variance of the data: $$SS_{\text{tot, WS}} =\sum_i{(WS_i - \overline{WS})^2.}$$ A positive correlation between IAV uncertainty and $SS_{\text{tot, WS}}$ emerges.

![Relationship between IAV uncertainty and the total sum of squares $SS_{\text{tot, WS}}$ of MERRA-2 wind speed data for the 472 projects considered.[]{data-label="dep_iav_spread"}](f11){width="8.3cm"}

At the same time, the linear regression $R^2$ coefficient also depends on the variance of the produced energy (and, equivalently, of wind speed) as it is defined as: $$R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}} % = 1 - \frac{\sum_i{(y_i - f_i)^2}}{\sum_i{(y_i - \overline{y})^2}}
\label{R2}$$ where $SS_{\text{res}}$ is the total sum of the residuals from the linear regression. Equation \[R2\] shows that when the total sum of squares $SS_{\text{tot}}$ increases, so does $R^2$, thus confirming the positive correlation between $R^2$ and the variance in the data.

Comparison Between Total Operational-Based AEP Uncertainty Under Different Assumptions
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After having revealed the correlations existing between different AEP uncertainty components and explained their sources, we can compare the total operational AEP uncertainty calculated when allowing for these correlations (Equation \[unc\_corr\]) with the total uncertainty calculated with the uncorrelated assumption using the conventional sum of squares approach (Equation \[unc\_unc\]).

![image](f12){width="16cm"}

Figure \[unc\_histogram\] shows the results of this comparison for the 472 wind plants considered as 