Daily-cycle patterns of angular errors in ERA5 wind direction: clustering and calibration using surface meteorological variables

Wind direction is critical for wind energy assessment, as it influences turbine yaw alignment, wake effects, and energy production estimates. This is especially relevant in mountainous regions, where complex terrain and atmospheric processes contribute to directional variability. Despite its importance, wind direction from global atmospheric reanalysis has received little attention in wind resource assessments, which mainly focus on wind speed. This study identified clusters of daily-cycle patterns of angular errors in hourly ERA5 wind direction and evaluated a machine-learning calibration using ERA5 surface meteorological variables. The analysis was applied in the complex terrain of the Ecuadorian Andes (3800 m a.s.l.), using one year of data (2021) of ERA5 wind direction (100 m height) and ground-based wind measurements (80 m). K-means clustering was applied to the sine and cosine components of wind direction from both reanalysis and observations. A Random Forest model was trained independently for each cluster using wind speed at 100 m, sine and cosine components of wind direction, 10 m wind gust, near-surface air temperature, dew point temperature, skin temperature, surface pressure, radiation fluxes, and precipitation. Results revealed three clusters related to the daily-cycle and the magnitude of the angular error: Cluster 1- predominantly nocturnal and early morning (8 pm-10 am, minimum at 4 pm); and small angular error (median 16°); Cluster 2 - daytime and predominantly afternoon (10 am - 8 pm, peak at 4 pm), and large angular error (80°); and Cluster 3 - evenly distributed throughout the day, with a slight maximum at 3 pm; and medium angular error (47°). The largest errors coincided with lower wind speed and post-midday decreases in air temperature, skin-surface temperature, and surface pressure. They also coincided with large variability in wind direction since Cluster 1 was dominated by easterly to southeasterly winds, Cluster 3 by westerly, while Cluster 2 showed a large dispersion from easterly to westerly flows. Calibration substantially improved wind direction representation. For the nocturnal cluster, the most informative predictors were 10 m wind gust, skin temperature, and surface pressure, reducing the median angular error to 8° and improving the wind direction distribution (Perkins Skill Score - PSS from 0.50 to 0.69). For the high-error afternoon cluster, wind speed, total precipitation, and surface pressure were the dominant predictors, decreasing the median angular error to 15° and improving PSS from 0.32 to 0.60. Finally, for the evenly-distributed cluster, surface pressure, dew point temperature, and wind speed were most relevant predictors, yielding a median angular error of 8° and PSS increase from 0.36 to 0.68. The findings highlight the strong dependence of the angular error of ERA5 wind direction on the daily-cycle and thermal processes.