Ten-Meter Wind Speed Forecast Correction in Southwest China Based on U-Net Neural Network

Abstract

Accurate forecasting of wind speed holds significant importance for the economic and social development of humanity. However, existing numerical weather predictions have certain inaccuracies due to various reasons. Therefore, it is highly necessary to perform statistical post-processing on forecasted results. However, traditional linear statistical post-processing methods possess inherent limitations. Hence, in this study, we employed two deep learning methods, namely the convolutional neural network (CNN) and the U-Net neural network, to calibrate the forecast of the Global Ensemble Forecast System (GEFS) in predicting 10-m surface wind speed in Southwest China with a forecast lead time of one to seven days. Two traditional linear statistical post-processing methods, the decaying average method (DAM) and unary linear regression (ULR), are conducted in parallel for comparison. Results show that original GEFS forecasts yield poorer wind speed forecasting performance in the western and eastern Sichuan provinces, the eastern Yunnan province, and within the Guizhou province. All four methods provided certain correction effects on the GEFS wind speed forecasts in the study area, with U-Net demonstrating the best correction performance. After correction using the U-Net, for a 1-day forecast lead time, the proportion of the 10-m U-component of wind with errors less than 0.5 m/s has increased by 46% compared to GEFS. Similarly, for the 10-m V-component of wind, the proportion of errors less than 0.5 m/s has increased by 50% compared to GEFS. Furthermore, we employed the mean square error-based error decomposition method to further diagnose the sources of forecast errors for different prediction models and reveal their calibration capabilities for different error sources. The results indicate that DAM and ULR perform best in correcting the Bias2, while the correction effects of all methods were variable for the distribution with the forecast lead time. U-Net demonstrated the best correction performance for the sequence.

1. Introduction

Wind is one of the most crucial meteorological elements [1], playing a significant role in weather and climate changes [2], with profound impacts on human life, production, and transportation. Suitable wind conditions can alleviate local air pollution, mitigate urban heat island effects [3], and facilitate wind power generation to reduce carbon emissions [4]. However, excessive wind speed can pose risks to the environment, transportation infrastructure, and even human lives and property [5,6]. Furthermore, wind speed variations are a crucial aspect of climate change research [7,8]. Therefore, accurate and reliable wind speed forecasting is of paramount importance. Among various time scales in meteorological forecasting, short-term weather forecasting (one to seven days) is an essential component of traditional operational forecasts, serving purposes such as issuing warnings and assisting government decision-making [9]. Thus, improving the accuracy of wind speed forecasts in the 1–7 day range holds great significance [10].

Numerical weather prediction models [11] have matured as a technology and represent the primary technical support for meteorological operational forecasts after years of development. However, numerical models are based on numerical approximations and do not encompass all physical processes in the real Earth system [12,13,14,15,16,17]. Additionally, the chaotic nature of the atmosphere [18] and random errors that arise during the integration of numerical models [19,20,21] result in inevitable errors in the numerical forecasts. Therefore, statistical post-processing methods must be applied to further improve the accuracy of forecasts based on numerical model outputs [22]. Traditional statistical post-processing methods primarily involve establishing point-to-point regression equations for individual corrections. However, the atmosphere is a highly nonlinear system, and traditional linear statistical post-processing methods have limitations in the correction process of these forecasts. In recent years, the wave of artificial intelligence has swept across the globe, and deep learning algorithms have been widely applied across various fields. They have demonstrated great potential in the earth sciences owing to their rapid learning capabilities and excellent nonlinear fitting abilities [23].

Convolutional neural networks (CNN) [24,25,26,27,28] are among the most representative algorithms of deep learning. Compared to traditional feed-forward neural networks, CNNs incorporate convolutional and pooling layers [29,30]. The convolution operation considers the interactions between adjacent points within the convolution range. Han et al. employed CNNs for the short-term forecasting of convective storms, and the forecast results outperformed traditional machine learning methods [31]. To address medical image segmentation problems, U-Net networks were developed based on CNNs [32]. U-Net retains the convolution and pooling layers of CNNs while adding skip connections. It can filter and extract the main features of the original field and recognize and retain features at different spatial scales, making it applicable in statistical downscaling and post-processing. Sha et al. used the U-Net neural network for downscaling experiments on the highest and lowest temperatures in the Midwest of the United States. They found that the U-Net network outperformed traditional methods in terms of the mean absolute error [33].

