*3.4. Diurnal Variation in Wind Forecast Errors*

Figure 5 presents the diurnal variation of the mean observations, and the forecasts and MAE of the wind speed for the ensemble groups driven by the GFS, GEOS, and GEM forecasts. During daytime (00:00–09:00 UTC), the mean wind speed increases from 6 m/s to 7 m/s from morning to evening. Overall, the bias of the wind forecasts of all three groups is small. The GEOS group shows a bias close to zero, the GEM group has a weak negative deviation, and the GFS group has a bias that gradually increases from a negative deviation of ~0.1 m/s to a positive deviation of 0.2 m/s.

**Figure 5.** (**a**) Diurnal variation in wind speed observations and forecasts, and (**b**) MAE of the ensemble groups driven by the GFS, GEOS, and GEM. The x-axis represents the time (UTC).

At ~11:00 UTC, the wind forecasts of all three ensemble groups experience a sharp increase toward a positive deviation. Within half an hour, the bias of the wind forecasts of the GEOS, GFS, and GEM groups increases to ~0.9, 1.1, and 1.3 m/s, respectively. Subsequently, at night, the mean wind speed gradually weakens and the mean bias of the wind speed forecasting of the GFS group remains roughly unchanged, but the mean deviation in the GEOS and GEM groups continues to increase. By 23:00 UTC, the positive wind forecast biases of all three groups decrease rapidly as the boundary layer starts to grow after sunrise.

The GEM ensemble group possesses the largest MAE of the wind forecasts during daytime, followed by the GEOS group, while the MAE of the GFS group is the lowest. After a brief increase, MAE stabilizes at ~1.5 m/s between 03:00 and 11:00 UTC. After sunset (11:00–13:00 UTC), the MAE of all three groups increases to ~2.2 m/s. After nightfall, the MAE of the wind speed forecast of the GEM group continues to increase significantly, to 2.7 m/s, while that of the GEOS and GFS groups only increases to 2.3 m/s. Finally, after sunrise at 22:00 UTC, the MAE of all three groups decreases rapidly. Overall, the MAE of the GFS group was smaller than that of the other two groups, and the MAE of the GEM group was the largest for both nighttime and daytime. The MAE of the GEOS group during nighttime is similar to that of the GFS group.

To further compare the distribution of the wind forecast errors of the three ensemble groups and their diurnal variations, the forecast deviations of each ensemble member were analyzed for four day-periods: daytime (00:00–10:00 UTC), sunset (10:00–12:00 UTC), nighttime (12:00–22:00 UTC), and sunrise (22:00–00:00 UTC); the results are summarized in Figure 6.

The error distributions of the wind forecasts of all three groups are quite wide. The forecast members of the GFS group have relatively smaller variance (i.e., smaller dispersion) than the other two groups. In contrast, the forecast members of the GEM group have relatively larger variance and median bias. During the daytime and sunset periods, the error distributions of the three ensemble groups are relatively similar, and the numbers of samples with positive and negative deviations are close. However, during the night and sunrise phases, most of the model forecasts in all groups overestimate the wind speed, and the positive deviations of the GEM group are significantly larger than those of the GFS and GEOS groups.

**Figure 6.** Boxplots of the wind forecast bias distributions for the ensemble groups driven by the GFS, GEOS, and GEM forecasts for daytime (00:00–10:00 UTC), sunset (10:00–12:00 UTC), nighttime (12:00–22:00 UTC), and sunrise (22:00–00:00 UTC). The black horizontal line marks the median bias, while the white triangle represents the mean bias.

