For the ground truth reference, the ASWS data comprise in situ observations with a 5 min time interval, which is the 2 min average of the 3 s wind measured using automatic weather stations (AWSs) (Fig. b) at a height of 10 m above the ground. Note that there are limited wind observation data available on the seacoast and over the sea, and as a result, this study focuses on gust forecasting in the land region of eastern China. To match the spatiotemporal resolution of the observed radar reflectivity mosaics (RMOSs), the ASWS data were first interpolated to 6 min using linear interpolation. Inverse distance-weighted (IDW) interpolation has the advantages of being fast to calculate and easy to understand, and it is suitable for eastern China, where the automatic stations are dense and evenly distributed. Thus, the IDW interpolation method was employed to regrid the ASWS data to a spatial resolution of 0.01∘ × 0.01∘ by using the four nearest stations within 15 km with a power of 2 (the details of the parameter choices can be found in the Supplement). The wind observation data on the seacoast and over the sea were set to 0. Subsequently, during the training process, we masked the wind data on the seacoast and over the sea by setting the weight of the loss function to 0. This ensures that the sea areas do not contribute to the backpropagation optimization. However, the values in the sea areas still participate in the convolutional operations during the forward-propagation process, which could lead to a slight underestimation of the ASWS or PWGS values in areas close to the seacoast. In this study, the interpolated wind data are assumed to be close to the true observed wind field.

ASWS data from 2016 to 2022 were considered. To further select ASWS data associated with CGs, the samples selected need to meet the following two concurrent principles: (1) more than 2 % of stations recorded ASWS >10.8 m s-1, and (2) the precipitation at more than 5 % of the stations was greater than 0.1 mm within the space of an hour.

In addition, observed peak wind gust speed (PWGS) from 2021 to 2022 was used in this study for subsequent gust factor calculation and model evaluation; it is the maximum 3 s average gust recorded over 1 h by the AWS. Samples from PWGS were taken from typical CG events recorded by the meteorological bureau.

Weather radar provides a highly detailed representation of the spatial structure and temporal evolution of thunderstorms over a large area . Weather radar data may also indicate the time and location of the CGs that occurred . In particular, the constant-altitude radar RMOSs at 3 km are less susceptible to ground clutter compared to radar data at other altitudes. This allows them to provide continuous and comprehensive coverage of the study area, as well as a more accurate representation of storm structure. Thus, these constant-altitude radar RMOSs at 3 km were used as auxiliary data along with observed wind data to forecast the speed of CGs. The RMOS data are from 10 weather radar stations in eastern China (Fig. a). The type of radar sensor is the CINRAD/SA Doppler weather radar . The RMOS is acquired through the operational Doppler weather radar 3-D digital mosaic system , which was developed by the Chinese Academy of Meteorological Sciences. This system determines the RMOS by projecting the base reflectivity factor onto equal longitude and latitude coordinates. The time interval of the RMOS data is 6 min, the spatial resolution is 0.01∘, and the grid data are arranged from west to east and north to south.

The workflow of this study is illustrated in Fig. . First, the RMOS data were preprocessed, and the ASWS data were interpolated and regridded as mentioned above. Second, the spatiotemporal resolutions of the RMOS and ASWS samples were matched, and the time of the RMOS samples was determined by the selected ASWS samples. Third, the dataset was divided into three parts (training, validation, and testing datasets) according to the observation time. Fourth, the ASWS data were clipped to be between 0 and 35 m s-1 and subsequently normalized to the range 0–1 through min–max normalization. Similarly, the RMOS values were clipped to be between 0 and 70 dBZ and subsequently normalized to be between 0 and 1. Fifth, the ASWS and RMOS data in the past 60 min were used as input data to train and validate the deep learning nowcasting model, and the outputs were the forecasted ASWSs with lead times of 6–120 min ahead, with a spatial resolution of 0.01∘ × 0.01∘ and a 6 min temporal resolution. Sixth, the performance of the deep learning model in forecasting ASWS was evaluated by different statistical variables. Seventh, the mean gust factor (GF) was determined by comparing the observed PWGS and ASWS. Subsequently, the PWGS forecasts were estimated by multiplying the GF by the forecasted ASWS. Finally, the PWGS forecasts were compared with INCA results, and two cases were also showed to demonstrate the accuracy of PWGS forecasts.

