Open AccessArticle

MIESTC: A Multivariable Spatio-Temporal Model for Accurate Short-Term Wind Speed Forecasting

Shaohan Li

Min Chen

^1,2,3,

Lu Yi

⁴

Qifeng Lu

^5,6 and

Hao Yang

^1,*

School of Computer Science, Chengdu University of Information Technology, Chengdu 610225, China

Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610213, China

University of Chinese Academy of Sciences, Beijing 100049, China

⁴

Key Laboratory of Coastal Environment and Resources Research of Zhejiang Province, School of Engineering, Westlake University, Hangzhou 310024, China

⁵

CMA Earth System Modeling and Prediction Centre (CEMC), China Meteorological Administration, Beijing 100081, China

⁶

China State Key Laboratory of Severe Weather, Beijing 100081, China

Author to whom correspondence should be addressed.

Atmosphere 2025, 16(1), 67; https://doi.org/10.3390/atmos16010067

Submission received: 17 December 2024 / Revised: 3 January 2025 / Accepted: 8 January 2025 / Published: 9 January 2025

(This article belongs to the Special Issue Applications of Artificial Intelligence in Atmospheric Sciences)

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Figure 1
Research area and five research sites. "> Figure 2
Correlation analysis of different factors with wind speed across five locations. A, B, C, D, and E represent the five research locations in the study. The chart shows that the correlation between the wind speed and various factors differs significantly across locations. The factors u10, v10, and t2m exhibit strong correlations with the wind speed at multiple locations, suggesting their importance as primary influencing factors, whereas sp and tp show relatively strong correlations at specific locations. "> Figure 3
An overview of the MIESTC model’s architecture. Subfigure (a) illustrates the overall workflow, including the independent encoding of multiple meteorological variables (WS, U10, V10, T2M, TP, SP), spatio-temporal feature extraction through the MSTC module to capture the spatio-temporal relationships between variables, and finally the decoding and prediction using the predictor module. The skip connection aids in preserving features from earlier stages. Subfigures (b–d) present the detailed structures of the encoder block, MSTC block, and predictor block. "> Figure 4
The data distribution of the meteorological variables. These variables clearly exhibit significant differences in their distributions, with distinct scales and semantic units. "> Figure 5
Model performance comparison. This figure presents the performances of various models at different prediction time horizons, evaluated with RMSE, PCC, MAE, and SSIM metrics. The results indicate that the MIESTC model consistently surpasses other models across all time steps and evaluation metrics, highlighting its superior effectiveness in short-term wind speed forecasting. "> Figure 6
Visual representation of wind speed prediction results across different models. The red boxes indicate areas where the prediction deviates significantly from the ground truth, highlighting the deficiencies in different models. "> Figure 7
Attention weight distribution of wind speed prediction variables. This heatmap illustrates the attention weight distribution of each meteorological variable (U10, V10, T2M, SP, TP, WS) across eight attention heads in the MSTC module. The attention heads (Head 1 to Head 8) represent different perspectives of the model in capturing variable relationships. Darker colors indicate higher attention weights, highlighting the relative importance of each variable for wind speed prediction. ">

Versions Notes

Abstract

Wind speed forecasting is an essential part of weather prediction, with significant value in economics, business, and management. Utilizing multiple meteorological variables can improve prediction accuracy, but existing methods face challenges such as mixing and noise due to variable differences, as well as difficulty in capturing complex spatio-temporal dependencies. To address these issues, this study introduces a novel short-term wind speed forecasting model named as MIESTC. The proposed model employs an independent encoder to extract features from each meteorological variable, mitigating the issues of noise that are caused by variable mixing. Then, a multivariate spatio-temporal correlation module is used to capture the global spatio-temporal dependencies between variables and model their interactions. Experimental results on the ERA5-LAND dataset show that, compared to the ConvLSTM, UNET, and SimVP models, the MIESTC model reduces RMSE by 14.60%, 8.64%, and 10.41%, respectively, for a 1 h prediction duration. For a 6 h prediction duration, the corresponding reductions are 13.91%, 8.20%, and 6.95%, validating its superior performance in short-term wind speed forecasting. Furthermore, an analysis of variable impacts reveals that U10, V10, and T2M play dominant roles in wind speed prediction, while TP exhibits a relatively lower impact, aligning with the results of the correlation analysis. These findings underscore the potential of MIESTC as an effective and reliable tool for short-term wind speed prediction.

Keywords:

wind speed forecasting; multiple meteorological variables; spatio-temporal dependencies; independent encoding; spatio-temporal forecasting

1. Introduction

Wind speed forecasting, as an important component of weather forecasting, plays a crucial role in economic, commercial, and management decisions. It not only influences decision-making processes and resource allocation across various industries but also aids in natural disaster prediction and provides insights for climate change analyses [1]. In recent years, with the growing demand for electricity, the importance of renewable energy, including wind energy [2], has become increasingly prominent. Despite the abundance of global wind energy resources, its utilization remains low due to current technological limitations [3]. Furthermore, the inherent variability and uncertainty of wind energy result in unstable acquisition and a low conversion efficiency [4]. The highly random and intermittent nature of wind speed variations poses significant challenges to the stability of power systems, necessitating reliable and timely wind speed forecasts to address these challenges [5].

Wind speed forecasting approaches are typically classified into physical methods [6], statistical methods [7], and artificial intelligence (AI) methods [8]. Physical methods rely on the atmospheric properties of the Earth, such as air pressure, temperature, and humidity, and estimate wind speeds by solving equations related to atmospheric dynamics. Numerical Weather Prediction (NWP) [9] technology represents a physical forecasting method, utilizing mathematical models and computer simulations to predict wind speeds in the atmospheric environment. These models can provide wind speed forecasts at different heights and times, but their accuracy is limited by the terrain, complex weather conditions, and the models themselves. Additionally, this method requires substantial computational power.

