Calibration of Typhoon Track Forecasts Based on Deep Learning Methods

Abstract

An accurate forecast of typhoon tracks is crucial for disaster warning and mitigation. However, existing numerical weather prediction models, such as the Weather Research and Forecasting (WRF) model, still exhibit significant errors in track forecasts. This study aims to improve forecast accuracy by correcting WRF-forecasted tracks using deep learning models, including Bidirectional Long Short-Term Memory (BiLSTM) + Convolutional Long Short-Term Memory (ConvLSTM) + Wide and Deep Learning (WDL), BiLSTM + Convolutional Gated Recurrent Unit (ConvGRU) + WDL, and BiLSTM + ConvLSTM + Extreme Deep Factorization Machine (xDeepFM), with a comparison to the Kalman Filter. The results demonstrate that the BiLSTM + ConvLSTM + WDL model reduces the 72 h track prediction error (TPE) from 255.18 km to 159.23 km, representing a 37.6% improvement over the original WRF model, and exhibits significant advantages across all evaluation metrics, particularly in key indicators such as Bias², Mean Squared Error (MSE), and Sequence. The decomposition of MSE further validates the importance of the BiLSTM, ConvLSTM, WDL, and Temporal Normalization (TN) layers in enhancing the model’s spatio-temporal feature-capturing ability.

1. Introduction

The northwestern Pacific, a highly active region for tropical cyclones, including typhoons, presents significant challenges for accurate track prediction. This predominantly tropical area is influenced by the East Asian Monsoon and the Western North Pacific Monsoon, which drive seasonal variability in typhoon activity, with most storms forming between June and October. The southwest monsoon brings hot, humid summers, while the northeast monsoon results in cooler, drier winters. Warm sea surface temperatures [1] fuel typhoon development, while prevailing wind patterns dictate their movement and eventual dissipation.

Several atmospheric mechanisms further complicate typhoon dynamics in this region. The Western Pacific Subtropical High (WPSH) often steers typhoons westward and northward, particularly as it shifts northward during the summer. The Intertropical Convergence Zone (ITCZ) enhances convection and cyclogenesis, while the Madden–Julian Oscillation (MJO) [2] modulates typhoon activity on intraseasonal timescales by influencing convection and the likelihood of formation.

Typhoons, as highly destructive natural disasters, cause significant economic losses and casualties worldwide each year [3]. Accurate prediction of typhoon tracks is crucial for mitigating disaster impacts and enhancing emergency response efficiency. Numerical Weather Prediction (NWP) models, such as the WRF model, have become primary tools for typhoon track forecasting. However, due to the high complexity of atmospheric systems and sensitivity to initial conditions [4], traditional NWP models still exhibit certain limitations in track prediction, especially under rapidly changing meteorological conditions.

In the field of typhoon track prediction, traditional methods remain significant. The Climatology and Persistence (CLIPER) model, serving as a benchmark approach, simulates the two-dimensional characteristics of typhoons by combining historical climatological data and persistence information [5]. Although its prediction accuracy is limited, the CLIPER model provides a simple yet effective reference in the absence of more complex numerical models. Additionally, the Kalman Filter [6] technique, known for its state estimation capabilities in dynamic systems, is frequently employed to correct the prediction errors of NWP models, thereby enhancing typhoon track forecast accuracy [7].

With the rise of machine learning, numerous data-driven approaches have been introduced to typhoon track prediction. Support Vector Machine (SVM), commonly used for classification and regression, has been applied to various meteorological forecasting tasks by effectively fitting nonlinear data through optimal hyperplane search [8]. Ensemble learning methods based on decision trees, such as Extreme Gradient Boosting (XGBoost) [9] and Light Gradient Boosting Machine (LightGBM) [10], have demonstrated strong performance in handling high-dimensional, large-scale data, excelling in both prediction accuracy and computational efficiency. The application of these machine learning methods in typhoon track prediction has expanded the range of predictive models and approaches, offering new possibilities for improving forecast accuracy and reliability.

Meanwhile, deep learning models, particularly Convolutional Neural Network (CNN) [11,12,13,14,15], Recurrent Neural Network (RNN) [16], and their variants such as Long Short-Term Memory (LSTM) networks [17] and ConvLSTM networks, have shown significant advantages in processing complex spatiotemporal data [18]. These models, by automatically learning intricate patterns from large-scale data, are capable of capturing the spatiotemporal evolution characteristics of typhoon tracks, thereby further enhancing prediction accuracy and model robustness [19].

Despite the considerable potential demonstrated by deep learning methods in typhoon track prediction, several unresolved challenges remain. Firstly, the reliance of deep learning models on large datasets means that their performance may be constrained by the quality and quantity of the available data. Secondly, effectively integrating deep learning models with traditional NWP models remains a critical challenge. Although some progress has been made in combining these approaches, fully leveraging the physical foundations of NWP models alongside the nonlinear fitting capabilities of deep learning models is an area that has not yet been thoroughly explored.

This study aims to enhance the accuracy of the WRF model in forecasting and correcting typhoon tracks. Specifically, by constructing a dataset based on the CLIPER method and a three-dimensional construction technique, this research compares the effectiveness of traditional methods, machine learning approaches [20], and deep learning techniques [21] in track correction. The study particularly focuses on the role of BiLSTM [22] and TN [23] in track correction, and it analyzes the performance of different network architectures, including WDL [24], Neural Factorization Machine (NFM) [25], and xDeepFM [26]. All these network architectures incorporate ConvLSTM modules to capture the spatiotemporal evolution characteristics of typhoon tracks. The primary objective of this study is to evaluate the performance of these different network structures in track correction and to identify the optimal approach.