We started by adapting the network structure proposed by , namely PhyDNet, which is a sequence-to-sequence network. Unlike traditional networks, PhyDNet steers the learning process toward identifying physically consistent solutions by introducing an appropriate inductive bias , that is, implicitly embedding prior knowledge in the network architecture and satisfying a given set of physical laws. It has a two-branch deep architecture, i.e., the newly proposed recurrent physical cell (PhyCell) and ConvLSTM (convolutional long short-term memory). Specifically, PhyCell is inspired by data assimilation techniques for performing partial differential equation (PDE)-constrained prediction in latent space. It explicitly disentangles PDE dynamics from unknown complementary information and allows for a generic class of linear PDEs through varying differential orders, e.g., wave equations. In PhyDNet, the physical knowledge is represented by PDEs, which can enforce physical constraints for future image prediction well. PhyDNet has been successfully employed in many fields, e.g., solar irradiance forecasting using fisheye images and nitrogen prediction .

The attention mechanism can focus on the important information among a large amount of input information and ignore most of the unimportant information . Thus, an attention mechanism is applied to improve the performance of PhyDNet for nowcasting CGs in this study. Here, the PhyDNet with an attention mechanism for CG nowcasting is called CGsNet, and its architecture is illustrated in Fig. . An input sequence {xt-Ka,r,…,xta,r} ∈ RK×n×l×c including ASWS (a) and RMOS (r) with K time steps, spatial size n×l, and c channels is projected into {ht-KE,…,htE} by the convolutional units and is processed by the recurrent block unfolded in time. This forms a sequence-to-sequence architecture suitable for multistep prediction, outputting T future ASWS (a), and RMOS (r) predictions {x^t+1a,r,…,x^t+Ta,r}. For time t, we learn a weight vector 〈αtk,…,αt1〉 for K hidden states {ht-Km,…,ht-1m}, where the weight αtk can be interpreted as the relative importance of the kth hm. Each weight αtk is computed by taking ht-kE as input, followed by a softmax operation. Then, we perform summation over the weighted hidden states to obtain an attention representation At, which will be incorporated into the decoder for prediction. The key equations for generating the attention representation At for the t+1th output prediction are summarized as follows: 1stk=W∗ht-kE+b,∀k∈[1,K],2αtk=exp⁡(stk)∑k=1Kexp⁡(stk),∀k∈[1,K],3At=∑k=1Kαtkhkm,4ht+1m=PhyCell([htE,At])+ConvLSTM([htE,At]), where “*” denotes the convolution operator, and the kernel matrices W and biases b are parameters to be learned. The high-level representation ht+1m is then fed into the deconvolutional units, and x^t+1a,r is calculated. Similarly, by inputting x^t+1a,r into the decoder, combined with the attention mechanism, the forecasted x^t+2a,r can be calculated. In this cycle, we can obtain the ASWS and RMOS forecasts in the future, i.e., {x^t+1a,r,…,x^t+Ta,r}. The effect of the attention mechanism operation is to find the most significant historical information from the input sequences; e.g., when predicting x^t+1a,r, the attention module can assign weights for {ht-Km,…,htm}. This can better model both short-term and long-term dependencies. The detailed convolutional encoder and decoder, the calculation process of PhyCell and ConvLSTM, and the feature maps of hidden states can be found in the Supplement. Note that we just focus on analyzing the forecasting results of ASWS, and the forecasted RMOS is a secondary result.