Statistical methods infer future wind speeds by analyzing historical meteorological data. These methods rely on statistical techniques such as time series analysis, regression analysis, and probabilistic models. Research by Cassola et al. [10] demonstrated that optimizing the time step and prediction range of the Kalman filter significantly enhances model performance, particularly for short-term forecasting. Singh et al. [6] proposed an ARIMA model utilizing repeated wavelet transform and validated its superiority across various time scales. Nonetheless, statistical methods depend heavily on the quality and consistency of historical data, with incomplete or anomalous data greatly impacting prediction accuracy. Overall, these methods are more suitable for short-term forecasts but lack flexibility and struggle to handle long-term predictions or complex future weather conditions.

Artificial intelligence (AI) methods use machine learning and deep learning technologies to predict wind speeds. These methods are widely applied in wind speed forecasting, because they can handle large amounts of complex meteorological data and identify nonlinear relationships between variables [11]. AI methods are generally capable of processing various types and resolutions of data, making them effective for both long-term and short-term predictions [12]. The flexibility and powerful data processing capabilities of these methods enable them to perform well under complex and variable meteorological conditions, thereby improving the accuracy and reliability of forecasts.

With the progress of deep learning, its applications have expanded across diverse domains [13,14,15,16], such as marine science [17], energy [18], weather forecasting [19,20,21], autonomous driving [22], and finance [23]. Deep neural networks (DNNs), including Long Short-Term Memory (LSTM) [24], Convolutional Neural Networks (CNNs) [25], Bidirectional LSTM (BiLSTM) [26], Gated Recurrent Units (GRUs) [27], and Bidirectional GRU (BiGRU) [28], have gained popularity in wind speed forecasting for their ability to address complex nonlinear challenges. Nana et al. [29] proposed a CNN-GRU hybrid model for short-term wind speed prediction, where CNNs extract features from multivariate weather data, which are then input into a GRU model for forecasting. Chen et al. [30] combined CNN and LSTM autoencoders for two-dimensional regional wind speed forecasting, where CNNs were used to extract high-dimensional features, and LSTMs were tasked with wind speed prediction. Shi et al. [31] combined a CNN and LSTM to propose the ConvLSTM model for precipitation forecasting. The experimental results indicated that this method could effectively capture spatio-temporal correlations, achieving commendable outcomes. This model has also been applied to two-dimensional regional wind speed forecasting [32]. Trebing et al. [33] proposed a CNN-based multidimensional wind speed forecasting model that learns the complex input–output relationships from multiple dimensions of the input data. Wu et al. [34] treated the multi-step wind speed forecasting problem as a sequence-to-sequence mapping issue, applying the Transformer model to multi-step wind speed forecasting. He et al. [35] combined ConvLSTM with a dual-attention mechanism, and integrating other meteorological variables, multi-step wind speed predictions were conducted on a two-dimensional space using grid data.

Moreover, wind speed forecasting can be divided into single-variable and multi-variable forecasting based on influencing factors [36]. Single-variable forecasting focuses on analyzing historical wind speed data and identifying temporal trends to accurately predict future wind speeds. In contrast, multivariate wind speed forecasting improves the accuracy by integrating multiple atmospheric variables, such as the temperature, relative humidity, and rainfall. By considering these additional factors, multivariate forecasting methods can more comprehensively reflect the complexity of the atmospheric environment, leading to more precise prediction results [37]. Extensive research by scholars has demonstrated that incorporating multiple atmospheric variables significantly enhances the forecasting performance [38,39,40,41]. For example, Meikha et al. [38] used a Temporal Convolutional Network (TCN) to predict wind speeds. This method, based on convolution operations, improves the prediction accuracy by utilizing the correlations between multiple atmospheric variables, such as the temperature, solar radiation, and relative humidity. Similarly, López and Arboleya [42] and Chengqing et al. [41] also introduced multiple atmospheric variables in wind speed forecasting. However, the limitation of these studies lies in the lack of effective methods to integrate and process these atmospheric variables, which restricts their potential for further improving the forecasting performance.

Despite the progress made in multivariate wind speed forecasting by previous research, different meteorological elements are usually treated as independent input channels. For instance, the temperature, humidity, and solar radiation are often input into the model as separate convolutional channels [33,35,37]. Although this approach is technically straightforward, it presents several key issues: 1. Differences in units, semantics, and scales—Different meteorological variables typically have varying physical units, semantics, and scales. Directly using them as equivalent inputs may introduce irrelevant noise, leading to inefficient model training or prediction bias. 2. Overlooking complex dynamic relationships between variables—Treating variables as independent input channels ignores the potentially complex dynamic relationships and interactions between them. For example, an increase in temperature might affect the stability of the local atmosphere, indirectly influencing the wind speed. Ignoring these relationships could negatively impact the accuracy of wind speed predictions. 3. Insufficient utilization of global information in time series and spatial distribution—Previous studies often focus on data processing at a single time point or location, without fully utilizing global information across time series and spatial distributions. This limits the model’s ability to capture long-term meteorological trends and regional climate characteristics, potentially resulting in suboptimal prediction performance across different time scales and geographic regions.

