Research on Short-Term Prediction Methods for Small-Scale Three-Dimensional Wind Fields

Abstract

The accurate prediction of small-scale three-dimensional wind fields is of great practical significance for aviation safety, wind power generation, and related fields. This study proposes a novel method for predicting small-scale three-dimensional wind fields by combining the mesoscale Weather Research and Forecasting (WRF) model with Computational Fluid Dynamics (CFD). The method consists of three components: the WRF module, the hybrid neural network prediction module, and the CFD module. First, mesoscale meteorological fields are simulated using the WRF module to establish a historical inflow boundary dataset for the CFD domain. Next, deep separable convolutions are incorporated, and convolutional long short-term memory (ConvLSTM) is combined with a deep separable convolution-gated recurrent unit (DSConvGRU) to construct a hybrid neural network prediction module named ConvLSTM-DSConvGRU. This module is employed for predicting inflow boundary data. Finally, the predicted inflow boundary conditions drive the CFD module to predict small-scale three-dimensional wind fields. The effectiveness of the WRF and CFD downscaling coupling method was validated using observed data from meteorological stations within the simulated domain, along with statistical indicators of errors. Additionally, a comparative evaluation was conducted between the proposed hybrid network model and the four commonly used spatiotemporal prediction models to assess its prediction performance. The results demonstrate that our proposed wind field prediction method achieves accurate simulation and short-term prediction of small-scale three-dimensional wind fields, and the hybrid network model exhibits comprehensive advantages in terms of model complexity and prediction accuracy.

1. Introduction

In recent years, with the rapid advancement of urbanization in China, the importance of three-dimensional wind field prediction has become increasingly prominent owing to the rapid developments in wind power generation, aviation transportation, and other fields. For example, in the field of wind power, factors such as wind speed, wind direction, and atmospheric pressure determine the electricity generation of wind turbines [1]. Meanwhile, for airports, the variation in wind fields has a direct impact on aircraft takeoff, landing, parking, and maintenance operations. The primary cause of most air traffic accidents is severe wind shear or wake flow encountered during the takeoff and landing phases [2,3]. Therefore, the accurate simulation and prediction of small-scale three-dimensional wind fields can not only better assess wind resources and predict the inflow volume for wind farm sites but also provide critical meteorological information and ensure aviation safety for airports.

With the continuous improvement of computational power, many scholars [4,5,6,7] have proposed Computational Fluid Dynamics (CFD) models to improve the spatial resolution of the Mesoscale Weather Research and Forecasting Model (WRF) in wind field research. As a widely used meteorological simulation software, WRF takes into consideration various physical processes such as atmospheric dynamics, boundary layer processes, turbulent processes, and radiation processes, and it can simulate large-scale meteorological phenomena at the kilometre scale [4]. On the other hand, CFD, as a numerical simulation method for fluid mechanics, can establish high-accuracy real building and terrain models and achieve the simulation of fine flow fields.

Several studies have been conducted on the coupling of WRF and CFD through regional nesting to obtain more accurate and refined wind field information. Yang Yi et al. used the output of the WRF model based on the Four-Dimensional Data Assimilation (FDDA) technology as the boundary condition for CFD flow field simulation [5]. They achieved a refined downscaling simulation of complex local wind fields on terrain with the Reynolds-averaged Navier–Stokes (RANS) method, verifying the effectiveness of the multi-scale coupling method in improving the accuracy of wind field simulation. Luo et al. adopted a one-way coupling method between WRF and CFD and proposed a method to maintain mass conservation in the CFD simulation process [6]. The simulated wind speed was close to the measured value, and they successfully reproduced the curvature of the airflow during typhoons. Chen et al. used a large-eddy simulation (LES) based on the data from the WRF model to accurately reproduce the variation trends of wind speed and wind direction in the airspace above airports under the influence of the terrain of Lantau Island [7]. They also effectively predicted the range of wind shear. However, most of the current research on WRF and CFD coupling focuses on the impact of complex terrain on the wind field. In fact, in addition to airflow disturbances caused by terrain, buildings can also cause sudden changes in wind direction for aircraft under certain weather conditions. A numerical simulation study using a nested mesoscale meteorological model and a CFD model showed that buildings can cause significant changes in wind direction and affect aircraft operation [8]. However, the above study only modelled a few buildings near the runway, and the accuracy needs to be improved.