First, the WRF model is used to forecast pressure and wind fields, from which typhoon tracks are extracted. These tracks are then used to generate high-quality datasets through the CLIPER method and three-dimensional construction techniques. Subsequently, traditional methods, machine learning approaches, and deep learning techniques are employed to correct the WRF-forecasted tracks to match the actual tracks. The study places special emphasis on the critical role of BiLSTM and TN in the correction process, as well as the performance of different network architectures incorporating ConvLSTM modules (including WDL, NFM, and xDeepFM). Additionally, to investigate the sources of error and improve model interpretability, this research adopts the error decomposition method proposed by Hodson et al. [27], decomposing the MSE [28] into Bias², distribution, and sequence components. Subsequently, error diagnosis and analysis are conducted for each correction scheme, providing insights for further model optimization.

The contributions of this study are as follows:

• A systematic comparison of traditional methods, machine learning approaches, and deep learning techniques in WRF track correction is conducted, clarifying the strengths and weaknesses of each method.
• The study emphasizes the importance of BiLSTM and TN in track correction and analyzes the performance of different deep learning frameworks after the integration of ConvLSTM modules.
• This research delves into the performance of WDL, NFM, and xDeepFM in typhoon track correction, significantly enhancing the ability to process complex meteorological data and improving the accuracy and efficiency of predictions. These optimized network architectures demonstrate the immense potential of deep learning techniques in improving typhoon track prediction accuracy.
• By introducing the error decomposition method, error diagnosis and analysis are performed for each correction scheme, enhancing model interpretability and providing valuable insights for further optimization.

2. Data

2.1. Best-Track Data

The Best-Track data used in this study are sourced from the China Meteorological Administration (CMA) [29,30]. This dataset has recorded the tracks and intensity information of tropical cyclones in the Western North Pacific (WNP) basin since 1949. The CMA dataset provides updates on typhoon center locations and intensity every six hours and serves as a crucial foundational data source for typhoon track prediction research.

2.2. Reanalysis Data

This study utilizes two reanalysis datasets: ERA-Interim and NCEP FNL, each applied at different stages.

The ERA-Interim dataset, provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), serves as a crucial data source for constructing the three-dimensional structure of typhoons. This dataset has been continuously recording 14 reanalysis variables of the global atmosphere since 1979, with data available four times daily (00:00, 06:00, 12:00, and 18:00) across 37 pressure levels. In this study, the geopotential height data with a 1° × 1° grid resolution is used to construct the three-dimensional structure of typhoons. Geopotential height refers to the gravitational potential energy per unit mass relative to mean sea level.

The NCEP FNL dataset is an operational global analysis dataset provided by the National Centers for Environmental Prediction (NCEP) in the U.S., primarily used for forecasting typhoon tracks with the WRF model. This dataset covers the globe (from 0° E to 359° E, and from 90° N to 90° S) with a grid resolution of 1° × 1°, including 26 standard vertical levels ranging from 1000 millibars to 10 millibars. The NCEP FNL data include various atmospheric parameters such as temperature, surface winds, upper-level winds, vertical wind speed and velocity, and potential temperature.

3. Methods

3.1. Numerical Model Forecast

In this study, the WRF (version 4.2.1) [31] model was utilized to forecast the tracks of tropical cyclones [32], providing part of the input data for the deep learning models. Given the substantial computational resources and extended integration time required for WRF forecasts, typhoons from June to November in the Western North Pacific (WNP) from 2000 to 2022 were selected [33]. Only typhoons reaching or exceeding tropical storm strength (≥34 kts) and lasting at least three days are included in the forecasts. A total of 452 typhoon cases (Figure 1). The tracks were forecast with integration times of 24 h, 48 h, and 72 h. The forecasts were conducted with a horizontal resolution of 27 km, and the computational domain was defined by a rectangular area with an additional 100 km added to both the length and width to ensure complete coverage.

Initial and boundary conditions were provided by NCEP-FNL data, with a resolution of 1° × 1°. The WRF parameterization settings were based on previous studies of typhoons in the WNP [35], including the WRF Single-Moment 6-class microphysics scheme (Hong and Lim 2006) [36], the Rapid Radiative Transfer Model (RRTM) longwave radiation scheme (Mlawer et al., 1997) [37], the Dudhia shortwave radiation scheme (Dudhia 1989) [38], the Kain–Fritsch cumulus parameterization scheme (Kain 2004) [39], the Yonsei University planetary boundary layer scheme (Hong et al., 2006) [40], and the thermal diffusion scheme (Dudhia 1996) [41]. Typhoon tracks were recorded every six hours, with the typhoon center determined by the minimum sea-level pressure [42].

3.2. Dataset and Preprocessing Method

The dataset used in this study comprises both two-dimensional data (

Table 1. Characteristics of the two-dimensional dataset, using the WRF model with a 72-h integration time as an example.

