A Hybrid Model of Variational Mode Decomposition and Long Short-Term Memory for Next-Hour Wind Speed Forecasting in a Hot Desert Climate

Abstract

Advancements in technology, policies, and cost reductions have led to rapid growth in wind power (WP) production. One of the major challenges in wind energy production is the instability of WP generation due to weather changes. Efficient power grid management requires accurate power output forecasting. New wind energy forecasting methods based on deep learning (DL) are delivering competitive performance versus traditional methods, like numerical weather prediction (NWP), statistical models and machine learning (ML) models. This is truer for short-term prediction. Since there is a relationship between methods, climates and forecasting complexity, forecasting methods do not always perform the same depending on the climate and terrain of the data source. This paper presents a novel model that combines the variational mode decomposition (VMD) method with a long short-term memory (LSTM) model for next-hour wind speed (WS) prediction in a hot desert climate, such as the climate in Saudi Arabia. The proposed model performance is compared to two other hybrid models, six DL models and four ML models using different feature sets. Also, the proposed model is tested on data from different climates, Caracas and Toronto. The proposed model showed a forecast skill (FS) between 61% and 74% based on mean absolute error (MAE), 64% and 72% based on root mean square error (RMSE), and 59% and 68% based on mean absolute percentage error (MAPE) for locations in Saudi Arabia.

1. Introduction

WP production has grown rapidly due to the evolutions in related technology and its decreasing cost. Onshore wind capacity rose from 178 gigawatts (GW) in 2010 to 699 GW in 2020, while offshore wind grew from 3.1 GW in 2010 to 34.4 GW in 2020. Industry forecasts expect onshore and offshore wind capacity will reach 1787 GW and 228 GW, respectively, by 2030. Wind energy, along with solar energy, would lead the way in transforming the global electricity sector and help the world meet Paris climate targets of CO₂ emissions reductions by 2050 [1] and the sustainable development goals of the United Nations. Therefore, Artificial Intelligence research should support renewable energy sources and sustain their progress.

Saudi Arabia plans to install 16 GW of wind capacity by 2030. In 2022, Dumat Al Jandal began generating electricity and became the first 400-megawatt (MW) onshore WP project in Saudi Arabia. Even though the Dumat Al Jandal wind farm will be the largest in the Middle East, it will account for only 2.5% of the total installed capacity target set by ‘Vision 2030′ (16 GW) [2,3]. Dumat Al Jandal is in the northwestern region of the country and it is the most recommended region for solar and wind energy in Saudi Arabia [4,5,6]. The Saudi government has announced three new wind projects as part of the National Renewable Energy Program. The first is the Yanbu project with a capacity of 700 MW, the second project is in Alghat with 600 MW and the third is in Waad Al Shamal with 500 MW [7]. To enhance the development of wind energy in Saudi Arabia and the Middle East, more studies should focus on developing advanced solutions suitable for the weather in the area.

WP output is proportional to the wind turbines’ rotor dimension and the cube of the WS. Theories show that when WS doubles, the WP potential increases by a factor of eight. Therefore, accurate prediction of WS helps in estimating the power generated by wind turbines. The hub heights of modern wind turbines may be up to 120 m. Hence, to carry out wind resource assessment at the hub height, one must measure or extrapolate WS to that height with minimal error [8]. Temperature (T), pressure (P) and other meteorological variables affect WS. Therefore, including these variables might increase the accuracy of WS and WP forecasting. Efficient management of power grids and energy markets relies on the accurate prediction of short-term power output. However, weather changes pose a challenge in wind energy production and cause instability in WP generation.

Sustaining WP as one of the affordable and clean energy sources has motivated researchers across the globe to develop advanced methods for WP forecasting. There are three kinds of models used in the WP prediction field: physical models, statistical models and ML models. Physical models, also called NWP models, forecast weather including WS based on mathematical modeling and physical principles of the atmosphere and oceans. Because they depend on computer simulations and require a vast amount of meteorological and geographical data, their operating costs are very expensive. Although they can generate accurate long-term forecasting results, they are not desirable in short-term forecasting tasks due to the high cost. On the other hand, Statistical models forecast the WS by using historical WS data and based on mathematical representation. They are better at dealing with short-term forecasting problems compared with physical models. Although they are simple and effective, they have a limited utility with nonlinear time series because that modeling assumes stationary and linear characteristics of time series. Therefore, using ML models has attracted many researchers recently, in particular, DL-based methods. They show superior performance compared to other types of forecasting methods [9,10,11,12] because of their ability to handle nonlinear characteristics of WS series. Hybrid models that combine a decomposition method and a DL forecaster have achieved higher forecasting accuracy in the wind energy forecasting field compared to single DL models [9,10,11,12]. The reason for that is the ability of decomposition methods to separate time series data into four components: level, trend, seasonality and noise. In hybrid models, one or more decomposition methods are used as a data processing step to decompose data into several subseries before training a forecasting model for each one. The final forecasting result is the sum of the results given by all the forecasters [13,14,15]. Hybrid models have shown performance superiority not only in the renewable energy forecasting field but also in other forecasting tasks and applications, such as wave forecasting [16,17,18], stock market index prediction [19] and traffic flow prediction [20].

In this work, a new model that comprises VMD and LSTM is developed to forecast next-hour WS in a hot desert climate. To test the superiority of the proposed model, using different feature sets, its performance is compared with other benchmark forecasting models: two hybrid models of decomposition methods and the LSTM model, six DL-based models and four traditional ML-based models. The purpose of this comparison is to identify the most important data features for WS forecasting in the hot desert climate and measure the performance gain of the proposed model over the benchmark models. Although hybrid models would provide more accurate forecasting, they require more processing time and significant computational resources since data are first decomposed into several subseries and separate models are trained for each subseries [15]. This results in a loss of efficiency.

Figure 1 provides a graphical abstract of the work. It shows the data inputs used to train and test the models, which include temporal and weather variables. Three groups of models are developed, and their performances are compared: ML-based models, DL-based models and hybrid models. Based on four evaluation metrics, the results show that the proposed hybrid model of VMD and LSTM achieves the best results.

The contributions of this paper are summarized as follows.

• Proposing a novel hybrid model of the VMD method and LSTM model for next-hour WS prediction in a hot desert climate. This is the first work, to our knowledge, proposing a hybrid model for this combination of task and weather.
• Identifying the most important dataset features and the most suitable ML models for three climates: hot desert, humid continental and tropical. This is achieved through a performance comparison of the proposed model and two hybrid models of data decomposition techniques and the LSTM model, six DL-based models and four ML-based models, using previous hours’ WS values only versus using weather variables besides WS values.
• Measuring the performance gain of the proposed hybrid model over benchmark models to justify the added complexity and help make an informed decision on the tradeoff between accuracy and efficiency.
• Providing the forecasting results for four different locations in Saudi Arabia and two international locations, Caracas and Toronto. The results are presented using visualization and several performance metrics, including MAE, RMSE, MAPE and FS.

This paper is organized into sections. Section 2 discusses the related works and highlights the research gap. Section 3 describes the methodology used in this paper, including the data preprocessing steps, models’ development process, implementation details and the evaluation metrics used to present the results. Next, Section 4 provides the results of WS forecasting based on the effect of using weather variables, the effect of seasonality, the effect of using decomposition methods and the FS of the models. Section 5 concludes the work.

2. Related Work

DL-based wind energy forecasting methods outperform other traditional methods, such as NWP, statistical and conventional ML models, when making short-term predictions [9,10,11,12]. Alkhayat and Mehmood performed an extensive literature review on DL-based wind energy forecasting methods in [13]. From this review and many other literature reviews of the renewable energy forecasting field [9,10,11,12], it is noted that there is a relationship between methods, terrain and forecasting complexity. The effectiveness of different methods varies with the climate and terrain of the data source, necessitating complex models in some cases. Since models’ structure and performance depend on data, there is a need to develop new models designed for WS prediction for data collected from a hot desert climate. The literature in this field lacks works that propose new DL-based models for such climate conditions or provide comparative studies that show how existing novel ML and DL models perform under this climate. Around fifty-five papers have been published from 2019 to October 2023, which proposed a variation of VMD and LSTM models for WS or WP prediction. Most of these papers proposed models for locations in China, such as [21,22,23,24,25,26,27,28]. Six works proposed models for locations in the USA [29,30,31,32,33,34] and nine works for locations in Europe, such as Spain and Belgium [35,36,37,38,39,40,41,42,43]. Only one work was found that targeted the hot desert climate in which data from a wind farm in Pakistan was used [44]. However, the proposed model in [44] was developed for WS forecasting in the next 10 min whereas this paper targets forecasting for the next hour. Also, the model proposed in [44] was developed using data from one location only, while data from four locations are used in this work. In some of these works, which proposed hybrid models of VMD and LSTM, additional methods were combined. For example, in [22], Lu et al. used VMD to decompose WP data into several modes, then used weighted permutation entropy (WPE) to reconstruct the modes to reduce data redundancy, whereas a combination of a convolutional neural network (CNN) and LSTM model was used for the prediction. In [33], Ma et al. used complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) for WS decomposition and LSTM for WS prediction. The resulting errors from subseries prediction were then decomposed by VMD and LSTM was used again for error prediction. Finally, the predicted error was used to correct the forecasting results and obtain the final forecasting.