According to recent studies, there are mainly two catalogues of methods for wind field prediction [9]. The first catalogue is based on dynamic physical models, which describe variables such as wind, pressure, density, and temperature in the atmosphere using the laws of fluid mechanics and solve or simplify the equations. In addition, data assimilation techniques are combined to predict the state of the atmosphere [10,11]. However, using this method for predicting high-accuracy wind fields requires large computational resources, which are currently unattainable [12]. The second catalogue is based on historical wind field data. The used historical wind field data can be from weather prediction models, e.g., GraphCast [13], PanguWeather [14], and FourCastNet [15]. The models are trained based on the reproduction weather data, ERA5. The short-term and long-term global weather prediction can be performed with high speed, high accuracy, and low loss. However, the mentioned models may perform the weather data prediction with 0.25° of the highest spatial resolution and one hour of the shortest time step, which are limited by the resolution of ERA [14]. The historical data can be also from observation stations and lidars. The machine learning methods such as Convolutional Neural Networks (CNNs), Support Vector Machines (SVMs), graph neutral networks, Long Short-Term Memory (LSTM) networks, and Gated Recurrent Units (GRUs) are used to realize weather predictions, employing data from observation stations and lidars [16,17,18,19,20]. It is hard to predict the three-dimensional wind field on a small scale using the observation station outputs due to their limited resolution and the limited number of the stations. On the other hand, although laser radar scanned data have a higher resolution, it is difficult to obtain a three-dimensional wind field from single-angle plan position indicator (PPI) scanned data using wind field inversion methods. Conducting multiple PPI scans of the environmental wind field may introduce a certain time delay, which reduces the real-time performance and accuracy of the three-dimensional predicted wind field obtained through inversion.

In summary, it is hard to predict the small-scale wind field precisely with ordinary computer resources based on the above-mentioned methods. Meanwhile, several studies have demonstrated the advantages of the WRF–CFD coupled method in simulating small-scale wind fields with high accuracy and precision [5,6,7,8]. However, most of the relevant work focuses on the data processing of the historical wind fields, while the output variables of the WRF model are directly used as the inputs to the CFD model for the simulation of small-scale wind fields. In this paper, we propose the ConvLSTM-DSConvGRU neutral network model to predict the wind speed and temperature with high speed. The prediction involves a limited number of parameters and does not cost much in terms of computer resources. The predicted wind speed and temperature are fed to the CFD model as the boundary conditions [21]. Consequently, the CFD model implements the wind field simulations and the predicted wind fields are obtained.

In this study, Hong Kong International Airport with a complex geographical location and wind field environment was selected as the research object, and a short-term prediction method for small-scale three-dimensional wind fields based on the coupling of WRF and CFD was proposed. First, the wind field simulation of the complex terrain area surrounding the Hong Kong International Airport was performed using the WRF–CFD coupled model. The wind speed and temperature information obtained from the WRF simulation were used to provide realistic boundary conditions for the CFD model. Then, the impacts of the nearest neighbour interpolation and inverse distance weighted interpolation on the CFD simulation results were compared and analysed to verify the accuracy and applicability of the numerical simulation. Finally, depthwise separable convolutions were introduced, and an encoder–decoder network model based on a hybrid of ConvLSTM and a depthwise separable ConvGRU was proposed. This model predicted the WRF output variables used as boundary conditions for the CFD model. The model performance was evaluated using error evaluation indicators.

2. WRF-CFD Coupled Small-Scale Wind Field Simulation

2.1. WRF Model Settings

In this study, WRF version 4.3.3 was used for simulation. The start and end times for the WRF model were 00:00 on 15 March 2022 and 12:00 on 31 March 2022, i.e., a duration of 16 days and a half. The simulated domain of the model is shown in Figure 1, with the centre located at Hong Kong International Airport (113.911° E, 22.314° N). The inputs for the WRF model were from the NCEP GFS 0.25 degree Global Forecast Grids Historical Archive. The NCEP GFS offers meteorological reanalysis resources with a spatial resolution of 0.25° × 0.25° which are updated every 6 h.

The WRF model adopts a 3-layer one-way nested grid configuration. The first 12 h of each nested domain is the spin-up time. The valid simulation time of the WRF model is regarded from the 12th hour. The time interval of the d01 and d02 nested domains is one hour, while the time interval of the d03 nested field is ten minutes. Correspondingly, as the simulation results, 385 meteorological sets are outputted for the d01 and d02 domains, each, while 2305 meteorological sets are outputted for the d03 domain. The parameters for the nested grids are shown in

Table 1. Parameter settings for nested grids for WRF simulations.

Nested Domain	dx/km	dy/km	Number of Regional Grid Points	Regional Integration Step/s
d01	9	9	61 × 61	36
d02	3	3	61 × 61	12
d03	1	1	61 × 61	4

. The dx and dy represent the grid spacing in the x and y directions, respectively. The vertical grid was divided into 60 layers using a vertically stretched grid approach, with 12 layers below 1 km and the 1st layer approximately 10 m above the ground. The model used the GMTED2010 elevation dataset with a resolution of 30 s for the topography data. The simulated domain was projected using the Mercator projection scheme. The selection of parameterization schemes for physical processes was as follows: WSM-5 for microphysics, RRTMG for longwave radiation, RRTMG for shortwave radiation, YSU for planetary boundary layer, and NOAH for land surface processes. Due to the high horizontal resolution of the model, the cumulus parameterization scheme was not used [22].

2.2. CFD Model Settings

Figure 2 is the schematic diagram of the CFD complex terrain and building modelling and grid partitioning. First, the ASTER GDEM elevation data of the simulated domain at a resolution of 30 m were transformed using ArcGIS software 10.7. Then, the data were imported into Blender software 3.5 along with OSM map data for the initial modelling of complex terrain and buildings. The models were further refined and adjusted using SCDM software 2022R1, incorporating the actual building data provided by the Hong Kong Lands Department for 225 buildings near the airport. The adjusted models are shown in Figure 2a, in which the red dots indicate the location of the Sha Chau Automatic Weather Station near Hong Kong International Airport. Finally, the models were imported into Fluent Meshing for grid partitioning, resulting in the computational domain grid model shown in Figure 2b. The simulated domain size was 15,000 m × 15,000 m, with a solution domain top height of 3000 m.

