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. For the first time an analytical solution for the quantification of the spatial variance of the second-order moment of correlated wind speeds wasdeveloped in this work. The spatial variance is defined as random differences in the sample variance of wind speed between different points inspace. The approach is successfully verified using simulation and field data. The impact of the spatial variance on three selected applicationsrelevant to the wind energy sector is then investigated including mitigation measures. First, the difference of the second-order moment betweenfront-row wind turbines of Lillgrund wind farm is investigated. The variance of the difference ranges between 25 % and 48 % for turbulenceintensities ranging from 7 % to 10 % and a sampling period of 10 min. It is thus suggested to use the second-order moment measured at eachindividual turbine as input to flow models of wind farm controllers in order to mitigate random error. Second, the impact of the spatial variance ofthe measured second-order moment on the verification of wind turbine performance is investigated. Misalignment between the mean wind direction andthe line connecting the meteorological mast and wind turbine is observed to result in an additional random error in the observed second-order momentof wind speed. In the investigated conditions the random error was up to 34 %. Such a random error adds uncertainty to the turbulenceintensity-based classification of the fatigue loads and power output of a wind turbine. To mitigate the random error, it is suggested to eitherfilter the measured data for low angles of misalignment or quantify wind turbine performance using the ensemble-averaged measurements of thesame wind conditions. Third, the verification of sensors in wind farms was investigated with respect to the impact of distant referencemeasurements. In the case of a misalignment between the wind direction and the line connecting sensor and reference, an increased random error willhamper the comparison of the measured second-order moments. The suggested mitigation measures are equivalent to those for the verification ofturbine performance.

Mitigating impact of spatial variance of turbulence in wind energy applications