An Automatic Jet Stream Axis Identification Method Based on Semi-Supervised Learning

Abstract

Changes in the jet stream not only affect the persistence of climate change and the frequency of extreme weather but are also closely related to climate change phenomena such as global warming. The manual way of drawing the jet stream axes in meteorological operations suffers from low efficiency and subjectivity issues. Automatic identification algorithms based on wind field analysis have some shortcomings, such as poor generalization ability, and it is difficult to handle merging and splitting. A semi-supervised learning jet stream axis identification method is proposed combining consistency learning and self-training. First, a segmentation model is trained via semi-supervised learning. In semi-supervised learning, two neural networks with the same structure are initialized with different methods, based on which pseudo-labels are obtained. The high-confidence pseudo-labels are selected by adding perturbation into the feature layer, and the selected pseudo-labels are incorporated into the training set for further self-training. Then, the jet stream narrow regions are segmented via the trained segmentation model. Finally, the jet stream axes are obtained with the skeleton extraction method. This paper uses the semi-supervised jet stream axis identification method to learn features from unlabeled data to achieve a small amount of labeled data to effectively train the model and improve the method’s generalization ability in a small number of labeled cases. Experiments on the jet stream axis dataset show that the identification precision of the presented method on the test set exceeds about 78% for SOTA baselines, and the improved method exhibits better performance compared to the correlation network model and the semi-supervised method.

1. Introduction

The atmospheric wind field jet stream is a narrow band of high-speed winds (typically exceeding 30 m/s) in the atmosphere. It is a vital component of atmospheric circulation. In temperate regions, the jet stream significantly impacts the movement of frontal zones and air masses, thus influencing ground-level weather. Towards the latter part of the Second World War, greater attention was given to jet streams when it was discovered that fighter planes were vulnerable to strong winds during air combat [1].

Understanding and visualizing the weather situation involves plotting jet stream axes, typically represented by lines with arrows on high-altitude weather maps. In meteorological operations, forecasters manually draw jet streams, especially in the MICAPS (Meteorological Information Comprehensive Analysis and Processing System) software developed by the China Meteorological Administration. However, this manual method is inefficient and prone to errors and subjectivity. To address these challenges, researchers have explored methods to calculate the jet stream axes from radar data to improve efficiency. Zhang et al. [2] used Doppler radar data and the VAD algorithm to determine average wind speed and direction at various heights, identifying potential jet stream altitudes and axes. Jin et al. [3] also employed Doppler radar data, applying 3D interpolation and velocity gradients to locate jet streams by combining wind speed, radial velocity, and gradient with a threshold condition.While radar data primarily provide radial wind speed, they have limitations in extracting the jet stream axes in high-space wind fields. Some researchers have made progress in defining the jet stream axes using mathematical methods to analyze the wind field. Wang et al. [4] used a quadratic transfer clustering algorithm and cubic Bessel curve to automatically identify and smooth the jet stream axes after preprocessing the data. Molnos et al. [5] designed a network-based approach utilizing Dijkstra’s shortest-path algorithm to identify the cores of the polar and subtropical jet streams. Gan et al. [6] identified jet streams using grid point wind field data, skeleton extraction, and center of gravity fine-tuning to connect and obtain the jet stream axes. Diao [7] processed automatic station data based on wind direction, then used the nearest neighbor propagation algorithm for clustering and the least squares method to fit and determine the jet stream axes. Lu et al. [8] employed traditional observation data, automatic station data, and MICAPS wind field information to automatically identify low-altitude jet streams on the 850 hPa surface through preprocessing, clustering, and fitting. Despite these advancements, these methods still exhibit poor generalization ability and struggle with bifurcation and merging of jet streams in certain conditions.

