Wavelet cross-correlation analysis of wind speed series generated by ANN based models

Abstract

To obtain, over medium term periods, wind speed time series on a site, located in the southern part of the Paris region (France), where long recording are not available, but where nearby meteorological stations provide large series of data, use was made of ANN based models. The performance of these models have been evaluated by using several commonly used statistics such as average absolute error, root mean square error, normalized mean square error, and correlation coefficient. Such global criteria are good indicators of the “robustness” of the models but are unable to provide useful information about their “effectiveness” in accurately generating wind speed fluctuations over a wide range of scales. Therefore a complementary wavelet cross coherence analysis has been performed. Wavelet cross coherence, wavelet cross-correlation and spectral wavelet cross-correlation coefficients, have been calculated and displayed as functions of the equivalent Fourier period. These coefficients provide quantitative measures of the scale-dependence of the model performance. In particular the spectral wavelet cross coherence coefficient can be used to have a rapid and efficient identification of the validity range of the models. The results show that the ANN models employed in this study are only effective in computing large-scale fluctuations of large amplitude. To obtain a more representative time series, with much higher resolution, small-scale fluctuations have to be simulated by a superimposed statistical model. By combining ANN and statistical models, both the high and the low-frequency segments of the wind velocity spectra can be simulated, over a range of several hours, at the target site.