Improving the Forecasts of Coastal Wind Speeds in Tianjin, China Based on the WRF Model with Machine Learning Algorithms

1.   Introduction

Strong wind is one of the primary meteorological disasters in coastal areas, resulting in reduced agricultural and fishery yields (Cleugh et al., 1998), air or vessel traffic accidents (Kim et al., 2015), and storm surges (Anarde et al., 2018), and this phenomenon poses a severe threat to the security of lives and property (Smith and Katz, 2013). Coastal wind-related disasters cause an annual economic loss of approximately 2.4 billion Yuan in China (Ministry of Natural Resources, 2023). The Bohai Sea is an inland sea region with many ports and natural resources that serves as a vital corridor connecting the Beijing–Tianjin–Hebei region and Northeast China economic zones, functioning as the Maritime Silk Road in the 21st century.

Accurate coastal wind forecasting is crucial for strengthening disaster prevention and mitigation efforts, ensuring energy security and stability, and promoting sustainable development. However, predicting the wind speed remains a challenge in both operational forecasting and research in this region. Liu et al. (2022) noted that the root-mean-square error (RMSE) of current 10-m wind speed forecasts over the Bohai Sea is approximately 1–3 m s⁻¹ and that of strong wind forecasts (> 10 m s⁻¹) could reach 5–8 m s⁻¹. Fan et al. (2017) reported that NCEP climate forecast system reanalysis (CFSR) data underestimate the wind speed by approximately 4 m s⁻¹ for strong winds.

The annual average wind speed in the circum-Bohai Sea region is 6.2 m s⁻¹, and it has been shown to increase over time (Zhang et al., 2011, 2013). Different synoptic weather systems and atmospheric processes influence wind patterns throughout the year, resulting in a distribution of strong winds during all four seasons in the circum-Bohai Sea (Qu et al., 2018). In winter, the Mongolian cold high-pressure system or the passage of cold fronts results in stable prevailing northwest winds, leading to strong winds in Tianjin (Zhang et al., 2022). The subsidence motion of cold flows caused by cold fronts can also trigger strong coastal winds by propagating cold air from high to low levels and causing downward momentum transport (Zhang and Zheng, 2004). In summer, influenced by low-pressure systems in Southeast China and subtropical high-pressure systems in Northwest Pacific, prevailing southern winds could lead to unstable wind directions and frequent convective systems (Zhang et al., 2021). Northward movement of tropical cyclones can produce a large-scale and powerful southeast jet stream, causing strong easterly winds in the coastal belt surrounding the Bohai Sea (Xing et al., 2018). In spring and autumn, frequent extratropical cyclones and low-level jets lead to unstable atmospheric conditions and the consequent enhancement in the wind speed (Qu et al., 2018). Apart from weather systems, the different thermal properties of land and sea surfaces cause obvious diurnal variations in the wind speed (Chaney et al., 2016). Atmospheric processes near the surface, such as turbulence, affect the wind speed and direction by altering momentum and heat flux transfer (Cheng and Steenburgh, 2005). Moreover, complex terrain can further enhance the complexity and uncertainty in strong coastal winds by forcing near-surface atmospheric processes and local circulations (Duan et al., 2018; Fernández-González, 2018).

The approaches for wind speed forecasting can be classified into four categories: empirical forecasting, statistical, physical, and artificial intelligence-based approaches (Ramage, 1993; Niu and Wang, 2019; Jiang et al., 2021). The empirical forecasting approach relies mainly on the experience of forecasters. Since some forecasting indices are difficult to quantify, the timeliness and applicability of the empirical forecasting approach in modern weather forecasting are limited (Ramage, 1993). In contrast, statistical methods compensate for the inability to understand atmospheric processes and their interactions. However, the assumption of linearity in statistical approaches results in inadequate predictions, particularly for existing refined, high-resolution, and medium-to-long-term weather forecasting methods (Chang, 2014; Yang et al., 2020). Physical approaches, mainly based on numerical weather prediction (NWP) models, provide detailed forecasts of the state of the atmosphere at a given time (Foley et al., 2012). The Weather Research and Forecasting (WRF) model is a classical NWP model widely employed in meteorological services for weather forecasting and research. However, the inherent deviation of NWP models necessitates the refinement of the output data (e.g., wind speed forecasts) according to on-site conditions to improve the forecast accuracy (Bhaskar and Singh, 2012; Hanifi et al., 2020).