The case adopted unstructured polyhedral hybrid grids. Slit control and curvature control were used to fit fine building features, and the BOI block was applied to locally refine the area below 600 m above the airport buildings to capture the wind field changes caused by buildings. Polyhedral grids were used to fit the model boundaries, ensuring a high-accuracy representation of complex geometries such as buildings and terrains while maintaining topological consistency. Hexahedral grids were used to partition the central wind field area to improve the efficiency and stability of subsequent numerical calculations. In the simulations, we used three grid partitioning schemes. For scheme 1, the maximum grid size in the refined area of the BOI block was set to be 50 m, the maximum grid spacing was set to be 150 m, and 1.83 million grids were generated. Li have demonstrated that a grid spacing of 150 m was sufficient to resolve the terrain-induced fluctuations in CFD simulations [23]. Finer grids were used for scheme 2. The maximum grid size was set to be 30 m, the maximum grid spacing was set to be 100 m, and 2.95 million grids were generated. Coarse grids were used for scheme 3 with a maximum grid size of 70 m, a maximum grid spacing of 200 m, and 1.02 million grids. For the three grid partitioning schemes, we used the output meteorological datasets at 2:00 on 27 March 2022 for the d03 domain as the boundary conditions for further wind speed simulations in the CFD model. We demonstrate the wind speed profile in Figure 3, taking a spot close to the airport runway as an example. It was noted that the wind speed was normally underestimated using the coarse grids, i.e., grid partitioning scheme 2, and the wind speed profiles almost coincided for scheme 1 and scheme 3. Hence, in the following discussions, we used grid partitioning scheme 1, considering both the computation precision and resources.

The coupling between WRF and CFD enables the interpolation of the output data from the WRF model to the inflow boundary of the CFD-simulated domain. There are two commonly used interpolation methods: nearest neighbour interpolation and inverse distance weighted interpolation. Nearest neighbour interpolation involves extracting the values of variables such as speed and temperature from the nearest grid points on the profiles obtained from the WRF model and directly assigning them to the grid points on the corresponding inflow boundary of the CFD model. Inverse distance weighted interpolation calculates the values of the grid points on the CFD inflow boundary by inversely weighting the variable values of the grid points on the aforementioned profiles from the WRF model based on their distances to the CFD grid points. The weight factors are inversely proportional to the distances between the grid points on the profiles obtained from the WRF model and the CFD grid points.

In this study, the WRF model output information from nested domain d03 with an output interval of 10 min was firstly processed. Secondly, we saved the wind speed components of longitude, latitude, and vertical directions, denoted by u, v, and w respectively, and temperature tk into an ASCII file. Then, the boundary profile module of the CFD model used the wind speed and temperature as the inflow boundary conditions.

The settings of the boundary conditions and solver parameters for the CFD model are listed in

Table 2. Settings of CFD solver parameter.

Type	Parameter	Setting
Boundary condition	Inflow boundary	Grid point speed and temperature
	Outflow boundary	Pressure outlet boundary
	Top boundary	Grid point speed and temperature
	Bottom boundary	Non-slip wall surface
Solving solution	Solver software	Fluent 2022R1
	Turbulence model	Realizable k-ε model
	Pressure–speed coupling scheme	SIMPLE
	Spatial discretization scheme	Second-order upwind scheme

. The eastern, western, southern, and top boundaries of the model were set as the inflow boundaries. The speed and temperature variables from the three-dimensional field obtained from the WRF model were interpolated and assigned to the CFD grid points. We employed Fluent as the solver of the CFD. Fluent incorporates RANS and LES turbulence models. Although the LES module exhibited better performance than the RANS model in cases of complex turbulence [24], LES may incur more computational cost than RANS by over ten times. Therefore, the RANS turbulence model remains popular in wind field investigations using the CFD coupled with WRF method, considering both computational cost and simulation precision [4,5]. Furthermore, we used the realizable k-ε of RANS in the computation, following ref. [8] and ref. [25]. The northern boundary was set as the outflow boundary, which was specified as a pressure outlet boundary. The bottom boundary was classified into three types: sea surface, airport island, and Lantau Island, as shown in Figure 2a. The corresponding surface roughness values of 0.0005 m, 0.005 m, and 0.5 m were set for each type, respectively [26].

2.3. Analysis of CFD Results

We compared the differences between direct simulation using the WRF model and coupled simulation with two different boundary value assignment methods for the period from 0:00 27 March 2022 to 24:00 29 March 2022. The objective was to quantitatively analyse the comparison between the measured wind speed at the 30 m height of the Sha Chau Automatic Weather Station (refer to Figure 2a) and the simulated wind speed at the 30 m height of the Sha Chau Automatic Weather Station using three different methods. The calculation case was solved using the Realizable k-ε model in the RANS method, and the specific parameter settings are shown in Table 2. Figure 4a,b show the comparison of using the nearest neighbour interpolation method and the inverse distance weighted interpolation method to interpolate the wind speed component (u) to the CFD east inflow boundary, respectively. Figure 5a,b) depict the comparison of using the nearest neighbour interpolation method and the inverse distance weighted interpolation method to interpolate the temperature variable to the CFD east inflow boundary, respectively. It can be seen that for both the speed and temperature variables, the inverse distance weighted interpolation method depicts the detailed characteristics of the variable distribution more accurately compared with the nearest neighbour interpolation method.