Currently, many researchers [34,35,36] have explored the application of deep learning algorithms in the correction of numerical wind field forecasts, achieving promising results. However, the use of the U-Net neural network in the correction of numerical wind field forecasts has been quite limited. Therefore, in this study, the U-Net neural network is employed for wind speed forecast correction in Southwest China. It is compared with a CNN correction model and traditional correction methods such as the Decaying Average Method (DAM) [37] and unary linear regression (ULR) [38] to explore potential improvements in forecast accuracy. Furthermore, to analyze the sources of errors and enhance the interpretability of the forecasting models, this study employs the error decomposition method proposed by Hodson et al. [39] to decompose the mean square error (MSE) into a bias, a distribution, and a sequence term. Subsequently, error diagnosis and analysis are conducted for each forecasting scheme, providing insights for further model optimization.

2. Data

The 10-m U- and V-components of the wind forecast data from the Global Ensemble Forecasting System (GEFS) of the National Centers for Environmental Prediction (NCEP) were selected as the forecast data. The data were obtained from the daily 00:00 UTC forecasts. The data spanned from 1 January 2000 to 31 December 2019, and covered Southwest China and its surrounding areas (96° E–111.75° E, 20° N–35.75° N). The horizontal resolution of the model is 0.25° × 0.25°, and the forecast lead time is from 24 to 168 h with a 24-h interval. For the observation data, the hourly 10-m U- and V-components of the wind data from the Fifth Generation of the European Centre for Medium-Range Weather Forecasts (ERA5) were selected. The data were available daily at 00:00 UTC and were transformed into daily data prior to use. The data cover the period from 1 January 2000 to 31 December 2020, and have the same horizontal resolution and spatial coverage as GEFS data.

The study region is located in Southwest China (Figure 1). According to previous studies [40], this region has experienced numerous meteorological disasters of varying degrees in the past 40 years. On average, more than 50 million people are affected by disasters each year, and the direct economic losses amount to nearly 100 billion RMB. Wind and hail disasters are among the most severe meteorological disasters in this region. Therefore, accurate wind speed forecasting is urgently needed in this area, making it a suitable focus for this study.

3. Methods

3.1. Correction Methods

3.1.1. Decaying Averaging Method (DAM)

The decaying average error is calculated at every grid point based on the forecast and observation during the training period:

$$\begin{array}{c}B\left(t\right)=\left(1-w\right)\times B\left(t-1\right)+w\times \left(F-a\right),\end{array}$$

(1)

where B(t) represents the decaying average error on the grid point, B(t − 1) is the decaying average error from the day before, and B(1) is the average bias over the entire training period, calculated as $B\left(1\right)=\frac{1}{n}\sum (F-a)$. Where n is the length of the training period, F is the forecast, and a is the observation for the current day. The weight coefficient w is calculated as w = 1/n. After obtaining the decaying average error, the corrected forecast is found by subtracting it from the forecast for the current day:

$$F_t^{\prime }=F_t-B\left(t\right)$$

(2)

3.1.2. Unary Linear Regression (ULR)

At each grid point, the ULR method is applied to establish an equation during the training period for a specific forecast lead time of the 10-m wind speed. The equation is defined as follows:

$$y_t=a+b{x}_{t, }$$

(3)

where $y_t$ represents the forecast at time t, $x_t$ represents the corresponding observation at time t, a is the constant term, and b is the regression coefficient. The values of a and b are determined based on the forecast and observation data during the training period and calculated as follows:

$$b=\frac{{{\displaystyle \sum }}_{t=1}^n{x}_t{y}_t-n\overline{x}\overline{y}}{{{\displaystyle \sum }}_{t=1}^n{x}_t^2-n{\overline{x}}^2},$$

(4)

$$a=\overline{y}-b\overline{x},$$

(5)

where n represents the length of the training period, $\overline{x}$ denotes the averages of the observations, and $\overline{y}$ denotes the averages of the forecast.

Regarding the selection of the training period, previous studies showed that using a sliding training period for statistical post-processing yields better correction results compared to a fixed training period [41]. Therefore, both the DAM and ULR methods in this study employ a sliding training period. Specifically, for each forecast lead time, the training period length varies from 10 to 100 days. The length corresponding to the minimum spatial-temporal average error is selected as the optimal training period length for DAM and ULR, ensuring that the correction results reach their optimum performance.