Based on the previous analysis, this paper proposes a new end-to-end wind speed forecasting model called MIESTC (Multivariate Independent Encoding and Spatio-Temporal Correlation). This model comprehensively considers the independence of each variable, as well as their global spatio-temporal correlations during the multivariate fusion process. This design enables the MIESTC model to efficiently capture and process the distinct characteristics of various meteorological variables and their interrelationships, thereby enhancing wind speed forecasting accuracy and overall model performance. The main contributions of this paper are as follows:

An innovative end-to-end framework is developed for forecasting wind speed utilizing multiple atmospheric variables. The framework is divided into three parts: first, an independent spatio-temporal encoder that separately encodes each variable; second, a spatio-temporal feature extractor that analyzes the spatio-temporal correlations of the input sequences across the entire study area; and finally, a predictor that integrates the extracted features to generate wind speed predictions. Through this design, the framework effectively captures the characteristics and interrelationships of each variable while avoiding the introduction of noise due to differences in semantics and scales between variables, thereby improving the accuracy of the wind speed prediction.
This study presents a multivariate spatio-temporal correlation (MSTC) feature extraction module, which enables the model to more effectively comprehend the relationships between different variables, thereby further enhancing the accuracy and reliability of the information that is required for wind speed prediction.
The proposed framework outperforms state-of-the-art algorithms, achieving superior forecasting performance. This outcome validates the effectiveness of the framework as the most reliable approach for wind speed forecasting using multiple atmospheric variables. A detailed analysis was also conducted on the impact on the wind speed prediction of adding different variables. The results indicate that U10, V10, and T2M play dominant roles in wind speed forecasting, while TP has a relatively lower impact, consistent with the findings of the correlation analysis.

2. Data

The data utilized in this study originate from the European Centre for Medium-Range Weather Forecasts (ECMWF), renowned for delivering the most accurate numerical model forecasts at a global level [43]. More specifically, the data are sourced from the ECMWF’s fifth-generation reanalysis product, the ERA5-Land dataset [44]. This dataset, founded on the terrestrial component of the ECMWF’s ERA5 climate reanalyses, synthesizes modeled data with global observations to yield a uniformly integrated dataset that is governed by the laws of physics. This dataset spans several decades, offering researchers an accurate representation of historical weather conditions. Notable characteristics of the ERA5-Land dataset encompass a spatial resolution of 0.1° × 0.1°, an hourly temporal resolution, and storage in the GRIB format.

Our study concentrates on the southwestern region of China, encompassing the provinces of Sichuan, Chongqing, Yunnan, and Guizhou, as depicted in Figure 1. This region is bounded by latitudes 23° to 37° N and longitudes 96° to 110° E. The southwestern region boasts abundant wind energy resources, making short-term wind speed prediction essential for enhancing the power generation efficiency and dispatch performance of wind farms. This plays a pivotal role in fostering regional clean energy development, optimizing the energy structure, and aiding China’s pursuit of its carbon neutrality objectives [45]. Characterized by its complex terrain, the region is susceptible to natural disasters, including flash floods and mudslides. Accurate short-term wind forecasts play a crucial role in enhancing the disaster prevention and mitigation system’s responsiveness, especially in the context of the rising frequency of extreme weather events caused by climate change [46]. Short-term wind speed prediction in Southwest China not only addresses a significant research gap but also advances wind speed prediction technology, particularly in regions with complex terrains.

This research utilizes the ERA5-LAND dataset spanning the years from 2019 to 2022. Specifically, data from 2019 to 2021 constituted the training set, whereas data spanning January to May 2022 served as the validation set, and observations from June to November of the same year were allocated for testing purposes. Consequently, the training set comprises 26,304 h of continuous data, while the validation and test sets contain 3624 and 5136 h of data, respectively.

To identify the meteorological factors associated with wind speed, correlation analyses were conducted for WS (wind speed) and multiple variables at five different locations. These variables include U10 (wind U-component at 10 m), V10 (wind V-component at 10 m), T2M (temperature at 2 m), SP (surface air pressure), and TP (hourly precipitation accumulation). The results are presented in Figure 2. The chart illustrates the relationship between the absolute values of these variables and wind speeds across five geographic points, with each line representing the correlation strength of a variable at different locations. The analysis shows that U10, V10, and T2M exhibit strong correlations with the wind speed at most locations, indicating their significant influence on the wind speed. For SP and TP, their impact on the wind speed is notably stronger in specific regions but relatively weaker in others. Overall, the correlation between different meteorological factors and wind speeds shows considerable variation across different locations. Notably, the U10 variable exhibits the strongest correlation at location B, while showing the weakest correlation at location D. This variability can be attributed to regional atmospheric conditions, topographical influences, and local climate differences. These findings underscore the importance of spatial information for wind speed prediction. Notably, the 10 m wind speed employed in this research is derived from the calculated u10 and v10 [20], utilizing the formulas presented below:

W S = \sqrt{{U 10}^{2} + {V 10}^{2}}

(1)

3. Methods

In this section, we present the methodology used for wind speed prediction based on multivariable meteorological data. The proposed approach involves processing historical data through an encoder–predictor framework to forecast future wind speeds. We begin by defining the problem statement, which involves using multiple meteorological factors to predict wind speeds over subsequent time frames. We then introduce the components of the model, including independent encoders for each variable, the multivariate spatio-temporal correlation (MSTC) module to capture spatio-temporal dependencies, and the predictor module for generating the forecast. The model architecture, as illustrated in Figure 3, is specifically designed to leverage the temporal, spatial, and multivariable relationships within the data to improve the prediction accuracy.

