seasonal patterns of downscaled results demonstrate the superiority of wavelet machine learning methods over QM. A spatial analysis indicates that the corrected NMME precipitation forecasts show the best skill in South China, with an average RMSE of about 30 mm, while the worst skill in Central and Southwest China with a RMSE of 80 mm. In spite of the correction, the uncertainties of seasonal precipitation forecasts in summer and extreme wet cases are still large. However, the WSVM and WRF methods may serve as an effective tool in the bias correction of NMME precipitation forecasts.


NMME Precipitation forecast Bias correction Wavelet Machine learning 



This work was supported by Grants from the National Key Research and Development Program of China (2017YFB0503803), Creative Research Groups of Natural Science Foundation of Hubei Province of China (2016CFA003), the Fundamental Research Funds for the Central Universities (2042017GF0057), the National Nature Science Foundation of China program (41771422, 41890822, 41601406, 41801339), the Nature Science Foundation of Hubei Province (2017CFB616), the China Meteorological Administration Drought Research Fund (IAM201704), LIESMARS Special Research Funding (201806), and the China Postdoctoral Science Foundation (No. 2017M620338, 2018T110804).

Supplementary material

382_2018_4605_MOESM1_ESM.docx (5.3 mb)
Supplementary material 1 (DOCX 5463 KB)


  1. Ahmad S, Kalra A, Stephen H (2010) Estimating soil moisture using remote sensing data: a machine learning approach. Adv Water Resour 33:69–80CrossRefGoogle Scholar
  2. Ahmadalipour A, Moradkhani H, Rana A (2018) Accounting for downscaling and model uncertainty in fine-resolution seasonal climate projections over the Columbia River Basin. Clim Dyn 50:717–733. CrossRefGoogle Scholar
  3. Bakshi BR (1999) Multiscale analysis and modeling using wavelets. J Chemom 13:415–434CrossRefGoogle Scholar
  4. Barbero R, Abatzoglou JT, Hegewisch KC (2017) Evaluation of statistical downscaling of North American multimodel ensemble forecasts over the western United States. Weather Forecast 32:327–341. CrossRefGoogle Scholar
  5. Barnston AG, Tippett MK, Ranganathan M, L’Heureux ML (2016) Deterministic skill of ENSO predictions from the North American multimodel ensemble. Clim Dyn. Google Scholar
  6. Becker E, den D Hv, Zhang Q (2014) Predictability and forecast skill in NMME. J Clim 27:5891–5906CrossRefGoogle Scholar
  7. Belayneh A, Adamowski J, Khalil B, Ozga-Zielinski B (2014) Long-term SPI drought forecasting in the Awash River Basin in Ethiopia using wavelet neural network and wavelet support vector regression models. J Hydrol 508:418–429CrossRefGoogle Scholar
  8. Benaouda D, Murtagh F, Starck J-L, Renaud O (2006) Wavelet-based nonlinear multiscale decomposition model for electricity load forecasting. Neurocomputing 70:139–154CrossRefGoogle Scholar
  9. Breiman L (2001) Random forests. Mach Learn 45:5–32. CrossRefGoogle Scholar
  10. Cannon AJ, Sobie SR, Murdock TQ (2015) Bias correction of GCM precipitation by quantile mapping: how well do methods preserve changes in quantiles and extremes? J Clim 28:6938–6959CrossRefGoogle Scholar
  11. Chen S-T, Yu P-S, Tang Y-H (2010) Statistical downscaling of daily precipitation using support vector machines and multivariate analysis. J Hydrol 385:13–22. CrossRefGoogle Scholar
  12. Cuo L, Pagano TC, Wang QJ (2011) A review of quantitative precipitation forecasts and their use in short- to medium-range streamflow forecasting. J Hydrometeorol 12:713–728. CrossRefGoogle Scholar
  13. Daubechies I (1992) Ten lectures on wavelets, vol 61. Siam, PhiladelphiaCrossRefGoogle Scholar