ID	Feature Name	Description
1–5	${\mathrm{LONG}}_0,{\mathrm{LONG}}_6,{\mathrm{LONG}}_{12},{\mathrm{LONG}}_{18},{\mathrm{LONG}}_{24}$	Longitude in the last 24 h
6–10	${\mathrm{LONG}}_0,{\mathrm{LONG}}_6,{\mathrm{LONG}}_{12},{\mathrm{LONG}}_{18},{\mathrm{LONG}}_{24}$	Longitude in the last 24 h
11–15	${\mathrm{WND}}_0,{\mathrm{WND}}_6,{\mathrm{WND}}_{12},{\mathrm{WND}}_{18},{\mathrm{WND}}_{24}$	Wind speed in the last 24 h
16	$\mathrm{MONTH}$	Current month
17–20	$\begin{array}{l}{\mathrm{LAT}}_0-{\mathrm{LAT}}_6,{\mathrm{LAT}}_6-{\mathrm{LAT}}_{12},\\ {\mathrm{LAT}}_{12}-{\mathrm{LAT}}_{18},{\mathrm{LAT}}_{18}-{\mathrm{LAT}}_{24}\end{array}$	1st-order difference in historical latitude
25–28	$\begin{array}{l}{\mathrm{WND}}_0-{\mathrm{WND}}_6,{\mathrm{WND}}_6-{\mathrm{WND}}_{12},\\ {\mathrm{WND}}_{12}-{\mathrm{WND}}_{18},{\mathrm{WND}}_{18}-{\mathrm{WND}}_{24}\end{array}$	1st-order difference in historical wind speed
29	${\displaystyle \sum _{i=0}^3{({\mathrm{LAT}}_{6i}-{\mathrm{LAT}}_{6(i+1)})}^2}$	Sum of squares of 1st-order latitude difference
30	${\displaystyle \sum _{i=0}^3{({\mathrm{LONG}}_{6i}-{\mathrm{LONG}}_{6(i+1)})}^2}$	Sum of squares of 1st-order longitude difference
31	$\sqrt{{\displaystyle \sum _{i=0}^3{({\mathrm{LAT}}_{6i}-{\mathrm{LAT}}_{6(i+1)})}^2}}$	Square root of feature 29
32	$\sqrt{{\displaystyle \sum _{i=0}^3{({\mathrm{LONG}}_{6i}-{\mathrm{LONG}}_{6(i+1)})}^2}}$	Square root of feature 30
33–34	$\sqrt{{\mathrm{LAT}}_0},\sqrt{{\mathrm{LONG}}_0}$	Square root of current latitude and longitude
35–38	$\begin{array}{l}\mathrm{Acc}({\mathrm{LOC}}_6,{\mathrm{LOC}}_0),\mathrm{Acc}({\mathrm{LOC}}_{12},{\mathrm{LOC}}_6),\\ \mathrm{Acc}({\mathrm{LOC}}_{18},{\mathrm{LOC}}_{12}),\mathrm{Acc}({\mathrm{LOC}}_{24},{\mathrm{LOC}}_{18})\end{array}$	Physical acceleration of historical location
39–42	$\begin{array}{l}\mathrm{Angle}({\mathrm{LOC}}_0,0^{°} \mathrm{N}),\mathrm{Angle}({\mathrm{LOC}}_6,0^{°} \mathrm{N}),\\ \mathrm{Angle}({\mathrm{LOC}}_{12},0^{°} \mathrm{N}),\mathrm{Angle}({\mathrm{LOC}}_{18},0^{°} \mathrm{N})\end{array}$	Zonal angle
43–46	$\begin{array}{l}\mathrm{Angle}({\mathrm{LOC}}_0,0^{°} \mathrm{E}),\mathrm{Angle}({\mathrm{LOC}}_6,0^{°} \mathrm{E}),\\ \mathrm{Angle}({\mathrm{LOC}}_{12},0^{°} \mathrm{E}),\mathrm{Angle}({\mathrm{LOC}}_{18},0^{°} \mathrm{E})\end{array}$	Meridional angle
47–50	$\begin{array}{l}\mathrm{Angle}({\mathrm{LOC}}_0,{\mathrm{LOC}}_6),\mathrm{Angle}({\mathrm{LOC}}_6,{\mathrm{LOC}}_{12}),\\ \mathrm{Angle}({\mathrm{LOC}}_{12},{\mathrm{LOC}}_{18}),\mathrm{Angle}({\mathrm{LOC}}_{18},{\mathrm{LOC}}_{24})\end{array}$	Angle of historical location
51–53	$\begin{array}{l}\mathrm{Angle}({\mathrm{PATH}}_{0,6},{\mathrm{PATH}}_{6,12}),\\ \mathrm{Angle}({\mathrm{PATH}}_{6,12},{\mathrm{PATH}}_{12,18})\end{array}$	Angle of historical path
54–56	${\mathrm{LAT}\left(\mathrm{WRF}\right)}_{24},{\mathrm{LAT}\left(\mathrm{WRF}\right)}_{48},{\mathrm{LAT}\left(\mathrm{WRF}\right)}_{72}$	TC center latitude forecasted by WRF (Integration time of 72 h) after 24 h, 48 h, 72 h
57–59	${\mathrm{LON}\left(\mathrm{WRF}\right)}_{24},{\mathrm{LON}\left(\mathrm{WRF}\right)}_{48},{\mathrm{LON}\left(\mathrm{WRF}\right)}_{72}$	TC center longitude forecasted by WRF (Integration time of 72 h) after 24 h, 48 h, 72 h

) and three-dimensional data (Figure 2). The two-dimensional data extend the dataset used in a previous study [34], incorporating additional latitude and longitude information for tropical cyclone centers forecasted by the WRF model at 24, 48, and 72 h. These data help correct the forecasted tracks, aligning them with the actual tracks in the best track dataset, thereby enhancing the accuracy of forecasts.