The statistical analysis of the simulation results obtained from the WRF model simulation coupled with the two interpolation methods is shown in

Table 3. Evaluation indicators of wind speed simulation at 30 m height of the Sha Chau Automatic Weather Station.

Error Assessment Indicator	WRF	WRF + CFD
		Nearest Neighbour Interpolation	Inverse Distance Weighted Interpolation
Average error (BIAS) (m·s−1)	2.952	0.819	0.333
Root mean square error (RMSE) (m·s−1)	4.684	2.844	2.724
Mean absolute error (MAE) (m·s−1)	4.052	2.334	2.080

. It can be seen that whether it is the results simulated directly by the WRF model or the results simulated by the coupling of interpolation and CFD, the average error is greater than zero, indicating that all three simulation methods overestimated the wind speed at the Sha Chau Automatic Weather Station. Compared with the simulation results of the WRF model, those of the coupled WRF and CFD model showed significantly reduced average error, root mean square error (RMSE), and mean absolute error. The error assessment indicators of the inverse distance weighted interpolation method were lower than those of the nearest neighbour interpolation method. Therefore, it can be concluded that the accuracy of simulating by coupling the inverse distance weighted interpolation method with WRF and CFD is superior to that of the nearest neighbour interpolation method and direct WRF simulation.

Figure 6a–d show the results of the planar wind field calculations using the inverse distance weighted interpolation method. Our analysis showed that due to the impact of airflow on the terrain and buildings near the ground, a large amount of turbulent vortex motion was generated. As a result, significant wind speed gradients were observed at elevations of 50 m and 200 m (Figure 6c,d)). However, a significant reduction in wind speed was observed on their lee side due to the obstruction of terrain and buildings. For example, in Figure 6a, at the location of 12,000–14,000 m in the x-direction, and in Figure 6b, at the location of 8000 m (dashed box) in the y-direction, there are evident deceleration features in wind speed on the lee side of the terrain and buildings. This also indicates that the grid partitioning and local refinement methods used in this study effectively capture the fluctuation phenomena caused by the terrain and buildings.

3. ConvLSTM-DSConvGRU Hybrid Prediction Model

We have seen that the key to the coupling of WRF and CFD to simulate the small-scale three-dimensional wind field is to interpolate the output data of the WRF model to the inflow boundary of the CFD-simulated domain. Moreover, the results in Section 2.3 show that the inverse distance weighted interpolation method is more suitable for the simulation and prediction of the three-dimensional wind field in the simulated domain of this study than the nearest neighbour interpolation method. The subsequent focus of this study was to construct a neural network prediction model to accurately predict the WRF output data as the CFD inflow boundary conditions. This study introduces the ConvLSTM model and a separable convolution to reconstruct the ConvGRU model as the DSConvGRU model and establishes a ConvLSTM-DSConvGRU hybrid prediction model based on an encoder–decoder architecture.

3.1. ConvLSTM

ConvLSTM is a hybrid variant model based on the LSTM network that is used for spatiotemporal prediction prob-lems such as predicting rainfall intensity in local areas [27]. Compared with the LSTM neural network, ConvLSTM replaces the fully connected operations between the input of the network to state and state to state with convolution operations, allowing ConvLSTM not only to address time series modelling problems but also to introduce multiple layers of convolution to better capture local spatial features. The operation of the ConvLSTM model is illustrated in Equations (1)–(5):

$$i_t=\sigma (W_{xi}\ast x_t+W_{hi}\ast h_{t-1}+W_{ci}\circ C_{t-1}+b_i)$$

(1)

$$f_t=\sigma (W_{xf}\ast x_t+W_{hf}\ast h_{t-1}+W_{cf}\circ C_{t-1}+b_f)$$

(2)

$$o_t=\sigma (W_{xo}\ast x_t+W_{ho}\ast h_{t-1}+W_{co}\circ C_t+b_o)$$

(3)

$$C_t=f_t\circ C_{t-1}+i_t\circ \tanh (W_{xc}\ast x_t+W_{hc}\ast h_{t-1}+b_c)$$

(4)

$$h_t=o_t\circ \tanh (C_t)$$

(5)

where $i_t$, $f_t$, and $o_t$ represent the input gate, forget gate, and output gate at time t, while $c_t$ and $h_t$ are the unit state and hidden state at time t, respectively; σ and tanh denote, respectively, the Sigmoid activation function and hyperbolic tangent activation function; W and b are the trainable weight matrix and bias term, respectively; and “$\circ$” and “*” represent the Hadamard product operation and convolution operation, respectively.