Deep learning is highly esteemed and advanced by researchers due to its remarkable ability to generalize effectively and achieve high accuracy. The model automatically identifies jet stream areas by learning from samples labeled by meteorologists. Fully supervised deep learning necessitates many high-quality samples, while semi-supervised deep learning can operate effectively with smaller samples. In 2015, Long et al. [9] proposed Fully Convolutional Networks (FCNs). The FCN extends image-level classification networks to pixel-level classification networks and realizes end-to-end network training, pioneering work applying deep neural networks to image semantic segmentation. As feature map receptive fields shrink during downsampling in FCN networks, some image spatial information is lost, and contextual information is not fully utilized. The DeepLab series networks [10] have been introduced to address this limitation. These networks excel at enlarging the receptive field and extracting more feature information. However, they come with drawbacks such as increased computational cost, loss of positional pixel information, and impact on the local consistency of feature maps. One potential approach to address the challenge of diminished image resolution and the loss of pixel space details caused by pooling operations is to implement the Encoder–Decoder structure. This structure also offers a solution to the issue of inter-pixel information loss. Various methods, such as U-Net [11], UNet++ [12], and SegNet [13], rely on the Encoder–Decoder structure to fuse low and high-level features for spatial dimension recovery and boundary information retrieval in images. However, these methods are complex in network structure, feature a large number of parameters, and may not effectively segment object boundaries. The nature of convolutional operations imposes inherent limitations on CNN-based methods, making it challenging for them to learn explicit global and long-term semantic information interactions. Swin-Unet [14] leverages Transformer to enable 2D image segmentation. It is the pioneering purely Transformer-based U-architecture with vital segmentation accuracy and robust generalization capabilities.

In semi-supervised learning methods, the fundamental concept behind the consistency learning method [15] involves introducing a perturbation to the unlabeled data. This perturbation is used to measure the disparity between the perturbed prediction and the unperturbed prediction. The absolute value of this difference is then utilized as a component of the loss function to enhance the model’s generalization capabilities. Input perturbation-based methods have demonstrated significant improvements in the generalization capability of models by employing various data augmentation techniques. These techniques, such as rotation, flipping, and CutMix [16], are applied to input images to generate multiple post-perturbation representations, encouraging models to yield consistent outputs for these manipulated inputs. Moreover, recent studies have introduced innovative input perturbation techniques, such as ComplexMix [17], which combines CutMix [16] and ClassMix [18], thereby contributing to further enhancement of model performance. Feature perturbation-based methods improve features by introducing perturbations to the encoder outputs within the segmentation network. For instance, Cross Consistency Training (CCT) [19] methods enhance the performance of semi-supervised semantic segmentation by perturbing the encoder outputs while training unlabeled samples. These methods also employ an auxiliary decoder to guarantee that the outputs align with the main encoder. Network perturbation-based methods generate perturbation predictions by utilizing networks with distinct initializations. For example, Cross Pseudo Supervised (CPS) [20] methods enhance semi-supervised semantic segmentation by employing two networks with identical structures but different initializations. This approach imposes similarity constraints on the outputs of the same input samples. However, existing methods do not subsequently incorporate the high-quality samples obtained into the dataset. On the other hand, the self-training method [21] utilizes all the pseudo-labels for training the model. If the confidence level of some pseudo-labels is too low, the model’s performance may deteriorate as the number of iterations increases, potentially leading to a crash.

This study introduces a semi-supervised deep learning technique that focuses on identifying the jet stream region of the atmospheric wind field and determining its axes through skeleton extraction. By leveraging manually labeled jet stream axes, the model learns the extended features of the jet stream region. It accurately calculates the shape trend and wind direction, leading to a more precise extraction of the jet stream axes. The method combines and enhances consistency learning and self-training, utilizing a substantial amount of unlabeled data to train the jet stream region segmentation axes identification model. This study uses MICAPS 11 class data (grid point vector data primarily used for drawing wind field streamlines, containing longitude, latitude, U-direction data, and V-direction data for each grid point) as the dataset. In the consistency learning phase, the Cross Pseudo Supervision (CPS) [20] strategy is employed, using two neural networks with the same structure but different initialization methods to supervise and reinforce each other’s learning. During the self-training [21] stage, high-confidence pseudo-labels are identified through feature perturbation based on the consistency principle, ensuring the use of reliable pseudo-labels for further learning. The consistency learning phase employs Unet [11] as the base network to model local information, while the self-training phase utilizes Swin-Unet [14] to capture long-range dependencies. This semi-supervised learning approach reduces the model’s reliance on labeled data and enhances its generalization capabilities. The automatic identification of jet stream axes can significantly enhance the efficiency of weather forecasting decisions. By leveraging samples annotated by meteorological experts, these automated identification methods can offer more objective and consistent results, given the critical role jet streams play in weather forecasting. Additionally, the automatic identification outputs can be encoded as inputs for weather prediction models, thereby improving the accuracy and interpretability of these models. This approach lays a solid methodological foundation for the future of smart weather forecasting. The main innovations of this paper are as follows:

1.

In addressing the challenges of limited generalization ability and the difficulty of obtaining many high-quality samples for identifying jet stream axes in atmospheric wind fields, a new semi-supervised automatic identification method has been proposed based on a semi-supervised approach. This method aims to accurately capture the shape of the jet stream area while aligning more consistently with wind direction.

2.

The issue of excluding high-quality samples from the dataset is tackled within the framework of consistency learning. This paper proposes an innovative semi-supervised learning methodology that amalgamates consistency learning with self-training techniques for jet stream area identification, also called segmentation.

3.

Addressing the challenge of model training deterioration due to low-confidence pseudo-labels within self-training methodologies, this study proposes a strategy predicated on feature perturbations for the filtration of high-confidence pseudo-labels. Empirical analyses substantiate that the proposed approach significantly enhances the efficacy of semi-supervised learning paradigms.

2. Methods

2.1. Overall Plan

The overall plan of the method in this paper is depicted in Figure 1. Initially, the raw data consisting of MICAPS 11 class data and manually labeled masks are transformed into model input data. The segmentation model produces the segmentation results, which are then used to identify the jet stream axes through the skeleton extraction method. Subsequently, the jet stream axes are transformed into a standard data format for the meteorological domain. The crucial step in this framework is segmenting the jet stream region to ensure it is consistent with the wind speed direction. Neural networks are primarily utilized for segmenting jet stream regions, a process akin to solving an image segmentation problem. Utilizing neural networks enables us to accurately extract the jet stream region from atmospheric data and subsequently determine the jet stream axes. This paper introduces a semi-supervised deep learning approach to segment the jet stream region and enhance the semi-supervised deep learning model.

2.2. Data Preprocessing

The MICAPS Class 11 data were preprocessed to transform the initial U and V data into more understandable and intuitive wind direction and speed features, which are crucial for manual labeling. Subsequently, we converted the wind direction and speed into image pixels, treating them as image channels to create the training dataset, with the image dimensions being 320 × 512 × 3. The wind speed (Speed) and wind direction (Direction) were calculated using the equations presented in (1) and (2).:

$$Speed=\sqrt{(U^2+V^2)}$$

(1)

$$\mathit{Direction}=\left\{\begin{array}{cc}0,\hfill & U=0,V>0\hfill \\ 90,\hfill & U>0,V=0\hfill \\ 270,\hfill & U<0,V=0\hfill \\ 180,\hfill & U=0,V<0\hfill \\ arctan\left({\displaystyle \frac{U}{V}}\right)\times {\displaystyle \frac{180}{\pi }},\hfill & U>0,V>0\hfill \\ arctan(-{\displaystyle \frac{U}{V}})\times {\displaystyle \frac{180}{\pi }}+270,\hfill & U<0,V>0\hfill \\ arctan\left({\displaystyle \frac{U}{V}}\right)\times {\displaystyle \frac{180}{\pi }}+90,\hfill & U>0,V<0\hfill \\ arctan(-{\displaystyle \frac{U}{V}})\times {\displaystyle \frac{180}{\pi }}+180,\hfill & U>0,V>0\hfill \end{array}\right.$$

(2)

As per the Technical Specification for Mesoscale Weather Map Analysis (Trial Version) released by the National Meteorological Center of China, if the observed wind speeds at two adjacent stations within the 500 hPa isobar exceed 20 m/s, the area is classified as a jet stream area. To accurately determine the boundaries of the jet stream area, a wind speed threshold of 14 m/s was established for the 500 hPa isobar.