In addition, published works that presented other types of hybrid models for WS prediction, which combine different decomposition methods rather than VMD, or other DL models rather than LSTM, did not target the hot desert climate either. For example, Liang et al. [45] developed a hybrid model targeting short-term WS forecasting for a wind farm in China, which comprises CEEMDAN, permutation entropy (PE), gated recurrent unit (GRU), radial basis function neural network (RBFNN) and an improved bat algorithm (IBA). In addition, Lv and Wang [46] developed a hybrid model for short-term WS forecasting in the Rocky Mountains, USA, which combined two decomposition methods of VMD and linear–nonlinear (LN) with the Multi-Objective Binary Back-tracking Search Algorithm (MOBBSA) for optimization and the LSTM autoencoder (LSTM-AE) for prediction. Yildiz et al. [47] combined VMD and a residual-based CNN model for WP forecasting using data from a wind farm in Turkey. Hu et al. [48] proposed a hybrid model that combines VMD and ESN optimized by Differential Evolution algorithm (DE) for WS forecasting using data from a wind farm in Galicia, Spain. As stated earlier, none of the aforementioned hybrid models were developed or tested using data from the targeted climate in this work.

Few studies compare the performance of ML methods using data gathered from different climates and terrains to reach a conclusion on the best method for certain data. For example, Manero et al. in [49] tested five DL models using wind data from around 126,000 locations in North America. They found that recurrent neural network (RNN) models perform better in desert areas. Also, they found that RNN and CNN models provide better performance than the multilayer perceptron (MLP) neural network model for 1 h ahead prediction, while the latter is better for 3 to 12 h ahead prediction. Peng et al. proposed a hybrid model for WS forecasting that combines wavelet soft threshold denoising (WSTD) and GRU [50]. They tested their model using data from four locations in the USA with different climates. They found that the worst performance is associated with desert rock. Alhussein et al. [51] developed a model to predict WS and solar irradiance based on a multi-headed CNN using data from three locations in the USA with different climates, but they noted that different seasons and climates do not affect WS prediction results as solar radiation prediction. However, there are no comparative studies that include the hot desert climate. This highlights the need for more studies that test advanced DL models on multiple climates including the hot desert climate.

Several studies in the literature used Saudi data or other locations with similar climates, but to the best of our knowledge, none of them proposed hybrid models. For example, the developed models for next-hour WS prediction in Saudi Arabia include CNN and bidirectional LSTM (BiLSTM) [52], echo state network (ESN) [53], BiLSTM [54], GRU [55] and feedforward neural network (FFNN) [56,57]. Additionally, some studies compared ML models to statistical methods for 1 h ahead WS forecasting, such as [58], in which ML methods provided better performance, specifically the support vector regression (SVR) model. Other ML model comparisons include studying the effect of including weather variables besides WS and wind direction (WD) on prediction performance, such as [59], in which kernel ridge regression (RR) outperformed SVR and artificial neural network models. Another work [60] studied the effect that using three exogenous variables had on LSTM model performance and found that the best performance is achieved with previous values of WS and T measured at 10 and 2 m. Although all mentioned works targeted the hot desert climate, none of them proposed or compared hybrid models. In addition, no work studied the effect that using exogenous variables on multiple DL models for such a climate.

Table 1. Summary of the related work.

Ref No.	Aim	Method	Features	Data	Climate	Results	Location	Limitation
[22]	WP	Hybrid of VMD + WPE + CNN LSTM	WP, WS, WD, Momentum flux	G	Dwa/Dwb, BSk	NRMSE = 4.19%, NMAE = 3.72%.	Four wind farms, China	A
						NRMSE = 4.96%, NMAE = 3.51%.
						NRMSE = 5.03%, NMAE = 4.89%.
						NRMSE = 5.13%, NMAE = 4.75.
[33]	WS	Hybrid of CEEMDAN + VMD + LSTM	WS	G	Dfb	RMSE = 0.23, MAE = 0.17, MAPE = 4.45% for series 3. RMSE = 0.29, MAE = 0.19, MAPE = 5.38% for series 4.	Colorado, USA	A
[45]	WS	Hybrid of CEEMDAN + PE + GRU + RBFNN + IBA	WS	G	BSk	MAE = 0.45, RMSE = 0.59, MAPE = 4.79%.	Zhangjiakou, China	A
[46]	WS	Hybrid of VMD + LN + MOBBSA + LSTM-AE	WS	G	Dfc	MAE = 0.08, RMSE = 0.11, MAPE = 2.95%.	Rocky Mountains, USA	A
[47]	WP	Hybrid of VMD+ CNN	WP, WS, WD	G	Cfa	R = 0.97, RMSE = 0.05, MAE = 0.04.	A location in Turkey	A
[48]	WS	Hybrid of VMD +ESN+ DE	WS, WD, T, P, RH,	G	Csb	RMSE = 0.12, MAE = 0.10, MAPE = 2.6%.	Galicia, Spain	A
[49]	WS	MLP, CNN, RNN	WS	S	Multiple	R2 for CNN and RNN model is higher than MLP.	Locations in USA	A, B
[50]	WS	Hybrid of WSTD + GRU	WS	G	Dwa, Cfa, BSk	RMSE = 0.38, MAPE = 0.01.	Bondvill, USA	A
						RMSE = 0.26, MAPE = 0.07.	Penn State, USA
						RMSE = 0.53, MAPE = 0.03.	Boulder, USA
						RMSE = 1.86, MAPE = 0.19.	Desert Rock, USA
[51]	WS	CNN	T, RH, P, WS, season, M, D, H	S	Csc	MAE = 0.09, RMSE = 0.13, sMAPE = 4.92.	San Francisco, USA	A, B
[52]	WS	CNN-BiLSTM	WS, SD, MAX	G	BWh	MAE = 0.30, RMSE = 0.43, MAPE = 115	Location in SA	B
[53]	WS	ESN	WS	S	BWh	MSE = 0.24.	Location in SA	B
[54]	WS	BiLSTM	WS, GHI, DNI, DHI, T	S	BWh	MAE = 0.4, RMSE = 0.6, MAPE = 15.	Dumat Al Jandal, SA	B
[55]	WS	GRU	WS, T	S	BWh	MAE = 0.48, RMSE = 0.66, MAPE = 5.		B
[56]	WS	FFNN	T, WD, P, GHI, RH, PWS	G	BWh	RMSE = 0.81, R2 = 0.92, MAE = 0.61.	Jeddah, SA	B
						RMSE = 1.12, R2 = 0.90.	Afif, SA
						RMSE = 0.54, R2 = 0.87.	Riyadh, SA
						RMSE = 0.86, R2 = 0.90.	Taif, SA
[57]	WS	FFNN	WS, T, RH	G	BWh	MAPE = 6.65%, MSE = 0.09.	Qaisumah, SA	B
[58]	WS	SVR	WS	G	BWh	MAE = 2.37, MAPE = 206.80.	Yanbu, SA	B
[59]	WS	RR	WS, WD, PWS, T, P, RH	S	BWh	MAE = 1.22, RMSE = 0.26, R2 = 0.9.	A city in SA	B
[60]	WS	LSTM	WS, T, P	G	BWh	MAE = 0.28, R2 = 0.97.	Dhahran, SA	B

RH: relative humidity, PWS: peak WS, SD: standard deviation, MAX: maximum, GHI: Global Horizontal Irradiation, DNI: Direct Normal Irradiance, DHI: Diffuse Horizontal Irradiance, M: month, D: day, H: hour, GA: genetic algorithm.

summarizes the related work by specifying the forecasting aim, whether it is WS or WP, the forecasting method, the features used as inputs, the data source, whether it is ground-based measurements (G) or simulation data (S), and the Köppen Climate classification of the data source (refer to [61] for the description of each climate code). Also, the table includes the main results and the location of the data used to calculate the results. If a work targets a prediction horizon other than the next-hour prediction, only the results of next-hour forecasting are included in the table because it is the target of this work. The last column defines the limitations of each study as (A) data not from a hot desert climate or (B) not a hybrid model of a decomposition method and DL model.