3.2. ConvGRU

Due to the large number of parameters in ConvLSTM, overfitting of the input data may occur during the training process. To address this issue, Ballas et al. [28] proposed the ConvGRU model. A ConvGRU introduces convolution operations to replace the original fully connected operations and extract local spatial features of the input data based on the one-dimensional GRU network. Compared with ConvLSTM, the gate mechanism of the ConvGRU model is simpler, with fewer parameters, higher computational efficiency, and faster network convergence speed. The operation of the ConvGRU model is illustrated in Equations (6)–(9):

$$z_t=\sigma (W_{xz}\ast x_t+W_{hz}\ast h_{t-1}+b_z)$$

(6)

$$r_t=\sigma (W_{xr}\ast x_t+W_{hr}\ast h_{t-1}+b_r)$$

(7)

$$h_t^{\prime }=\tanh \left(W_{xh}\ast x_t+r_t\circ (W_{hh}\ast h_{t-1})+b_h\right)$$

(8)

$$h_t=(1-z_t)\circ h_t^{\prime }+z_t\circ h_{t-1}$$

(9)

where $z_t$, $r_t$, and $h_t^{\prime }$ represent the update gate, reset gate, and candidate gate at time t, respectively; f is the activation function; and $h_t$ is the output at time t.

3.3. Depthwise Separable Convolution

Depthwise separable convolution decomposes the conventional convolution operation in two processes: depthwise convolution and pointwise convolution. This greatly reduces the number of parameters in the convolutional layer while maintaining the model’s ability to extract input features [29]. The schematic diagram is shown in Figure 7.

Depthwise convolution splits the convolution kernel into single-channel form and convolves each input channel separately. The output feature map has the same number of channels as the input channels. Then, a 1 × 1 convolution kernel is used for the pointwise convolution operation, which combines the feature maps generated by the depthwise convolution in the depth direction. The comparison of computational complexities between the depthwise separable convolution and conventional convolution is shown in Equations (10)–(12).

$$Z_{DSC}=K\times K\times H\times W\times C+Q\times H\times W\times C$$

(10)

$$Z_{CONV}=K\times K\times H\times W\times C\times Q$$

(11)

$$\frac{Z_{DSC}}{Z_{CONV}}=\frac{1}{Q}+\frac{1}{K\times K}$$

(12)

where K and Q represent the size and number of convolution kernels, respectively; H, W, and C represent the height, width, and number of channels of the input features, respectively; $Z_{DSC}$ represents the computational complexity of depthwise separable convolution; and $Z_{CONV}$ represents the computational complexity of conventional convolution. Taking the convolution kernel size $K=3$ used in this study as an example, Equation (12) shows that depthwise separable convolution reduces the computational complexity by approximately 88%.

3.4. Improved Hybrid Network

To reduce the network model parameters and prevent the overfitting caused by many parameters, this study introduces depthwise separable convolution to reconstruct the ConvGRU network layer, which replaces the standard convolution in the ConvGRU layer with depthwise separable convolution and constructs the DSConvGRU. Many studies [30,31,32] have confirmed that the differences in structure between LSTM and a GRU result in different ways of processing input. Compared with LSTM, a GRU is faster and has fewer model parameters. Therefore, combining LSTM and GRU models can alleviate the gradient vanishing problem to a certain extent, while also speeding up model training and convergence. The performance of hybrid models obtained by combining LSTM and GRU models is also superior. Therefore, this study combined the ConvLSTM network layer and the DSConvGRU network layer to improve the prediction performance of the model, enhance the representation and generalization capabilities of the model, and reduce the risk of overfitting.

This study developed a neural network based on an encoder–decoder architecture, and its detailed structure is shown in Figure 8. In equation $a^2\times b$ next to the network layer in the figure, $a^2$ is equivalent to $a\times a$, indicating the size of the convolution kernel for that network layer, while $b$ represents the number of convolution kernels for that network layer. The optimal values for the size and number of convolution kernels in the network layers of the model were determined through manual parameter tuning. The network structure consists of two parts:

(1)

The encoder module consists of two ConvLSTM layers and one DSConvGRU layer. A BatchNorm layer is added after each of the network layers to regularise the output results and accelerate the training process while improving the model stability. The encoder is used to receive samples of WRF output variables and extract the spatiotemporal features of the variable sequence, compressing the high-dimensional input frame sequence into a low-dimensional vector that contains historical spatiotemporal information.

(2)

The decoder module consists of one DSConvGRU layer, two ConvLSTM layers, and one Conv3D layer. The DSConvGRU layer and ConvLSTM layers are used to decode the spatiotemporal feature vector output from the encoder module. Finally, the Conv3D layer compresses the last dimension of the decoded feature vector and unfolds it into an output frame sequence.