After analyzing the wind speed data for all grid points, it was found that only a tiny percentage (0.435%) of grid points had wind speeds exceeding 40 m/s. As a result, 40 m/s was established as the maximum wind speed value for all grid points, with any points exceeding this threshold being assigned a value of 40 m/s. Considering that the maximum pixel value in the image is 255, the wind speed was multiplied by 6.375, and this value was assigned to the image’s R channel. For grid points with wind speeds less than 14 m/s, the red channel pixel value was set to 0. For grid points with wind speeds greater than or equal to 14 m/s, the wind speed value was multiplied by 6.375 to determine the corresponding red channel pixel value. Wind direction indicates a direction—just a number without quantitative meaning—and cannot be directly used as an input feature for deep learning models. For example, 0° wind direction and 359° wind direction are directions, but the quantized numbers are very different. To handle wind direction, it is converted to a point on a two-dimensional plane located on the circumference of a circle using the function $x^2+y^2=1$. The angle $\theta$ from the positive direction of the y-axis to that point corresponds to the wind direction. The x-coordinate and y-coordinate of the point fall within the range of [−1, 1], and these coordinates are converted to pixel values for the green and blue channels of the image. This is achieved by adding 1 to the x and y coordinates and multiplying by 127.5 to obtain values in the range [0, 255]. During the construction of the training image, the RGB pixel values are calculated using Equations (3)–(5), as shown in the paper.

$$R(i,j)=\left\{\begin{array}{cc}0,\hfill & \mathrm{if}Speed(i,j)<14\mathrm{m}/\mathrm{s}\hfill \\ Speed(i,j)\times 6.375,\hfill & \mathrm{if}Speed(i,j)\ge 14\mathrm{m}/\mathrm{s}\hfill \end{array}\right.$$

(3)

$$G(i,j)=\left[cos\left({\displaystyle \frac{2\pi \times Direction(i,j)}{359}}\right)+1\right]\times 127.5$$

(4)

$$B(i,j)=\left[sin\left({\displaystyle \frac{2\pi \times Direction(i,j)}{359}}\right)+1\right]\times 127.5$$

(5)

2.3. Semi-Supervised Method Structure

The presented method structure includes two states, i.e., consistency learning and self-training stage, as shown in Figure 2.

In the first stage of consistency learning, a Cross Pseudo Supervised structure is employed. Two Unet neural networks are initialized using Kaiming initialization and Xavier initialization, respectively. Each batch comprises labeled and unlabeled data. In consequence, the neural network produces two distinct outputs: a labeled output for the labeled data and an unlabeled output for the unlabeled data. For a pixel, a pseudo-label is generated for the unlabeled data by selecting the highest probability of segmentation classes from the unlabeled outputs of the two neural networks, which are then utilized as supervised signals. As illustrated in Figure 2, unlabeled output1 utilizes pseudo2 as a supervised signal, while unlabeled output2 uses pseudo1 as a supervised signal. The labeled outputs of both neural networks are subject to the supervisory loss function for the labeled data.

In the phase of self-training, Swin-Unet undergoes initial training using labeled data. Subsequently, the network is further trained using an augmented dataset, integrating high-confidence pseudo-labels derived from the first module’s output into the training set. Iterating the addition of high-confidence pseudo-labels and training the neural network until no further improvement is observed.

2.4. Screening for High-Confidence Pseudo-Labels

Algorithm 1 describes the method used for the screening process. Unlabeled samples corresponding to pseudo-labels are encoded via the encoder trained in the consistency learning phase. This encoder uses the encoder from the Unet network. Various perturbations, such as Gaussian noise, random masks, and spatial transformations, are added to the encoded embedding vectors. Subsequently, both the perturbed embedding vectors and the embedding vectors without added perturbations are decoded using a decoder. IoU and average IoU values are calculated using decoded images with and without added perturbation into embedding vectors. A threshold value is set for comparison with the computed average value. If the average value exceeds the threshold value, the corresponding pseudo-label is regarded as a high-confidence pseudo-label.