The three-dimensional data capture the atmospheric environment. It is generated for each time instance in the two-dimensional dataset, with geopotential height [43] being the primary feature. These data are instrumental in capturing the three-dimensional evolution of tropical cyclones, further enhancing the model’s capability for track correction.

Typhoons from 2000–2017 were used for training, and those from 2018–2022 as the test set, with the final 10% of the training set designated for validation. All data underwent preprocessing before being input into the model. The two-dimensional data were normalized, while the three-dimensional data were standardized to ensure consistency and stability during model training. This dataset supported the training and validation of the deep learning model, ultimately enhancing prediction accuracy.

Figure 3 illustrates the methodological workflow of this study, covering data acquisition, preprocessing, model training, and evaluation.

3.3. Temporal Normalization and BiLSTM

TN is a preprocessing technique designed to standardize data across different time periods, eliminating inconsistencies. Time series data often contain nonlinear trends, seasonal fluctuations, and noise, which can negatively impact model performance. By applying TN, the input data achieve improved generalization capability. TN helps the model predict future trends by balancing information across different periods.

BiLSTM improves accuracy by processing time series bidirectionally. Traditional LSTM networks process data in a forward direction, whereas BiLSTM uses two parallel LSTM layers to capture both forward and backward information. This allows BiLSTM to strengthen the model’s understanding of sequences. In tasks like typhoon track prediction, BiLSTM boosts accuracy by integrating information from both the past and future. BiLSTM is also more robust in handling long-term dependencies and complex patterns.

In summary, TN ensures input data consistency, while BiLSTM optimizes predictions through bidirectional processing. This combination offers significant advantages in time series modeling.

3.4. Network Architecture

3.4.1. WDL

The WDL model combines a wide linear model with a deep neural network. The wide component captures interactions among high-dimensional sparse features, while the deep component learns complex nonlinear interactions. By jointly training both, the WDL model generalizes to unseen feature combinations while retaining high memorization capacity.

In this study, the WDL architecture (Figure 4) consists of feature extraction via a linear layer, fused with the deep component’s output. The final latitude and longitude predictions are made through a fully connected layer. The deep component includes ConvLSTM layers and a residual channel attention mechanism, processed with TimeDistributed layers to capture spatiotemporal characteristics of typhoon tracks.

Batch normalization and dropout are used to prevent overfitting. The output layer predicts typhoon track latitude and longitude using linear regression. By training both components, the WDL model efficiently captures historical path patterns and applies broader feature combinations, leading to accurate typhoon track prediction.

3.4.2. NFM

The NFM model combines the strengths of Factorization Machine (FM) and Deep Neural Network (DNN) to capture both low-order and high-order feature interactions. The FM component models second-order interactions, while the DNN component extracts higher-order, more complex interactions through neural network layers.

In this study, the NFM architecture (Figure 5) divides input features into Wide Features and Deep Features. Deep Features are processed through ConvLSTM layers with channel attention and pooling operations, then mapped into an embedding space and processed by a Bi-Interaction Pooling layer, which explicitly models second-order interactions. Wide Features are processed through a linear layer and fused with the Bi-Interaction Pooled Deep Features. The final output, predicting typhoon track latitude and longitude, is generated through a linear layer.

NFM’s Bi-Interaction Pooling layer captures nonlinear interactions without additional feature engineering, while deep learning layers enhance high-order interaction capture. Compared to traditional models, NFM is flexible in feature extraction and efficient with sparse data, providing a reliable solution for modeling complex spatiotemporal features in typhoon track prediction.

3.4.3. xDeepFM

In this study, the xDeepFM model was employed to capture complex typhoon track features. xDeepFM integrates both explicit and implicit high-order feature interactions. The explicit component includes the Compressed Interaction Network (CIN), which captures multi-level feature relationships through layer-by-layer interactions. CIN models high-order interactions with increasing network depth.

As shown in Figure 6, the CIN component processes embedded input features through compressed interaction layers. The CIN output is fused with other interaction outputs, and final predictions are generated through a fully connected layer. xDeepFM combines Factorization Machines (FM) with high-order interaction learning via CIN, enhancing the model’s expressiveness and prediction accuracy.

This architecture effectively captures spatiotemporal interactions, supporting accurate typhoon track prediction.

3.5. Performance Evaluation

3.5.1. Evaluation Metrics

To comprehensively evaluate the performance of the model in typhoon track correction, this study employs various statistical metrics that help quantify the predictive accuracy of the model and reveal its performance under different conditions. The primary evaluation metrics include Mean Bias Error (MBE), Root Mean Square Error (RMSE), correlation coefficient $R^2$, and Track Position Error (TPE).

MBE is used to measure the systematic bias between the model’s predictions and actual observations. The formula for calculating MBE is as follows:

$$\mathrm{MBE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n(y_i-{\widehat{y}}_i)},$$

(1)

where $y_i$ represents the ith predicted value, ${\widehat{y}}_i$ represents the ith observed value, and n is the number of samples. MBE can reveal whether there is an overall bias in the model, making it one of the key indicators for evaluating the quality of model predictions.