Recently, with the development of artificial intelligence (AI) and enhanced computing capacity, various AI-based methods for wind speed prediction have been explored and applied (De Freitas et al., 2018). As one category of AI-based methods, machine learning techniques can capture the nonlinear and complex statistical relationships between the input and output data (Chang, 2014). However, these methods rely on selected parameters, are resource intensive, and lack interpretability. Hence, they are often combined with parameter selection and optimization algorithms and data pre- and postprocessing methods to construct synergetic models (Yang B. et al., 2021).

Considering the limitations of each approach, individual forecasting approaches are insufficient for accurately forecasting wind speeds. It has been revealed that machine learning and NWP methods complement each other and should be integrated to achieve better forecasting (Zhao et al., 2012; Xiong et al., 2023). Previous studies have focused mainly on utilizing machine learning to improve the parameterization and data assimilation capabilities of NWP models (Gentine et al., 2018; Yuval and O’Gorman, 2020; Farchi et al., 2021); few studies have focused on the use of machine learning (ML) to directly correct the NWP forecast bias. In contrast, the random forest (RF), support vector machine (SVM), and backpropagation neural network (BP) models, which are representative of the three most common ML algorithms, have been applied as postprocessing tools to mitigate the model forecast bias, but their bias correction performance levels are still unclear.

In this study, the aforementioned three ML algorithms are employed as postprocessing tools to correct the bias of WRF model forecasts of the wind speed, and their correction capacities are compared, with the objective of providing helpful operational forecasting references for obtaining improved coastal wind speed forecasts. In addition, the main influencing factors of the wind speed forecast bias are analyzed to better understand its origins in terms of the wind speed.

2.   Data and methods

2.1   Data description

Meteorological in-situ data, including the 2-m air temperature (T₂), 2-m relative humidity (RH₂), and 10-m wind speed (u₁₀ and v₁₀), were obtained from the Meteorological Assimilation Data Ingest System (MADIS; https://madis.ncep.noaa.gov/), which is an observational database with global coverage.

The initial and boundary conditions of the WRF model were derived from the NCEP Global Forecast System (GFS; https://rda.ucar.edu/datasets/ds084.1/), with a horizontal resolution of 0.25° × 0.25° and 27 vertical levels. GFS analysis/initial data are available at 0000, 0600, 1200, and 1800 UTC daily, and the forecast data extend from the initial time to 384 h.

In this study, four months (January, April, July, and October) during 2015–2019 were selected to represent the four seasons in those years, as widely considered in previous studies (Chang et al., 2019; Su et al., 2019). At 0000 UTC on each day of the selected months, the WRF model was started and operated for 168 h with a forecast output interval of 1 h. In total, there were 123 sets of forecasts every year, with each set containing 169-h forecast data.

2.2   Model setup

The WRF model is a state-of-the-art mesoscale NWP system that has been widely applied for both atmospheric research and operational forecasting applications. In this study, the WRF model was used to forecast the wind speed and other meteorological variables from 0000 UTC in January, April, July, and October 2015–2019 to the subsequent 168 hours.

Three nested domains were applied in WRF model forecasting, with 50 vertical layers extending from the surface to 50 hPa (Fig. 1). The parent domain (D01) has a horizontal resolution of 27 × 27 km² (160 × 160 grids) and includes a large part of East Asia. These data can reflect the main weather systems affecting the Bohai Sea during each season. The intermediate domain (D02) covers Tianjin and nearby areas and sea areas, with a horizontal resolution of 9 × 9 km² (223 × 223 grids), providing reliable boundary conditions for the inner domain. The inner domain (D03) with a 3-km resolution (202 × 202 grids) includes most of the Beijing–Tianjin–Hebei (BTH) region and the Bohai Sea. Table 1 provides an overview of the schemes used in the WRF model forecasts. Note that the cumulus parameterization was switched off in D03, and an explicit cloud microphysics scheme, i.e., the Morison 2-moment scheme, was used.

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Fig  1.  (a) Three nested WRF simulation domains and topography, and (b) topography in D03 and location of Tianjin City. The purple cross indicates the observation site.

Table  1.  Main physical parameterization schemes used in the WRF forecast runs

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Parameter	WRF option
Microphysics	Morrison 2-moment scheme (Morrison et al., 2009)
Boundary 　layer	YSU scheme (Hong et al., 2006)
Land surface	Unified Noah scheme (Tewari et al., 2004)
Surface layer	Revised MM5 Monin–Obukhov scheme (Jiménez et al., 2012)
Shortwave 　radiation	RRTMG scheme (Iacono et al., 2008)
Longwave 　 radiation	RRTMG scheme (Mlawer et al., 1997)
Cumulus	Grell 3D ensemble scheme (Grell, 1993)
Urban	UCM scheme (Chen et al., 2011)

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2.3   Machine learning (ML)

The observed wind speed was selected as the dependent variable, and a total of 29 WRF-output variables were selected as independent variables for the ML algorithm because of their close relationship with the wind speed (Qu et al., 2018; Wang Y. N. et al., 2020) and because of the higher orthogonality of the predicted quantities as ML input variables. All the variables used in this study are summarized in Table 2.

