Low-frequency wind spectrum

Figure 3-8 shows the wind speed spectrum in the low-frequency domain at the σ995 level

over Toronto. Three pronounced peaks are noticeable. The peak associated with the highest frequency has a period of 2 to 4.5 days. This local maximum in the spectrum has previously been reported in a number of wind studies (see discussion in Introduction and Figure 3-1). The passage of large scale pressure systems, such as depressions and cyclones, is associated with the energy production with the period of 3-4 days (Estoque 1955; Van der Hoven 1957). The Great Lake region is an area where two major North American cyclonic tracks merge (Zishka and Smith 1980) and afterwards take northeasterly trajectories. The same study reported that these cyclones are most frequent in winter, which has been later

128 confirmed in the study by Zhang et al. (2004). Their findings are in a good agreement with the presented results that winter is the windiest month in Toronto.

Figure 3-8. Low-frequency wind speed spectrum for Toronto based on the mean daily wind speeds.

The second pronounced peak in the spectra possesses a period of 1 year. This peak is associated with alternation of seasons throughout the year. As already demonstrated, winds over Toronto are the strongest in winter and weakest in summer. The existence of a 1-year peak is reported by many researchers (Gomes and Vickery 1977; Harris 2008; Belu and Koracin 2013). The autocorrelation function of the wind speed series also resembles the 1- year periodicity, as shown in Figure 3-9.

129 Figure 3-9. Autocorrelation of the mean daily wind speed. The horizontal red lines represent the 95% confidence intervals. Note that the x-axis starts at the time lag of 1.

A striking feature in the spectrum, however, is the presence of the third peak corresponding to the 11-year period. This finding required further investigation. To begin with, it should be noticed that very low frequencies correspond to very long time periods, which consequentially means that the lowest frequency oscillations often lack statistical significance. For example, the left end of the spectrum in Figure 3-7 corresponds to a period of approximately 22 years. Knowing that the input data cover only 67 years, such a (hypothetical) process could not occur more than three times in the timespan of the dataset. Thus, the presence of this last peak is not yet conclusive. Nevertheless, an astronomical process that possesses an 11-year period is the solar activity (Hathaway et al. 1994).

130 Since the observed 11-year peak in wind spectrum has the same period as the maximum of solar activity, combining these two time series seems to be a logical step. Data representing the monthly mean total sunspot number are obtained from the World Data Center SILSO at the Royal Observatory of Belgium, Brussels, Belgium (SILSO World Data Center, 1948), at: http://sidc.be/silso/. As we are not concerned with the inter-annual oscillations of the number of sunspots, the mean monthly wind speed as well as the total monthly number of sunspots were smoothed by applying a moving average with a 13-month low- pass filter (n), as described by Eq. (3-7).

The results of the moving average procedure are depicted in Figure 3-10. It can be observed that there were seven solar cycles in the analyzed period. The wind speed time series, although noisier, also contains some major peaks in 1958, 1977, 1989, as well as lower peaks in 1981 and 2002. An absolute wind speed minimum in 2005 is also evident. The same peaks, but not that pronounced, have been observed in the mean annual wind speed data series presented in Figure 3-5. The overlaps between the solar activity, on one side, and wind speed peaks, on the other side, can easily be observed in the years 1958, 1981, 1989 and 2002. It seems, however, that the absolute maximum in the wind speed series, recorded in 1977, does not directly coincide with a solar maximum. A peak in solar activity rather occurred some 8 years prior to the 1977 wind speed peak.

131 Figure 3-10. 13-month moving average of the mean monthly wind speeds above Toronto

(black line) and the total monthly number of sunspots (red line)

An interesting occurrence is that this solar maximum has been the weakest maximum in the 1949 to 2002 period. In order to statistically quantify the strength of the observed relationship between the mean annual wind speed and the solar activity, a cross-correlation analysis between the two data sets is carried out. The results are portrayed in Figure 3-11.

132 Figure 3-11. Cross-correlation between the 13-month moving averages of the mean

monthly wind speed above Toronto and total monthly number of sunspots

The cross-correlation analysis confirms that there is a significant similarity between the two time series. The highest correlation is observed at zero time lag and reaches 0.82. A second and less pronounced peak in the correlation curve is located around 8.5 years in the direction of the positive lags; at the time lag equal 100 months. This may indicate that the response in wind speed maximum is considerably delayed after the period of the maximum solar activity. Examining Figure 3-10 again, it can be seen that the time lag between the peaks in the monthly number of sunspots in 1969 and the wind speed peak in 1977 occurred with the 8-year time shift in between them. Another example is the solar minimum that

133 took place in 1997 and the most pronounced wind speed minimum recorded in 2005. The 8-year periodicity is also noticeable in the 5-year moving average series of mean annual wind speeds in Figure 3-4. However, the last three peaks in the moving average series in Figure 3-4 are 11 years apart. The above results seem to indicate that the solar activity either has instantaneous or time-delayed impact on the monthly wind speed over Toronto area.