3.2. Comprehensive Performances of WSPD Models
In this section, we evaluate the performances of different wind speed probability distribution (WSPD) models, as listed in
Table 1, at two different heights (10 m ASL and 100 m ASL) over a 20-year period. To ensure computational efficiency, data from four representative times each day (00:00, 06:00, 12:00, and 18:00 UTC) were used, capturing the key characteristics of wind speed variation.
The results, summarized in boxplots (
Figure 2), show that the WEI-class models (WEI2 and WEI3) consistently perform well, with higher R
2 values and lower RMSE. At 10 m ASL, WEI2 slightly outperforms WEI3, although this difference is less significant in the European seas. However, at 100 m ASL, WEI3 outperforms WEI2, demonstrating its better ability to handle wind speed distributions at higher altitudes. The GEV model also performs competitively, especially in regions with high variability and extreme wind events. In contrast, the NO and LNO models show higher RMSE and lower R
2 values, indicating poor fit for the wind speed distributions in these regions. The WEI-class models better capture the wind speed patterns, reflecting the moderate to high wind speeds with occasional extremes.
The wind speed distributions in coastal areas of China exhibit significant variability at 10 m ASL (
Table 3). Specifically, at N1 (Bohai Bay), the mean wind speed is 5.35 m/s with a skewness of 0.68, indicating occasional strong winds. At N2 (Shandong Peninsula), the mean wind speed is 6.13 m/s with a skewness of 0.54, indicating a more stable wind profile. In contrast, at N5 (Taiwan Strait), the mean wind speed is 7.97 m/s with a variance of 15.33, reflecting higher wind energy potential coupled with frequent extreme wind events. At 100 m ASL, the mean wind speeds increase significantly, with 6.55 m/s at N1, 7.48 m/s at N2, and 9.57 m/s at N5, but the variability remains notable, particularly in the N5 and N6 regions. Offshore regions exhibit more stable wind conditions. For example, at O1 (Bohai Sea), the mean wind speed at 10 m ASL is 5.98 m/s with a skewness of 0.58. It rises to 7.39 m/s at 100 m ASL with a skewness of 0.53. At O5 (South East China Sea), the mean wind speed at 10 m ASL is 7.53 m/s with a skewness of 0.59. It increases to 8.68 m/s at 100 m ASL with a skewness of 0.83, indicating a more uniform wind profile. However, at O8 (South China Sea), the wind speed at 100 m ASL shows significant variability, with a variance of 22.45. This phenomenon indicates that considerable fluctuations could emerge at higher altitudes.
The histogram analysis reveals that the wind speed distributions at N5, O6, and O8 exhibit distinct multimodal patterns, indicating complex wind speed characteristics that cannot be adequately captured by common unimodal distribution models (such as WEI-class or GAM). Multimodal distributions typically suggest that wind speed variations in these areas may be influenced by multiple factors, such as seasonal changes, alternating climate systems, or topographical effects [
27]. Therefore, in these regions, the evaluation of models based on single-peak distributions may not be appropriate, and a different approach is needed to reflect the complex wind speed variability.
In contrast, at N6 (eastern Taiwan), the wind speed distribution shows a significant right-skewed pattern, particularly at 10 m ASL. The mean wind speed is relatively low, resulting in a more pronounced right skew. This wind speed distribution is distinct from other locations. For such distributions, the Gamma distribution model provides a better fit compared to the WEI-class models, as the GAM model is more suitable for low wind speeds with right-skewed characteristics. Overall, coastal regions in China are influenced by monsoons and typhoons, leading to significant wind speed fluctuations, especially at lower altitudes. Offshore areas, particularly at higher altitudes, exhibit more stable wind conditions, making them more suitable for large-scale wind farm development.
- 2.
Wind speed patterns in European seas.
The statistical properties of wind speed at 10 m and 100 m ASL across selected EU points show consistently slightly right-skewed distributions, in contrast to the more variable, multimodal distributions in China’s coastal regions (
Table 4). At 10 m ASL, the mean wind speeds range from 6.36 m/s at N1 (Baltic Sea) to 8.75 m/s at N8 (Western Ireland). As the altitude increases, the variance also rises, reflecting more pronounced wind speed fluctuations. At 100 m ASL, the mean wind speed increases, reaching 9.68 m/s at N5 (near the Netherlands) and 10.99 m/s at O6 (offshore UK). Offshore sites exhibit relatively stable wind conditions despite considerable variance at some locations (e.g., variance of 27.28 at O6). Despite this, the distributions remain right-skewed.
Given these characteristics, the WEI-class models (such as WEI2 and WEI3) provide the best fit for the data. These models are particularly well-suited to the stable distributions in the European sea areas.