Table  2.  Description of the predictor parameters used in this study

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Variable	Description (unit)
T2	2-m temperature (°C)
RH2	2-m relative humidity (%)
u10	10-m u-component of wind (m s−1)
v10	10-m v-component of wind (m s−1)
HGT	Terrain height (m)
SLP	Sea level pressure (hPa)
CAPE	Convective available potential energy (J kg−1)
CIN	Convective inhibition (J kg−1)
LCL	Lifting condensation level (m)
LFC	Level of free convection (m)
rmax	Maximum reflectivity (dBZ)
T500	500-hPa temperature (°C)
RH500	500-hPa relative humidity (%)
u500	500-hPa u-component of wind (m s−1)
v500	500-hPa v-component of wind (m s−1)
w500	500-hPa w-component of wind (m s−1)
T700	700-hPa temperature (°C)
RH700	700-hPa relative humidity (%)
u700	700-hPa u-component of wind (m s−1)
v700	700-hPa v-component of wind (m s−1)
w700	700-hPa w-component of wind (m s−1)
T850	850-hPa temperature (°C)
RH850	850-hPa relative humidity (%)
u850	850-hPa u-component of wind (m s−1)
v850	850-hPa v-component of wind (m s−1)
w850	850-hPa w-component of wind (m s−1)
T925	925-hPa temperature (°C)
RH925	925-hPa relative humidity (%)
u925	925-hPa u-component of wind (m s−1)
v925	925-hPa v-component of wind (m s−1)
w925	925-hPa w-component of wind (m s−1)

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2.3.1   Random forest

The random forest (RF) algorithm is a decision tree-based ML algorithm that aims to construct multiple decision trees during training and can output the class that is the mode of all classes (classification) or mean prediction (regression) of the individual trees (Biau, 2012). In the RF model, decision trees are constructed by using a random subset of the training data and a random subset of the input features at each split. By randomly selecting subsets of the data and features, the RF algorithm reduces the risk of overfitting and improves the accuracy and robustness of the model (Liaw and Wiener, 2002). In addition, the RF model provides feature importance measures, which allow the user to better understand the relative importance of each feature in the prediction process (Breiman, 2001).

The number of decision trees (N_tree), number of variables in each subset at each split (M_try), and minimum number of observations at a terminal node (N_min) are three important customization parameters that affect the performance and efficiency of the RF algorithm (Yao et al., 2020). N_tree in the algorithm should be large enough to ensure the diversity of the classifiers, but an increase in N_tree increases the complexity and reduces the interpretability of the algorithm. The smaller M_try is, the higher the randomization of the model and the lower the classification accuracy of a single tree. In contrast, the larger M_try is, the higher the classification accuracy of a single tree and the lower the diversity. Considering the model accuracy and calculation cost and combining the classification performance and generalization ability of the model, we constructed a prediction model with N_tree = 500, M_try= $\sqrt{M}$, and N_min = 5, where M is the number of features.

2.3.2   Support vector machine

The support vector machine (SVM) is a supervised learning algorithm that can be used for classification and regression tasks. The main idea of SVMs is based on the Mercer kernel expansion theorem, which uses a nonlinear mapping function to map the sample space into a high-dimensional feature space. A hyperplane is then established as the decision surface, transforming the algorithm for establishing the optimal linear regression hyperplane into a convex programming problem subject to convex constraints, ultimately yielding the global optimal solution (Hearst et al., 1998).

The mathematical model of regression analysis can be understood as follows: for a given set of k independent and identically distributed training observation samples {(x_i, y_i) | i = 1, 2, 3, ..., k}, where x_i∈R_N denotes the predictor values and y_i∈R denotes the forecast object values. A training process is performed to obtain the optimal function relationship y = f (x). This function relationship is subsequently used to forecast future data from a set of forecast samples {(x_i, y_i) | i = k + 1, k + 2, …, n}. If the obtained function y = f (x) is linear, it is referred to as linear regression; if it is a nonlinear function, it is called nonlinear regression (Vapnik, 1999).