Root Mean Square Error (RMSE) is another commonly used accuracy metric, which assesses the average difference between predicted and actual values. The formula for RMSE is:

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}},$$

(2)

A smaller RMSE indicates that the model’s predictions are more accurate and better reflect the actual data.

The correlation coefficient is used to evaluate the linear correlation between the model’s predictions and actual observations. Its formula is:

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}{{\displaystyle \sum _{i=1}^n{(y_i-\overline{y})}^2}}},$$

(3)

where $\overline{y}$ is the mean of the predicted values. The closer the $R^2$ value is to 1, the stronger the model’s explanatory power and the higher the agreement between the predicted and actual values.

TPE, calculated following the method outlined in [44], is a metric specifically designed to assess the error in typhoon track predictions, representing the geographical deviation between the predicted and actual tracks. It serves as a crucial metric for evaluating typhoon track prediction performance, effectively reflecting the model’s overall error at different time steps and is one of the key evaluation metrics in this study. In addition to TPE, the combined use of these evaluation metrics provides a multidimensional framework for assessing the model’s performance, ensuring the reliability and accuracy of the prediction results.

Based on the literature [6,45,46,47,48,49,50,51,52], other commonly used evaluation metrics for assessing differences between predicted and actual paths after model processing include Mean Absolute Error (MAE), RMSE, MBE, Mean Squared Error (MSE), R², Mean Distance Error (MDE), Mean Spherical Distance (MSD), and Spherical Distance (SD). These metrics are widely applied due to their effectiveness in measuring spatial errors and are complementary to TPE, which specifically assesses spatial discrepancies between predicted and actual paths. Generally, the smaller the error, the better the model’s performance, which is the primary reason for selecting these metrics.

Among various evaluation methods, this study specifically chose MBE, RMSE, R², and TPE based on their frequent use in the literature and their clarity. MBE and RMSE reflect the model’s bias and overall error magnitude, while R² measures goodness-of-fit, indicating the linear relationship between predicted and actual values. TPE, as a spatial error metric, directly reflects the accuracy of the predicted path. By combining these metrics, this study comprehensively evaluates the model’s performance from multiple perspectives.

Additionally, to address the limitations of relying on a single evaluation method, this study employs MSE decomposition. By breaking down MSE into Bias², Distribution, and Sequence components, the study provides a detailed analysis of different sources of error, offering a more thorough model evaluation. This approach not only enhances the depth of evaluation but also strengthens the understanding of model performance, ensuring the reliability and academic value of the findings. Thus, the combined use of traditional and decomposed metrics offers a comprehensive framework to robustly assess model performance across different scenarios.

3.5.2. Error Decomposition

Conventional metrics like Mean Squared Error (MSE) quantify overall error but may not explain specific aspects of model performance. To enhance interpretability, this study follows Hodson et al.’s approach and decomposes MSE into a Bias Term [53], Distribution Term, and Sequence Term. This method enables detailed error diagnosis and guides future optimization.

MSE is calculated using the following formula:

$$\mathrm{MSE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{(f_i-o_i)}^2},$$

(4)

where $f_i$ represents the forecasted value and $o_i$ represents the observed value on the ith time point. According to the decomposition method proposed by Geman et al. [27], MSE can be decomposed into a bias term and a variance term:

$$\mathrm{MSE}(e)=\left(E(e^2)-E{(e)}^2\right)+E{(e)}^2=\mathrm{Var}(e)+\mathrm{Bias}{(e)}^2,$$

(5)

where $e$ represents the model’s prediction error, $\mathrm{Var}(e)$ is the variance component of the error, and $\mathrm{Bias}{(e)}^2$ is the bias component. The variance term evaluates the model’s ability to reproduce the variability of the observed values, while the bias term assesses the model’s ability to reproduce the mean characteristics of the observations.

Next, the variance term is further decomposed into a sequence term and a distribution term. To calculate these error components, the forecasted and observed values need to be sorted, and the new error is calculated:

$$w=\mathrm{sort}(f)-\mathrm{sort}(o),$$

(6)

where $\mathrm{sort}(f)$ denotes the sorted forecasted values and $\mathrm{sort}(o)$ denotes the sorted observed values, with $w$ being the error after sorting. Consequently, the new MSE can be expressed as:

$$\mathrm{MSE}(w)=\mathrm{Bias}{(w)}^2+\mathrm{Var}(w),$$

(7)

where $\mathrm{Var}(w)$ represents the difference in data distribution, i.e., the distribution term. According to this formula, the distribution term can be expressed as:

$$\mathrm{Var}(w)=\mathrm{Distribution}(e),$$

(8)

The sequence term is then expressed as:

$$\mathrm{Sequence}(e)=\mathrm{MSE}(e)-\mathrm{MSE}(w),$$

(9)

Thus, the final decomposition of MSE can be expressed as:

$$\mathrm{MSE}(e)=\mathrm{Bias}{(e)}^2+\mathrm{Sequence}(e)+\mathrm{Distribution}(e),$$

(10)

In this formula, $\mathrm{Bias}{(e)}^2$ quantifies the model’s ability to reproduce the mean characteristics of the observations, $\mathrm{Sequence}(e)$ represents the errors induced by temporal sequence variations, and $\mathrm{Distribution}(e)$ reflects the errors caused by differences in the distribution between forecasted and observed values. By using this decomposition method, a more comprehensive understanding of error sources can be obtained, allowing for more targeted model optimization.