  14. DeChant CM, Moradkhani H (2014) 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. CrossRefGoogle Scholar
  15. Deka PC (2014) Support vector machine applications in the field of hydrology: a review. Appl Soft Comput 19:372–386CrossRefGoogle Scholar
  16. Fowler HJ, Blenkinsop S, Tebaldi C (2007) Linking climate change modelling to impacts studies: recent advances in downscaling techniques for hydrological modelling. Int J Climatol 27:1547–1578CrossRefGoogle Scholar
  17. Ghosh S, Mujumdar PP (2008) Statistical downscaling of GCM simulations to streamflow using relevance vector machine. Adv Water Resour 31:132–146CrossRefGoogle Scholar
  18. Gizaw MS, Gan TY (2016) Regional flood frequency analysis using support vector regression under historical and future climate. J Hydrol 538:387–398. CrossRefGoogle Scholar
  19. Goyal MK, Burn DH, Ojha C (2012) Evaluation of machine learning tools as a statistical downscaling tool: temperatures projections for multi-stations for Thames River Basin, Canada. Theor Appl Climatol 108:519–534CrossRefGoogle Scholar
  20. Gudmundsson L, Bremnes J, Haugen J, Engen-Skaugen T (2012) Downscaling RCM precipitation to the station scale using statistical transformations—a comparison of methods. Hydrol Earth Syst Sci 16:3383CrossRefGoogle Scholar
  21. Hao Z, AghaKouchak A, Nakhjiri N, Farahmand A (2014) Global integrated drought monitoring and prediction system. Sci Data 1:140001CrossRefGoogle Scholar
  22. Hao Z, Singh Vijay P, Xia Y (2018) Seasonal drought prediction: advances, challenges, and future prospects. Rev Geophys. Google Scholar
  23. Im J, Park S, Rhee J, Baik J, Choi M (2016) Downscaling of AMSR-E soil moisture with MODIS products using machine learning approaches. Environ Earth Sci 75:1120CrossRefGoogle Scholar
  24. Infanti JM, Kirtman BP (2014) Southeastern US rainfall prediction in the North American multi-model ensemble. J Hydrometeorol 15:529–550CrossRefGoogle Scholar
  25. Jha B, Kumar A, Hu Z-Z (2016) An update on the estimate of predictability of seasonal mean atmospheric variability using North American multi-model ensemble. Clim Dyn. Google Scholar
  26. Jung M et al (2010) Recent decline in the global land evapotranspiration trend due to limited moisture supply. Nature 467:951CrossRefGoogle Scholar
  27. Ke Y, Im J, Park S, Gong H (2016) Downscaling of MODIS one kilometer evapotranspiration using Landsat-8 data and machine learning approaches. Remote Sens 8:215CrossRefGoogle Scholar
  28. Khajehei S, Ahmadalipour A, Moradkhani H (2017) An effective post-processing of the North American multi-model ensemble (NMME) precipitation forecasts over the continental US. Clim Dyn. Google Scholar
  29. Kirtman BP et al (2014) The North American multimodel ensemble: phase-1 seasonal-to-interannual prediction; phase-2 toward developing intraseasonal prediction. Bull Am Meteorol Soc 95:585–601CrossRefGoogle Scholar
  30. Köksal G, Batmaz İ, Testik MC (2011) A review of data mining applications for quality improvement in manufacturing industry. Expert Syst Appl 38:13448–13467. CrossRefGoogle Scholar
  31. Lafon T, Dadson S, Buys G, Prudhomme C (2013) Bias correction of daily precipitation simulated by a regional climate model: a comparison of methods. Int J Climatol 33:1367–1381CrossRefGoogle Scholar
  32. Lau K-M, Weng H (1995) Climate signal detection using wavelet transform: how to make a time series sing. Bull Am Meteorol Soc 76:2391–2402CrossRefGoogle Scholar
  33. Lavers D, Luo L, Wood EF (2009) A multiple model assessment of seasonal climate forecast skill for applications. Geophys Res Lett. Google Scholar