In this study, the RBF (radial basis function) was selected as the kernel function, and the regularization parameter C and kernel coefficient γ were determined as 100 and 0.1, respectively; these values were obtained via the systematic grid search method through 10-fold cross-validation on the training set (Su et al., 2020).

2.3.3   Back propagation neural network

The back propagation (BP) neural network is a commonly used neural network with a notable nonlinear regression capability (Sawaitul et al., 2012; Han et al., 2022). The BP neural network involves two main steps: forward propagation and backward propagation. In the forward propagation step, the neural network adopts an input and produces an output using the existing weights. In the backward propagation step, the gradient of the loss function with respect to the weights is calculated by using the output of the forward propagation step. This gradient is subsequently used to update the weights in the network.

In this study, the Adam solver was selected for weight optimization (Kingma and Ba, 2014), the ReLU activation function was adopted, and the number of dense layers was set to 2, with 100 and 50 neurons in the respective layers. The strength of the L2 regularization term was set to 0.01, and the maximum number of iterations was set to 1000. All of these parameters were obtained by a systematic grid search method using 10-fold cross-validation on the training set.

2.3.4   Key idea and differences among the three ML algorithms

Utilization of the aforementioned three algorithms facilitates an understanding of the postprocessing performance within the context of three prominent ML algorithms, each underpinned by fundamentally different internal structures.

The RF algorithm is an ensemble learning method based on decision trees. It consists of multiple decision trees trained on various subsets of the dataset (bootstrap samples) and combines their outputs through averaging (for regression tasks) or voting (for classification tasks). Each tree in the forest independently makes a prediction, and the final prediction is based on the aggregation of individual tree predictions.

The SVM algorithm aims to find the hyperplane that best separates different classes or approximates a regression function with a defined margin. Kernel functions can be used to transform the data into higher dimensions to achieve better separation in nonlinear cases. The SVM algorithm seeks to identify the optimal hyperplane that maximizes the margin between classes. Support vectors are the data points that lie closest to the decision boundary. This algorithm manage handle high-dimensional data well.

The BP model is a type of artificial neural network used for various ML tasks. It consists of an input layer, one or more hidden layers, and an output layer. The neurons in each layer are interconnected, and the network uses backpropagation to adjust the weights to minimize the error between the predicted and actual outputs.

2.4   Data preprocessing steps

All the data from 2015 to 2018, accounting for approximately 80% of the total data, were selected as the training set for ML. The data for 2019 were selected as the test set for ML. The observation data in our study were based on ground-based measurements at the observation site indicated in purple in Fig. 1b. Hence, each ML method was applied at this point in D03. To improve the performance of the ML algorithms, three data preprocessing steps were used before the training step:

(1) Data cleaning: This step involved both outlier elimination and missing value substitution for the observation data. First, observation data exceeding three standard deviations were defined as missing values based on the 3-sigma rule. All missing values, accounting for 2.1% of the total dataset (including missing values and outliers of the original observations), were replaced by linear interpolation.

(2) Data normalization: All variables were normalized to [0,1] as follows:

where $x$ is the original variable, ${x}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ and ${x}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ are the minimum and maximum values of variable, and $y$ is the variable transformed by normalization.

(3) Dimensionality reduction: Principal component analysis (PCA) was employed to reduce the dimensionality of the high-dimensional data in our study.

Note that data normalization and dimensionality reduction were only applied in the SVM and BP algorithms because only parameter-based models or distance-based algorithms must be normalized because the parameters or distances must be calculated. However, tree-based algorithms (e.g., the RF model) do not require these steps.

2.5   Classification of synoptic weather patterns

T-mode principal component analysis (PCT) within the COST733 software framework (Philipp et al., 2016) was employed for objective classification of weather systems. COST733, a weather classification software developed under the European Cooperation in Science and Technology (EU COST) 733 program, represents a significant tool in this regard. Currently, PCT is the prevailing objective classification method. Huth (1996) underscored the temporal and spatial stability characteristics of the PCA method, highlighting its reduced reliance on preset parameters and enhanced capacity to preserve the original field information. This characteristic renders PCA a more promising objective classification method. PCT, an extension of PCA, was further refined by Huth et al. (2008). In the T-mode configuration, daily patterns constitute the columns in the input data matrix, while grid-point values form its rows. The versatility of the PCT method is evident in its widespread application across various research domains, including precipitation, ozone, and haze classification (Dong et al., 2020; Yang Y. J. et al., 2021). In this study, the hourly geopotential height at 850 hPa was selected to identify synoptic patterns, aligning with methodologies employed in prior research (Li W. J. et al., 2021; Zong et al., 2021).