Research Gap

There are two research gaps identified in the related work discussion. The first is the need to develop new hybrid models designed for WS prediction in a hot desert climate. None of the published works have developed hybrid models for such a climate, except one paper that targeted a different forecasting horizon. To our knowledge, this is the first work proposing a hybrid model of a decomposition method and a DL model for this climate and for the next-hour forecasting horizon. The second gap is the lack of comparative studies across different climates. Few studies compare the performance of the novel methods using data gathered from different climates and terrains, and none of these comparative studies consider the hot desert climate. Therefore, the secondary objective of this paper is to compare the performance of several ML and DL models besides hybrid models for three different climates (hot desert, humid continental, tropical) using different datasets and features. This comparison quantifies the improvement in the accuracy of DL models over ML with and without exogenous variables to show important data features for each climate. Also, it quantifies the performance gains of hybrid models over single models to justify their complexity and aid in decisions regarding accuracy–efficiency tradeoff.

3. Methodology

First, data preprocessing steps are described in Section 3.1, including data collection, feature engineering, data normalization and portioning, and data decomposition methods. Then, Section 3.2 describes the development process of seven DL models, which are LSTM, GRU, BiLSTM, bidirectional GRU (BiGRU), LSTM-AE, CNN-LSTM and the hybrid model of decomposition methods and LSTM. Also, four ML-based models, which are SVR, random forest regression (RFR), eXtreme gradient boosting (XGB) and multiple linear regression (MLR), are described. Section 3.3 explains the implementation details of the models developed in this work. Section 3.4 clarifies the performance evaluation metrics used for comparison.

3.1. Data Preprocessing

In this section, four data preprocessing steps are described: data collection, feature engineering, data normalization and portioning, and data decomposition methods.

3.1.1. Data Collection

Six datasets were used in this work from the National Solar Radiation Database (NSRDB) accessed through the National Renewable Energy Laboratory (NREL) website [62]. NREL notes the data are gathered by the METEOSAT IODC satellite and simulated by the Physical Solar Model (PSM) version 3 with a one-hour temporal resolution and 4 KM spatial resolution. The datasets cover the years 2017, 2018 and 2019. Four datasets were collected from locations in Saudi Arabia (refer to Figure S1 in the Supplementary File), and two international datasets were collected from Caracas, Venezuela and Toronto, Canada (refer to Figure S2 in the Supplementary File). The climate classification of the Saudi locations is hot desert climate (BWh), whereas the climate classification of Toronto is humid continental (Dfb) and that of Caracas is tropical (A), according to the Köppen classification. Saudi locations were chosen as per the planned places for wind farms by the Saudi government whereas international locations were chosen because they represent very different climates.

Table 2. Saudi dataset location information.

Location No.	Location Name	Latitude (N)	Longitude (E)	Elevation (m)
1	Alghat	26.32	43.45	674
2	Dumat Al Jandal	29.52	39.58	618
3	Waad Al Shamal	31.37	38.46	747
4	Yanbu	23.59	38.13	10

clarifies Saudi dataset location information, while

Table 3. International dataset location information.

Location Name	Latitude (N)	Longitude (E)	Elevation (m)
Caracas, Venezuela	10.49	−66.9	942
Toronto, ON, Canada	43.65	−79.38	93

shows the international dataset location information.

3.1.2. Feature Engineering

Besides date and time information, all the datasets contain hourly values of 10 attributes:

• Output: WS in meters per second (m/s);
• WD in degrees (°);
• Clear-sky GHI in watts per square meter (w/m²);
• Clear-sky DHI in w/m²;
• Clear-sky DNI in w/m²;
• Precipitable Water (PW) in millimeters;
• T in Celsius (°C);
• Dew Point (DP) in Celsius (°C);
• P in millibars;
• RH as a percentage (%).

Since GHI, DNI and DHI are all related to solar radiation information and are correlated, one of them was nominated to represent radiation in each dataset based on the highest Pearson correlation coefficient with WS. In addition, weather variables in the forecasting time (t) would not be available in reality; therefore, the last hour’s weather variables (at time t − 1) were used as features to train the forecasting models, which include GHI_lag1, DP_lag1, RH_lag1, P_lag1 and PW_lag1. These features were created using the shift method in the Pandas library.

Temporal variables (month, day, hour) of the forecasting time (t) are also important inputs. The day attribute was converted to the day of the year. This eliminated the need to include the month number while also representing seasonality. For example, the first day of January will become day 1, and the last day of December will become day 365. Second, temporal variables have a cyclical nature. For example, hour 23 is close to hour 1 and day 1 is close to day 365. Treating temporal variables as regular numbers would make hour 1 far from hour 23, even though the difference is small. To avoid this problem that might affect the models’ learning, the effect of the cyclical nature of temporal variables was eliminated by encoding them into sine and cosine using the following equations [63]. The result is an additional four features: hour sine (HS), hour cosine (HC), day sine (DS) and day cosine (DC). The denominator for hour is 23 and for day is 365 in Equations (1) and (2) because 23 is the MAX hour in the datasets, whereas 365 is the MAX day of the year.

WD also has a cyclical nature. For example, WD of value 10° is close to WD of value 360°. Therefore, Equations (1) and (2) were applied and an additional two features were created: WD sine (WDS) and WD cosine (WDC).

$$\tilde{\mathcal{X}}=\sin \left(\frac{2\mathsf{\pi }\mathcal{X}}{\mathrm{MAX}\left(\mathcal{X}\right)}\right)$$

(1)

$$\tilde{\mathcal{X}}=\cos \left(\frac{2\mathsf{\pi }\mathcal{X}}{\mathrm{MAX}\left(\mathcal{X}\right)}\right)$$

(2)

Lagged values of WS are essential inputs for making accurate forecasting. Therefore, WS lagged values were created with the shift method in the Pandas library. To guide the decision on lag, the autocorrelation function (ACF) was used for WS in each dataset. Figure 2 displays the ACFs of three datasets as an example: Alghat, Caracas and Toronto. Saudi datasets including Alghat show a significant correlation of WS with its five past values. The correlation drops below 0.5 after lag 5. Therefore, only WS values of the previous five hours were added to the feature set of Saudi datasets (WS_lag1, WS_lag2, WS_lag3, WS_lag4, WS_lag5). In addition, the same hour on the last day’s WS value might be important for forecasting, so it was included in the feature set (WS_1D) after checking its correlation with WS. The situation with Caracas and Toronto is different. In Caracas (see Figure 2b), WS is significantly correlated with its 72 past values. Thus, WS_lag6 and WS_lag7 were added to the feature set. However, the correlation coefficient after WS_lag7 has the same value up to WS_1D; thus, only WS_1D was included in the feature set to represent the trend and WS_lag8 to WS_lag23 were eliminated. In Toronto (Figure 2c), WS is significantly correlated with its 12 past values and correlation decreases afterward, so WS_lag8 to WS_lag12 were added to the feature set.

The final number of features in Saudi datasets after the feature engineering process is 18, as listed in

Table 4. Saudi dataset features.

Time t Features	$\mathbf{Time}\mathbf{t}-1$ Features	WS Lagged Features
WS (output)	T_lag1	WS_lag1
	DHI_lag1	WS_lag2
HS	DP_lag1	WS_lag3
HC	RH_ lag1	WS_lag4
DS	P_lag1	WS_lag5
DC	PW_lag1	WS_1D
	WDS_lag1
	WDC_lag1

, whereas it is 20 in the Caracas dataset and 24 in the Toronto dataset.

Table 5. Caracas and Toronto dataset features.

Common Features			Caracas Only	Toronto Only
WS (output)	T_lag1	WS_lag1	WS_1D	WS_lag8
	DP_lag1	WS_lag2	DNI_lag1	WS_lag9
HS	RH_ lag1	WS_lag3		WS_lag10
HC	P_lag1	WS_lag4		WS_lag11
DS	PW_lag1	WS_lag5		WS_lag12
DC	WDS_lag1	WS_lag6		GHI_lag1
	WDC_lag1	WS_lag7

lists the common features among the Caracas and Toronto datasets and shows the different features of each one.