3.5. Small-Scale Wind Field Prediction Model

The small-scale wind field prediction method proposed in this study consists of three parts: the WRF module, the ConvLSTM–DSConvGRU hybrid prediction module, and the CFD module. The overall framework is shown in Figure 9. In the WRF module, the NCEP meteorological reanalysis data, land data, and terrain data are used to drive WRF for mesoscale meteorological field simulation. The ARWpost tool is then used to extract the wind speed components along the longitude, latitude, and vertical directions, i.e., u, v, w, and temperature tk, as historical boundary conditions from the WRF outputs. Further, the ConvLSTM–DSConvGRU hybrid prediction module with an encoder–decoder structure is used to predict the boundary conditions of wind speed and temperature. Using the proposed model, the boundary conditions of wind speed and temperature are predicted with a limited number of parameters and high speed. In the CFD module, DEM elevation data, OSM map data, and real building information are first combined to accurately model the terrain and buildings. Then, the model is subjected to unstructured body grid partitioning, and the boundary conditions predicted by the neural network are assigned to the inflow boundary grid points using the inverse distance weighting method. Finally, the CFD module is driven to solve and complete the wind field prediction.

4. Experimental Simulation and Result Analysis

4.1. Construction of Datasets

To verify the effectiveness of the proposed prediction model, the output results of the WRF model for domain d03 at a frequency of every 10 min from 15 March 2022 12:00 to 31 March 2022 12:00, i.e., a duration of 16 days, were used as the initial data (Table 1). A total of 2305 outputs were obtained in this duration. To make it convenient for network training and to save computational resources, this study selected the ARWpost tool to post-process the initial data. The data below the height of 3000 m (the top height of the CFD domain) in the vertical direction of the WRF output were interpolated into 60 layers in a sparse-to-dense manner, while 60 grid point data closer to the boundaries of the CFD model were selected in both the east–west and north–south directions. Regardless of whether the grid point information was extracted from the horizontal or vertical profiles, the number of grid points in the profiles was 60 × 60. Based on the statistical analysis of the post-processed data, Equation (13) was used to transform the grid point data in the profiles into greyscale pixel values through linear projection:

$$I_t=f(G_t^D)=255\ast \frac{G_t^D-G_{\min }^D}{G_{\max }^D-G_{\min }^D},$$

(13)

where $G_t^D$ represents all the speed or temperature grid point data in a profile at time t; $I_t$ represents all the transformed grayscale pixel values in the same profile at time t; $G_{max}^D$ and $G_{min}^D$ respectively indicate the maximum and minimum values of the speed or temperature grid point data in the profile during the simulation period. Since the data transformation is linear, Equation (14) can also be used to project the predicted pixel values outputted by the hybrid network model back into the profile grid point data to drive the CFD module for prediction:

$$G_t^D=f^{-1}(I_t)=\frac{G_{\max }^D-G_{\min }^D}{255}\ast I_t+G_{\min }^D$$

(14)

In this experiment, the longitude component of the wind speed u and the temperature variable tk on the vertical profile of the WRF post-processed grid point data closest to the eastern inflow boundary of the CFD model were selected to generate two greyscale image datasets, which were used to evaluate the performance of the network model. The images generated after visualising the two datasets are shown in Figure 10a,b. Since the WRF model had a total of 2305 outputs for the d03 domain during the simulation period, both datasets contained 2305 greyscale images.

The objective of the experiment was to predict the next five consecutive frames based on a continuous sequence of five previous input frame images. In other words, it aimed to use the past 50 min of WRF output variables to predict the next 50 min of WRF output variables. Specifically, this means using the input frame sequence $\left\{I_{t-4},I_{t-3},\cdots I_t\right\}$ to obtain the predicted frame sequence $\left\{{\widehat{I}}_{t+1},{\widehat{I}}_{t+2},\cdots {\widehat{I}}_{t+5}\right\}$ in an interval of 10 min.

To reduce the amount of data processing for model learning, the experiment adopted the method of rolling prediction [33]. First, the predicted frame sequence $\left\{{\widehat{I}}_{t-3},{\widehat{I}}_{t-2},\cdots {\widehat{I}}_{t+1}\right\}$ was obtained using the input frame sequence $\left\{I_{t-4},I_{t-3},\cdots I_t\right\}$. Then, the frames $I_{t-4}$ were removed from the original input frame sequence $\left\{I_{t-4},I_{t-3},\cdots I_t\right\}$, and the frame ${\widehat{I}}_{t+1}$ from the predicted frame sequence was appended to the end of the input frame sequence. This resulted in a newly constructed frame sequence $\left\{I_{t-3},I_{t-2},I_{t-1},I_t,{\widehat{I}}_{t+1}\right\}$. Next, the new frame sequence $\left\{I_{t-3},I_{t-2},I_{t-1},I_t,{\widehat{I}}_{t+1}\right\}$ was used to obtain a new predicted frame sequence $\left\{{\widehat{I}}_{t-2},{\widehat{I}}_{t-1},\cdots {\widehat{I}}_{t+2}\right\}$. Then, the newly constructed frame $I_{t-3}$ was removed, and ${\widehat{I}}_{t+2}$ from the new prediction frame sequence was appended to the end of the input frame sequence. This process continued, and finally, the predicted frame sequence $\left\{{\widehat{I}}_{t+1},{\widehat{I}}_{t+2},\cdots {\widehat{I}}_{t+5}\right\}$ was obtained.