Algorithm 1 High-Confidence pseudo-label screening with multiple perturbations

Require:  Input image X, Encoder $E(·)$, Decoder $f(·)$, Set of perturbation functions $\{{\mathrm{Noise}}_1(·),{\mathrm{Noise}}_2(·),\dots ,{\mathrm{Noise}}_n(·)\}$, IoU threshold $\theta$ Ensure:  High-confidence pseudo-label Y for X 1: $E\leftarrow E\left(X\right)$ {Encode the input image to get the embedding} 2: $Y\leftarrow f\left(E\right)$ {Generate pseudo-label without perturbation} 3: Initialize IoU_sum←0 4: for  $i=1$  n  do 5:    ${\tilde{E}}_i\leftarrow E+{\mathrm{Noise}}_i\left(E\right)$ {Apply the i-th perturbation to the embedding} 6:    ${\tilde{Y}}_i\leftarrow f\left({\tilde{E}}_i\right)$ {Generate pseudo-label with the i-th perturbed embedding} 7:    IoU_sum←IoU_sum+${\displaystyle \frac{|Y\cap {\tilde{Y}}_i|}{|Y\cup {\tilde{Y}}_i|}}$ {Accumulate IoU} 8: end for 9: IoU_avg←${\displaystyle \frac{\mathrm{IoU}\_\mathrm{sum}}{n}}$ {Calculate average IoU} 10: if IoU_avg ≥ θ  then 11:    Y is accepted as a high-confidence pseudo-label 12: else 13:    Reject Y as a low-confidence pseudo-label 14: end if

The introduction of various perturbations, based on clustering assumptions and consistency principles, can be considered a data enhancement technique that can improve the model’s generalization ability. The model’s generalization ability and accuracy can be improved by screening pseudo-labels in this manner and incorporating them into the training set. The IoU value, representing the intersection over the union between the perturbed and unperturbed outputs, indicates the representativeness of the corresponding sample’s pseudo-label. A higher IoU value signifies stronger representativeness and higher pseudo-label quality. High-quality samples can improve the model’s accuracy and accelerate the convergence speed during training.

2.5. Loss Function

In supervised learning for semantic segmentation tasks, Cross-Entropy and Dice loss functions are frequently employed as loss functions. Nonetheless, using Cross-Entropy or Dice loss functions in isolation can sometimes lead to suboptimal outcomes. Consequently, this section presents a combined approach, using both Cross-Entropy and Dice loss functions as the supervised loss function, as shown in (6):

$$L_{Sup}=\lambda L_{CE}+\mu L_{Dice}$$

(6)

where $L_{Sup}$ denotes the supervised loss function, $L_{CE}$ represents the Cross-Entropy loss function, and $L_{Dice}$ signifies the Dice loss function. $\lambda$ and $\mu$ are the weighting coefficients. In the semi-supervised learning loss function, only the Cross-Entropy loss is utilized. The loss function for the consistency phase is expressed as (7):

$$L_{Con}=L_{Sup}+L_{UnSup}$$

(7)

where $L_{Con}$ denotes the consistency learning loss function, $L_{Sup}$ represents the supervised loss function, and $L_{UnSup}$ represents the unsupervised loss function.

For self-training, A combination of the Cross-Entropy loss function and the Dice loss function continues to be used. The total loss function of our method is defined as (8):

$$L_{Total}=L_{Con}+L_{Self}$$

(8)

where $L_{Total}$ denotes the total loss function, $L_{Con}$ denotes the loss function in the consistency learning phase, $L_{Self}$ denotes the loss function in the self-training phase.