3.1. Problem Statement

We define the problem of wind speed prediction using multivariable data as follows: Given a sequence of data at time t with T past frames,

X^{t - T : t} = x_{t - T + 1}^{t}

. The goal is to predict the subsequent

T^{'}

frames from time

t + 1

Y^{t + 1 : T^{'}} = x_{t + 1}^{t + T^{'}}

, where

x \in R^{N \times H \times W}

represents the multivariate data with N variables, height H, and width W. In our experiments, we denote the input observation sequence and the output prediction sequence as tensors:

X^{t - T : t} \in R^{T \times N \times H \times W}

Y^{t + 1 : T^{'}} \in R^{T^{'} \times N \times H \times W}

. A model with learnable parameters

θ

is designed to capture the dependencies between multiple meteorological variables, as well as the temporal and spatial dependencies that are essential for accurate wind speed prediction. This mapping process can be represented as follows:

F_{θ} : X^{t - T : t} \to Y^{t + 1 : T^{'}}

(2)

In this work, the mapping

F_{θ}

is implemented using a neural network model that minimizes the discrepancy between the predicted future frames and the actual frames. The optimal parameters

θ^{*}

are determined as follows:

θ^{*} = arg min_{θ} L (F_{θ} (X^{t - T : t}), Y^{t + 1 : T^{'}})

(3)

L

represents the loss function that is used to evaluate the difference between the predicted and actual values, which in this work is implemented as the Mean Squared Error (MSE). Since the ERA5 data used in this study have a temporal resolution of one hour, one frame corresponds to one hour in this context.

3.2. Independent Encoding of Multiple Meteorological Variables

Figure 4 shows the data distributions of various meteorological variables (U10, V10, T2M, SP, TP, WS). Significant differences are observed in the distribution shapes, scales, and semantic units of these variables. For example, the distributions of TP and T2M are notably different from the other variables, indicating considerable differences in data ranges and statistical properties. These disparities suggest that directly mixing these variables in the channel dimension could introduce irrelevant noise, leading the model to learn ineffective semantic features, which may, in turn, reduce the predictive performance [37]. Therefore, it is necessary to encode each meteorological variable independently to better capture the specific patterns and characteristics of each variable, laying a solid foundation for accurately capturing the spatio-temporal relationships among variables.

To achieve the goal of independent encoding for each variable, we employ a simple yet effective reshaping operation. Specifically, we reshape the variable dimension into the batch dimension, ensuring that there is no information exchange between different variables during the encoding process. This achieves the intended independence of variables while also allowing them to share the encoder’s parameters, promoting efficiency in parameter usage. Furthermore, we treat the temporal dimension as the channel dimension to facilitate rapid spatio-temporal encoding without the need for introducing specific temporal processing modules. This approach enables the encoder to learn temporal features directly by leveraging its inherent capabilities. Formally, given an input tensor

X \in R^{B \times N \times T \times H \times W}

, where N represents the number of meteorological variables, we reshape it as follows:

X^{'} \in R^{(B \times N) \times T \times H \times W}

By moving the variable dimension N into the batch dimension, the new batch size becomes

B \times N

. This guarantees that each variable is independently encoded without interference from other variables. Simultaneously, the temporal dimension T is treated as the new channel dimension, allowing the encoder to learn temporal and spatial features efficiently in a unified manner. This simple reshaping operation achieves independent encoding of each meteorological variable, retains parameter sharing for efficient learning, and effectively facilitates spatio-temporal feature extraction without additional temporal-specific modules.

In the specific implementation of the encoder, it is composed of

N_{s}

basic blocks, where each block contains a convolutional layer (Conv), group normalization (GroupNorm), and an activation function (Leaky ReLU). These basic blocks are stacked to extract features progressively from lower to higher levels.The overall encoding process can be described as follows:

X_{l + 1} = Leaky ReLU (GroupNorm (Conv (X_{l})))

(4)

where l represents the layer index of the encoder. By stacking

N_{s}

of such basic blocks, the encoder incrementally learns rich feature representations, providing a solid foundation for the subsequent prediction module.

3.3. Spatio-Temporal Correlation Between Multiple Variables

To capture the global spatio-temporal correlation between multiple meteorological variables, we employ an MSTC (multivariate spatio-temporal correlation) module after the independent encoding process. The purpose of this module is to model the relationships between variables based on their spatio-temporal features, following the independent extraction of these features for each variable.

When modeling the complex dynamic dependencies between multiple meteorological variables, we utilize a self-attention mechanism to effectively capture the correlations among variables. Before processing with the MSTC module, the feature dimensions extracted by the encoder are first reshaped from

(B \times N) \times D \times H \times W

B \times N \times D \times H \times W

, denoted by

Z \in R^{B \times N \times D \times H \times W}

, where D represents the embedding dimension. The attention matrix over the variable axis reads as follows [47]:

A = softmax (\frac{Q K^{⊤}}{\sqrt{d}})

(5)

in which

Q, K \in R^{B \times N \times D \times H \times W}

are the query and key, which are extracted by two different 2D-CNNs, and

\sqrt{d}

is a scaling term. After the softmax function,

A \in R^{N \times N}

demonstrates the global dependencies among the variables. Subsequently, the fusion is performed using the following equation:

Z^{'} = A V

(6)

where

V \in R^{B \times N \times D \times H \times W}

is the value term, extracted by another 2D-CNN, and

Z^{'} \in R^{B \times N \times D \times H \times W}

is the fused embeddings.

The aforementioned operations correspond to the 2D Multi-Head Self-Attention mechanism (MHSA) shown in Figure 3. After the fusion, the fused features are processed through a 2D Feedforward Network (FFN), implemented by two layers of Depthwise Convolutions to enhance the feature representation. The entire MSTC block can be represented as follows:

Z_{m} = FFN (MHSA (Z))

(7)

The entire MSTC module is composed of

N_{h}

of such blocks that are stacked together.

3.4. Decoding Features for Wind Speed Prediction

The purpose of the predictor is to decode the fused features and generate the final wind speed prediction. Before processing with the predictor, the fused feature dimensions are reshaped from

B \times N \times D \times H \times W

B \times (N \times D) \times H \times W

to fully exploit the previously learned global correlations among variables, thereby facilitating the subsequent spatial decoding and wind speed prediction. This transformation merges the embedding features of each variable, allowing the predictor to more effectively perform information fusion and feature extraction along the spatial dimensions and ultimately enhancing the predictive accuracy of the model.