To be brief, three datasets that represent different climates were chosen to show their correlation matrices: Alghat, Caracas and Toronto. Figure 3 shows the correlation matrix of the Alghat dataset with these final features. If the threshold for significant correlation is +/−0.5, only the correlations between WS and its past four hours’ values (WS_lag1 to WS_lag4) are significant. Figure 4 displays the correlation matrix of the Caracas dataset in which the correlation between WS and DS is significant, showing that the season has a strong effect on WS at Caracas. Also, the correlations between WS and its past hours’ values (WS_lag1 to WS_1D) are significant. Figure 5 displays the correlation matrix of Toronto in which the correlations between WS and its past 12 h’ values (WS_lag1 to WS_lag12) are significant.

From the correlation matrices of Alghat, Caracas and Toronto, it is noted that last hour’s weather variables have weak correlations with WS. In Section 4.1, the effect of using such variables on forecasting is studied. The models’ performance is compared with and without using these features to show their effect.

Most of the features’ correlations with WS that appear in Figure 3, Figure 4 and Figure 5 above are weak, except correlations with WS lagged features. However, Pearson correlation measures only linear relationships; therefore, mutual information (MI) correlation, which measures both linear and nonlinear correlations [64,65], was used as the feature selection method. Any feature with an MI correlation above zero was kept. All the features listed in Table 4 and Table 5 passed this threshold. To be brief, three datasets that represent different climates were chosen to show their MI correlation scores: Alghat, Caracas and Toronto. Figure 6 shows MI scores for Alghat dataset’s features. The top five features are WS_lag1, WS_lag2, WS_lag3, WS_lag4 and DS. Figure 7 shows MI scores for Caracas dataset’s features, while Figure 8 shows the same for Toronto dataset’s features. The top five features for both datasets are WS_lag1, WS_lag2, WS_lag3, WS_lag4 and WS_lag5. From all three figures, it is noticeable that weather variables have the lowest MI scores. Therefore, Section 4.1 discusses the effect of eliminating these features on forecasting accuracy.

3.1.3. Data Normalization and Portioning

All features were normalized to the range of [0, 1] using a min–max scaler, then denormalized to the normal range after the training process was complete and before calculating the evaluation metrics. Data were portioned into 70% for training, 15% for validation and 15% for testing. Empirical studies show that the best results are obtained if 20–30% of the data are used for testing, and the remaining 70–80% of the data are used for training [66]. The total number of records for each dataset was 26,255, out of which 18,410 records were used for training, 3906 were used for validation and 3939 were used for testing.

Table 6. Dataset descriptions.

Dataset		WS Mean	WS SD	WS VAR	WS MIN	WS MAX
Alghat	Train:	3.03	1.53	2.33	0.1	10
	Val:	3.13	1.58	2.50	0.2	8.6
	Test:	3.01	1.43	2.04	0.2	9.2
	All:	3.04	1.52	2.31	0.1	10
Dumat Al Jandal	Train:	2.65	1.40	1.97	0.1	9.8
	Val:	2.79	1.55	2.39	0.1	10.3
	Test:	2.62	1.37	1.87	0.1	7.3
	All:	2.66	1.42	2.02	0.1	10.3
Waad Al Shamal	Train:	3.08	1.56	2.44	0.2	10.6
	Val:	3.40	1.69	2.86	0.4	11.1
	Test:	2.97	1.39	1.93	0.2	9.3
	All:	3.12	1.56	2.44	0.2	11.1
Yanbu	Train:	3.17	1.61	2.58	0.1	11.2
	Val:	3.31	1.70	2.89	0.1	9.9
	Test:	3.06	1.58	2.50	0.2	9.6
	All:	3.17	1.62	2.62	0.1	11.2
Caracas	Train:	1.63	0.42	0.17	0.1	2.9
	Val:	1.76	0.34	0.12	0.8	2.7
	Test:	1.39	0.39	0.15	0.1	2.6
	All:	1.62	0.42	0.17	0.1	2.9
Toronto	Train:	4.38	2.37	5.60	0.1	14.7
	Val:	3.85	2.49	6.17	0.3	15.6
	Test:	4.28	2.07	4.29	0.3	14.1
	All:	4.28	2.35	5.52	0.1	15.6

describes each dataset used in this work. It defines the mean, standard deviation, variance (VAR), minimum (MIN) and MAX values of WS in each data portion and in the entire dataset.

3.1.4. Data Decomposition Methods

Two tests were performed to check the stationarity of WS data, which are the Dickey–Fuller (AD) test and the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) test. Even though both tests showed data are stationary, data decomposition methods were tried to check their effect on forecasting. Section 4 shows the improvement in prediction results after using three methods: empirical mode decomposition (EMD), CEEMDAN and VMD. In this section, these three methods are described.

EMD

The EMD method decomposes a time series into a set of intrinsic mode functions (IMFs) with different frequency bands and a residue based on the local properties of the time series. EMD’s effectiveness is proven in a broad range of applications for analyzing nonlinear and nonstationary processes. However, there are still some limitations to applying EMD. One of the major limitations is the mode-mixing problem. Mode mixing means that a signal of different scales exists in one IMF or a signal of a similar scale exists in different IMFs [15,67].

Without limiting the number of IMFs, EMD decomposes WS into eleven IMFs and a residue. However, the MAX number of IMFs was set to 4 after the trial-and-error process because no improvement in forecasting has been observed with a larger number. The EMD result of WS decomposition for Alghat dataset is illustrated in Figure S3 in the Supplementary File.

CEEMDAN

To address the mode-mixing problems in EMD, various improved EMD methods have been proposed and CEEMDAN is one of the latest versions. CEEMDAN can solve the mode-mixing problem without adding extra noise to the reconstructed signal [15,67].

Without limiting the number of IMFs, CEEMDAN decomposes WS into eleven or twelve IMFs and a residue. However, the MAX number of IMFs was set to 4 after the trial-and-error process because no improvement in forecasting has been observed with a larger number. CEEMDAN result of WS decomposition for Alghat dataset is illustrated in Figure S4 in the Supplementary File.

VMD

VMD is an effective decomposition algorithm that decomposes a time series into several modes, which have specific sparsity properties while producing the original time series [15,67]. VMD-based models show better noise robustness and more precise component separation.

The number of modes was set to 4 based on the trial-and-error process because no improvement in forecasting has been observed with a larger number. The VMD result of WS decomposition for Alghat dataset is illustrated in Figure S5 in the Supplementary File.

3.2. Models’ Development

Section 3.2.1 describes seven DL-based models: LSTM, GRU, BiLSTM, BiGRU, LSTM-AE, CNN-LSTM and the hybrid model of a decomposition method and LSTM. Section 3.2.2 describes four ML-based models: SVR, RFR, XGB and MLR.

3.2.1. DL-Based Models

Seven DL-based models are described here, which are used for next-hour WS forecasting. These models are LSTM, GRU, BiLSTM, BiGRU, LSTM-AE, CNN-LSTM and the hybrid model of a decomposition method and LSTM.

LSTM

LSTM is a special type of RNN that can learn long-term dependencies. It performs better than traditional RNN in diverse tasks. Besides the hidden state, LSTMs contain the cell state that conveys important inputs from previous steps to later steps. Meanwhile, new inputs are added to or deleted from the cell state through input and forget gates. The output gate determines if the current memory cell will be output. More details on LSTM are in [68,69].

An LSTM model for the next-hour WS forecasting is implemented in this work (refer to Figure S6 in the Supplementary File), which comprises two LSTM layers with dropout for feature extraction and two dense layers to make WS prediction. The activation function of the LSTM model is ReLU. Further implementation details are given in Section 3.3.

GRU

GRU is like LSTM because it captures long-term dependencies but does not contain the cell state. The update gate in GRU determines the amount of past information that needs to be kept because the reset gate determines how much to forget. GRUs are often faster and need less computation time and memory than LSTMs [70].

A GRU model for the next-hour WS forecasting is implemented in this work. It has the same structure that appears in Figure S6 in the Supplementary File, except that each LSTM layer is replaced with a GRU layer. More implementation details are given in Section 3.3.

BiLSTM

BiLSTM is an adjusted version of LSTM that contains two layers: one to process inputs in a forward direction and another to process inputs in a backward direction. This structure allows learning from past and future information. More details on BiLSTMs are in [54,68].