Here, we aim to forecast 0–2 h CGs; thus, 10 historical ASWS and RMOS grid fields {x1a,r,…,x10a,r}∈R10×480×560×2 were taken as the inputs, and the subsequent 20 ASWS and RMOS grid fields {x11a,r,…,x30a,r}∈R20×480×560×2 were the ground truth outputs. The ASWS and RMOS grid fields from 2016 to 2020 were used for model training, and the fields from June to September 2021 and April to May 2021 were employed for ASWS validation and testing, respectively. The fields from May to July 2022 were used for PWGS testing. Correspondingly, we obtained 15 629 CG samples, including a training set of 13 155 samples, a validation set of 1236 samples, and the testing sets of 1184 and 54 samples for ASWS and PWGS.

Regarding the training settings, Adam was used as the optimizer, and the batch size was set as 2. The learning rate was initially set to 0.001 and then multiplied by 0.3 if the loss did not decrease when the model was trained for 2 epochs. The model was trained for a total of 50 epochs, and the model weight with the minimum loss on the validation set was selected and saved. Then the evaluation experiments were implemented on the testing set. Detailed hyperparameter choices can be found in the Supplement. All experiments in this study were conducted using Python and PyTorch and were executed on four NVIDIA GeForce RTX 3090 GPUs with the CUDA-11.1 library.

The loss function is used to adjust the weights of the deep learning model, and it is an instructive function that guides one on how to improve the weight coefficients. Most previous studies used the mean absolute error (MAE) loss or mean squared error (MSE) loss as the default to train their models . However, these losses will result in smoothing effects in the predicted fields, since they may make a good assumption about the global similarity of the two fields, meaning that the field's details may be lost . Notably, with increasing forecast time, the problem of underestimating high values becomes more obvious, such as underestimating heavy rain or radar reflectivity. To address these problems and make the predictions sharper and more realistic, the weighted MAE loss was adopted in this study. The weights for the MAE loss function are shown in Table  (further details on parameter choices are available in the Supplement). These weights are determined based on the six ASWS and RMOS value ranges. The weighted MAE loss is designed to ameliorate the problem of data imbalance caused by the scarcity of strong gust data, as it gives a large weight to strong gusts and a small weight to weak gusts. Thus, this setting has a better effect on forecasting CGs than loss without weights. The weighted loss function can be calculated as follows: 5loss=1N∑n=1N∑i=1480∑j=1560wn,i,jyn,i,ja-y^n,i,ja+1N∑n=1N∑i=1480∑j=1560wn,i,jyn,i,jr-y^n,i,jr, where N is the number of samples, and i and j are the width and length of the ASWS and RMOS, respectively. Moreover, yn,i,ja, yn,i,jr, y^n,i,ja, and y^n,i,jr are the observed ASWS, observed RMOS, forecasted ASWS, and forecasted RMOS values, respectively. wn,i,ja and wn,i,jr denote the weights of the ASWS and RMOS values, respectively.

To quantify the capabilities of CGsNet, the critical success index (CSI), probability of detection (POD), false-alarm rate (FAR), bias score, and Heidke skill score (HSS) were implemented for evaluating the CGsNet forecasts. The following equations describe these indices: 6CSI=TPTP+FP+FN,7POD=TPTP+FN,8FAR=FPTP+FP,9Bias=TP+FPTP+FN,10HSS=(TP×TN-FN×FP)(TP+FN)×(FN+TN)+(TP+FP)×(FP+TN), where TP, TN, FN, and FP are the numbers of true positives, true negatives, false negatives, and false positives, respectively. Moreover, the MAE and RMSE are also used for model evaluation and are calculated as follows: 11MAE=1Q∑i=1Q|yi-y^i|,12RMSE=1Q∑i=1Q(yi-y^i)2, where Q is the number of predicted ASWS pixel values. yi and y^i represent the observations and forecasts, respectively. Note that the value of the bias is greater than 0, and the closer to 1 the value is, the better. The remaining indices range between 0 and 1. An excellent model should present high CSI, POD, and HSS values but low FAR, MAE, and RMSE values.

The bootstrapping method is used to generate the 95 % confidence intervals for the mentioned indices. The confidence interval (CI) helps to provide a measure of the uncertainty associated with the results and allows for a better understanding of the range of possible values for the indices. Besides, the use of bootstrapping allows us to estimate the variability of the indices and helps to ensure that the results are robust and reliable.The detailed calculation process can be found in the Supplement.