2.6   Metric definitions

We evaluated the WRF forecasts and ML-corrected meteorological conditions using the metrics listed in Table 3.

Table  3.  Metrics used to evaluate the model simulations

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Metric	Abbr.	Equation
Mean bias	MB	$\dfrac{1}{n}\sum _{1}^{n}(M-O)$
Mean error	ME	$\dfrac{1}{n}\sum _{1}^{n}|M-O|$
Root-mean-square error	RMSE	$\sqrt{\dfrac{\sum _{1}^{n}{(M-O)}^{2}}{n}}$
Pearson correlation coefficient	R	$\dfrac{\sum _{1}^{n}(M-\overline{M})(O-\overline{O})}{\sqrt{\sum _{1}^{n}({M-\overline{M})}^{2}}\sqrt{\sum _{1}^{n}({O-\overline{O})}^{2}}}$
M denotes the model-predicted value; O denotes the observed value.

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3.   Results

3.1   Performance of the WRF forecast

Figure 2 shows the overall statistical parameters for the meteorological variables of the WRF model. The forecast of T₂ by the WRF model agreed well with the observations, with an MB value of 0.32 and an R value of 0.98. The model generally captured the trend in RH₂ (R = 0.78) but overestimated the value on average (MB = 12.04). Regarding u₁₀ and v₁₀, the ME meets the recommended standard (ME ≤ ±2.0) in Boylan and Russell (2006) but the correlation coefficient is far below that of T₂ and RH₂, indicating the obvious inaccuracy of the WRF model in forecasting wind speeds.

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Fig  2.  Scatter density plots of the observed (OBS) and simulated (SIM) values of the WRF model for (a) T₂, (b) RH₂, (c) u₁₀, and (d) v₁₀ in the training set.

The variations in the RMSE and R values of the WRF model for the various meteorological variables with forecast time are shown in Fig. 3. Notably, the RMSE increased and the correlation coefficient decreased with forecast time for all meteorological variables. Nevertheless, the WRF model forecasting results are comparable to those of previous studies (Zhang et al., 2019; Li H. D. et al., 2021), demonstrating the reliability of the WRF model in simulating meteorological variables.

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Fig  3.  Variations in (a, c, e, g) RMSE and (b, d, f, h) R with forecast time for (a, b) T₂, (c, d) RH₂, (e, f) u₁₀, and (g, h) v₁₀ in the training set.

3.2   Factors affecting the wind speed and forecast bias

The relative importance of multiple forecast factors in influencing the wind speed and the forecast bias were investigated in this study through the RF approach. Regarding wind speed forecasts (Fig. 4a), the 10-m meridional wind speed (v₁₀) was identified as the most important factor influencing wind speed forecasting because meridional airflows are often accompanied by severe weather systems such as cold fronts (Bao and Zhang, 2013) and typhoon troughs (Qian et al., 2014; Liu et al., 2021), which significantly impact the wind speed. RH₂ plays a crucial role in wind speed prediction through dynamic or thermodynamic processes, as it is closely related to the temperature, pressure, and water vapor (Cheruy et al., 2013). The variable u₉₂₅ is an indicator closely related to strong winds because a low-level jet has been suggested as a key factor leading to strong near-surface winds via downward momentum transportation (Stensrud, 1996) and severe convection systems (Marion and Trapp, 2019; Luo and Du, 2023). The SLP plays a crucial role in wind speed prediction, as the pressure gradient force resulting from the uneven distribution of pressure fields is the main cause of wind generation from a weather system development perspective (Andrews, 2010; Emeis, 2018). Moreover, T₅₀₀ is a significant reference for determining the frontal surface temperature during severe weather events such as cold fronts (Schultz and Steenburgh, 1999; Kolstad et al., 2009), rendering it a critical factor in wind speed prediction.

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Fig  4.  Feature importance of the variables for (a) wind speed forecasting and (b) determining the wind speed bias via the RF algorithm.

Figure 4b shows the impact of the different meteorological variables on the forecast bias of the wind speed. The results indicated that the 10-m zonal wind speed (u₁₀) is the most influential physical variable of the forecast bias of the wind speed, while its importance in predicting the wind speed (Fig. 4a) ranks only ninth. This suggests that the accuracy of forecasting u₁₀ may significantly influence the forecast accuracy of the wind speed, which may result from the influence of midlatitude westerlies, distribution of underlying land–sea surfaces, and corresponding thermal properties. In addition, v₁₀, u₉₂₅, RH₂, and SLP, which exert significant impacts on the wind speed, greatly influenced the forecast bias. Moreover, T₂ is an essential factor affecting both the wind speed and forecast bias, as a local increase in the temperature causes the near-surface atmosphere to rise due to thermal expansion, resulting in uneven changes in the pressure field and wind production driven by elements such as the pressure gradient force (Oke, 1995; Mohajerani et al., 2017).