A BiLSTM model for the next-hour WS forecasting is implemented in this work (refer to Figure S7 in the Supplementary File). It comprises one BiLSTM layer and one LSTM layer, followed by two dense layers to make WS prediction. More implementation details are given in Section 3.3.

BiGRU

Similar to BiLSTM, BiGRU comprises two GRUs, which process the input sequence from two directions, then merge their representations [71].

A BiGRU model for the next-hour WS forecasting is implemented in this work. It has the same structure that appears in Figure S7 in the Supplementary File, except that each LSTM layer is replaced with a GRU layer. More implementation details are given in Section 3.3.

LSTM-AE

AE is a neural network that comprises two parts: the encoder and the decoder. The encoder compresses inputs into a feature vector called latent space, and the decoder decompresses it into outputs. This data reconstruction process helps the model extract the most important features. The LSTM-AE model is an AE in which both the encoder and decoder comprise LSTM layers to learn temporal dependencies in sequence data. Work in [38,39] contains more on LSTM-AE [72,73].

An LSTM-AE model for the next-hour WS forecasting is implemented in this work, (refer to Figure S8 in the Supplementary File). Both the encoder and decoder have two LSTM layers, followed by two dense layers to make WS prediction. More implementation details are given in Section 3.3.

CNN-LSTM

In the CNN and LSTM structure, convolutional and pooling layers are followed by LSTM layers, then one or more dense layers to generate the output [74].

A CNN-LSTM model for the next-hour WS forecasting is implemented in this work (refer to Figure S9 in the Supplementary File), which comprises two 1D convolutional layers with a kernel size equaling 2, a max-pooling layer, a flatten layer, a repeat vector layer, an LSTM layer, a dropout layer and two dense layers. Section 3.3 provides more implementation details.

Hybrid Model of Decomposition Methods and LSTM

The LSTM model, combined with the decomposition methods (EMD, CEEMDAN, VMD), is the same model explained earlier. However, the activation function is Tanh instead of ReLU, as appears in Figure 9, because the decomposition process produces negative values for which Tanh is more suitable (refer to Figures S3–S5 in the Supplementary File to see the range of decomposition results). To understand how the hybrid model works, Figure 10 clarifies the forecasting process, which starts with applying a decomposition method on WS original data series, then uses a separate LSTM model for each subseries. The results of these separate LSTM models are totaled to provide the final WS forecasting.

3.2.2. ML-Based Models

This section describes four ML-based models used in this work for performance comparison, which are SVR, RFR, XGB and MLR.

SVR

SVR is a supervised ML algorithm for regression problems, which recognizes nonlinearity in the data. It predicts values instead of predicting classes as a support vector machine that is used for classification problems. In SVR, the best-fit line is the hyperplane that has the MAX number of points [41].

In this work, the SVR was built using Scikit-learn library with radial basis function kernel, with the parameter settings: C = 100; epsilon = 0.001. The random search method was used to select the hyperparameters, which requires setting up a grid of values and selecting random combinations of these values to train the model. The combination that gives the best results is chosen. SVR was trained and tested using the same training and testing sets of the datasets described in Table 6.

RFR

Random forest is a non-parametric, supervised and ensemble-based learning method used for both classification and regression tasks. Its final output is the average of multiple decision trees’ outputs. Therefore, it produces a more accurate prediction than a single decision tree [75].

In this work, the RFR, which was built using Scikit-learn library, has 600 estimators with a MAX depth equal to 50. It was trained and tested using the same training and testing sets of the datasets described in Table 6. The random search method was used to select the hyperparameters.

XGB

XGB is a scalable, distributed gradient-boosted decision tree. It is an ensemble learning algorithm, like a random forest for classification and regression. Gradient boosting improves a single weak model by combining it with several other weak models to generate a strong ensemble model. XGB is an accurate and efficient implementation of gradient boosting that uses computing power for building trees in parallel [76].

In this work, the XGB, which was built using XGBoost library, has 500 estimators with a learning rate equal to 0.1. It was trained and tested using the same training and testing sets of the datasets described in Table 6. The random search method was used to select the hyperparameters.

MLR

MLR is a conventional statistical method to define the relationship between multiple independent variables and one dependent variable [77].

In this work, the MLR was built using Scikit-learn library and the same training and testing sets of the datasets described in Table 6.

3.3. Implementation

In this work, the Keras Library, a DL API written in Python and running on top of the TensorFlow platform, was used to create DL models, where Python3 was employed as the programming language. The PyEMD library was used for EMD and CEEMDAN, whereas the vmdpy library was used for VMD. The experiments were performed on a laptop with Intel Core i7-11800 H CPU, NVIDIA GeForce RTX 3070 GPU and 16 GB memory. However, all DL models were developed using the GPU.

Table 7. DL-based models’ hyperparameters and optimization methods.

Hyperparameter	Value	Optimization
Learning Rate	0.001	Adam Optimizer
Number of Epochs	100	Activation Function = ReLU, Tanh *
Dropout	0.1	Loss Function = MSE
Batch Size	500	Early Stopping
Weight Decay	0.000001	Kernel Initializer = glorot uniform

* In hybrid LSTM model with decomposition methods.

specifies the hyperparameters used in developing all DL models, besides the optimization methods. The structures of all DL models, including the type and number of layers and their neurons, are explained in Section 3.2.1 and illustrated in Figures S6–S9 in the Supplementary File. The algorithm for developing the hybrid model of VMD and LSTM is shown in Figure 11.

3.4. Evaluation Metrics

In this work, four performance evaluation metrics were used to evaluate the forecasting models.

MAE is the mean of the absolute values of the individual forecast errors on overall examples (N) in the test set. Each forecasting error is the difference between the actual value (actual WS) and the forecast value (forecast WS). A lower value of MAE is better. It is calculated as follows [44].

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\left|{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{W}\mathrm{S}}_{\mathrm{i}}-{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{t} \mathrm{W}\mathrm{S}}_{\mathrm{i}}\right|$$

(3)

RMSE is the standard deviation of the residuals or the forecast errors. It measures residual spread and how the data are concentrated around the line of regression. A lower value of RMSE is better. RMSE is calculated as follows [78].

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{({\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{W}\mathrm{S}}_{\mathrm{i}}-{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{t} \mathrm{W}\mathrm{S}}_{\mathrm{i}})}^2}$$

(4)

MAPE is a measure of forecasting accuracy. This percentage shows the average difference between the forecasted value and the actual value. Smaller MAPE provides better forecasts. MAPE is calculated as follows [79].

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\left|\frac{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l} {\mathrm{W}\mathrm{S}}_{\mathrm{i}}-{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{t} \mathrm{W}\mathrm{S}}_{\mathrm{i}}}{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l} {\mathrm{W}\mathrm{S}}_{\mathrm{i}}}\right|\times 100\%$$

(5)

FS is used to compare a proposed forecasting model performance metric with a reference model performance metric. An often-used reference model in the literature is the persistence method. The evaluation metric could be RMSE, MAE, or others. FS is calculated as follows [80].

$$\mathrm{F}\mathrm{S}=1-\frac{{\mathrm{M}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d}}}{{\mathrm{M}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}}_{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}}}\times 100\%$$

(6)

4. Results and Discussion

This section presents and discusses the results of the models’ forecasting performance in four aspects: the effect of using weather variables besides lagged WS features on forecasting accuracy (Section 4.1); the effect of seasonality on forecasting accuracy (Section 4.2); the effect of using three decomposition methods with the LSTM model for forecasting accuracy (Section 4.3); and the percentage of the forecasting improvement in all models over the persistence method, known as the FS (Section 4.4).

4.1. Effect of Using Last Hour’s Weather Variables on Forecasting

To study this effect on Saudi datasets, ten forecasting models (LSTM, GRU, BiLSTM, BiGRU, LSTM-AE, CNN-LSTM, SVR, RFR, XGB, MLR) were trained and tested twice with the same records. First, training was conducted using 18 features, as shown in Table 4, which include temporal features (HS, HC, DS, DC), the last hour’s weather variables (T_lag1, DHI_lag1, DP_lag1, RH_ lag1, P_lag1, PW_lag1, WDS_lag1, WDC_lag1), and the WS values of the previous 5 h (WS_lag1, WS_lag2, WS_lag3, WS_lag4, WS_lag15) besides the WS value of the same hour last day (WS_1D). In the second trial, only WS values of the previous 5 h were used. For the Caracas dataset, 20 features were used in the first trial (with WS_lag6 and WS_lag7 added to Table 4 features) and 7 features in the second trial (WS_lag1 to WS_lag7). For the Toronto dataset, 24 features were used in the first trial (with WS_lag8 to WS_lag12 added to Table 4 features and WS_1D removed). In the second trial for the Toronto dataset, only 12 features were used (WS_lag1 to WS_lag12).