3. Experiments

3.1. Dataset

The dataset consists of 1000 instances of the 11th MICAPS format at the 500 hPa level, spanning the years 2019 to 2022. Experts in meteorology label the samples; 10% of the data are allocated to a test set, while the remaining data are split into a training set and a validation set at an 8:1 ratio.

3.2. Experimental Setup

All experiments were conducted on a computer with an Intel Core i9 10900K CPU, NVIDIA RTX A5000 graphics, and 64 GB of RAM. Development and training were conducted using PyTorch 1.13.0, Python 3.10.8, CUDA 11.7, and PyCharm 2021.3.3. During the consistency learning phase, the optimizer was Adam, with a learning rate of 0.01. The batch size was 24 for labeled data and 12 for unlabeled data. The initial consistency and boost were set to 0.1 and 200, respectively. In the self-training phase, the Adam optimizer was utilized with a batch size of 24 and a learning rate of 0.01.

3.3. Ablation Study

We have analyzed the proposed method using various combinations of consistency learning and self-training to assess the effectiveness of the semi-supervised method integrating consistency learning and self-training. The results of the ablation experiments are presented in

Table 1. Results of ablation studies using different combinations.

Methods	IoU (%)	Dice (%)	Pre (%)
U-Net	40.81	53.57	58.34
Swin-UNet	50.24	64.12	61.52
ST	56.71	69.42	63.36
CPS	58.15	74.11	67.73
Ours	68.85	79.00	78.90

. In these experiments, CPS denotes the Cross Pseudo Supervised method, ST denotes the self-training method, and a 30% labeled dataset is utilized. We have selected the following evaluation metrics to gauge the model’s performance: Intersection over Union (IoU), Dice coefficient (Dice), and Precision (Pre). These metrics measure the level of overlap between the prediction results and the actual annotations, as well as the similarity and accuracy of the predictions, respectively.

As indicated in Table 1, when no semi-supervised learning method is employed, U-Net and Swin-Unet yield relatively poor performance, with corresponding IoU values of 40.81% and 50.24%. This suggests that models based solely on supervised learning can only achieve satisfactory results when the dataset is extensively labeled. The IoU, Dice, and Pre values of ST, CPS, and our proposed method surpass those of U-Net and Swin-Unet, indicating that incorporating consistency learning and self-training enhances the models’ performance. Notably, our paper’s method yields the highest results across all three metrics, demonstrating that a combination of consistency learning and self-training leads to superior performance. In Figure 3 and Figure 4, the visualization results of the ablation experiments illustrate that the subjective quality of the findings of the various methods can generally identify the jet stream axes, while the subjective quality of our paper’s method better visualizes the jet stream axes. The results of the ablation experiments confirm that our proposed jet stream identification method achieves the best performance in identifying a dataset containing only 30% labeling.

In

Table 2. Impact of whether to screen for high-confidence pseudo-labels.

Screening Pseudo-Labels	IoU (%)	Dice (%)	Pre (%)
	60.26	72.45	69.05
✓	68.85	79.00	78.90
Improvement	8.59	6.55	9.85

, the comparison of experiment results with and without high-quality pseudo-label screening reveals that the three metrics significantly improved after screening. This suggests that the screening of high-confidence pseudo-labels, as proposed in this paper, enhances the performance of the semi-supervised method.

3.4. Comparison with State-of-the-Art Methods

To illustrate the effectiveness of the presented model, it is compared with segmentation baselines, i.e., U-Net [11], UNet++ [12], DeepLabv3+ [10], SegNet [13], and Swin-UNet [14].

Table 3. Performance comparison results of different segmentation models.

Methods	IoU (%)	Iou Deviation with Ours (%)	Dice (%)	Dice Deviation with Ours (%)	Pre (%)	Pre Deviation with Ours (%)
U-Net	53.81	15.04	65.25	13.75	63.26	15.64
UNet++	60.30	8.55	72.03	6.97	70.37	8.53
DeepLabv3+	60.44	8.41	73.46	5.54	71.19	7.71
SegNet	63.26	5.59	76.18	2.82	73.73	5.17
Swin-UNet	66.54	2.31	77.48	1.52	76.91	1.99
Ours	68.85	0.00	79.00	0.00	78.90	0.00

presents a performance comparison of these models, highlighting the highest score for each evaluation metric in bold.