3.3   Performance of the three ML algorithms

As indicated in Table 4 and Fig. 5, the WRF model-forecasted wind speeds were acceptable, but there was still room for improvement (MB = 0.57 and 0.57 m s⁻¹, ME = 1.58 and 0.58 m s⁻¹, RMSE = 2.15 and 0.66 m s⁻¹, and R = 0.40 and 0.91 for the whole test set and the 7-day forecast set, respectively). After correction by the three machine learning algorithms, the results showed great improvement. The RF performed well in reducing the ME and RMSE values and increasing the R value (ME = 1.33 and 0.20 m s⁻¹, RMSE = 1.78 and 0.26 m s⁻¹, R = 0.59 and 0.97 for the whole test set and the 7-day forecast set, respectively), and the SVM exhibited a similar but slightly lower ability than the RF algorithm (ME = 1.35 and 0.36 m s⁻¹, RMSE = 1.84 and 0.47 m s⁻¹, and R = 0.57 and 0.95, respectively). The BP algorithm significantly improved the forecast average closer to the observed value (MB = 0.04) but was nowhere near enough to improve the ME, RMSE, and R values. In summary, regardless of whether the entire forecast ensemble or the average 7-day forecast was considered, the three ML methods could effectively improve the forecast performance of the NWP model. Note that all the results passed the significance test with the 99% confidence level (p < 0.01). Moreover, from the perspective of the training time, RF model training was incredibly fast, lasting only 21 s with a single thread, while the training times of the SVM and BP models were 313 and 184 s, respectively, indicating the feasibility of the RF algorithm in forecasting operations.

Table  4.  Comparison of the forecast performance levels of the WRF model with/without correction by the three ML algorithms

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Dataset	Approach	MB	ME	RMSE	R
Testing set	WRF	−0.57	1.58	2.15	0.40
	WRF + RF	−0.09	1.33	1.78	0.59
	WRF + SVM	−0.34	1.35	1.84	0.57
	WRF + BP	−0.04	1.56	2.06	0.49
7-day averaged	WRF	−0.57	0.58	0.66	0.91
	WRF+RF	−0.09	0.20	0.26	0.97
	WRF + SVM	−0.34	0.36	0.47	0.95
	WRF + BP	−0.04	0.18	0.22	0.96

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Fig  5.  Taylor diagram of the forecast performance levels of the WRF model with and without correction by the three ML algorithms.

Figure 6 shows the variation in the wind speed forecast error with the wind speed on the Beaufort scale. The WRF model overestimates the wind speed under weaker wind conditions and underestimates it under stronger wind conditions. In addition, except for weak wind conditions (< force 2), the WRF model exhibits a trend toward increasing the forecast RMSE with increasing wind speed. After correction by the RF algorithm, significant improvements are achieved for forecast values with a wind force > 2, and the correction effect improves with increasing wind speed. For wind forcings above 6, the RMSE of the forecast values is reduced from 3.37 to 3.11, and the mean bias is reduced from −3.49 to −2.36. The SVM method yielded similar correction results to those of the RF model, but the correction effect for stronger winds was slightly worse. For wind forces above 6, the RMSE of the forecast values was reduced from 3.37 to 3.21, and the mean bias was reduced from −3.49 to −2.43 after correction by the SVM algorithm. Moreover, the BP algorithm only reduced the RMSE of the forecast values for wind forcings above 6, indicating that it could not significantly reduce or even increase the dispersion of the forecast values. Nevertheless, this approach achieved the greatest effect in reducing the mean bias of the forecast values, with the mean bias of the forecast values for wind forces above 6 decreasing from −3.49 to −1.74 after correction by the BP algorithm. This indicates that when the wind speed is high (force > 2), the predicted wind speed corrected by the BP method is closer to the observed mean value. In addition, regarding the frequency of the wind speed in each interval, the WRF model overestimated the number of weaker wind samples (forces < 3) and vastly underestimated that of strong wind samples, especially for wind forces > 6, which generated a difference in magnitude (Figs. 6b, c). The BP model exhibited a desirable performance at most wind scales, especially for strong winds (forces > 6). The RF algorithm exhibited satisfactory performance for moderate winds (force 3).