Figure 12 shows the average MAE results of 20 runs of the forecasting models when weather features were used besides WS lagged features, whereas Figure 13 shows the same when only WS lagged features were used.

For the Alghat dataset, it is noted that using weather features improved the MAE results for all DL-based forecasting models by 33% at most, as with the GRU model, and 20% at least, as with the CNN-LSTM model. Using weather features with ML-based models improved the MAE results for all by 30% at most, as with the XGB model, and 5% at least, as with MLR model. The best MAE value was 0.14, achieved by the LSTM, GRU, BiLSTM, BiGRU, and XGB models, while the worst MAE value was 0.20 and associated with the MLR model.

For the Dumat Al Jandal dataset, using weather features improved the MAE results for all DL-based forecasting models by 25% at most, as with the LSTM, BiLSTM, BiGRU, and LSTM-AE models, and 15% at least, as with the CNN-LSTM model. Using weather features with the ML-based models improved the MAE results for all models by 24% at most, as with the XGB model, and 5% at least, as with MLR model. The best MAE value was 0.15, achieved by the LSTM, BiLSTM, BiGRU, and LSTM-AE models, while the worst MAE value was 0.20 and associated with the MLR model.

For the Waad Al Shamal dataset, using weather features improved the MAE results for all DL-based forecasting models by 32% at most, as with the BiLSTM model, and 16% at least, as with the CNN-LSTM model. Using weather features with ML-based models improved the MAE results for all models by 27% at most, as with the RFR model, and 5% at least, as with the MLR model. The best MAE value is 0.13, achieved by BiLSTM, while the worst MAE value is 0.20 and associated with the MLR model.

For the Yanbu dataset, using weather features improved the MAE results for all DL-based forecasting models, except CNN-LSTM model, by 18% at most as with LSTM, GRU, BiLSTM, and BiGRU models. Using weather features with ML-based models improved the MAE results for all models by 18% at most, as with SVR and 6% at least as with the MLR model. The best MAE value is 0.14, achieved by LSTM, GRU, BiLSTM, BiGRU, and SVR models, while the worst MAE value is 0.20 and associated with the MLR model.

For the Caracas dataset, using weather features did not improve the MAE results, except for the GRU and RFR models, which were improved by 14%. The best MAE value is 0.06, achieved by all models with weather features.

For the Toronto dataset, using weather features did not improve the MAE results, except for CNN-LSTM and MLR models, which were improved by 5%. In fact, the LSTM, GRU, BiLSTM, and LSTM-AE models achieved better results using only lagged features. Weather features worsened the results. The best MAE value is 0.18, achieved by the SVR model with only lagged features.

From the MAE results of Saudi datasets, it is concluded that using weather features improved all models for all four locations, but the improvement percentage was the highest with the Alghat dataset and the lowest with the Yanbu dataset. The low improvement with the Yanbu dataset might be related to its location as it is the only coastal city among the four Saudi locations, and there are no significant changes in Yanbu’s weather from season to season. For example, the average T is 32 °C in August and 21 °C in January. With weather features, all models had similar MAE results, except the MLR model, which achieved the worst MAE value for all four datasets. The BiLSTM model was the best, which attained the best MAE value for all Saudi locations.

To summarize the MAE results for the Caracas dataset, weather features did not improve the MAE results because WS has strong correlations with its seven lagged features (see Figure 2), which makes it easy to predict the next value with no extra features. Also, the MAE value was 0.06 for all models. This is a low value compared to other locations because the MAX WS in Caracas was 2.9 (see Table 6). Using weather features in the Toronto dataset made the MAE results worse in most of the cases because WS has strong correlations with its lagged 12 features (see Figure 2). Also, MAE values for Toronto are the largest because the MAX WS is 15.6—the highest among all locations (see Table 6).

Figure 14 shows the average RMSE results of 20 runs of the forecasting models when weather features were used besides WS lagged features, whereas Figure 15 shows the same when only WS lagged features were used.

For the Alghat dataset, it was noted that using weather features improved the RMSE results for all DL-based forecasting models by 32% at most, as with the GRU model, and 21% at least, as with the CNN-LSTM model. Using weather features with ML-based models improved the RMSE results for all models by 27% at most, as with the RFR model, and 4% at least, as with the MLR model. The best RMSE value was 0.19 achieved by the LSTM, GRU, BiLSTM, and BiGRU models, while the worst RMSE value was 0.27 and associated with the MLR model.

For the Dumat Al Jandal dataset, using weather features improved the RMSE results for all DL-based forecasting models by 25% at most, as with the LSTM model, and 18% at least, as with the CNN-LSTM model. Using weather features with ML-based models improved the RMSE results for all models by 24% at most, as with the XGB model, and 3% at least, as with MLR model. The best RMSE value was 0.21, achieved by the LSTM, BiLSTM, and LSTM-AE models, while the worst RMSE value was 0.28 and associated with the MLR model.

For the Waad Al Shamal dataset, using weather features improved the RMSE results for all DL-based forecasting models by 33% at most, as with the LSTM, GRU, and BiLSTM models, and 19% at least, as with the CNN-LSTM model. Using weather features with ML-based models improved the RMSE results for all models by 30% at most, as with the XGB model, and 3% at least, as with the MLR model. The best RMSE value was 0.18, achieved by the LSTM, GRU, BiLSTM, and BiGRU models, while the worst RMSE value was 0.28 and associated with the MLR model.

For the Yanbu dataset, using weather features improved the RMSE results for all DL-based forecasting models, except the CNN-LSTM model, by 22% at most, which was achieved by the LSTM model. Using weather features with ML-based models improved the RMSE results for all models by 18% at most, as with SVR, and 8% at least, as with the MLR model. The best RMSE value was 0.18, achieved by LSTM, BiLSTM, and SVR models, while the worst RMSE value was 0.23 and was associated with the RFR model.

For the Caracas dataset, using weather features improved the RMSE results only for the LSTM, GRU, SVR, MLR, and XGB models, by 13%, and the RFR model, by 22%. The best RMSE value was 0.07, achieved by the LSTM, GRU, SVR, RFR, XGB, and MLR models with weather features.

For the Toronto dataset, using weather features did not improve the RMSE results, except for the CNN-LSTM, SVR, and XGB models, which were improved by 3% at least. In fact, the GRU, BiLSTM, and LSTM-AE models achieved better results with lagged features only, and using weather features worsened the results. The best RMSE value was 0.30, achieved by the XGB model with weather features and achieved by the GRU and BiLSTM models with lagged features only.

From the RMSE results of Saudi datasets, it is concluded that weather features improved all models for all four locations. However, the improvement percentage was the highest with the Alghat and Waad Al Shamal datasets and the lowest with the Yanbu dataset. The low improvement with the Yanbu dataset might be related to its location as it is the only coastal city among the four Saudi locations, and there are no significant changes in Yanbu’s weather from season to season. For example, the average T is 32 °C in August and 21 °C in January. With weather features, DL-based models had similar RMSE results, except the CNN-LSTM model, and ML-based models had similar RMSE results, except the MLR model. The MLR model achieved the worst RMSE value for three datasets, while the LSTM and BiLSTM models attained the best RMSE value for all Saudi locations.

To summarize the RMSE results for the Caracas dataset, weather features did not improve the RMSE results because WS has strong correlations with its seven lagged features (see Figure 2), which makes it easy to predict the next value with no extra features. Also, the RMSE value was 0.07 or 0.08 for all models, which is a low value compared to other locations because the MAX WS in Caracas was 2.9 (see Table 6). Using weather features in the Toronto dataset did not improve the RMSE results for most of the models because WS has strong correlations with its twelve lagged features (see Figure 2). Also, the RMSE values for Toronto were the largest because the MAX WS was 15.6, which was the highest among all locations (see Table 6).

Figure 16 shows the average MAPE results of 20 runs of the forecasting models when weather features were used besides WS lagged features, whereas Figure 17 shows the same when only WS lagged features were used.