  34. Li H, Sheffield J, Wood EF (2010) Bias correction of monthly precipitation and temperature fields from Intergovernmental Panel on Climate Change AR4 models using equidistant quantile matching. J Geophys Res Atmos 115:D10101. CrossRefGoogle Scholar
  35. Liaw A, Wiener M (2002) Classification and regression by randomForest. R News 2:18–22Google Scholar
  36. Ma F et al (2016) Evaluating the skill of NMME seasonal precipitation ensemble predictions for 17 hydroclimatic regions in continental China. Int J Climatol 36:132–144CrossRefGoogle Scholar
  37. Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11:674–693CrossRefGoogle Scholar
  38. Manganello JV, Cash BA, Hodges KI, Kinter JL (2017) Seasonal forecasts of North Atlantic tropical cyclone activity in the North American multi-model ensemble. Clim Dyn. Google Scholar
  39. Materia S et al (2014) Impact of atmosphere and land surface initial conditions on seasonal forecasts of global surface temperature. J Clim 27:9253–9271. CrossRefGoogle Scholar
  40. Meinke H, Stone RC (2005) Seasonal and inter-annual climate forecasting: the new tool for increasing preparedness to climate variability and change. Agric Plan Oper Clim Change 70:221–253. CrossRefGoogle Scholar
  41. Mo KC, Lyon B (2015) Global meteorological drought prediction using the North American multi-model ensemble. J Hydrometeorol 16:1409–1424CrossRefGoogle Scholar
  42. Molteni F et al (2011) The new ECMWF seasonal forecast system (System 4). European Centre for Medium-Range Weather Forecasts, ReadingGoogle Scholar
  43. Nason GP, Von Sachs R (1999) Wavelets in time-series analysis. Philos Trans R Soc Lond A Math Phys Eng Sci 357:2511–2526CrossRefGoogle Scholar
  44. Nasrabadi NMP (2007) Recognition and machine learning. SPIE, San FranciscoGoogle Scholar
  45. Roundy JK, Yuan X, Schaake J, Wood EF (2015) A framework for diagnosing seasonal prediction through canonical event analysis. Mon Weather Rev 143:2404–2418. CrossRefGoogle Scholar
  46. Saha S et al (2014) The NCEP climate forecast system version 2. J Clim 27:2185–2208CrossRefGoogle Scholar
  47. Shastri H, Ghosh S, Karmakar S (2017) Improving global forecast system of extreme precipitation events with regional statistical model: application of quantile-based probabilistic forecasts. J Geophys Res Atmos 122:1617–1634. CrossRefGoogle Scholar
  48. Shukla S, Roberts J, Hoell A, Funk CC, Robertson F, Kirtman B (2016) Assessing North American multimodel ensemble (NMME) seasonal forecast skill to assist in the early warning of anomalous hydrometeorological events over East Africa. Clim Dyn. Google Scholar
  49. Slater LJ, Villarini G, Bradley AA (2016) Evaluation of the skill of North-American multi-model ensemble (NMME) global climate models in predicting average and extreme precipitation and temperature over the continental USA. Clim Dyn 1–16Google Scholar
  50. Slater LJ, Villarini G, Bradley AA (2017) Weighting of NMME temperature and precipitation forecasts across Europe. J Hydrol 552:646–659. CrossRefGoogle Scholar
  51. Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222. CrossRefGoogle Scholar
  52. Srivastava PK, Han D, Ramirez MR, Islam T (2013) Machine learning techniques for downscaling SMOS satellite soil moisture using MODIS land surface temperature for hydrological application. Water Resour Manag 27:3127–3144CrossRefGoogle Scholar
  53. Tan X, Gan TY, Shao D (2016) Wavelet analysis of precipitation extremes over Canadian ecoregions and teleconnections to large-scale climate anomalies. J Geophys Res Atmos 121:14469–14486. CrossRefGoogle Scholar
  54. Teutschbein C, Seibert J (2012) Bias correction of regional climate model simulations for hydrological climate-change impact studies: review and evaluation of different methods. J Hydrol 456:12–29CrossRefGoogle Scholar
