# Region-Based Convolutional Neural Network for Wind Turbine Wake Characterization in Complex Terrain
## 2 Materials and Methods
### Sensitivity to Scan Resolution and Flow Conditions  
As lidar technology evolves and scan resolutions vary per campaign, it is pertinent to examine how the model, and the subsequent wake characteristics, are affected when applied to lower resolution scans. To assess the model's performance under a variation in range gate resolution, each of the radial velocity fields in each scan in the testing dataset was down-sampled such that every other value was removed, reducing the range gate resolution from 50 m to 100 m. Wake characteristics were then calculated for down-sampled scans and compared to full resolution scans.  
As wake geometries are dependent on atmospheric conditions and flow field velocities, variations in wake characteristics and model accuracy were assessed by classifying the atmospheric conditions under which each scan was performed (Table 2). Scans were defined as \"low\" wind speed if the median horizontal wind speed is <9 ms\({}^{-1}\) in the 59 testing scans. Scans captured during lower velocity conditions result in higher thrust coefficients, which yield relatively larger magnitude wakes. In addition, lower velocities are most often associated with higher turbulence intensities [48]. Scans performed during the daytime (8 a.m.-8 p.m., local time) are placed into a class of unstable stratification.  
After wakes and wake fragments in each atmospheric class were identified for both scan image resolutions (full, half) based on the threshold for IoU, three wake characteristics were analyzed: asymmetry, length and width. These metrics are defined below, and depend on the characterization of the wake or wake fragment's _skeleton_, which is otherwise known as the medial axis of the object. The skeleton (the mathematical process to calculate the skeleton is described in detail in [49]) is a simplified shape representation used often in image processing applications and is utilized herein as an approximation for the geometric wake centerline (Figure 8).  
\begin{table}
\begin{tabular}{c c c} \hline
**Class** & **Atmospheric Stability Indicator (Time of Day in Local Time)** & **Wind Speed Bracket (Classified by Scan Bulk Wind Speed, V)** \\ \hline I & Nighttime & Low \\ \hline II & Daytime & Low \\ \hline III & Nighttime & High \\ \hline IV & Daytime & High \\ \hline \end{tabular}
\end{table}
Table 2: Atmospheric classes used in the analysis of varying scan resolution on wake characteristics.  
Width: In this analysis, wakes propagate along an approximate west-east axis, so an approximation of the mean wake width (perpendicular to the skeleton) was computed as the sum of the number of pixels in the y-direction (south-north) that are enclosed by the wake boundary at a given point along the skeleton divided by the total number of points along the skeleton;  
Asymmetry: After the wake/wake fragment's skeleton was identified, the pixels above and below the skeleton (in the north-south [y] direction) were projected to two histograms, where each bin represents the point along the skeleton, and the histogram width is the number of pixels above (or below) the skeleton. Each projected histogram thus represents the distribution of pixels in the y direction along the length of the skeleton, with one histogram representing the distribution of pixels above the skeleton and one histogram representing the distribution of pixels below. The correlation of these projected histograms was then assessed through evaluation of the Pearson correlation coefficient. A high correlation coefficient corresponds to high north-south symmetry along the skeleton (approximate wake centerline), i.e., the width of the pixels in the upper half of the wake correlate with the width of the pixels in the lower half of the wake for each point along the skeleton;  
Length: The wake length was assessed through calculating the distance between the easternmost and westernmost wake skeleton locations for east-west propagating wakes, or the westernmost and easternmost wake skeletons for west-east propagation cases.