4. Result

4.1. Analysis of WRF Model Track Forecast Results

We used the WRF model to forecast typhoon tracks at different time scales and evaluated its performance using a series of metrics. Figure 7 compares the forecasted latitude and longitude results from the WRF model at 24-h, 48-h, and 72-h time scales with the actual tracks. To comprehensively analyze the model’s performance, we employed metrics such as TPE, RMSE, and MBE.

Figure 7 illustrates the bar charts of track error and RMSE at each time scale. As shown, both TPE and RMSE increase as the forecast time extends. This trend indicates that the error in WRF-forecasted typhoon tracks gradually increases over time, with the maximum error at the 72-h mark.

Specifically, the TPE was 223.57 km at 72 h, 183.46 km at 48 h, and 104.57 km at 24 h. This indicates that the WRF model performs better on shorter time scales (24 h) than longer time scales (48 and 72 h). Similarly, the RMSE for both latitude and longitude increased at 72 h, with RMSE values of 2.0882° for latitude and a notably high 3.2427° for longitude. At 48 and 24 h, RMSE values decreased. For the 24-h forecast, the RMSE values for latitude and longitude were 1.4783° and 1.8422°, respectively, indicating more accurate predictions over shorter periods.

Notably, at all time scales, the RMSE for longitude consistently exceeded that for latitude, likely due to more pronounced lateral shifts in typhoon tracks. The longitudinal path is influenced by more complex weather systems and topography, increasing prediction difficulty and leading to higher errors. Optimizing longitudinal direction forecast errors could be key to improving overall accuracy.

Figure 8 illustrates year-by-year TPE variations from 2000 to 2022. TPE volatility increases at longer time scales (72 h), consistent with earlier analysis. In years like 2007 and 2015, the 72-h TPE was significantly higher, indicating particularly pronounced errors at longer time scales.

Finally, Figure 9 compares WRF-forecasted latitude and longitude with actual tracks at different time scales. In the 24-h forecast, the R² value was 0.9884, indicating high model fit and minimal error over short time scales. At 72 h, the R² value dropped to 0.9328 (latitude) and 0.9641 (longitude), with corresponding increases in RMSE and MBE, indicating larger errors at longer time scales.

In summary, the WRF model performs best in forecasting typhoon tracks over short time scales (24 h), with errors increasing significantly as the time scale extends. Thus, greater emphasis should be placed on leveraging the model’s short-term prediction capabilities, while optimizing long-term forecasts to enhance overall accuracy.

4.2. Analysis of Deep Learning-Based Track Correction Results

We conducted a comparative analysis of the performance of different deep learning models and traditional methods in typhoon track correction, focusing on their advantages over directly using WRF model forecast results.

Table 2. Comparison of TPE (km) Across Different Models at 72 h, 48 h, and 24 h on the 2018–2022 Test Set.

Method	72 h	48 h	24 h
WRF	255.18	236.41	94.80
BiLSTM	207.67	150.01	112.86
BiLSTM (TN = False)	428.72	156.49	126.42
Linear	305.13	276.10	145.79
Linear (TN = False)	328.61	423.81	305.58
GRU	244.15	212.43	182.26
GRU (TN = False)	362.08	347.98	230.93
Transformer	394.74	331.51	186.14
Transformer (TN = False)	425.48	398.28	239.78

Bold values represent the best result.

shows that the TPE values for the WRF model are 255.18 km, 236.41 km, and 94.80 km at 72 h, 48 h, and 24 h, respectively. These values differ somewhat from the TPE obtained by directly using the WRF model forecasts, mainly due to the reprocessing and filtering of data during dataset construction, which affects the observed errors.

From Table 2, it is evident that the BiLSTM model performs better across all time scales, especially in track correction at 72 h, 48 h, and 24 h, with TPE values of 207.67 km, 150.01 km, and 112.86 km, respectively. This is mainly due to BiLSTM’s ability to better capture temporal dependencies in typhoon tracks, maintaining high accuracy even over longer time scales. Additionally, the performance of the BiLSTM model improves when the TN layer is enabled. Without the TN layer, the TPE values for the BiLSTM model are 428.72 km, 156.49 km, and 120.10 km at 72 h, 48 h, and 24 h, respectively—significantly higher than what the TN layer enabled. This indicates that the TN layer plays a crucial role in mitigating seasonal variations and noise, significantly enhancing the model’s generalization capability.

In

Table 3. Comparison of TPE (km) Across Different Models at 72 h, 48 h, and 24 h Integration Times on the 2018–2022 Test Set.

Method	72 h	48 h	24 h
WRF	255.18	236.41	94.80
BiLSTM + ConvGRU + WDL	186.87	174.59	81.02
BiLSTM + ConvGRU + NFM	198.22	186.38	88.45
BiLSTM + ConvGRU + xDeepFM	905.10	700.69	691.30
BiLSTM + ConvLSTM + WDL	159.23	148.25	75.31
BiLSTM + ConvLSTM + NFM	1143.48	1004.39	911.28
BiLSTM + ConvLSTM + xDeepFM	822.03	693.49	648.87
SVM	667.09	331.50	323.73
XGBoost	258.86	252.44	243.87
LightGBM	226.75	212.09	204.81
Kalman Filter	603.09	568.95	543.38

Bold values represent the best result.