To effectively recover spatial information and capture fine-grained details, the predictor is composed of

N_{S}

basic blocks, each consisting of an upsampling convolution (UNConv2D), group normalization (GroupNorm), and an activation function (Leaky ReLU). The upsampling convolution is used to progressively increase the spatial resolution of feature maps, while the group normalization stabilizes the training process, and the Leaky ReLU introduces nonlinearity to enhance the model’s expressive power. Additionally, the final layer of the predictor includes a skip connection, which passes low-level features directly from the encoding phase to the decoding phase. This design helps the model retain fine details from the input data, thus improving the prediction accuracy. The entire decoding process can be represented as follows:

Y = Leaky ReLU (GroupNorm (UNConv 2 D (Z_{m}))) + Z_{skip}

(8)

With this design, the predictor can effectively generate high-accuracy wind speed predictions while retaining important spatio-temporal information. Here, the term

Z_{m}

represents the output features of the MSTC module, while

Z_{skip}

denotes the output features of each encoder layer.

4. Experiment

4.1. Implementation Details

Through the analysis of correlations among meteorological variables across diverse locations, the meteorological factors and research methodologies to be employed in this study were established. Six meteorological variables were selected for this study, U10, V10, T2M, SP, TP, and 10 m wind speed, based on the past 12 h data, to predict the 10 m wind speed for the subsequent six hours.

Given that the selected dataset encompasses various meteorological elements that are characterized by diverse magnitudes and units, this study employs the maximum–minimum normalization method for data processing. This normalization process not only effectively mitigates the differences in magnitude among the elements but also facilitates the acceleration of model convergence and the enhancement of training precision. The formula is presented below [35]:

x^{'} = \frac{x - x_{m i n}}{x_{m a x} - x_{m i n}}

(9)

where

x_{m a x}

represents the maximum value of the training set, and

x_{m i n}

represents the minimum value of the training set.

During the training phase, all models employed the Adam optimizer and the MSE loss function. The learning rate was established at 0.0001, with a cosine annealing strategy being implemented for its adjustment. A batch size of 16 was specified, and the total training iterations were capped at 100.

4.2. Evaluation Metrics

In this study, the root mean square error (RMSE), mean absolute error (MAE), and Pearson correlation coefficient (PCC) were selected as the evaluation metrics for the model. These metrics t are defined at a single time step as shown below:

\begin{matrix} R M S E_{t} & = \sqrt{\frac{1}{N} {\sum_{i = 1}^{N} ({\hat{y}}^{i}_{t} - y_{t}^{i})}^{2}} \\ {M A E}_{t} & = \frac{1}{N} \sum_{i = 1}^{N} |{\hat{y}}_{t}^{i} - y_{t}^{i}| \\ P C C_{t} & = \frac{\sum_{i = 1}^{N} (y_{t}^{i} - {\bar{y}}_{t}) ({\hat{y}}_{t}^{i} - {\bar{\hat{y}}}_{t})}{\sqrt{\sum_{i = 1}^{N} {(y_{t}^{i} - {\bar{y}}_{t})}^{2} \cdot \sum_{i = 1}^{N} {({\hat{y}}_{t}^{i} - {\bar{\hat{y}}}_{t})}^{2}}} \\ S S I M_{t} & = \frac{(2 {\bar{\hat{y}}}_{t} {\bar{y}}_{t} + C_{1}) (2 σ_{{\hat{y}}_{t} y_{t}} + C_{2})}{({\bar{\hat{y}}}_{t}^{2} + {\bar{y}}_{t}^{2} + C_{1}) (σ_{{\hat{y}}_{t}}^{2} + σ_{y_{t}}^{2} + C_{2})} \end{matrix}

(10)

where

{\hat{y}}^{i}_{t}

and

y_{t}^{i}

represent the predicted value and the true value at time t, respectively.

{\bar{\hat{y}}}_{t}

and

{\bar{\hat{y}}}_{t}

represent the mean of the true and predicted values at time t, respectively.

σ_{{\hat{y}}_{t}}^{2}

and

σ_{y_{t}}^{2}

represent the variance of the predicted and true values at time t, respectively.

σ_{{\hat{y}}_{t} y_{t}}

represents the covariance between the predicted and true values at time t.

C_{1}

and

C_{2}

are constants to stabilize the result.

4.3. Baseline Model

This study selects four models—ConvLSTM [31], UNET [48], PhyDNet [49], and SimVP [50]—as benchmarks. ConvLSTM, integrating the strengths of LSTM and CNN, has gained widespread application in wind speed forecasting in recent years. Originally designed for image segmentation, UNET has recently showcased excellent performance in 2D spatial wind speed forecasting [51,52,53]. PhyDNet [49], integrating physical principles with deep learning, emerges as a robust tool for spatio-temporal sequence forecasting tasks like wind speed prediction, offering predictions that are not only more accurate and reliable but also richer in explanatory power. SimVP, a purely CNN-based model that was introduced at CVPR 2022 as a novel benchmark, has shown considerable promise in video forecasting and achieved impressive outcomes in wind speed prediction. These models underwent training within a standardized experimental setup, adhering to a consistent training regimen and a fixed number of iterations, with the top-performing models later chosen for in-depth comparison and assessment.

4.4. Comparison of Results

To validate the efficacy of the method proposed herein, data spanning from June to November 2022 served as the test set, against which a comparative analysis with the baseline model was executed for forecast intervals ranging from 1 to 6 h. The experimental outcomes are delineated in Table 1.

The data presented in the table indicate that the MIESTC model exhibits superior performance across the RMSE, MAE, PCC, and SSIM evaluation metrics at all forecast intervals, thereby affirming its efficacy in wind speed forecasting. Furthermore, the IMP (%) value underscores the MIESTC model’s performance improvement relative to other models, evidencing its pronounced superiority. Specifically, the MIESTC model achieved a reduction, and hence an improvement, in the 1 h forecast RMSE by 14.60%, 8.64%, 11.78%, and 10.41% relative to the ConvLSTM, UNET, PhyDNet, and SimVP models, respectively.

