## 3 Results and Discussion  
We analysed three data sets (Table 1), one (Howard) containing both wind speed and wind power time series, and the other two (Big Bear Lake and Atacama) containing only wind speed time series. Figure 3a plots the standard deviations of wind speed \(\sigma_{v}\) and wind power \(\sigma_{P}\) versus mean wind speed  
Figure 2: Statistical convergence of (**a**) mean wind speed; and (**b**) mean wind power versus number of samples contributing to the average. Each trace represents a separate data set generated with a bootstrap protocol by randomly shuffling values of the original Howard time series (Table 1). The averages approach asymptotic convergence around 400 samples. \(\overline{v}\) and wind power \(\overline{P}\), respectively, for the Howard data set. The standard deviation of wind speed \(\sigma_{v}\) (solid red circles in Figure 3a) scales algebraically relative to the mean wind speed \(\overline{v}\) with a power-law fit that follows the form \(\sigma_{v}=0.25\times\overline{v}^{0.73}\) (solid line in Figure 3a). The standard deviation of wind power fluctuations \(\sigma_{P}\) (solid blue squares in Figure 3a) also exhibits algebraic scaling, albeit shallower than wind speed, with a power-law fit of the form \(\sigma_{P}=3.9\times\overline{P}^{0.49}\) (dashed line in Figure 3a). Wind speed standard deviation \(\sigma_{v}\) for the Big Bear Lake data set plotted in Figure 3b (red solid circles) exhibits a similar algebraic scaling, but with a different power-law exponent (\(\sigma_{v}=0.4\times\overline{v}^{0.6}\), solid black line in Figure 3b) from the Howard data set. Finally, for the Atacama data set, although \(\sigma_{v}\) exhibits a systematic increase with \(\overline{v}\) (solid blue squares in Figure 3c), we find that the scatter is too high to make a conclusive determination of power-law scaling. We do include a power-law fit (dashed line in Figure 3c), but one should not derive any inferences from this fit. Be that as it may, the fact that \(\sigma_{v}\) exhibits monotonic increase with \(\overline{v}\) for all data sets establishes the scenario of multiplicative variability. The observed scaling for power fluctuations (\(\sigma_{P}=3.9\times\overline{P}^{0.49}\)) is significant given that [PERSON] et al. [18] have recently reported the same \(\sigma_{P}\sim\overline{P}^{0.5}\) scaling for a single turbine as well as for wind farms at various planetary locations. They interpreted this scaling within the context of the \"Taylor Rule\" [19] (not to be confused with Taylor's Hypothesis in turbulence theory [20]), also called \"Fluctuation Scaling\" [21] in physics, where the \(1/2\) scaling exponent forms one of two limiting cases. However, based on additional empirical evidence for wind speed fluctuations and calculations resulting in Equation (7), we proffer an alternative interpretation for this scaling. Consider a time-varying signal \(x(t)\) with a signal correlation time \(\tau_{0}\). The mean \(\overline{x}\) and standard deviation \(\sigma_{X}\) become truly time-independent when the average is taken over several multiples of the correlation time \(\tau_{0}\). Instead, if the averaging interval \(\tau<\tau_{0}\), residual correlations persist in \(\overline{x}_{\tau}\) and \(\sigma_{x_{\tau}}\) (subscript \(\tau\) now denotes the averaging interval) which vary with averaging time \(\tau\). Wind speed (and therefore wind power) fluctuations which reflect atmospheric turbulence possess long time correlations extending up to 24 h timescales [22; 23; 24; 25; 26], whereas the IEC standard [3] specifies a 10 min time average for calculation of \(\overline{v}\) and \(\overline{P}\). Even our bootstrap protocol specifically tests for statistical convergence in the absence of temporal correlations; generating a new randomised time series from the original time series destroys temporal correlations in the signal.