In addition, the baseline methods, PhyDNet and INCA , are compared with CGsNet in forecasting ASWS and PWGS in CGs, respectively. INCA is a nowcasting system developed with complex-terrain adaptability at the Austria National Weather Service. In this study, the nowcasts start with a three-dimensional analysis based on a first guess obtained from the output of the numerical weather prediction model (here, the PWAFS model is used), with observation corrections superimposed. It can provide wind forecasts, for which the update frequency (temporal resolution) is 1 h.

In particular, we concentrate on evaluating ASWS at thresholds of 8.0–13.9 m s-1 (e.g., ASWS >8.0 m s-1 or ASWS >13.9 m s-1) and PWGS at thresholds of 10.8–20.8 m s-1 in CG events, which has broad value for disaster warning in meteorological operations and aviation applications.

To validate and evaluate the effectiveness of the CGsNet in forecasting ASWS in CGs, the baseline model, PhyDNet, was used for the comparison. The evaluation results of CGsNet and PhyDNet in terms of the CSI, HSS, POD, MAE, and RMSE are given in Table  for the investigated nowcasting lead time. The thresholds at 8.0, 10.8, and 13.9 m s-1 of ASWS are evaluated, and the results reveal that CGsNet outperformed PhyDNet on these criteria. In detail, for an ASWS threshold of 8.0 m s-1, CGsNet has better performance with HSS = 0.54 (95 % CI: 0.47; 0.61), POD = 0.59 (95 % CI: 0.51; 0.66), MAE = 1.6 (95 % CI: 1.46; 1.80) m s-1, and RMSE = 2.26 (95 % CI: 2.00; 2.54) m s-1 compared to PhyDNet (HSS =  0.52 (95 % CI: 0.44; 0.59), POD = 0.55 (95 % CI: 0.46; 0.62), MAE = 1.71 (95 % CI: 1.55; 1.91) m s-1, and RMSE = 2.40 (95 % CI: 2.14; 2.68) m s-1). When the threshold is raised to 10.8 m s-1, the forecast ability of both CGsNet and PhyDNet degrades slightly. For strong wind (the threshold is at 13.9 m s-1), CGsNet still has a certain forecasting ability, with an HSS of 0.20 (95 % CI: 0.07; 0.24) and a POD of 0.22 (95 % CI: 0.10; 0.31), which is superior to the performance of PhyDNet. This means that the developed attention module can effectively enhance the modeling ability of CGsNet, making CGsNet a valuable tool for nowcasting ASWS during CG events, particularly for strong gusts that are typically challenging to forecast using traditional methods.

We further investigated the performance of models by drawing the CSI, HSS, MAE, and RMSE curves at all nowcasting lead time stamps. As shown in Fig. , in the cases with ASWS >8.0 m s-1, the prediction quality of both CGsNet and PhyDNet gradually decreases as the forecasting time increases. The CSI and HSS of CGsNet always retain top positions at any time. Specifically, for CGsNet, the value of CSI and HSS drops from approximately 0.56 and 0.70 (lead time at 6 min) to 0.40 and 0.45 (lead time at 120 min) in the nowcasting results, and the RMSE (MAE) increases from approximately 2.5 (1.7) m s-1 for the first lead time to 5.1 (3.7) m s-1 for the last lead time. The case of ASWS >10.8 m s-1 is similar to that of ASWS >8.0 m s-1; the prediction quality of both models gradually decreases as the lead time increases, but the performances are degraded compared to that with a threshold of 8.0 m s-1.

In addition, the evaluation curves are depicted with respect to different nowcasting lead times at the 13.9 m s-1 threshold (Fig. ). The results are similar to the ASWS at the other two thresholds. It is also clear that CGsNet always has the superior performance in terms of CSI and HSS for all steps. In the first 12 min, the performance of CGsNet decreases rapidly and then gradually decreases slowly. For PhyDNet, there is a slow decline in both CSI and HSS during the 0–2 h forecasting period. It is worth noting that the nowcasting performance of PhyDNet is close to CGsNet after 108 min, but on the whole, CGsNet with the additional attention mechanisms is better than that of PhyDNet. Although the performance of CGsNet is worse than that with the other two thresholds, it still exhibits forecasting skill within 2 h. Overall, the above results confirm the effectiveness of the developed attention mechanism, which has potential for nowcasting ASWS in CG events.