By comparing the performance of the MIESTC model with baseline models across four key performance metrics—RMSE, MAE, PCC, and SSIM—we can observe that the MIESTC model exhibits the lowest errors and highest correlations in 1 to 6 h multi-step predictions. As shown in Figure 5, this study visually presents the trends of RMSE, PCC, MAE, and SSIM across the 1 to 6 h forecasting periods through four subplots. These metrics provide essential criteria for comprehensively evaluating the accuracy of the models, further demonstrating the significant advantage of the MIESTC model in short-term multi-step wind speed forecasting.

4.5. Case Study

Figure 6 displays a visual comparison between various prediction models and actual observational data from 25 March 2022. The figure clearly illustrates the significant performance advantage of the MIESTC model compared to the baseline model. In the initial hour of predictions, the MIESTC model, along with ConvLSTM, UNET, PhyDNet, and SimVP, accurately predicted areas of high wind speed. Notably, as the prediction period extended to two hours, ConvLSTM, UNET, PhyDNet, and SimVP experienced a marked decline in their ability to detect high wind speed areas, deteriorating further by the third hour to almost complete ineffectiveness. Conversely, the MIESTC model consistently and effectively captured high wind speed areas throughout the entire prediction period, from one to six hours.

4.6. Comparison Experiments of Relevant Variables

To further verify the positive impact of the added meteorological variables on the experimental results, we conducted a controlled experiment to ensure consistency in the number of variables used. As shown in Table 2, when the forecast duration was 1 h, removing TP, SP, T2M, U10, and V10 resulted in reductions in RMSE of 2.33%, 2.54%, 4.73%, 4.38%, and 5.24%, respectively. For a forecast duration of 4 h, the corresponding reductions were 0.74%, 0.73%, 3.62%, 2.86%, and 3.01%. When the forecast duration was extended to 6 h, these reductions became 0.85%, 0.84%, 2.94%, 2.60%, and 3.04%, respectively. It can be observed that, for all forecast durations, the reduction in RMSE was more significant when removing T2M, U10, and V10 compared to removing TP and SP. This finding is consistent with the conclusions from our initial correlation analysis of the meteorological variables.

To further analyze the impact of different combinations of meteorological variables on the wind speed forecasting performance of the MIESTC model, this experiment conducted comparisons based on various variable combinations. Table 3 presents the RMSE and PCC performance metrics for the MIESTC model using different combinations of meteorological variables in 1 to 6 h multi-step predictions. As shown in the table, as more meteorological variables are introduced, the model’s prediction error (RMSE) gradually decreases, while the correlation (PCC) steadily increases. Notably, when all variables, including wind speed, horizontal wind components, temperature, air pressure, and precipitation, are used (TP column), the model exhibits the best performance in short-term multi-step predictions. This highlights the superiority of the MIESTC model, which integrates multiple meteorological variables, in enhancing the accuracy and reliability of wind speed predictions.

Figure 7 depicts the distribution of attention weights assigned to different meteorological variables in the MSTC module, specifically in the context of wind speed prediction. Each row corresponds to one of the eight attention heads, and each column represents a variable. The attention heads (Head 1 to Head 8) serve to capture diverse aspects of spatio-temporal dependencies and variable interactions. The distribution reveals that T2M and V10 receive higher attention weights in most of the heads, indicating their dominant roles in the prediction process. In contrast, variables such as TP show lower attention weights, suggesting their relatively minor contributions. This analysis confirms that the model effectively uses multiple attention heads to focus on the most influential variables, aligning with the correlation analysis results and improving the interpretability of the prediction mechanism.

4.7. Module Ablation Study

Table 4 presents the results of an ablation study on the MIESTC model, evaluating the impact of removing specific components on the model’s performance across different prediction hours. In the table, “-” indicates the exclusion of a particular component, whereas “SC” represents skip connections, “IE” stands for independent variable encoding, and “MSTC” denotes multivariate spatio-temporal correlation encoding. The complete MIESTC model consistently achieves the best performance in terms of RMSE and PCC at all prediction times, indicating that retaining each component contributes to improved model performance. Additionally, the SimVP-Trans model does not utilize our newly proposed training framework; instead, it integrates a transformer into the SimVP framework to enhance the temporal feature extraction. Although SimVP-Trans outperforms the standard SimVP, its performance still falls short of that of the full MIESTC model. This underscores the effectiveness of our newly proposed framework for short-term wind speed forecasting using multivariate data.

5. Conclusions

This paper proposes a multivariable-based short-term wind speed prediction model, MIESTC, which utilizes independent encoding of variables and models the global spatio-temporal correlations among variables. This approach effectively addresses the issues of variable mixing and inadequate modeling of complex spatio-temporal dependencies in traditional wind speed forecasting. The experimental results demonstrate that MIESTC exhibits significant advantages in short-term wind speed forecasting, achieving substantial improvements in prediction accuracy compared to existing models. Specifically, MIESTC reduces the RMSE and MAE by up to 8.64% and 14.36%, respectively, for a 1 h prediction horizon and maintains consistent superiority across longer prediction durations. These results validate the model’s effectiveness and robustness in accurately capturing spatio-temporal dependencies. Furthermore, a detailed analysis of the impact of different meteorological variables on the wind speed prediction was conducted. Variables such as T2M and V10 were found to play dominant roles, while TP exhibited relatively lower contributions, aligning with the findings from the correlation analysis.

