## 1 Introduction  
The wind turbine power curve relates the speed of wind blowing past a turbine to the power generated by the turbine. Wind plant operators forecast the power they expect to generate by feeding wind speed forecasts from numerical weather models to these power curves [1, 2]. The power curves are supplied to operators by turbine manufacturers, who calibrate them under standards specified by the International Electrotechnical Commission (IEC) [3]. The IEC standard considers the average behaviour between the mean wind speed \(\overline{v}\) (\(\overline{x}\) being the time-average of a time-varying quantity \(x(t)\)) and mean power output \(\overline{P}\), and hence does not locally hold in time for instantaneous measurements. Indeed, instantaneous values of wind speed \(v(t)\) and wind power \(P(t)\) exhibit significant scatter about the mean profile (Figure 1). Several studies [4, 5, 6, 7, 8] have focused on the factors contributing to this variability, including turbulent fluctuations, wind shear, directional shear, directional fluctuations, etc., with the aim of accurately modeling the \"mean\" profile of the wind turbine power curve [9, 10, 11, 12]. In this article, we first establish that the wind turbine power curve has features that are sensitive to local environmental factors. We then employ a combination of theory and empirical results to self-consistently account for this dependence on local factors. Our proposed approach was especially developed within the framework of IEC standard 614001-12-1 to ensure its easy adoption by wind plant operators. In particular, we present a minimal parameter description of wind speed variability \(\sigma_{v}=\sqrt{\overline{(v(t)-\overline{v})^{2}}}\) and wind power variability \(\sigma_{P}=\sqrt{\overline{(P(t)-\overline{P})^{2}}}\) in terms of the mean wind speed \(\overline{v}\). Our objective here is to remain faithful to the IEC standard [3] that prescribes the power curve with mean wind speed \(\overline{v}\) as its only parameter. We present empirical evidence that the standard deviation in wind speed \(\sigma_{v}\) systematically varies with mean wind speed \(\overline{v}\). At least in some instances, this monotonic variation follows algebraic scaling of the form \(\sigma_{v}=C\times\overline{v}^{\alpha}\), where \(C\) is a constant and \(\alpha\) is a fractional power. This scaling form--which we attribute to residual signal correlations that remain post-averaging--then affords a description of mean wind power \(\overline{P}\) and its standard deviation \(\sigma_{P}\) in terms of \(\overline{v}\) alone. Our analysis of wind data obtained from three different planetary locations (Table 1) reveals that in instances when the above scaling form is satisfied, the power-law exponent \(\alpha\) varies with geographic location, and hence must reflect local environmental factors not captured by manufacturer-supplied calibration power curves. Consequently, when these calibration power curves are applied to forecast wind power, wind speed variability transforms into power forecast uncertainty. Since the variability always increases in tandem with mean speed, the resulting forecast error is multiplicative, so it substantially increases uncertainty in wind power forecasts. We conclude with a proposal that wind plant operators should recalibrate turbine power curves at the plant location to properly account for variability arising from local environmental factors. This will help to reduce the uncertainty of wind power forecasts. At first sight, the monotonic increase in wind speed variability \(\sigma_{v}\) with mean speed \(\overline{v}\) seems at odds with the general belief that the turbulence intensity \(I=\frac{\sigma_{v}}{\overline{v}}\) decreases with speed. In many instances, one observes that fluctuations \(\sigma_{v}\) exhibit non-monotonic behaviour with steady increase in mean speed \(\overline{v}\) (and Reynolds number \(Re\)) [13]. In particular, frictional losses with the walls cause loss of pressure head in water flow down a river or pipe.