The experiment followed a 7:3 ratio, in which the first 35 consecutive frames out of every 50 frames were assigned to the training set, and the last 15 consecutive frames were assigned to the test set. A sliding window with a width of six frames and a step size of one was then used to generate training and test sequences from the training and test sets, resulting in a dataset containing 1380 training sequences and 460 test sequences. On this basis, 5 consecutive test sequences were concatenated to evaluate the model performance in rolling predictions of 5 frames, resulting in a total of 276 test sequences with a width of 10 frames.

4.2. Experimental Environment

A workstation with an Intel Core i7-10700 processor, NVIDIA Quadro P400 4 GB graphics card, and 512 GB RAM was used for the computations. The software environment was a Tensorflow 2.4 deep learning framework, which is based on Windows 10. Since the greyscale pixel values are linearly related to grid point data, the loss function during the training process was directly calculated based on the pixel values using mean square error (MSE). The batch size was set to 16, the Adam optimiser was used, the learning rate was set to $1\times {10}^{-4}$, and the number of training epochs was set to 60 during the training.

4.3. Evaluation Indicators for Prediction Performance

The prediction performance of the neural network model was evaluated by calculating the Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) of the test sequence profile data using Equations (15) and (16):

$$RMSE=\sqrt{\frac{1}{M}{\displaystyle \sum _{m=1}^{M_{test}}{\displaystyle \sum _{n=1}^N{\displaystyle \sum _{h=1}^H{\displaystyle \sum _{w=1}^W{(f^{-1}({\widehat{I}}_{m,n})-G_{m,n}^D)}^2}}}}}$$

(15)

$$MAPE=\frac{100\%}{M}{\displaystyle \sum _{m=1}^{M_{test}}{\displaystyle \sum _{n=1}^N{\displaystyle \sum _{h=1}^H{\displaystyle \sum _{w=1}^W\left|\frac{f^{-1}({\widehat{I}}_{m,n})-G_{m,n}^D}{G_{m,n}^D}\right|}}}},$$

(16)

where $M=M_{test}\times N\times H\times W$; $M_{test}$ = 276 represents the number of test sequences; “n” denotes the profile grid point data of the nth frame in the mth test sequence, with “h” and “w” representing the vertical and horizontal grid points corresponding to the profile; and $f^{-1}\left({\widehat{I}}_{m,n}\right)$ indicates the projection of the predicted pixel value of the nth frame in the mth test sequence to the predicted profile grid point value, using Equation (10).

4.4. Ablation Experiment

To validate the prediction performance of the improved ConvLSTM–DSConvGRU hybrid network model, ablation experiments were conducted, and the results are shown in

Table 4. Results of the ablation experiment test set.

Model	Conv- LSTM	Conv- GRU	DSConv- GRU	Number of Parameters	Runtime (s)	RMSE1 (m/s)	MAPE1 (%)	RMSE2 (K)	MAPE2 (%)
1	√	×	×	5.804 M	0.968	1.509	22.1643	0.494	0.109
2	×	√	×	4.354 M	0.768	1.449	20.2898	0.471	0.105
3	×	×	√	0.494 M	0.353	1.475	21.5941	0.480	0.107
4	√	√	×	5.243 M	0.859	1.386	19.2707	0.470	0.104
5	√	×	√	3.767 M	0.735	1.384	18.3817	0.465	0.102

. The experiments were based on the ConvLSTM network, where the “√” in the table indicates the utilization of that network layer in constructing the network model, while “×” indicates the absence of that network layer. Runtime refers to the time that the prediction model takes to obtain five frames within one prediction. RMSE1 and MAPE1 are for wind speed, while RMSE2 and MAPE2 are for temperature.

The results of the ablation experiments on the speed component dataset and the temperature variable dataset are shown in Figure 11a,b, and combined with Table 4, the following conclusions can be drawn: (1) The prediction performance of the five network models on the temperature variable dataset was superior to that on the speed component dataset because the temperature variables were more uniformly and stably distributed in time and space compared with the speed components. (2) Compared with the other four models, the ConvLSTM model showed the poorest performance using the two datasets. On the one hand, as seen in Figure 11a,b, the ConvLSTM model performed relatively well in the first two predicted frames, but its performance deteriorated significantly over time, with the highest errors in the fourth and fifth predicted frames among all five models. This indicates that the ConvLSTM model has poor generalization ability. On the other hand, although the prediction performance of the DSConvGRU model was reduced compared with ConvGRU, it achieved a reduction of approximately 88% in the number of parameters. Additionally, although DSConvGRU exhibited the highest error in the first two predicted frames, its error accumulated at a slower speed over time compared with ConvLSTM and ConvGRU, demonstrating a stronger generalization ability. Specifically, for both datasets, the slopes of the blue lines in Figure 11a,b are smaller than those of the red and green lines. (3) The prediction performance of the hybrid models formed by combining ConvLSTM with ConvGRU or DSConvGRU was superior to that of the individual models. Among them, the ConvLSTM–DSConvGRU model proposed in this study performed slightly better than the ConvLSTM–ConvGRU model.