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Fig  6.  Sample size for each wind speed band in the (a) observations and variations in (b, d, f, h) RMSE and (c, e, g, i) MB of the forecasted wind speed values with the forecasted wind speed (red solid line) and sample size for each wind speed interval (purple bars).

Figure 7 shows the variation in the wind speed forecast errors with the forecast lead time. Notably, the RMSE of the WRF model forecast results increases with forecast lead time, and the correlation coefficient between the forecast and observation values decreases with forecast lead time, with significant fluctuations in the error. The value of R declines below 0.2 at approximately 60 h but can increase to 0.2 at approximately 72 h and decrease to 0.05 at 140 h. The RF algorithm exerts the best correction effect on the WRF model forecast results, with a significantly reduced RMSE and smaller fluctuations with forecast time. R is also significantly improved after correction, with values above 0.40 maintained within 48 h and still exceeding 0.2 at 168 h. The correction effect of the SVM method was similar to that of the RF model but with a slightly larger RMSE and higher fluctuations in the RMSE with forecast lead time. The correlation coefficient for the 0–168-h forecast wind speed was greater than 0.2 for both methods. After correction by the BP algorithm, the wind speed forecast values were still better than those of the WRF model, but the correction effect was inferior to that of the RF and SVM models, with an RMSE that could exceed 2.5 and a correlation coefficient that decreased below 0.2 after 160 h.

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Fig  7.  Variations in (a, c, e, g) RMSE and (b, d, f, h) R with forecasting time for different wind speeds.

3.4   Performance of the three ML algorithms under different conditions

We employed obliquely rotated principal component analysis in the T mode (T-PCA) and applied this method to the 850-hPa geopotential fields to identify three dominant synoptic patterns (Fig. 8). Type 1 accounts for 68.2% of the total area and is characterized by northwest air flow behind the cold vortex, leading to strong westerly winds in the circum-Bohai Sea region. Type 2 represents a typical summer synoptic pattern, characterized by a subtropical high-pressure system located over Northwest Pacific. Type 3, while accounting for only 9.4% of the total patterns, exhibits the highest wind speeds. For Type 3, a cold vortex resides in northeastern Asia, alongside a subtropical high-pressure system in the southeast. This configuration leads to the convergence of northerly cold air and southerly warm-wet air over the circum-Bohai Sea region, consequently inducing thunderstorm gales.

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Fig  8.  The 850-hPa geopotential height (GH) fields (colored areas) in January, April, July, and August from 2015 to 2020 for (a) Type 1, (b) Type 2, and (c) Type 3. The occurrence frequency of each synoptic pattern is shown at the top right of each panel.

Table 5 provides the performance of the different machine learning algorithms across the three types of synoptic patterns. Notably, with increasing wind speed, the MB also increases. In a manner similar to that observed in Table 4, the RF model demonstrated the most comprehensive performance across all synoptic patterns, with the SVM model exhibiting a lower performance than the RF model. The BP neural network achieved the most significant reduction in the MB but could hardly reduce the RMSE effectively.

Table  5.  As in Table 4, but for the different synoptic types

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Type	Approach	MB	ME	RMSE	R
1	WRF	−0.66	1.61	2.21	0.47
	WRF + RF	−0.11	1.30	1.84	0.64
	WRF + SVM	−0.38	1.37	1.89	0.63
	WRF + BP	0.04	1.53	2.04	0.56
2	WRF	−0.47	1.59	2.13	0.27
	WRF + RF	−0.25	1.28	1.70	0.48
	WRF + SVM	−0.40	1.33	1.75	0.46
	WRF + BP	−0.10	1.42	1.85	0.45
3	WRF	−0.70	1.47	2.01	0.39
	WRF + RF	0.19	1.32	1.75	0.50
	WRF + SVM	−0.26	1.61	2.10	0.39
	WRF + BP	−0.24	1.42	1.88	0.39

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As shown in Fig. 9, the error trends following the application of ML algorithm correction exhibited a close correlation with those observed in the WRF model. In terms of the MB, the WRF model consistently underestimated the wind speed during the daytime but improved the wind speed forecasts at night. All three ML algorithms contributed to the enhancement in the WRF forecasting results, with the BP method demonstrating the most significant improvement. The SVM method was less effective than the BP and RF methods. The RMSE of the WRF forecasts indicated a distinctive double-peak pattern, with one peak occurring in the afternoon and another occurring during the midnight. These observations suggest the significant influence of the temperature on the RMSE. Among the ML algorithms, the RF algorithm excelled in reducing the RMSE, while the SVM algorithm demonstrated a comparable performance to the RF model. The BP model notably reduced the RMSE when it was initially high, although in some cases, it led to an increase in the RMSE.