Despite its strengths, MIESTC has certain limitations. For instance, while the model performs well in short-term wind speed forecasting, its performance for longer prediction horizons could be further optimized. Additionally, the computational cost of the MSTC module might be a concern in real-time applications. Future research could explore more efficient architectures or hybrid approaches to balance performance and efficiency, as well as extend the model to other meteorological applications.

Author Contributions

Conceptualization, Q.L. and H.Y.; Methodology, S.L.; Validation, M.C., L.Y. and Q.L.; Investigation, S.L., M.C. and L.Y.; Data Curation, S.L., M.C. and L.Y.; Writing—Original Draft Preparation, S.L.; Writing—Review and Editing, S.L., M.C., L.Y., Q.L. and H.Y.; Supervision, Q.L. and H.Y.; Project Administration, H.Y.; Funding Acquisition, H.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This research was partly supported by the Natural Science Foundation of Sichuan (Grant No. 2024NSFJQ0035), the Talents Program by the Sichuan Provincial Party Committee Organization Department, and the Chengdu—Chinese Academy of Sciences Science and Technology Cooperation Fund Project (Major Scientific and Technological Innovation Projects). Additional support was provided by the Sichuan Provincial Science and Technology Achievement Transfer and Transformation Demonstration Project, 2024ZHCG0026.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All original contributions presented in this study, including data, methods, and results, are included in the article. No additional data are available, and further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Research area and five research sites.

Figure 2. Correlation analysis of different factors with wind speed across five locations. A, B, C, D, and E represent the five research locations in the study. The chart shows that the correlation between the wind speed and various factors differs significantly across locations. The factors u10, v10, and t2m exhibit strong correlations with the wind speed at multiple locations, suggesting their importance as primary influencing factors, whereas sp and tp show relatively strong correlations at specific locations.

Figure 3. An overview of the MIESTC model’s architecture. Subfigure (a) illustrates the overall workflow, including the independent encoding of multiple meteorological variables (WS, U10, V10, T2M, TP, SP), spatio-temporal feature extraction through the MSTC module to capture the spatio-temporal relationships between variables, and finally the decoding and prediction using the predictor module. The skip connection aids in preserving features from earlier stages. Subfigures (b–d) present the detailed structures of the encoder block, MSTC block, and predictor block.

Figure 4. The data distribution of the meteorological variables. These variables clearly exhibit significant differences in their distributions, with distinct scales and semantic units.

Figure 5. Model performance comparison. This figure presents the performances of various models at different prediction time horizons, evaluated with RMSE, PCC, MAE, and SSIM metrics. The results indicate that the MIESTC model consistently surpasses other models across all time steps and evaluation metrics, highlighting its superior effectiveness in short-term wind speed forecasting.

Figure 6. Visual representation of wind speed prediction results across different models. The red boxes indicate areas where the prediction deviates significantly from the ground truth, highlighting the deficiencies in different models.

Figure 7. Attention weight distribution of wind speed prediction variables. This heatmap illustrates the attention weight distribution of each meteorological variable (U10, V10, T2M, SP, TP, WS) across eight attention heads in the MSTC module. The attention heads (Head 1 to Head 8) represent different perspectives of the model in capturing variable relationships. Darker colors indicate higher attention weights, highlighting the relative importance of each variable for wind speed prediction.

Table 1. Results of the performance comparison. ‘↑’ means the higher the better, and ‘↓’ means the inverse. The values in bold are the top 1 results. The underlined values are suboptimal results. ‘IMP(%)’ is the percent of improvements of MIESTC over the suboptimal ones.

	Hour	ConvLSTM	UNET	PhyDNet	SimVP	MIESTC	IMP(%)
RMSE $(↓)$	1	0.24850	0.23230	0.24057	0.23688	0.21222	8.64
	2	0.36172	0.33808	0.33354	0.33613	0.30499	8.56
	3	0.43101	0.40212	0.39661	0.40011	0.36284	8.51
	4	0.47660	0.44414	0.44154	0.44312	0.40340	8.64
	5	0.51051	0.47641	0.47652	0.47498	0.43540	8.33
	6	0.53945	0.50586	0.50592	0.49905	0.46439	6.95
MAE $(↓)$	1	0.17021	0.15861	0.16859	0.16469	0.14453	8.88
	2	0.25295	0.23522	0.23311	0.23585	0.21333	8.48
	3	0.30233	0.27946	0.27473	0.27956	0.25318	7.84
	4	0.33451	0.30797	0.30352	0.30775	0.27996	7.76
	5	0.35822	0.33012	0.32603	0.32885	0.30105	7.66
	6	0.37836	0.35048	0.34522	0.34531	0.32055	7.15
PCC $(↑)$	1	0.96446	0.96934	0.96707	0.96735	0.97396	0.48
	2	0.92486	0.93510	0.93687	0.93452	0.94603	0.98
	3	0.89323	0.90814	0.91148	0.90799	0.92423	1.40
	4	0.86915	0.88774	0.89074	0.88768	0.90676	1.80
	5	0.84971	0.87072	0.87288	0.87153	0.89167	2.15
	6	0.83241	0.85414	0.85665	0.85824	0.87681	2.16
SSIM $(↑)$	1	0.92865	0.93896	0.93214	0.93207	0.94693	0.85
	2	0.87265	0.89232	0.89216	0.88719	0.90409	1.32
	3	0.83878	0.86517	0.86727	0.86027	0.87924	1.38
	4	0.81767	0.84822	0.85045	0.84398	0.86276	1.45
	5	0.80228	0.83529	0.83732	0.83147	0.84979	1.49
	6	0.78881	0.82251	0.82586	0.82167	0.83657	1.30

Table 2. Results of experiments controlling for consistency in the number of meteorological variables used each time. “−” indicates the removal of a variable; “ALL” indicates the use of all variables. ‘↑’ means the higher the better, and ‘↓’ means the inverse.