For the Alghat dataset, we noted that using weather features improved the MAPE results for all DL-based forecasting models by 25% at most, as with the LSTM and GRU models, and 15% at least, as with the CNN-LSTM model. Using weather features with the ML-based models improved the RMSE results for all models by 25% at most, as with the XGB and RFR models, and 2% at least, as with the MLR model. The best MAPE value was 5.91, achieved by the LSTM model, while the worst MAPE value was 8.31 and was associated with the MLR model.

For the Dumat Al Jandal dataset, using weather features improved the MAPE results for all DL-based forecasting models by 18% at most, as with the LSTM model, and 11% at least, as with the CNN-LSTM model. Using weather features with the ML-based models improved the MAPE results for the RFR model by 15% and for the XGB and SVR models by 9% at least. The best MAPE value was 7.66, achieved by the LSTM model, while the worst RMSE value was 10.05 and was associated with the MLR model.

For the Waad Al Shamal dataset, using weather features improved the MAPE results for all DL-based forecasting models by 31% at most, as with the BiLSTM model, and 15% at least, as with the CNN-LSTM model. Using weather features with the ML-based models improved the MAPE results for all models by 28% at most, as with the XGB model, and 3% at least, as with the MLR model. The best MAPE value was 5.41, achieved by the BiLSTM model, while the worst MAPE value was 8.22 and was associated with the MLR model.

For the Yanbu dataset, using weather features improved the MAPE results for all DL-based forecasting models by 23% at most, as with the LSTM model, and by 5% at least, as with the CNN-LSTM model. Using weather features with the ML-based models improved the MAPE results for all models by 17% at most, as with SVR, and 6% at least, as with the MLR model. The best MAPE value was 6.67, achieved by the LSTM model, while the worst MAPE value was 8.25 and was associated with the RFR model.

For the Caracas dataset, using weather features improved the MAPE results, except for the BiLSTM and CNN-LSTM models. The highest improvement percentage was 12% for the RFR model and the lowest was 2% for the MLR model. The best MAPE value was 4.68, achieved by the SVR model with weather features.

For the Toronto dataset, using weather features did not improve the MAPE results, except for the ML-based models, which were improved by 2% at most. In fact, the DL-based models achieved better results with lagged features only, and using weather features worsened the results. The best MAPE value was 5.37, achieved by the SVR model with weather features.

From the MAPE results of Saudi datasets, it is concluded that weather features improved all models for all locations. However, the improvement percentage was the highest with the Alghat and Waad Al Shamal datasets and the lowest with the Yanbu dataset. The low improvement with the Yanbu dataset might be related to its location as it is the only coastal city among the four Saudi locations, and there are no significant changes in Yanbu’s weather from season to season. For example, the average T is 32 °C in August and 21 °C in January. With weather features, all models had similar MAPE results, except the MLR and RFR models. The MLR model achieved the worst MAPE value for three datasets, while LSTM attained the best MAPE value for three datasets out of the four Saudi locations.

To summarize the MAPE results for the Caracas dataset, weather features improved the MAPE results because WS has strong correlations with its seven lagged features (see Figure 2), which makes it easy to predict the next value with no extra features. Using weather features in the Toronto dataset did not improve the MAPE results for most of the models because WS has strong correlations with its twelve lagged features (see Figure 2).

From the MAE, RMSE, and MAPE results in this section, it can be observed that using weather features improved the forecasting results of all models for Saudi locations by around 30% at most. However, the DL-based models experienced greater improvement than the ML-based models did. This may be related to DL-based models’ ability to handle high dimensionality. Also, the Yanbu dataset had the smallest improvement percentage because, as explained earlier, Yanbu is a coastal city, unlike the other three locations, and there are no significant changes in Yanbu’s weather from season to season. This makes weather features less important than WS lagged features in predicting the next value of WS. Weather features with Caracas improved the forecasting results slightly, while it worsened the results for Toronto for most of the models. The reason behind this is strong WS correlations with its lagged features. Seven lagged features were used for Caracas and twelve for Toronto. Therefore, the results of the ML-based models are better or similar to the results of DL-based models for both locations. It can be concluded that when WS has very strong correlations with its lagged values, ML-based models’ performance would be satisfactory (i.e., SVR and XGB models) while DL-based models are needed with less strong or weak correlations. The same applies to weather features, which can improve the forecasting results more if there are less strong correlations between WS and its lagged features.

4.2. The Effect of Seasonality on Forecasting

The datasets used in this work cover the period from January 2017 to December 2019. As mentioned earlier in Section 3.1.3, 15% of the size of the datasets was used for testing; hence, the testing set spanned from 20 July to 31 December 2019, and it only contained complete data for the last five months of the year 2019. In this section, the changes in MAE, RMSE, and MAPE are presented for August, September, October, November, and December to note the effect of seasonality on next-hour WS forecasting.

Figure 18 shows the WS hourly average per month for all datasets. Saudi Arabia has only two seasons and, as shown in the figure, the WS hourly average does not differ from month to month, ranging from 2.42 to 3.6 m/s. In Alghat, the WS hourly average is above 3 m/s in March, April, June, July, August, and November, whereas in Dumat Al Jandal, it has not reached 3 m/s. In Yanbu, the WS hourly average is above 3 m/s in all months, except May, September, October, and November. Among the Saudi locations, Yanbu has the highest average and Dumat Al Jandal has the lowest. As noted in [81], the western region of Saudi Arabia, where Yanbu is located, has more potential for wind energy than other regions do. In Caracas, the WS hourly average is low compared to other locations and the highest value is 1.94 m/s in February. It drops below 1.5 from July to October. In contrast, the WS hourly average in Toronto is high compared to other locations and the highest value is 5.95 m/s in January. It drops below 4 from May to September.

Figure 19 shows the MAE, RMSE, and MAPE results for five months (August, September, October, November, and December) for Saudi datasets. Alghat results (a) and (b) show that, according to the MAE and RMSE results of all models, November and December results are worse than the remaining months, except for the MLR model, which performs worse in August and December. The MAPE results of all models, as shown in (c), show that October has the worst results, followed by November and December. Dumat Al Jandal’s results in (d), (e), and (f) show that the October results are the worst for all models. For the Waad Al Shamal results in (g) and (h), the October results are the worst for all models, except for the MLR model, whereas the MAPE results in (i) show that besides October, December has the worst results. Yanbu’s results in (g), (k), and (l) show performance differences across months from model to model. However, September and October have higher errors than other months for most of the models.

Figure 20 shows MAE, RMSE, and MAPE results for five months (August, September, October, November, and December) for Caracas and Toronto. Caracas’s results in (a), (b), and (c) show that September is the most difficult month for forecasting. The Toronto MAE results in (d) show that October and December have the highest error, while the RMSE results in (e) show a significant increase in the October error. The Toronto MAPE results in (f) show that August and September’s results are even worse than October.

To conclude, it is unnecessary to worry about seasonality effects unless the hourly average of WS varies from one month to another or from one season to another. In the Saudi locations covered, there was no significant variance in the results from August to December, despite higher errors in some months, such as October. However, longer testing sets that cover a whole year should validate this observation. Caracas had the lowest WS hourly average in September. It also had the highest forecasting error. In Toronto, the MAPE results showed the same inverse relationship in which August and September had the lowest WS hourly average and the highest forecasting error. However, this observation cannot be validated without a test set covering a whole year.

4.3. The Effect of Using Decomposition Methods on Forecasting

To study this effect, three decomposition methods, EMD, CEEMDAN, and VMD (described in Section 3.1.4), were combined with the LSTM model. Section 3.2.1. describes the structure of these hybrid models in detail. The features used to train and test the three hybrid models were the last five hours’ WS values in Saudi locations, the last seven values in Caracas, and the last twelve values in Toronto. The forecasting results of the three hybrid models were compared to the results of the LSTM, GRU, BiLSTM, BiGRU, LSTM-AE, CNN-LSTM, SVR, RFR, XGB, and MLR models (the same results appeared in Section 4.1 in Figure 13, Figure 15 and Figure 17).

Figure 21 shows the MAE results of all forecasting models for six datasets when only WS lagged features were used. From the figure, it is noted that the best-performing model for all Saudi locations was the VMD-LSTM model, and the worst was the RFR model. The hybrid model of VMD-LSTM achieved an MAE value equal to 0.12, which improved the forecasting results over the LSTM model by 40% for Alghat, Dumat Al Jandal, and Waad Al Shamal. It also achieved an MAE value equal to 0.09 for Yanbu, which improved the forecasting results over the LSTM model by 47%. Regarding the Caracas dataset, all three hybrid models achieved the same MAE value equal to 0.03, which provided 50% improvement over the LSTM model’s result. With the Toronto dataset, the hybrid model of CEEMDAN-LSTM achieved a better MAE value than the other two hybrid models, which provided a 42% improvement over the LSTM model’s result.