3.1.3. CNN

CNN is a common algorithmic model in deep learning, consisting of input, convolutional, pooling, and fully connected layers. The key feature of CNN is the addition of convolutional and pooling layers in the hidden layers between the input and output layers. The convolutional layer performs convolution operations on the grid variables within subregions, enabling better exploration of the relationships between neighboring grid variables and the two-dimensional features within the region. The pooling layer is mainly used to enhance the network’s robustness to system scaling, translation, and rotation. The convolutional and pooling layers are usually connected in an alternating pattern, reducing the interconnections between neurons in different layers, thus reducing the number of computational parameters and making it feasible to train large-scale networks. This led to widespread applications of CNN in image processing. The structured grid data can be presented as an image composed of a group of pixels, which can be input into the CNN model for training. This approach facilitates a better exploration of spatial information among grid point meteorological data.

Figure 2 illustrates the architecture of the CNN used in this study. Three convolutional layers are followed by three pooling layers, and then three fully connected layers with 4096 neurons each. The input layer has dimensions of 64 × 64 × 1, and the pooling layers employ max pooling. The first convolutional layer has 64 channels, the second convolutional layer has 128 channels, and the third convolutional layer has 256 channels. The grid point meteorological data enters the network and first goes through convolutional layers to extract relevant information, followed by pooling layers to reduce resolution. Then, it enters the fully connected layers, where it is reconstructed before being output.

The CNN model was trained using data from 2000 to 2017, with the data from 2018 serving as the validation set. The model was used to correct wind speed forecasts in the southwestern region of China in 2019. Some parameter details of the model are given in the detailed outlined below.

The activation function employed here is the rectified linear unit (ReLU):

$$ReLU\left(x\right)=\max \left(0,x\right)$$

(6)

The Adam optimizer is used. The size of the convolutional kernel is set as 3 × 3, and the size of the pooling kernel is set as 2 × 2. MSE is used as the loss function to reflect the magnitude of the error during training and can be calculated using the following:

$$Loss=\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(f_i-o_i\right)}^2,$$

(7)

where $o_i$ is the observed value, $f_i$ is the forecasted value, and N is the total number of grid points in each training.

The learning rate is determined empirically, and different learning rates may be set for different problems before training. In this study, the initial learning rate is set at 0.0001. The batch size, i.e., the number of samples trained at each iteration, is set to 32, and the number of epochs is set to 20.

3.1.4. U-Net Neural Network

U-Net is an evolved form of CNN originally proposed to solve medical image segmentation problems. Owing to its powerful spatial information extraction capabilities, it has gradually been applied in meteorological research. The U-Net network model consists mainly of convolutional layers, pooling layers, upsampling layers, and skip connections. The overall network structure resembles the letter “U”, hence the name U-Net.

Figure 3 illustrates the U-Net model structure employed in this research. Both the input and output are 64 × 64 × 1 size images. The left half represents the downsampling process, also known as the “encoding” process, where the spatial resolution decreases with depth. The right half represents the upsampling process, or the “decoding” process, where the spatial resolution gradually increases. Convolutional layers do not alter the size of feature maps but change their number, i.e., channels. A max-pooling layer follows after every two convolutional layers. Pooling layers do not change the number of feature maps but reduce the output image size to half of the original, i.e., decreasing spatial resolution. The convolution and pooling operations act as filtering and downsampling operations while preserving the main data features. As the spatial resolution decreases, the number of channels in the convolutional layers after pooling usually increases to compensate for the loss in spatial information. The original data is compressed to a minimum after several pooling operations before entering the upsampling process. Each upsampling layer uses interpolation and convolution to double the size of the feature maps, resulting in higher spatial resolution while reducing the number of feature maps. Additionally, skip connections in the network preserve the high-resolution information extracted during the downsampling process and transmit it to the corresponding upsampling layers to retain features of different scale spatial fields. As the resolution gradually increases during the upsampling process, the model eventually outputs the forecast correction results for the entire spatial field. The grid point meteorological data enters the network and goes through the downsampling layer to extract relevant information and reduce resolution. Then, it enters the upsampling layer to further extract relevant information and increase resolution, until the data is fully reconstructed before being output.