  55. Themeßl MJ, Gobiet A, Heinrich G (2012) Empirical-statistical downscaling and error correction of regional climate models and its impact on the climate change signal. Clim Change 112:449–468CrossRefGoogle Scholar
  56. Thober S, Kumar R, Sheffield J, Mai J, Schäfer D, Samaniego L (2015) Seasonal soil moisture drought prediction over Europe using the North American multi-model ensemble (NMME). J Hydrometeorol 16:2329–2344CrossRefGoogle Scholar
  57. Thrasher B, Maurer EP, McKellar C, Duffy P (2012) Bias correcting climate model simulated daily temperature extremes with quantile mapping. Hydrol Earth Syst Sci 16:3309CrossRefGoogle Scholar
  58. Tripathi S, Srinivas V, Nanjundiah RS (2006) Downscaling of precipitation for climate change scenarios: a support vector machine approach. J Hydrol 330:621–640CrossRefGoogle Scholar
  59. Vapnik V (2013) The nature of statistical learning theory. Springer Science & Business Media, New YorkGoogle Scholar
  60. Voyant C, Notton G, Kalogirou S, Nivet M-L, Paoli C, Motte F, Fouilloy A (2017) Machine learning methods for solar radiation forecasting: a review. Renew Energy 105:569–582. CrossRefGoogle Scholar
  61. Wilby RL, Wigley T (1997) Downscaling general circulation model output: a review of methods and limitations. Prog Phys Geogr 21:530–548CrossRefGoogle Scholar
  62. Wilby RL et al (2000) Hydrological responses to dynamically and statistically downscaled climate model output. Geophys Res Lett 27:1199–1202CrossRefGoogle Scholar
  63. Wilcke RAI, Mendlik T, Gobiet A (2013) Multi-variable error correction of regional climate models. Clim Change 120:871–887CrossRefGoogle Scholar
  64. Wood EF, Yuan X, Roundy JK, Sheffield J (2015) Seasonal forecasting of global hydrologic extremes using the North American multi-model ensemble system. In: EGU general assembly conference abstractsGoogle Scholar
  65. Wu T et al (2014) An overview of BCC climate system model development and application for climate change studies. J Meteorol Res 28:34–56Google Scholar
  66. Wuest T, Weimer D, Irgens C, Thoben K-D (2016) Machine learning in manufacturing: advantages, challenges, and applications. Prod Manuf Res 4:23–45. Google Scholar
  67. Xu L, Chen N, Zhang X (2018a) A comparison of large-scale climate signals and the North American multi-model ensemble (NMME) for drought prediction in China. J Hydrol 557:378–390. CrossRefGoogle Scholar
  68. Xu L, Chen N, Zhang X, Chen Z (2018b) An evaluation of statistical, NMME and hybrid models for drought prediction in China. J Hydrol 566:235–249. CrossRefGoogle Scholar
  69. Yao M, Yuan X (2018) Superensemble seasonal forecasting of soil moisture by NMME. Int J Climatol. Google Scholar
  70. Yu S et al (2016) Anthropogenic aerosols are a potential cause for migration of the summer monsoon rain belt in China. Proc Natl Acad Sci 113:E2209–E2210CrossRefGoogle Scholar
  71. Yuan X, Wood EF (2013) Multimodel seasonal forecasting of global drought onset. Geophys Res Lett 40:4900–4905CrossRefGoogle Scholar
  72. Zhang X et al (2018) Geospatial sensor web: a cyber-physical infrastructure for geoscience research and application. Earth Sci Rev 185:684–703. CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote SensingWuhan UniversityWuhanChina
  2. 2.Collaborative Innovation Center of Geospatial TechnologyWuhanChina
  3. 3.Institute of Arid MeteorologyCMA, Key Laboratory of Arid Climatic Change and Reducing Disaster of CMA, Key Laboratory of Arid Climatic Change and Reducing Disaster of Gansu ProvinceLanzhouChina
  4. 4.Faculty of Information EngineeringChina University of Geosciences (Wuhan)WuhanChina

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