- 3.
Summary.
The comparison of wind speed distributions between the Chinese and European coastal and offshore regions reveals some differences. The Chinese coastal areas show higher variability and multimodal distributions, particularly in the Taiwan Strait and South China Sea. In contrast, the European regions exhibit more stable, slightly right-skewed distributions, which are well captured by the WEI-class models. Offshore areas in Europe, especially at higher altitudes, offer more stable and predictable wind conditions, where large-scale wind energy development is feasible.
3.3. Distributions of Optimal and Suboptimal WSPD Models
In this section, we assess the performances of the selected wind speed probability distribution (WSPD) models by calculating their normalized scores based on R
2, RMSE, AIC, and BIC values. Each metric was equally weighted, yielding a total score ranging from 0 to 4, where higher scores indicate better model performances. The distribution of these scores at both 10 m ASL and 100 m ASL across the Chinese and European offshore regions is shown in
Figure 4.
The results reveal significant regional differences. In both regions, the WEI-class models consistently achieve the highest scores. In China, the distribution of model scores is less uniform compared to Europe. Although WEI2 and WEI3 have the best performances, the broad spread of scores suggests that the wind speed characteristics with greater spatial and temporal variability are more challenging to model. This is likely due to China’s complex coastal topography and the high variability in wind speeds. In contrast, the distribution in Europe is more uniform, reflecting stable wind speed patterns.
To further assess the models’ performances, we examined the frequency of the most optimal and suboptimal models across different grid points.
Figure 5 illustrates the frequency distribution of the optimal and suboptimal models at both 10 m ASL and 100 m ASL. In China, WEI2, WEI3, and GEV are the most frequent optimal models. The spatial distributions of the optimal and suboptimal models, shown in
Figure 6 and
Figure 7, reveal that the GEV model is mainly found in the East China Sea, the adjacent western Pacific, and the southern sea region of Hainan Island. In these regions, GUM is always the suboptimal model, suggesting that GEV and GUM share similar characteristics. This is supported by the behavior of the O5 point (
Section 3.2) in the East China Sea, where GEV fits the wind speed distribution, which is characterized by high kurtosis and relatively low mean wind speeds. This distribution indicates local low wind speeds with occasional extreme events, which is effectively captured by the GEV model, known for modeling extreme values or tail events. The GUM model, selected as a suboptimal model, shares similarities with the GEV model in capturing high peak and moderate tail behavior. However, as a two-parameter distribution, GUM is less flexible compared with the GEV model. Since the GEV model is a three-parameter distribution, it is more suitable in terms of extreme wind events and tail behavior modeling, making GEV the optimal choice in these cases. Similarly, WEI3 often outperforms WEI2 for similar reasons, as its additional parameter provides greater flexibility in capturing complex wind speed distributions.
In Europe, the WEI-class models again dominate the optimal and suboptimal model selections. The consistent performance across regions further highlights the stability of wind conditions in Europe, where WEI2 and WEI3 emerge as the most suitable models for wind speed distributions at both altitudes. This suggests that wind speed distributions in the European offshore areas are more uniform, making them easier to model with simpler, well-established distributions like WEI-class models. The stability of wind conditions in Europe allows for a more simple application of these models, while in China, the complex variability in wind speeds requires a more flexible modeling approach.
3.4. Guidelines for Selecting the Optimal WSPD Model
Wind speed characteristics, including mean wind speed, variance, skewness, and kurtosis, vary significantly across different regions, influencing the selection of the optimal wind speed probability distribution (WSPD) model. In the Chinese seas (
Figure 8), wind speed distributions are more variable, with higher skewness and kurtosis values, particularly in coastal areas like the Taiwan Strait and the South China Sea, where extreme wind events are more frequent. In contrast, the European seas (
Figure 9) are characterized by higher variance, indicating more fluctuations in wind speed, but with lower skewness and kurtosis compared to China. These regional differences underline the importance of considering specific wind speed characteristics when choosing the most suitable WSPD model.
In the analysis of wind speed characteristics at 10 m ASL and 100 m ASL in the Chinese seas (
Figure 10), most models, particularly those based on Weibull distributions, exhibit a positive correlation between the mean wind speed and variance. This suggests that as the mean wind speed increases, the variance in the wind speed also increases. Concurrently, as the mean wind speed rises, both skewness and kurtosis tend to decrease. This implies that at higher wind speeds, the distributions become more symmetric with lighter tails. This indicates that the frequency of extreme high wind speed events is lower. On the contrary, the GEV model’s concentration in regions with high skewness and kurtosis suggests that this model may be more effective in capturing the positively skewed characteristics. Therefore, it might have good performances in regions where extreme wind speed events are more frequent.