The U-Net model was trained using data from 2000 to 2017, with 2018 data used as the validation set for the forecast correction in the southwestern region of China in 2019. Some parameter descriptions for the model are given are described below.

The ReLU function is used as the activation function. Adam is selected as the optimizer. The convolution and pooling kernel sizes are set to 3 × 3, 2 × 2, respectively. MSE is used as the loss function. The initial learning rate is set at 0.0001. The batch size is set to 32, and the number of epochs is set to 40.

3.2. Evaluation Metrics

To quantitatively evaluate the wind field correction effect of statistical post-processing, four forecast verification methods were employed in this study: the root mean square error (RMSE) [42], the mean absolute error skill score (MAESS) [43], the hit rate (HR) [44], and the pattern correlation coefficient (PCC) [45]. The corresponding formulas are as follows:

$$\begin{array}{c}RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n}{\left(f_i-o_i\right)}^2}\end{array}$$

(8)

$$\begin{array}{c}MAESS=\frac{MA{E}_{eva}-MA{E}_{ref}}{0-MA{E}_{ref}}=1-\frac{MA{E}_{eva}}{MA{E}_{ref}}\end{array}$$

(9)

$$\begin{array}{c}HRe=\frac{N_{bias<e}}{N}\times 100\%\end{array}$$

(10)

$$PCC=\frac{{{\displaystyle \sum }}_{i=1}^m\left(f_i-\overline{f}\right)\left(o_i-\overline{o}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^m{\left(f_i-\overline{f}\right)}^2{{\displaystyle \sum }}_{i=1}^m{\left(o_i-\overline{o}\right)}^2}},$$

(11)

where n is the number of days, m is the number of grid points, $f_i$ represents the forecast values, and $o_i$ represents the observation values of the i-th sample. $\overline{f}$ represents the regional average forecast values, and $\overline{o}$ represents observation values. $MAE=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\left|f_i-o_i\right|$, ${\mathrm{MAE}}_{eva}$ represents the MAE of the evaluated correction model. ${\mathrm{MAE}}_{ref}$ is the MAE of the reference forecast. RMSE reflects the square root of the ratio between the square of the forecast deviation from the observation and the square of the number of observations n. A smaller RMSE indicates higher forecast skill. MAESS reflects the improvement of the evaluated correction model compared to the reference forecast in terms of MAE. MAESS > 0 indicates positive improvement, while MAESS < 0 indicates negative improvement. A larger MAESS indicates a better correction effect. $N_{bias\le e}$ represents the number of samples with an absolute forecast error not exceeding e m/s, where e = 1, N represents the total number of samples, and HR1 reflects the percentage of samples with a forecast error within 1 m/s compared to all samples. A higher HR1 indicates better forecast skill, which is an important indicator for verifying and evaluating wind speed forecasts in operational forecasting. PCC reflects the spatial correlation between the forecast and observation fields. A higher PCC indicates a closer similarity between the structure of the forecast field and that of the observation field, indicating better forecast skill.

3.3. Error Decomposition

The forecast evaluation metrics mentioned earlier compress the forecast and observation into a single comprehensive score, making it difficult to understand in which specific aspects the model performs “well” or “poorly”. There is a lack of interpretability. By decomposing the errors into interpretable error components, the interpretability of the model’s forecast performance is effectively improved. Therefore, based on the error decomposition method proposed by Hodson et al., this study decomposes the MSE into a bias term, a distribution term, and a sequence term. This analysis enables error diagnostic analysis of different forecast schemes and provides directions for future optimization.

At every grid point, the MSE is calculated as follows:

$$MSE=\frac{1}{n}{\displaystyle \sum }_{i=1}^n{\left(f_i-o_i\right)}^2,$$

(12)

where $f_i$ is the forecast, and $o_i$ is observation on day i. Based on the decomposition approach introduced by Geman et al. [46], the MSE can be broken down into a bias term and a variance term:

$$MSE\left(e\right)=\left(E\left(e^2\right)-E{\left(e\right)}^2\right)+E{\left(e\right)}^2$$

