### Jacob Coburn

The feasibility of wind energy installations at a given location are dictated in large part by the wind resource (‘power in the wind’) which may change as a result of global climate non-stationarity. We seek to improve the wind farm lifetime wind power production by developing more efficient tools to make projections of annual energy production (AEP) under climate change scenarios. We develop and apply new statistical tools to make projections of energy production at 23 operating wind farms across North America (15-60°N, 60-125°W). A unique component of this research is that the statistical models are developed using actual daily production data corrected for operations and maintenance losses and curtailment. This avoids introducing uncertainties associated with deriving power estimates from downscaled wind speeds and relates directly to the variable of interest to the wind energy owner/operators. A potential disadvantage is that, in contrast to wind speeds that commonly fit a two-parameter Weibull distribution, the daily power production data from different sites do not conform to a single probability distribution. This and the short data record of observed power production (< 6 years) requires careful selection of appropriate statistical models. Here we develop and apply statistical models for each operating wind farm that employ a synoptic classification and apply them to make projections of future production for the 21st Century (2015-2100). The models are applied to an ensemble of 4 different CMIP6 Earth System Models (ESM) with 3 to 10 members for each ESM (total of 23 model runs) and to 4 different Shared Socioeconomic Pathways (SSPs).

The statistical models that link geophysical variables (e.g. sea level pressure) to daily power production expressed as capacity factors (CF) at each operating wind farm are derived using output from the ERA5 reanalysis. The suite of potential predictors considered are sea level pressure (SLP) as well as geopotential height and thickness, wind components and speed, air temperature, lapse rate and specific humidity at 500 and 700 hPa. The methodology used to select the predictors and build the statistical downscaling models at each site is as follows:

1) K-means hierarchical clustering is applied to daily mean patterns of each geophysical predictor over a 6° × 6° area centered on the wind farm. The clustering is applied using random initial centroids (days selected from within the dataset) and bootstrapped to obtain 500 realizations of the clustering and timeseries of the synoptic type to which each calendar date belongs.

2) The median CF for each synoptic type is calculated from the observed daily CF values. Timeseries of downscaled CF values are produced by assigning the median CF of each synoptic type to all days in the ERA5 record 1979-2014 on which the given synoptic type occurs. The result of this analysis is a sample of projected CF for the historical period.

3) The degree to which CF differ between the 20 clusters (synoptic types) is quantified for each potential predictor. The optimum predictor for each wind farm site is chosen using measures of clustering efficiency and the degree to which the daily CF from observations agree with the synoptic timeseries from Step 2 as measured by the Pearson correlation. For most sites, SLP or wind speed at 700 hPa emerge as the optimal predictors.

4) Mean spatial patterns for each synoptic type are computed for the 20 clusters of the optimal predictors. These act as the initial centroids for Kmeans clustering the ESM output for the historical period (1979-2014) as well as for the projections of the 21^{st} Century (2015-2100). This is done for each of the 500 timeseries from Step 1, resulting in 500 timeseries for each ESM run and scenario.

5) The daily type-index timeseries are converted to downscaled CF timeseries using the same assignment of median CF values to each day established in Step 2 for each of the 500 iterations. This results in the synoptic CF timeseries.

6) Clustering extracts and classifies days with similar spatial features but does not fully capture pattern intensity. Accordingly, residuals (predicted CF from the synoptic CF models developed using ERA5 versus the observed values) are strongly correlated with the daily pressure gradient (dP), calculated here as the difference between the maximum and minimum SLP values for each daily grid. Hence, a linear regression model is derived from ERA5 dP and CF residuals for each of the 500 iterations and applied to the ESM dP data for each site.

7) The full downscaled CF values are calculated by adding the synoptic CF timeseries and the pressure gradient CF timeseries, resulting in 500 daily CF timeseries for each ESM run and scenario. Thus, each day in the downscaled timeseries is characterized by a synoptic type and pressure gradient and a range of estimated CF values. The 50^{th} percentile of the 500 downscaled CF values for each day are used as the central estimate of daily CF for this assessment while the 10^{th}, 25^{th}, 75^{th} and 90^{th} percentiles provide the uncertainty range.

8) These timeseries of CF projections for each day 2005-2100 from each ESM realization, are used to quantify changes annual cumulative production (e.g., P50(AEP) and P90(AEP)), as well as changes in extremes such as storm events and wind ‘droughts.’ Changes in synoptic types and pressure gradients are used to diagnose causes of projected changes in CF over time.

In the near-term, the ensemble projections (23 ESM runs, 4 climate forcing scenarios) indicate relative stability in energy production. However, many model runs exhibit significantly larger changes by the end of the century, particularly under higher emissions scenarios, as well as much larger divergence in projected CF across the four ESMs. There is also clear evidence of coherent spatial variability in the wind futures, with specific regions experiencing markedly different trends. These results offer critical clues to utilities and planners as more information is sought on potential future shifts in the wind energy resource our society has become increasingly reliant on to combat the growth in emissions responsible for climate change.