, the BiLSTM + ConvLSTM + WDL model shows higher accuracy in typhoon track correction. Specifically, its TPE values are 159.23 km, 148.25 km, and 75.31 km at 72 h, 48 h, and 24 h, respectively, outperforming the standalone BiLSTM model. This suggests that the inclusion of ConvLSTM and WDL enhances the model’s ability to process three-dimensional input data and significantly improves track correction accuracy.

Further analysis reveals that the BiLSTM + ConvLSTM + WDL model outperforms other deep learning methods, machine learning methods, and the traditional Kalman Filter across all time scales. The BiLSTM + ConvGRU + NFM model ranks just below the BiLSTM + ConvGRU + WDL and BiLSTM + ConvLSTM + WDL models, showing some advantages in feature interaction and track correction. However, the BiLSTM + ConvLSTM + NFM model performs worse, especially at longer time scales (72 h and 48 h), with significantly higher TPE values. This suggests that NFM works better with ConvGRU but underperforms when paired with ConvLSTM.

The BiLSTM + ConvLSTM + WDL model consistently yields lower TPE values across all time scales compared to the BiLSTM + ConvLSTM + NFM and BiLSTM + ConvLSTM + xDeepFM models, validating WDL’s superiority in feature combination and nonlinear processing. WDL’s efficient handling of wide and deep feature combinations gives it an edge, whereas the complex feature interactions in NFM and xDeepFM do not yield significant performance improvements.

Table 4. Performance Comparison of Models in Longitude Direction Based on MBE (°), RMSE (°), and R² Across Multiple Time Scales on the 2018–2022 Test Set.

Evaluation Metrics	MBE			RMSE			R2
Integration Times	72 h	48 h	24 h	72 h	48 h	24 h	72 h	48 h	24 h
WRF	−0.8580	−0.8234	−0.2791	6.5923	6.1243	2.2350	0.8850	0.8969	0.9857
BiLSTM	−0.1757	−0.2150	−0.0641	3.5686	2.6131	2.2450	0.9663	0.9813	0.9856
BiLSTM (BN = False)	0.4024	−0.1068	−0.4794	6.0829	2.6533	1.8189	0.9021	0.9807	0.9905
Linear	−0.9187	0.1725	0.1134	3.7212	3.5113	1.6634	0.9633	0.9662	0.9921
Linear (BN = False)	−0.1158	−0.2076	−0.3326	4.8270	4.8597	3.5960	0.9383	0.9353	0.9631
GRU	−0.2162	−0.3655	−0.3548	3.3737	2.9878	2.0765	0.9699	0.9755	0.9877
GRU (BN = False)	0.2917	−0.2531	0.0416	4.8137	4.3212	2.8944	0.9387	0.9488	0.9761
Transformer	−0.9189	−0.9964	−0.3940	5.0485	4.6480	2.8076	0.9326	0.9408	0.9775
Transformer (BN = False)	−0.5368	0.0071	−0.4009	5.4069	4.9531	3.5501	0.9227	0.9328	0.9641
BiLSTM + ConvGRU + WDL	−0.3510	−0.2597	0.0643	2.9687	2.9477	1.1559	0.9766	0.9762	0.9961
BiLSTM + ConvGRU + NFM	0.0387	0.0028	−0.1931	3.3989	3.1412	1.6646	0.9694	0.9729	0.9921
BiLSTM + ConvGRU + xDeepFM	−6.4661	2.0634	1.3869	11.4131	9.0480	8.9276	0.6555	0.7758	0.7731
BiLSTM + ConvLSTM + WDL	−0.1654	−0.2661	0.0454	2.7000	2.7549	1.1039	0.9807	0.9792	0.9965
BiLSTM + ConvLSTM + NFM	−10.2760	−2.5333	−5.4385	12.8171	10.2671	9.7558	0.5656	0.7113	0.7290
BiLSTM + ConvLSTM + xDeepFM	4.9756	1.8617	1.9114	10.9262	8.6066	7.6774	0.6843	0.7971	0.8322
SVM	−0.1267	−0.3982	−0.3485	7.4554	4.3049	4.3001	0.8571	0.9494	0.9472
XGBoost	−0.5818	−0.4998	−0.3843	4.0085	4.0167	3.9538	0.9587	0.9560	0.9554
LightGBM	−0.4862	−0.4172	−0.3555	3.7029	3.5201	3.5342	0.9647	0.9662	0.9643
Kalman Filter	−0.2304	−0.1806	−0.1616	8.2721	7.7675	7.3244	0.8241	0.8355	0.8470

Bold values represent the best result.

and

Table 5. Performance Comparison of Models in Latitude Direction Based on MBE (°), RMSE (°), and R² Across Multiple Time Scales on the 2018–2022 Test Set.