(13)

$$=Var\left(e\right)+E{\left(e\right)}^2$$

(14)

$$=Var\left(e\right)+Bias{\left(e\right)}^2,$$

(15)

where e denotes the forecast error of the model, which is the difference between the forecast and the observation, and E(e) is the mean forecast error. Var(e) is the variance of the forecast error. The variance term assesses the model’s variability in replicating observations, while the bias term assesses the model’s capability to reproduce their average characteristics. For a more comprehensive understanding of the error sources, the variance term can undergo further decomposition. Utilizing the error decomposition method introduced by Hodson et al., the variance term can be broken down into a sequence term and a distribution term. To calculate the error components, the forecasts and observations are sorted, and the new error is calculated as follows:

$$w=sort\left(f\right)-sort\left(o\right)$$

(16)

$$MSE\left(w\right)=Bias{\left(w\right)}^2+Var\left(w\right),$$

(17)

where sort(f) denotes the sorted forecasts, sort(o) denotes the sorted observations, and w is the sorted forecast error. Considering that changing the order of the data does not alter their average error, the bias remains the same before and after sorting. The sorted observations and forecasts share the same time series, and Var(w) represents the error resulting from differences in data distribution, which is the distribution term. Therefore, the following equation can be derived:

$$Var\left(w\right)=Distribution\left(e\right)$$

(18)

$$MSE\left(w\right)=Bias{\left(e\right)}^2+Distribution\left(e\right)$$

(19)

The difference between MSE(e) and MSE(w) arises only from the variation in the time series, and it denotes the error resulting from it, which is the sequence term. Therefore, the following equation can be derived:

$$MSE\left(e\right)-MSE\left(w\right)=Var\left(e\right)-Var\left(w\right)$$

(20)

$$=Sequence\left(e\right)$$

(21)

In conclusion, the overall decomposition formula of MSE can be represented as follows:

$$MSE\left(e\right)=Bias{\left(e\right)}^2+Var\left(e\right)$$

(22)

$$=Bias{\left(e\right)}^2+\left(Var\left(e\right)-Var\left(w\right)\right)+Var\left(w\right)$$

(23)

$$=Bias{\left(e\right)}^2+Sequence\left(e\right)+Distribution\left(e\right),$$

(24)

where $Bias{\left(e\right)}^2$ represents the bias term, quantifying the model’s ability to replicate the average characteristics of the observations. Sequence(e) represents the sequence term, measuring the error caused by the forecast being ahead of or behind the observations. Distribution(e) represents the distribution term, indicating the error resulting from variances in data distribution between the forecast and observation.

4. Results

4.1. Forecast Correction Evaluation

Figure 4 presents the average RMSE, HR1, and PCC of the 1–7 day forecast lead time for the 10-m U- and V-components of wind in southwest China by GEFS and the results after correction by DAM, ULR, CNN, and U-Net models for the period from 1 January to 31 December 2019. From the graph, it can be observed that GEFS, DAM, ULR, CNN, and U-Net exhibit similar variations in RMSE, HR1, and PCC with an increase in the forecast lead time, showing a gradual increase, decrease, and further decrease. The four correction methods all demonstrate certain correction effects on wind speed forecasts in Southwest China. The correction effects of the two deep learning methods are superior to those of the traditional DAM and ULR methods. U-Net achieves the best correction effect, followed by CNN, while DAM performs the poorest.

To depict the spatial distribution characteristics of forecast errors by GEFS, DAM, ULR, CNN, and U-Net, Figure 5 shows the spatial distribution of RMSE for the 1, 4, and 7-day forecast lead times of the 10-m U- and V-components of wind in southwest China. Figure 6 presents the spatial distribution of MAESS for DAM, ULR, CNN, and U-Net compared to GEFS for the same forecast lead time and wind fields. From Figure 5, it can be deduced that GEFS has larger RMSE values in the western and eastern parts of the Sichuan province, eastern Yunnan province, and within the Guizhou province, while exhibiting smaller RMSE values in the southwestern part of Yunnan province. The difference becomes more significant with increasing forecast lead times. The overall RMSE values for the 10-m U-component are higher than those for the 10-m V-component. The four correction methods exhibit similar RMSE distributions to GEFS but with significantly reduced values and ranges. ULR, CNN, and U-Net have smaller RMSE values compared to DAM, with U-Net exhibiting the smallest RMSE distribution, followed by CNN. Figure 6 shows that, overall, the four correction methods yield the best improvement in the western part of Sichuan province, western Yunnan province, and northeastern Chongqing province. Locally, DAM exhibits some negative improvement in the Sichuan Basin and parts of the Yunnan-Kweichow Plateau. ULR and CNN also exhibit similar patterns in certain areas, but with a significantly reduced range compared to DAM. U-Net shows positive improvement throughout the study area.