For the European seas (
Figure 10), the Weibull-based models dominate. Different from the Chinese seas, the GAM distribution model is more effective in regions with higher variance, kurtosis, and skewness, such as the eastern Greenland seas. This suggests that the wind speed distribution in these regions is positively skewed, probably influenced by the unique climatic conditions (e.g., polar and marine climates [
47,
67]), topographic features (e.g., Greenland’s mountains [
68]), and ocean dynamics (e.g., ocean currents, tides, and vortices [
69]), which directly influence wind loads [
70,
71]. As a result, the wind speed distribution in this region shows higher volatility and a right-skewed pattern, which is similar to the eastern Taiwan seas, where the GAM model is also suitable (point N6 in
Figure A36).
Overall, the GEV model seems more suitable for capturing extreme wind speed events, as it is specifically designed to model the tail behavior of the distribution. In contrast, the GAM model may be a better choice for describing the general characteristics of wind speed distributions, especially in regions where the distribution is positively skewed and exhibits significant variability. The WEI-class models are likely to perform better in simulating wind speed distributions with moderate skewness, especially in the European seas. Aiming at an appropriate selection of distribution model, it is crucial to consider the wind speed distribution characteristics of the target sea area.
The analysis of wind speed characteristic importance rankings across Chinese and European offshore regions at 10 m and 100 m ASL utilized three distinct methodologies: Random Forest (RF), XGBoost, and Permutation Feature Importance (PFI). This combined approach ensured a comprehensive evaluation and validated the robustness of our findings.
The feature importance rankings for wind speed characteristics are shown in
Table 5. It should be noted that in the RF and XGBoost models, the sum of feature importances equals one due to normalization, allowing for direct comparison of feature importance scores. In contrast, PFI does not normalize the scores, so their sum may not equal one. In fact, PFI evaluates feature importance by assessing the impact of feature shuffling on model performance. This means that PFI scores represent the actual impact of features on the model’s predictive accuracy rather than their relative importance compared to other features. Consequently, PFI scores may not be directly comparable across models or datasets.
From
Table 5, it is clear that skewness is the most significant factor in both regions at both heights. This finding highlights the importance of considering distribution asymmetry when modeling wind speeds. Kurtosis also emerged as a significant factor, reflecting the influence of extreme wind events. While the mean and variance are important, they are consistently ranked lower in importance compared to skewness and kurtosis. This suggests that while the central tendency and variability in wind speeds are informative, they may not be as critical as the distribution’s shape in determining model accuracy.
In addition, the agreement between the PFI and tree-based model rankings (RF and XGBoost), as well as across the datasets from different regions and heights, highlights the impact of skewness and kurtosis on wind speed distribution modeling. This consistency indicates that these models effectively capture underlying data patterns crucial for accurate wind resource predictions.
3.5. Recommendations
Based on the analysis of the wind speed probability distribution models and their performances in the Chinese and European offshore areas, the following recommendations are provided to enhance the accuracy and applicability of wind speed modeling for wind energy assessments.
For regions with moderate skewness and kurtosis, particularly in the European offshore areas, the Weibull-class models (WEI2 and WEI3) are recommended due to their simplicity and effectiveness.
In areas with higher variability and extreme wind events, such as the East China Sea and the adjacent western Pacific, the Generalized Extreme Value (GEV) model is suggested for its ability to capture extreme values effectively. For regions exhibiting positively skewed wind speed distributions and significant variability, such as the eastern Greenland seas, the Gamma (GAM) distribution model is advised.
- 2.
Consideration of altitude in model application.
At 10 m ASL, the performance of WEI2 slightly surpasses WEI3 in Chinese coastal areas, while at 100 m ASL, WEI3 shows better performance, indicating the importance of altitude in model selection. In the European seas, the WEI-class models perform consistently well at both altitudes, reflecting the stability of wind conditions.
- 3.
Importance of skewness and kurtosis.
Skewness is identified as the most significant factor influencing model selection, emphasizing the need to model right-skewed distributions, especially in regions with occasional high wind speed events. Kurtosis also plays a crucial role, particularly in areas with frequent extreme wind events, indicating the occurrence of more frequent extreme wind events.
- 4.
Regional variability and model flexibility.
The complex variability in wind speeds in the Chinese coastal areas necessitates a more flexible modeling approach compared to the more uniform wind conditions in Europe, where simpler models, like WEI-class models, can be effectively applied.
- 5.
Future research directions.
Future studies should explore the integration of machine learning techniques and hybrid models to better capture complex wind patterns and enhance model accuracy. The long-term performance and adaptability of these models under changing climate conditions also need to be assessed.
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Yanan Chen www.mdpi.com