4.5. Comparison between Different Prediction Models

To further verify the prediction performance of the hybrid model proposed in this study, a comparative experiment was conducted using the ConvLSTM–DSConvGRU model and commonly used spatiotemporal prediction models such as 2D-CNN, 3D-CNN, 3D-ConvLSTM, and SA-ConvLSTM [34]. In this experiment, the structures and parameters of the 2D-CNN and SA-ConvLSTM models remained consistent with those of the proposed model, while the 3D convolution kernel size of the 3D-CNN and 3D-ConvLSTM models were optimised according to Gao et al. [9], with the remaining parameters being consistent with those of the proposed model. The experimental results are shown in

Table 5. Results of the comparative experiment using different models.

Method	Number of Parameters	Runtime (s)	RMSE1 (m/s)	MAPE1 (%)	RMSE2 (K)	MAPE2 (%)
2D-CNN	0.697 M	0.198	1.678	28.688	0.596	0.226
3D-CNN	2.475 M	0.370	1.549	23.669	0.537	0.121
3D-ConvLSTM	11.596 M	1.735	1.448	18.778	0.462	0.100
SA-ConvLSTM	5.933 M	1.194	1.545	23.509	0.499	0.111
The algorithm of this study	3.767 M	0.735	1.384	18.382	0.465	0.102

:

As shown in the table, among the five spatiotemporal prediction models, 2D-CNN showed the poorest prediction performance using the two datasets. 3D-CNN showed some improvement over 2D-CNN, possibly due to its better ability to capture temporal information compared with two-dimensional convolution [35]. 3D-ConvLSTM outperformed the other three commonly used prediction methods and 2D-ConvLSTM in the ablation experiment, and it also showed a slightly lower RMSE and MAPE with the temperature dataset compared with the proposed algorithm. However, its number of parameters was more than three times that of the proposed algorithm, and the training time was much longer, which indicates that the model has excessive algorithm complexity. The SA-ConvLSTM method, which incorporates a self-attention mechanism memory module, performed worse than the traditional ConvLSTM using the two datasets. Therefore, considering all factors, the proposed algorithm not only ensures superior prediction performance but also maintains a relatively small number of parameters, making it more practical.

4.6. Visualisation of Boundary Condition Prediction Results

During the selected simulation period, the wind field and temperature field were stable for the majority of the time. Taking the wind field as an example, Figure 12a is a visualisation of the wind speed component obtained from WRF for the period from 21:20 to 22:50 on 23 March 2022. It can be seen that the overall trend of the wind field during this period was relatively stable. The black dashed box in the figure indicates the process of the wind speed component gradually decreasing over time at that location. Figure 12b shows the visualisation of the wind speed component from 22:10 to 22:50 predicted based on the visualisation of the wind speed component from 21:20 to 22:00 using the ConvLSTM–DSConvGRU model. The RMSEs of the predicted frames ${\widehat{I}}_6–{\widehat{I}}_{10}$ were 0.464 m/s, 0.664 m/s, 0.848 m/s, 1.059 m/s, and 1.311 m/s, respectively. Figure 12b shows that the hybrid model accurately predicted the overall structure and distribution of the wind field, while also providing a good prediction of the gradual decrease in wind speed at the location indicated by the black dashed box. Figure 12c shows the absolute error between the wind field component distribution images from the WRF output and the predicted images. The prediction errors of each frame are mainly concentrated in the lower right area where significant changes in the wind field occurred. Furthermore, these errors tended to increase over time, which is consistent with the results shown in Figure 11a.

However, the wind field underwent dramatic changes over a large area during certain periods, as shown in Figure 13a. The variation in the wind speed component in frames $I_1–I_7$ of the image was relatively stable, but in frame $I_8$, the wind speed component in the upper half suddenly increased and continued to grow over time. This resulted in significant errors in frames ${\widehat{I}}_8–{\widehat{I}}_{10}$ of the predicted images of the hybrid network, as shown in Figure 13b. Specifically, the RMSEs for frames ${\widehat{I}}_6–{\widehat{I}}_{10}$ were 0.930 m/s, 1.300 m/s, 1.825 m/s, 2.226 m/s, and 2.633 m/s, respectively. Figure 13c shows that the errors are primarily concentrated in the upper half of the predicted frames. This result is reasonable because the wind field was stable and calm most of the time compared with the cases where the wind field underwent large and dramatic changes. As a result, the proportion of wind field variations with significant changes in the training dataset was relatively small, resulting in a poor prediction performance of the hybrid network.

5. Discussion

To achieve short-term predictions of small-scale three-dimensional wind fields, this study proposed a prediction method based on the multi-scale coupling of WRF and CFD. In response to the characteristics of the historical inflow boundary dataset, this study proposed a hybrid neural network model, ConvLSTM–DSConvGRU, to predict CFD boundary conditions. After training, this network is capable of accurately predicting the wind speed and temperature as boundary conditions for the next five time steps, enabling predictions of small-scale three-dimensional wind fields up to the next 50 min. The experimental results indicate that compared with the nearest neighbour interpolation method, the inverse distance weighted interpolation method is more suitable for the simulation and prediction of three-dimensional wind fields in the simulated domain of this study. In addition, the proposed hybrid network prediction model exhibits excellent spatiotemporal feature extraction capabilities, with comprehensive advantages in terms of the number of parameters and prediction accuracy. In the next steps, the configuration and parameters of the prediction model will be further optimised to enhance the wind field prediction accuracy, particularly for different locations and meteorological conditions.