Further, Figure 7 presents the spatial distribution of HR1 for the 1, 4, and 7-day forecast lead times of the 10-m U- and V-components of wind in southwest China by GEFS, DAM, ULR, CNN, and U-Net. The graph indicates that GEFS has smaller HR1 values in the western and eastern parts of Sichuan province, eastern Yunnan province, and within Guizhou province, while exhibiting larger HR1 values in the southwestern part of Yunnan province. The overall HR1 values for the 10-m U-component are smaller than those for the 10-m V-component, which is consistent with the RMSE distribution. DAM exhibits a similar HR1 distribution to GEFS, but with increased values and range. ULR, CNN, and U-Net have higher HR1 values in most regions outside of eastern Sichuan province, eastern Yunnan province, and Guizhou province, with the majority being above 90%.

To evaluate the systematic biases of the original GEFS and U-Net corrected forecasts, Figure 8 presents the percentage of absolute error samples within different ranges for the one-day forecast lead time of the 10-m U- and V-components of wind, as well as the forecast-observation scatter plots for GEFS and U-Net. In the forecast-observation scatter plots, the distance from the points to the diagonal line represents the absolute error of the forecast. Points above the diagonal line indicate a bias toward westward meridional or southward zonal winds, while points below the diagonal line indicate a bias toward eastward meridional or northward zonal winds. Figure 8a shows that after correction by the U-Net neural network, the proportion of errors greater than 1 m/s decreases significantly, while the proportion of errors below 0.5 m/s increases noticeably. For the 10-m U-component, the proportion of errors lower than 0.5 m/s increases by 46% for U-Net compared to GEFS in the one-day forecast lead time. For the 10-m V-component, the proportion of errors lower than 0.5 m/s increases by 50% for U-Net compared to GEFS in the one-day forecast lead time. In turn, Figure 8b shows that for the original GEFS forecasts, both U- and V-components exhibit a higher frequency of positive and negative extreme biases, especially the positive ones. Meanwhile, Figure 8c shows that after the U-Net correction, extreme biases are significantly reduced, and the distribution of errors appears more concentrated and symmetrical.

4.2. Evaluations of Error Decomposition

The error evaluation methods discussed in Section 3.1 provide an overall score but lack interpretability. In this section, based on Hodson’s MSE decomposition method, the errors are decomposed into three components: the bias term (Bias2), the distribution term (Distribution), and the sequence term (Sequence). Bias2 represents the average bias of the forecast compared to the observation; Distribution denotes the error resulting from the inconsistency between the forecast and observation data distributions; and Sequence represents the error caused by the forecast leading or lagging compared to the observation. Decomposing the errors into interpretable components helps diagnose the sources of errors in the model and provides insights for further improvements.

Figure 9 presents the average MSE, Bias2, Distribution, and Sequence for the 1–7 days forecast lead time of the 10-m U- and V-components of wind in southwest China obtained by GEFS, DAM, ULR, CNN, and U-Net for the period from 1 January to 31 December 2019. Figure 9a shows that the MSE of DAM, ULR, CNN, and U-Net exhibits similar characteristics to GEFS with an increase in the lead time, yielding an increasing trend. Under the same forecast lead time, GEFS consistently has the highest MSE, while all four correction methods show significant improvements compared to the original GEFS forecasts. U-Net consistently has the lowest MSE, indicating the best improvement in the U- and V-components of wind, followed by CNN.