To further prove the usefulness of CGsNet in detail, we show examples in two meteorologically important weather cases produced by CGsNet and PhyDNet. The first case occurred on 30 April 2021, when eastern China was affected by cold air due to the influence of the northeast China cold vortex. This cold air accompanied by the cold vortex moved eastward and southward, intersecting with some warm and humid air currents in eastern China. Then, the areas along the Yangtze River and north of Jiangsu suffered from SCW, including sudden CGs and hail. Because of the small-scale and rapid development of these CGs, numerical models usually cannot forecast this process accurately.

Specifically, hail and large-scale thunderstorms occurred from 18:00 to 22:00 BJT in parts of Nantong, Jiangsu, with a maximum wind speed of up to 47.9 m s-1 in some areas. Figure 5 shows the in situ observations and forecasted ASWS during this period. The CGs developed strongly at 20:12 BJT, and the ASWS exceeded 17.2 m s-1 in some areas. Then, the ASWS gradually decreased after 20:12 BJT for 120 min. It is clear that the CGsNet model has better forecasting skill than PhyDNet (Fig. ). CGsNet accurately forecasts the weakening trend of the CGs, while PhyDNet tends to overestimate the weakening trend of CGs. Additionally, the observed strong gusts continuously moved to the southeast as the lead time continued. CGsNet forecasts this phenomenon precisely, although in the later stage, the locations of the forecasted strong gusts are not exactly the same as in the observations. Specifically, the CGsNet model struggles to accurately forecast regions with strong gusts (ASWS >10.8 m s-1) and produced nowcasts that are slightly north (approximately 50 km) of the observed locations. Additionally, in regions with strong gusts (ASWS >10.8 m s-1), both CGsNet and PhyDNet underestimate the ASWS values, with PhyDNet showing a larger underestimation. Some false reports are also found from both models in the areas where 8.0 m s-1 < ASWS < 10.8 m s-1, indicating that the modeling ability of CGsNet is limited.

The second case is also typical convection weather. It was influenced by the low-level shear lines and strengthened by southwest warm and humid airflow on 15 May 2021. This process occurred in central and eastern Jiangsu, accompanied by heavy precipitation and strong gusts, causing serious economic losses. The observations and forecasts of ASWS for this case are presented in Fig. .

In the second case, CGs are produced with the development of the squall line in the Jiangsu area. The strong gust position is linearly distributed, moving eastward from western Jiangsu to central Jiangsu between 13:00 and 15:00 BJT. Figure 6 clearly shows that, in most of the forecasting period, CGsNet outperforms PhyDNet due to its improved modeling capability. The results demonstrate that CGsNet can accurately forecast the ASWS values in most areas, although the strong gust values are slightly smaller than the observations in some areas. For PhyDNet, it shows a more pronounced underestimation of ASWS values compared to CGsNet. Furthermore, it is worth noting that, in the later stages of prediction (e.g., lead time at 120 min), the forecasted CG positions by PhyDNet are closer to the observations. Similar results can also be found in the RMOS forecasts (Figs. S1 and S2 in the Supplement), which are the other output variables of CGsNet. Overall, the results further confirm that CGsNet is effective and accurate for ASWS nowcasting. Based on the reliable ASWS forecasts, nowcasting on the PWGS of CGs may be conducted.

ASWS reflects the average speed of CGs, which is not sufficient to determine the actual impact of CGs. The maximum momentary wind speed (e.g., PWGS) can reflect the actual peaks of CGs and is the key factor for the assessment and analysis of weather hazards. Thus, this section focuses on evaluating the reliability and accuracy of CGsNet on nowcasting PWGS.