# Linear and nonlinear regression prediction of surface wind components

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## Abstract

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.

## Keywords

Statistical prediction Linear regression nonlinear regression Predictability of surface winds## Notes

### Acknowledgements

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.

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