	Hour	ALL	−TP	−SP	−T2M	−U10	−V10
RMSE $(↓)$	1	0.21222	0.21717	0.21762	0.22225	0.22152	0.22333
	2	0.30499	0.30841	0.30937	0.31802	0.31578	0.31613
	3	0.36284	0.36562	0.36606	0.37714	0.37417	0.37462
	4	0.40340	0.40640	0.40633	0.41799	0.41495	0.41553
	5	0.43540	0.43897	0.43882	0.44966	0.44758	0.44893
	6	0.46439	0.46832	0.46828	0.47804	0.47648	0.47851
PCC $(↑)$	1	0.97396	0.97295	0.97283	0.97150	0.97179	0.97147
	2	0.94603	0.94501	0.94454	0.94128	0.94200	0.94195
	3	0.92423	0.92326	0.92281	0.91792	0.91896	0.91903
	4	0.90676	0.90564	0.90542	0.89939	0.90073	0.90083
	5	0.89167	0.89035	0.89023	0.88375	0.88507	0.88484
	6	0.87681	0.87534	0.87503	0.86838	0.87026	0.86936

Table 3. Performance comparison of the MIESTC model in wind speed forecasting using different meteorological variables. The column names represent the meteorological variables that have been added based on the previous column. ‘↑’ means the higher the better, and ‘↓’ means the inverse.

	Hour	WS	+U10,V10	+T2M	+SP	+TP
RMSE $(↓)$	1	0.24133	0.22666	0.21887	0.21717	0.21222
	2	0.35196	0.32662	0.31262	0.30841	0.30499
	3	0.42194	0.38869	0.37129	0.36562	0.36284
	4	0.47027	0.43163	0.41246	0.40640	0.40340
	5	0.50597	0.46456	0.44449	0.43897	0.43540
	6	0.53606	0.49406	0.47305	0.46832	0.46439
PCC $(↑)$	1	0.96698	0.97060	0.97242	0.97295	0.97396
	2	0.92861	0.93856	0.94323	0.94501	0.94603
	3	0.89765	0.91365	0.92073	0.92326	0.92423
	4	0.87302	0.89387	0.90282	0.90564	0.90676
	5	0.85301	0.87724	0.88760	0.89035	0.89167
	6	0.83527	0.86075	0.87268	0.87534	0.87681

Table 4. Ablation study examining MIESTC model components. “−” indicates the removal of a specific component; “SC” represents skip connections. “SimVP-Trans” indicates that the SimVP framework is used without adopting a new architecture; instead, a transformer is integrated into the SimVP framework to enhance the temporal feature extraction. The results, measured using the RMSE and PCC over six prediction hours, demonstrate that the full MIESTC model consistently achieves the lowest RMSE and highest PCC, highlighting the role of each component in improving the predictive performance. ‘↑’ means the higher the better, and ‘↓’ means the inverse.

	Hour	MIESTC	−MSTC	−IE	−SC	SimVP-Trans
RMSE $(↓)$	1	0.21222	0.23158	0.22216	0.22322	0.23444
	2	0.30499	0.33417	0.31740	0.30523	0.33307
	3	0.36284	0.39848	0.37718	0.35953	0.39037
	4	0.40340	0.44469	0.41774	0.39970	0.42812
	5	0.43540	0.48145	0.45461	0.43235	0.45635
	6	0.46439	0.51456	0.48165	0.46187	0.48045
PCC $(↑)$	1	0.97396	0.96975	0.97184	0.97057	0.96897
	2	0.94603	0.93610	0.94222	0.94548	0.93682
	3	0.92423	0.90867	0.91932	0.92516	0.91367
	4	0.90676	0.88583	0.90118	0.90810	0.89657
	5	0.89167	0.86628	0.88538	0.89295	0.88274
	6	0.87681	0.84828	0.87004	0.87793	0.86974

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Li, S.; Chen, M.; Yi, L.; Lu, Q.; Yang, H. MIESTC: A Multivariable Spatio-Temporal Model for Accurate Short-Term Wind Speed Forecasting. Atmosphere 2025, 16, 67. https://doi.org/10.3390/atmos16010067

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Li S, Chen M, Yi L, Lu Q, Yang H. MIESTC: A Multivariable Spatio-Temporal Model for Accurate Short-Term Wind Speed Forecasting. Atmosphere. 2025; 16(1):67. https://doi.org/10.3390/atmos16010067

Chicago/Turabian Style

Li, Shaohan, Min Chen, Lu Yi, Qifeng Lu, and Hao Yang. 2025. "MIESTC: A Multivariable Spatio-Temporal Model for Accurate Short-Term Wind Speed Forecasting" Atmosphere 16, no. 1: 67. https://doi.org/10.3390/atmos16010067

APA Style

Li, S., Chen, M., Yi, L., Lu, Q., & Yang, H. (2025). MIESTC: A Multivariable Spatio-Temporal Model for Accurate Short-Term Wind Speed Forecasting. Atmosphere, 16(1), 67. https://doi.org/10.3390/atmos16010067

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MIESTC: A Multivariable Spatio-Temporal Model for Accurate Short-Term Wind Speed Forecasting

Abstract

1. Introduction

2. Data

3. Methods

3.1. Problem Statement

3.2. Independent Encoding of Multiple Meteorological Variables

3.3. Spatio-Temporal Correlation Between Multiple Variables

3.4. Decoding Features for Wind Speed Prediction

4. Experiment

4.1. Implementation Details

4.2. Evaluation Metrics

4.3. Baseline Model

4.4. Comparison of Results

4.5. Case Study

4.6. Comparison Experiments of Relevant Variables

4.7. Module Ablation Study

5. Conclusions

Author Contributions

Funding

Institutional Review Board Statement

Informed Consent Statement

Data Availability Statement

Conflicts of Interest

References

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