To showcase the effectiveness of the proposed approach, we conducted performance comparison experiments on the jet stream axes dataset using four commonly used semi-supervised learning methods. These methods included Mean Teacher (MT) [22], Uncertainty Aware Mean Teacher (UAMT) [23], Cross Pseudo Supervision (CPS) [20], and Deep Co-Training (DCT) [24]. The performance of different semi-supervised segmentation methods for labeled data percentages of 5%, 10%, 20%, and 30% is presented in

Table 4. Performance comparison results of different semi-supervised methods.

Proportion of Labeled Data	Methods	IoU (%)	Dice (%)	Pre (%)
5%	MT	49.50	64.40	55.12
	UAMT	53.09	67.46	61.75
	DCT	47.78	62.74	51.99
	CPS	51.64	65.62	58.69
	Ours	55.23	66.81	65.34
10%	MT	49.95	64.11	57.82
	UAMT	54.69	69.13	61.72
	DCT	50.68	65.77	56.36
	CPS	54.54	68.90	60.90
	Ours	60.68	74.06	68.53
20%	MT	52.79	68.32	59.16
	UAMT	55.14	70.48	63.81
	DCT	51.29	65.11	57.72
	CPS	55.12	71.23	62.81
	Ours	63.52	77.43	74.46
30%	MT	53.96	68.03	60.71
	UAMT	55.52	71.72	66.41
	DCT	56.71	71.39	66.16
	CPS	58.15	74.11	67.73
	Ours	68.85	79.00	78.90

. The results demonstrate that at a labeled data proportion of 5%, the method in this paper achieves the highest scores in the IoU and Pre metrics compared to other models. Our method is more sensitive to data distribution. In the case of very small data volumes, the model may be more susceptible to noise or data distribution bias, which can lead to performance degradation. The UAMT method better maintains the overall consistency of the segmented region at low data volumes. Furthermore, when the proportion of labeled data exceeds 10%, our method consistently outperforms the methods in all three evaluation metrics. The findings indicate that our method demonstrates superior identification performance on the jet stream axes dataset compared to the four semi-supervised learning methods.

4. Conclusions

Addressing the challenges of inadequate generalization capabilities and the shortcomings in traditional methodologies for the automatic extraction of jet stream axes via wind field analysis, this study introduces a novel approach. The proposed semi-supervised jet stream axis identification technique synergizes consistency learning and self-training methodologies to overcome the issues of merger and bifurcation inherent in jet stream analysis. Predominantly, the semi-supervised deep learning model is structured around two phases: first, the phase of consistency learning, followed by the self-training phase. A notable concern this study addresses is the low-confidence pseudo-labels, which potentially destabilize the training framework of the semi-supervised learning model. A feature perturbation-based screening mechanism is meticulously designed to sift through and screen high-confidence pseudo-labels during semi-supervised learning. This strategy facilitates the enhancement of the dataset for the self-training phase with these high-fidelity pseudo-labels mined during the consistency learning phase. By judicious adoption of limited labeled data complemented by a voluminous quantum of unlabeled data, the semi-supervised learning technique markedly diminishes the reliance on extensively labeled datasets. This approach, therefore, substantially augments the model’s generalization capacity. Empirical evaluations underscore the superiority of the methodology proposed in this manuscript, evidencing an identification precision exceeding 78% on the test set, surpassing conventional semantic segmentation methodologies. Notwithstanding, this study acknowledges the limitations inherent in its identification approach, mainly manifest in regions characterized by subdued jet stream features or complex altitudinal fields, where the deviation from manually annotated results becomes perceptible. Future iterations of this research may benefit from integrating neural networks boasting enhanced feature extraction capabilities, thereby refining jet stream axis identification and extraction proficiency.