After decomposing the MSE, significant differences are observed in the characteristics of different error components. Bias2 and Distribution of GEFS show relatively small fluctuations with an increase in the lead time. Bias2 for the 10-m U-component remains stable around 0.12 ${\mathrm{m}}^2/{\mathrm{s}}^2$, while Bias2 for the 10-m V-component remains stable around 0.14 ${\mathrm{m}}^2/{\mathrm{s}}^2$. Distribution for the 10-m U-component remains stable around 0.13 ${\mathrm{m}}^2/{\mathrm{s}}^2$, while for the 10-m V-component, it remains stable around 0.2 ${\mathrm{m}}^2/{\mathrm{s}}^2$. Sequence shows similar changes to MSE. In terms of Bias2 (Figure 9b), the Bias2 values of all four correction methods are smaller than GEFS, with DAM and ULR exhibiting the smallest values, stable around 0.001 ${\mathrm{m}}^2/{\mathrm{s}}^2$. However, the Bias2 for CNN and U-Net exhibits noticeable fluctuations with an increase in the lead time. In terms of Distribution (Figure 9c), DAM has a smaller Distribution than GEFS, and its fluctuations are similar to those of GEFS. The Distribution values for ULR, CNN, and U-Net gradually increase with the lead time. For one- to four-day lead times, the Distribution of ULR is smaller than that of GEFS, while for five- to seven-day lead times, it exceeds GEFS. The Distribution for CNN is consistently lower than GEFS, while for U-Net, the 10-m V-component is consistently lower than GEFS, whereas for the 10-m U-component, it is lower than GEFS for the one- to six-day lead times and exceeds GEFS for the six-day lead time. In terms of Sequence (Figure 9d), all four methods show an increasing trend with an increase in the lead time, similar to GEFS. The Sequence for DAM is similar to GEFS, while ULR, CNN, and U-Net have lower Sequence values than GEFS, with U-Net having the smallest value, followed by CNN.

In summary, for Bias2, DAM and ULR show the best correction effects. For Distribution, CNN and U-Net perform better in correcting the distribution error in the first to five days. For Sequence, U-Net achieves the best correction effect.

To reflect the main error sources in different regions under various forecasting schemes, Figure 10 presents the spatial distribution of the percentage contribution of different error components in the total error of the 10-m U- and V-components of wind in southwest China for a one-day forecast lead time. Therein, the Bias2 of GEFS accounts for around 30% in most areas of western Sichuan province, western Yunnan province, and northeastern Chongqing province, while it is mostly below 20% in other locations. The Distribution of GEFS accounts for approximately 30% in the western Sichuan province and western Yunnan province and below 20% in other areas. The Sequence of GEFS accounts for around 50% in the western Sichuan province and western Yunnan province, while it is generally above 70% in other regions. After correction, all schemes are primarily dominated by the Sequence, with its contribution exceeding 80% in most places. The Bias2 of DAM and ULR is below 3%, while CNN and U-Net only exhibit a Bias2 of around 10% in localized areas. The Distribution of DAM accounts for around 30% in the western Sichuan province and western Yunnan province and below 20% in other regions. The Distribution of ULR remains between 10% and 30%, while CNN and U-Net exhibit a Distribution below 20%.

To illustrate the correction of different error components achieved by each forecasting scheme, Figure 11 presents the spatial distribution of Bias2 in the forecasts of 10-m U- and V-components of wind in southwest China by GEFS, DAM, ULR, CNN, and U-Net for one, four, and seven-day forecast lead times. GEFS exhibits large Bias2 values in the western Sichuan province, western Yunnan province, and northeastern Chongqing province, with maximum values exceeding 0.16 ${\mathrm{m}}^2/{\mathrm{s}}^2$. Bias2 values across various regions do not show significant changes as the forecast period increases. After correction, the Bias2 of each scheme decreases in most areas. DAM and ULR exhibit similar and smallest Bias2 values, followed by U-Net. CNN exhibits the largest Bias2 values, and in the central part of Guizhou province, the Bias2 values exceed those of GEFS.

Figure 12 displays the spatial distribution of Distribution in the forecasts of 10-m U- and V-components of wind in southwest China by GEFS, DAM, ULR, CNN, and U-Net for one, four, and seven-day forecast lead times. The Distribution of GEFS does not show significant spatial changes as the forecast lead time increases, with the high-value areas mainly located in the western Sichuan and northern Yunnan provinces. After correction, the spatial distribution of the Distribution of DAM is consistent with that of GEFS, but with reduced values and range. The Distribution of ULR, CNN, and U-Net exhibits increased values and spatial distribution as the forecast lead time increases. In ULR, the Distribution values exceed those of GEFS in the eastern Sichuan province, the eastern Yunnan province, the western Chongqing province, and within the Guizhou province, while they are lower than GEFS in other areas. CNN and U-Net exhibit cases where the Distribution values exceed those of GEFS in localized areas for the one- and four-day forecast lead times, and in eastern Sichuan province, eastern Yunnan province, and within Guizhou province for the seven-day forecast lead times.