Figure 22 shows the RMSE results of all forecasting models for six datasets when only WS lagged features were used. From the figure, it is noted that the best-performing model for all Saudi locations was the VMD-LSTM model, and the worst was the RFR model. The hybrid model of VMD-LSTM achieved an RMSE value equal to 0.15, which improved the forecasting results over the LSTM model by 44% for Alghat and Waad Al Shamal. It also achieved an RMSE value equal to 0.16 for Dumat Al Jandal and 0.13 for Yanbu, which improved the forecasting results over the LSTM model by 43%. Regarding the Caracas and the Toronto datasets, the hybrid model of CEEMDAN-LSTM achieved a slightly better RMSE value than the other two hybrid models, showing a 63% improvement in Caracas’s forecasting results and a 39% improvement in Toronto’s over the LSTM model.

Figure 23 shows the MAPE results of all forecasting models for six datasets when only WS lagged features were used. From the figure, it is noted that the best-performing model for all Saudi locations was the VMD-LSTM model, and the worst was the RFR model. The hybrid model of VMD-LSTM achieved a MAPE value equal to 4.81 for Alghat and 5.39 for Dumat Al Jandal, which improved the forecasting results over the LSTM model by 39% and 37% for both locations. It also achieved a MAPE value equal to 4.7 for Waad Al Shamal and 4.66 for Yanbu, which improved the forecasting results over the LSTM model by 41% and 46% for both locations. Regarding the Caracas and Toronto datasets, the hybrid model of CEEMDAN-LSTM achieved a better MAPE value than the other two hybrid models, showing a 58% improvement in Caracas’s forecasting results and a 41% improvement in Toronto’s over the LSTM model.

From the MAE, RMSE, and MAPE results in this section, it is concluded that using a hybrid model of LSTM and a decomposition method always achieves better results than using the LSTM model alone. In Saudi locations, the best hybrid model is VMD-LSTM according to all evaluation metrics, with the improvement percentage ranging from 39% to 47% over the LSTM model. This observation agrees with the performance comparison conducted in [48] between EMD, ensemble EMD, wavelet packet decomposition, and VMD, in which VMD achieved the most accurate and stable performance. Also, in [82], VMD was compared to empirical wavelet transform, complementary ensemble empirical mode decomposition, and ensemble intrinsic time-scale decomposition. VMD outperformed EMD in [83]. In this field, many works show that VMD-based models perform better compared with Wavelet Transform-based and EMD-based models [48,84,85]. The reason behind VMD’s superiority is its ability to decompose nonstationary and nonlinear time series and its robustness in handling data noise.

Regarding the Caracas and Toronto datasets, the best hybrid model is CEEMDAN-LSTM according to all evaluation metrics, with the improvement percentage ranging from 50% to 63% over the LSTM model in Caracas and from 39% to 42% over the LSTM model in Toronto.

Decomposition methods for forecasting were studied by comparing the results of hybrid models to the results of DL and ML-based models using only lagged WS values. Which method is better: hybrid models with decomposition methods in which only WS lagged values were used, or single DL-based models in which both weather variables and WS lagged values were used? To answer this question, the best-performing hybrid models VMD-LSTM and CEEMDAN-LSTM were compared to the LSTM model that was trained and tested using weather variables for each dataset in Figure 24.

Figure 24 compares the effect of using decomposition methods to the effect of using weather variables on the MAPE results of VMD-LSTM, CEEMDAN-LSTM, and LSTM. From the figure, it can be seen that the VMD-LSTM model achieved the best forecasting accuracy for the Saudi datasets, while the CEEMDAN-LSTM model achieved the same for the Caracas and Toronto datasets. Therefore, it can be concluded that hybrid models with only WS lagged values achieved better results than the LSTM model with both weather variables and WS lagged values.

4.4. The FS of All Models

This section presents the FS of all forecasting models, which measure the improvement in forecasting compared to the persistence method. This metric (refer to Equation (6)) not only shows the feasibility of a proposed model for the same dataset but also helps to evaluate a model’s performance compared to other models developed using different datasets. The results presented in this section are for the forecasting models that were trained and tested using WS lagged features.

Figure 25 shows the FS of all models using the MAE metric for all six datasets. From the figure, it is noted that the highest FS values for the Saudi datasets were achieved by the VMD-LSTM model, and the worst are associated with the RFR model. For Caracas, only the three hybrid models achieved an improvement over the persistence method by 50%. For Toronto, the EMD-LSTM model and CEEMDAN-LSTM model attained 63% as the highest FS value, whereas the worst was 30%, associated with the CNN-LSTM model.

Figure 26 shows the FS of all models using the RMSE metric for all six datasets. From the figure, it is noted that the highest FS values for the Saudi datasets were achieved by the VMD-LSTM model, and the worst are associated with the RFR model. For Caracas, the CEEMDAN-LSTM model achieved the best FS of 67%. The remaining two hybrid models attained an FS equal to 56%, while other models could not improve the FS by more than 11%. For Toronto, the CEEMDAN-LSTM model attained 56% as the highest FS value, whereas the worst was 23%, associated with the CNN-LSTM and SVR models.

Figure 27 shows the FS of all models using the MAPE metric for all six datasets. From the figure, it is noted that the highest FS values for the Saudi datasets were achieved by the VMD-LSTM model, and the worst are associated with the RFR model. For Caracas, the CEEMDAN-LSTM model achieved the best FS equal to 57%. The remaining two hybrid models attained an FS equal to 48% and 44%, while most of the remaining models are worse than the persistence method. For Toronto, the CEEMDAN-LSTM model attained 62% as the highest FS value, whereas the worst was 31%, associated with the RFR model.

From the figures above, it can be concluded that the highest FS percentages of all metrics are achieved by hybrid models. The VMD-LSTM model is the best with the Saudi datasets, and the CEEMDAN-LSTM model is the best with the Caracas and Toronto datasets. Also, apart from the hybrid models for Caracas, other models are worse, equal to, or just slightly better than the persistence method. The significant correlation between WS and its last value in Caracas makes prediction with the persistence method easier and more accurate.

5. Conclusions

This paper presents a novel hybrid model combining VMD and LSTM, developed for next-hour wind speed prediction in hot desert climates like Saudi Arabia’s. Additionally, the paper demonstrates how DL models, both with and without exogenous variables, improve accuracy over ML models, offering insights into crucial data features for hot desert climates. Finally, the paper highlights the superior performance of hybrid models over single models, justifying their complexity and aiding in decisions regarding the accuracy–efficiency tradeoff. These objectives are achieved through the performance comparison of three hybrid models, six DL-based models, and four ML-based models, which cover several aspects, such as seasonality and using different features and decomposition methods. The proposed hybrid model of VMD and LSTM is not only suitable for Saudi Arabia; rather, it is applicable to locations with the same or similar climate. In fact, the results show that the VMD and LSTM model delivers better performance than all single models for the Caracas and Toronto datasets, which have totally different climates. The findings are summarized as follows:

• The best forecasting model for the Saudi locations, according to MAE, RMSE, MAPE, and FS, is the hybrid model of VMD and the LSTM model.
• The best forecasting model for Caracas and Toronto, according to MAE, RMSE, MAPE, and FS, is the hybrid model of CEEMDAN and the LSTM model.
• All DL-based models have similar performance, but complex structures like the LSTM-AE and CNN-LSTM models have higher errors.
• Using the last hour’s weather variables, besides the last values of WS, improved the forecasting results for all models. However, the hybrid models with decomposition methods achieved better forecasting results.
• If seasons do not affect the hourly average of WS at the data source location, forecasting results would not show large variance either. Here, it is unnecessary to partition the datasets according to seasons and train separate forecasters.

Future work will involve developing a DL-based auto-selective tool, similar to the approach in [86] for solar energy, to predict the best-performing DL model for wind energy forecasting. The datasets, sourced from the NSRDB website and spanning three years, were satellite-collected, highlighting the need for more extensive, ground-based data in future research. Testing the proposed model on datasets gathered from locations with similar climates and for different forecasting horizons, such as the next 6 h or the next day, is another future research direction. Also, the model might be tested for the prediction of solar radiation data, solar power and WP data, and other renewable energy datasets. In addition, more decomposition methods and different DL-based models might be tested and compared for prediction in the hot desert climate.