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Fig  9.  Diurnal cycles of the (a) MB and (b) RMSE of the wind speed forecasts under the different approaches.

Table 6 provides the performance of the various ML algorithms across the different seasons. It is readily observed that the WRF model exhibited a suboptimal performance in January but displayed improved results in April and July. All three ML algorithms substantially enhanced the forecasting capability of the WRF model across all four seasons. Specifically, the RF algorithm yielded the best results in January, April, and October, whereas the SVM algorithm performed best in July. Moreover, the BP algorithm provided a comprehensive enhancement in the MB during all four seasons, albeit with less success in reducing the RMSE.

Table  6.  As in Table 4, but for the different seasons

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Month	Approach	MB	ME	RMSE	R
January	WRF	−0.91	1.83	2.40	0.39
	WRF + RF	−0.40	1.54	2.07	0.54
	WRF + SVM	−0.63	1.59	2.11	0.55
	WRF + BP	−0.11	1.73	2.29	0.50
April	WRF	−0.37	1.40	1.86	0.32
	WRF + RF	−0.08	1.14	1.52	0.42
	WRF + SVM	−0.22	1.21	1.60	0.38
	WRF + BP	0.04	1.30	1.69	0.36
July	WRF	−0.36	1.54	2.11	0.42
	WRF + RF	0.27	1.32	1.74	0.65
	WRF + SVM	−0.01	1.29	1.79	0.61
	WRF + BP	0.40	1.55	2.03	0.53
October	WRF	−0.69	1.59	2.18	0.39
	WRF + RF	−0.20	1.33	1.79	0.60
	WRF + SVM	−0.52	1.36	1.87	0.59
	WRF + BP	−0.26	1.46	1.95	0.52

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4.   Conclusions and discussion

In this study, a postprocessing system was developed based on several ML algorithms to enhance the wind speed forecasting ability of the WRF model, and the performance levels of different ML algorithms in reducing the forecast bias of the WRF model were compared by using 5-yr data.

The results revealed that the ML algorithms commonly captured the nonlinear relationship between the forecasted wind speed and its influencing factors and produced a satisfactory performance in mitigating the WRF model bias of the wind speed forecasts. The three ML algorithms reduced the MB of the wind speed forecasts by 40%–92% and 40%–92%, decreased the RMSE of the wind speed forecasts by 4%–17% and 28%–66% and increased the R value by 22.5%–47.5% and 4.3%–6.6% for the whole test set and the average 7-day forecast set, respectively. For a wind force > 6, the ML algorithms decreased the RMSE from 3.37 to 3.11–3.21 m s⁻¹ and the MB from −3.49 to −1.74 to −2.43 m s⁻¹. Overall, the RF algorithm achieved the best comprehensive performance due to its ability to substantially mitigate the model bias and reduce the computing cost. The SVM algorithm exhibited a similar but slightly lower ability than the RF algorithm but required approximately 15 times the computing time than the RF algorithm. The BP algorithm significantly increased the similarity of the forecast average to the observed average but insufficiently reduced the RMSE. Moreover, the BP algorithm required approximately 9 times more computing time than the RF model. Regarding the frequency of the wind speed, the RF algorithm commendably corrected the frequency for moderate wind speeds (wind force 3), and the BP model showed a desirable capability for stronger winds (wind force > 6).

We also investigated the possible causes of wind speed fluctuations in the WRF model. The effects of v₁₀, u₁₀, v₉₂₅, u₉₂₅, RH₂, SLP, and T₂ on the wind speed forecast bias were demonstrated by the WRF model. These results highlighted the importance of dynamic/thermodynamic processes in regulating the wind speed.

Overall, this study demonstrated the potential of combining ML algorithms and the NWP model for forecasting coastal wind speeds, and the RF model is suggested for use as a postprocessing tool for mitigating WRF model deviations. However, there are still uncertainties and certain deficiencies in this study. First, the combination of different input variables may lead to different correction capabilities for NWP wind speed forecasts over different types of underlying surfaces and climates. Second, the observation data in our study were based on only one ground-based site, and a greater improvement in wind speed forecasting might be achieved if multisite and radiosonde observation data were integrated. Furthermore, the use of three separate ML algorithms for coastal wind correction may be limited. It has been noted that iterative ML methods (Ma et al., 2020), combinations of ML and deep learning methods (Wang G. et al., 2020), and horizontal combination approaches with ML (Yang B. et al., 2021) may yield better results.