Figure 13 presents the spatial distribution of the Sequence in the forecasts of 10-m U- and V-components of wind in southwest China by GEFS, DAM, ULR, CNN, and U-Net for one, four, and seven-day forecast lead times. The Sequence values in GEFS forecasts show an increasing trend with forecast lead time in all regions, with maximum values mainly concentrated in the eastern Sichuan province, eastern Yunnan province, and central Guizhou province. The range of high-value areas significantly expands with increasing forecast periods. Under the seven-day forecast lead time, the maximum Sequence value exceeds 2.4 ${\mathrm{m}}^2/{\mathrm{s}}^2$. After correction, the Sequence distributions of all schemes are generally consistent with those of GEFS. DAM exhibits a Sequence distribution similar to GEFS, while ULR, CNN, and U-Net show decreased Sequence values in all regions. Among them, U-Net yields the smallest Sequence values, followed by CNN.

5. Discussion and Conclusions

In this study, the forecast accuracy of GEFS for surface 10-m wind speed in southwest China in 2019 was evaluated for a forecast lead time of one to seven days. Correction experiments were conducted using U-Net and CNN neural networks based on the original GEFS forecasts. The corrected results were evaluated and compared with two traditional linear statistical post-processing methods, namely, DAM and ULR. Finally, an error decomposition method was applied to diagnose and analyze error sources in the original and corrected forecasts, leading to the following main conclusions:

(1)

The original GEFS forecasts exhibit poor performance in predicting wind speeds in the Western and Eastern Sichuan provinces, Eastern Yunnan province, and Guizhou province, with better predictions for the 10-m U-component of wind compared to the 10-m V-component.

(2)

The DAM, ULR, CNN, and U-Net methods all show certain correction effects on GEFS wind speed forecasts in the region under study. While DAM, ULR, and CNN exhibit some negative corrections in specific local areas, U-Net achieves positive corrections throughout the entire study area. CNN and U-Net show significantly better correction performance than traditional DAM and ULR methods, with U-Net demonstrating the best overall correction effect. After correction using the U-Net, for a 1-day forecast lead time, the proportion of the 10-m U-component of wind with errors less than 0.5 m/s has increased by 46% compared to GEFS. Similarly, for the 10-m V-component of wind, the proportion of errors less than 0.5 m/s has increased by 50% compared to GEFS.

(3)

The changes in MSE for DAM, ULR, CNN, and U-Net over different lead times are similar to those of GEFS, increasing with the lead time. GEFS’s Bias2 and Distribution show little variation with the lead time, while the Sequence changes consistently with MSE. This suggests that the increase in MSE with lead time is primarily driven by the Sequence. After correction, all schemes are mainly driven by the Sequence. DAM and ULR show the best correction performance for Bias2. CNN and U-Net exhibit better correction for Distribution in the first five days, while U-Net achieves the best correction for Sequence.

Based on the above analysis, traditional methods perform better in correcting Bias2, while deep learning methods excel in correcting Sequence. Therefore, combining these two approaches to further improve forecasting skills may be a future task to be considered. Additionally, a study [47] has pointed out that different geographic locations may require different neural network architectures. Considering the complex terrain and the fact that wind field forecast errors are primarily concentrated in high-altitude areas in the southwestern China region, it would be worth exploring the inclusion of geographical information, such as elevation, as input data for training neural networks to examine whether it can further enhance the forecast skill. Furthermore, it is well known that the size of the training dataset significantly impacts training outcomes. In this study, an 18-year dataset was employed for training, but in practical scenarios, obtaining such long time-series samples might be challenging. Therefore, it could be considered to investigate the influence of varying sample sizes on the training outcomes to explore the minimum reasonable length of a time series for a meaningful study of related issues. Lastly, besides wind speed, it is possible to explore whether this model can effectively correct other meteorological elements in the region, such as temperature, precipitation, humidity, and more. Such investigations would hold meaningful implications for enhancing the accuracy of meteorological element forecasts in this area.