Climate Dynamics

, Volume 51, Issue 9–10, pp 3291–3309 | Cite as

Linear and nonlinear regression prediction of surface wind components

  • Yiwen MaoEmail author
  • Adam Monahan


This study compares the statistical predictability by linear regression of surface wind components using mid-tropospheric predictors with predictability by three nonlinear regression methods: neural networks, support vector machines and random forests. The results, obtained at 2109 land stations, show that more complex nonlinear regression methods cannot substantially outperform linear regression in cross-validated statistical prediction of surface wind components. As well, predictive anisotropy (variations in statistical predictive skill in different directions) are generally similar for both linear and nonlinear regression methods. However, there is a modest trend of systematic improvement in nonlinear predictability for surface wind components with fluctuations of relatively small magnitude or large kurtosis, which suggests weak nonlinear predictive signals may exist in this situation. Although nonlinear predictability tends to be higher for stations with low linear predictability and nonlinear predictive anisotropy tends to be weaker for stations with strong linear predictive anisotropy, these differences are not substantial in most cases. Overall, we find little justification for the use of complex nonlinear regression methods in statistical prediction of surface wind components as linear regression is much less computationally expensive and results in predictions of comparable skill.


Statistical prediction Linear regression nonlinear regression Predictability of surface winds 



The authors gratefully acknowledge helpful comments and suggestion from two anonymous reviewers. This research was supported by the Discovery Grants program of the Natural Sciences and Engineering Research Council of Canada.


  1. Amari SI, Murata N, Müller KR, Finke M, Yang HH (1996) Statistical theory of overtraining-is cross-validation asymptotically effective? In: Advances in neural information processing systems, pp 176–182Google Scholar
  2. Breiman L (2001) Random forests. Mach Learn 45(1):5–32CrossRefGoogle Scholar
  3. Csáji BC (2001) Approximation with artificial neural networks. Faculty of Sciences, Eötvös Loránd University, Hungary 24:48Google Scholar
  4. Culver AM, Monahan AH (2013) The statistical predictability of surface winds over western and central Canada. J Clim 26(21):8305–8322CrossRefGoogle Scholar
  5. Davy RJ, Woods MJ, Russell CJ, Coppin PA (2010) Statistical downscaling of wind variability from meteorological fields. Boundary-layer Meteorol 135(1):161–175CrossRefGoogle Scholar
  6. Hastie TJ, Tibshirani RJ, Friedman JH (2009) The elements of statistical learning: data mining, inference, and prediction. Springer, New YorkCrossRefGoogle Scholar
  7. He Y, Monahan A, Jones C, Dai A, Biner S, Caya D, Winger K (2010) Land surface wind speed probability distributions in North America: observations, theory, and regional climate model simulations. J Geophys Res 115(D04):103Google Scholar
  8. Holtslag A, Svensson G, Baas P, Basu S, Beare B, Beljaars A, Bosveld F, Cuxart J, Lindvall J, Steeneveld G et al (2013) Stable atmospheric boundary layers and diurnal cycles: challenges for weather and climate models. Bull Am Meteorol Soc 94(11):1691–1706CrossRefGoogle Scholar
  9. Hsieh WW (2009) Machine learning methods in the environmental sciences: neural networks and kernels. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  10. van der Kamp D, Curry CL, Monahan AH (2012) Statistical downscaling of historical monthly mean winds over a coastal region of complex terrain. II. Predicting wind components. Clim Dyn 38(7–8):1301–1311CrossRefGoogle Scholar
  11. Kanamitsu M, Ebisuzaki W, Woollen J, Shi-Keng Y et al (2002) NCEP-DOE AMIP-II reanalysis (r-2). Bull Am Meteorol Soc 83(11):1631CrossRefGoogle Scholar
  12. Liaw A, Wiener M (2002) Classification and regression by randomforest. R News 2(3):18–22Google Scholar
  13. Mao Y, Monahan A (2017) Predictive anisotropy of surface winds by linear statistical prediction. J Clim 30(16):6183–6201CrossRefGoogle Scholar
  14. MathWorks (2017b) Getting Started with Neural Network Toolbox.
  15. MathWorks (2017c) Understanding Support Vector Machine Regression.
  16. Mohandes M, Halawani T, Rehman S, Hussain AA (2004) Support vector machines for wind speed prediction. Renew Energy 29(6):939–947CrossRefGoogle Scholar
  17. Monahan AH (2012) Can we see the wind? Statistical downscaling of historical sea surface winds in the subarctic northeast Pacific. J Clim 25(5):1511–1528CrossRefGoogle Scholar
  18. Platt J (1998) Sequential minimal optimization: A fast algorithm for training support vector machines. Tech. rep, Microsoft ResearchGoogle Scholar
  19. Python (2016) RandomForestRegressor-scikit-learn 0.18.1 documentation.
  20. Ripley B, Venables W (2016) Package ’nnet’.
  21. Sailor D, Hu T, Li X, Rosen J (2000) A neural network approach to local downscaling of GCM output for assessing wind power implications of climate change. Renew Energy 19(3):359–378CrossRefGoogle Scholar
  22. Salameh T, Drobinski P, Vrac M, Naveau P (2009) Statistical downscaling of near-surface wind over complex terrain in southern France. Meteorol Atmos Phys 103(1–4):253–265CrossRefGoogle Scholar
  23. Stull RB (2000) Meteorology for scientists and engineers: a technical companion book with Ahrens’ Meteorology Today. Brooks/ColeGoogle Scholar
  24. Sun C, Monahan A (2013) Statistical downscaling prediction of sea surface winds over the global ocean. Journal of Climate 7938–7956CrossRefGoogle Scholar
  25. Vapnik V (2013) The nature of statistical learning theory. Springer Science & Business Media, New YorkGoogle Scholar
  26. Wolfram (2016) WeatherData source information. Accessed 1 Jan 2016
  27. Yuval Hsieh W (2002) The impact of time-averaging on the detectability of nonlinear empirical relations. Quarterly Journal of the Royal Meteorological Society 583(1609–1622)Google Scholar
  28. Zhao P, Yu B (2006) On model selection consistency of Lasso. Journal of Machine learning research 7(Nov):2541–2563Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Earth and Ocean SciencesUniversity of VictoriaVictoria Canada

Personalised recommendations