#### *3.5. Forecast Errors in Seven Regions*

The previous analysis indicates that the ensemble members driven by the three global model forecasts perform differently at different sites (Figure 3). To further investigate the regional differences in these ensemble groups, the wind farms in the study area were divided into seven sub-areas, according to geographical location, from west to east (see Figure 1). As shown in Figure 1, the wind farms are mainly built along the narrow mountain ridges that span the Inner Mongolia region. Based on the topography and wind farm distribution in the seven areas, they can be divided into four main types:


Figure 7 demonstrates that (1) the diurnal variation in the average wind speed and the forecast bias of the three ensemble groups in the four representative areas are quite different, (2) the trend of the wind speed forecast bias of the three ensemble groups is consistent, and (3) the average bias of the wind speed forecasting of all three ensemble groups is negatively correlated with the magnitude of the wind speed, i.e., the higher the wind speed, the smaller the bias.

Area 1 (Figure 7) is located on the north slope of a mountain. The wind in this region displays a very complex diurnal evolution, and the bias of the wind forecasts of all three ensemble groups presents similar, negatively correlated evolution of the mean wind speed. Among the three ensemble groups, the GEOS group has the smallest bias in the daytime and the largest late at night. The GEM group possesses the largest bias during most times, except for a 2-hour period around 18:00 UTC.

**Figure 7.** The BIAS of the wind forecasts of the three ensemble groups in the seven sub-areas. The x-axis represents the time (UTC).

Area 3 (Figure 7) is on the southern slope of the Hetao Plain, with a relatively low altitude. This area is affected by the prevailing westerly and northwesterly winds. Blocked by the Langshan Mountain tens of kilometers away to the northwest, the wind speed is smaller during the daytime and higher at nighttime compared to other areas, and the area is prone to strong winds. The nighttime wind speeds in this area gradually increase from 6.1 m/s at sunset to 7.1 m/s before sunrise, and a peak occurs at night (18:00 UTC). The bias of the wind speed forecasting of the three ensemble groups is small during daytime, at close to 0 for the GFS group, and with slight negative bias for the GEOS and GEM groups. In the evening, with the adjustment with the atmospheric boundary layer, the wind speed forecasts of the three ensemble groups grow rapidly to positive bias, reaching a maximum at ~13:00 UTC, and then gradually decreasing. The wind forecast biases of the GFS and GEOS groups are close, but the forecast bias of the GEM group has a much larger amplitude of diurnal variations, with a positive bias 0.3–0.4 m/s larger than that of the GFS group at night. It should be noted that the CC of the sites in Areas 1 and 3 is high (0.7~0.85).

The diurnal variations in the average wind speed and the wind forecast verification in Areas 2, 4, 5, and 6 are relatively similar. Unlike Area 3, the wind speed in these areas is characterized by high wind speeds during daytime, gradually strengthening after sunrise, reaching a peak around 9:00 UTC, and then decreasing to a minimum in the early morning. The bias of the wind speed forecasting of the three ensemble groups exhibits a very similar diurnal trend, with very little bias during daytime and a stable positive deviation of ~1.4 m/s at night. The GEOS group has a higher percentage of superior forecasts in Areas 2 and 4, mainly in the middle of the pass and on the northern slopes of the mountains in Area 4. The GFS group dominates better forecasts on the high slopes. The western part of Area 6, which is on the eastern part of the mountain peak, is a leeward slope where the forecast errors—mainly with negative bias—are relatively larger.

Area 7 (Figure 7) is a high plain characterized by flat terrain. The wind speed is characterized by a peak wind speed in the afternoon (08:00 UTC) and a shallow trough in the evening at 13:00 UTC. The wind speed forecasts of the three ensemble groups possess an obvious positive bias, except for the enhanced wind speed period in the afternoon (06:00–09:00 UTC), when the bias is smaller. The biases of the wind speed forecasts of the GFS and GEOS groups in this area are generally close to one another throughout the day, at ~0.5 m/s during daytime and close to 1.5 m/s at night. The GEM group underestimates the wind speed during daytime and overestimates the wind speed during nighttime, both of which errors are significantly larger than those of the GFS and GEOS groups. On average, the GFS group performs the best in this area, with a high CC of ~0.75.