Evaluation Metrics	MBE			RMSE			R2
Integration Times	72 h	48 h	24 h	72 h	48 h	24 h	72 h	48 h	24 h
WRF	−0.5869	−0.0547	0.0204	2.1927	2.3586	1.4154	0.9571	0.9483	0.9804
BiLSTM	−0.4274	−0.1121	−0.1045	1.8803	0.9956	1.0337	0.9684	0.9908	0.9895
BiLSTM (BN = False)	−0.8436	−0.0706	−0.0435	3.4579	1.0808	0.9270	0.8933	0.9891	0.9916
Linear	−0.4207	−0.2008	−0.2043	2.0460	1.7598	1.3299	0.9626	0.9713	0.9827
Linear (BN = False)	−0.6643	−0.4310	−0.0942	2.4424	2.6394	1.7988	0.9468	0.9355	0.9684
GRU	−0.6968	−0.3578	−0.4574	1.9796	1.4512	1.5308	0.9650	0.9805	0.9771
GRU (BN = False)	−0.6137	−0.8096	−0.5025	1.9777	2.4024	1.4817	0.9651	0.9466	0.9786
Transformer	−1.3834	−0.4780	−0.3452	3.3038	2.6558	1.7801	0.9026	0.9347	0.9691
Transformer (BN = False)	−0.9524	0.0587	−0.2639	3.1170	3.3044	1.7611	0.9133	0.8989	0.9698
BiLSTM + ConvGRU + WDL	−0.4735	−0.0644	−0.1287	1.4486	1.2587	0.9061	0.9812	0.9853	0.9920
BiLSTM + ConvGRU + NFM	−0.2782	−0.1518	−0.1182	1.5519	1.3800	1.0189	0.9785	0.9823	0.9898
BiLSTM + ConvGRU + xDeepFM	−1.1432	1.3622	0.4167	4.2574	2.9565	3.4487	0.8383	0.9191	0.8841
BiLSTM + ConvLSTM + WDL	−0.3333	−0.1077	−0.0585	1.2574	1.0809	0.8662	0.9859	0.9891	0.9926
BiLSTM + ConvLSTM + NFM	−2.2929	−3.0105	0.3350	4.5378	6.9031	4.8951	0.8164	0.5591	0.7666
BiLSTM + ConvLSTM + xDeepFM	1.9433	0.6772	0.3962	3.9412	3.0528	2.9718	0.8615	0.9137	0.9140
SVM	−1.3585	−0.5819	−0.5307	4.9184	2.8527	2.8442	0.7914	0.9248	0.9213
XGBoost	−0.7504	−0.6587	−0.5567	2.8311	2.6730	2.5929	0.9309	0.9340	0.9346
LightGBM	−0.6070	−0.5169	−0.4121	2.6081	2.3594	2.3057	0.9413	0.9485	0.9483
Kalman Filter	−0.0386	−0.0301	−0.0155	4.5448	4.3618	4.2370	0.8219	0.8242	0.8255

Bold values represent the best result.

summarize the prediction performance of different models in the longitude and latitude directions, evaluated using MBE, RMSE, and R² across three time scales (72, 48, and 24 h). Overall, the BiLSTM + ConvLSTM + WDL model excels, particularly in R² and RMSE. For example, in the 24-h longitude prediction, it achieves an R² of 0.9965, while in the 72-h latitude prediction, it shows an RMSE of 1.2574°, demonstrating high accuracy.

As the prediction time shortens (from 72 to 24 h), most models show improved accuracy, with decreasing RMSE and increasing R², indicating smaller errors for shorter-term forecasts. Notably, the evaluation metrics for longitude are generally higher than for latitude, suggesting that longitude predictions may be less stable. Overall, the BiLSTM + ConvLSTM + WDL model excels in both stability and accuracy across all time scales.

In conclusion, the BiLSTM + ConvLSTM + WDL model performs best in typhoon track correction, particularly with three-dimensional input data and long-term track predictions. WDL outperforms NFM and xDeepFM in combining wide and deep features, suggesting that a simple yet efficient feature combination strategy is more crucial in track correction. This analysis provides valuable insights for optimizing typhoon track prediction models.

4.3. Evaluations of Error Decomposition

Based on the overall performance illustrated in Figure 10, we observe the trends in MSE, Bias², Distribution, and Sequence across different time scales (72 h, 48 h, 24 h).

For MSE, both the line charts and scatter plots (Figure 10 and Figure 11) show a clear upward trend in MSE values as the forecast time increases from 24 to 72 h, with higher MSE values in the longitudinal direction compared to the latitudinal direction. This indicates that models tend to incur greater errors when forecasting longitude tracks. Specifically, the LSTM + ConvLSTM + WDL model (B) consistently shows the lowest MSE values across all forecast times, especially at the 72-h mark, where its errors are significantly lower than those of other models. In contrast, the Kalman Filter (E) and BiLSTM + ConvLSTM + xDeepFM (D) models exhibit higher MSE values across all forecast times, with this trend being particularly pronounced at 72 h, indicating larger errors in long-term forecasts. In the MSE-Latitude and MSE-Longitude scatter plots (Figure 11), the BiLSTM + ConvLSTM + WDL model shows relatively low MSE in both latitude and longitude, especially in the 24-h prediction, where regions such as the southeast coast and southern China exhibit smaller MSE values, indicated by green areas in the plots. In comparison, the BiLSTM + ConvGRU + WDL model’s MSE performance is slightly inferior but still surpasses that of the BiLSTM + ConvLSTM + xDeepFM model. Notably, the BiLSTM + ConvLSTM + xDeepFM model exhibits significantly higher MSE values in longitude, especially along the eastern coast of China and the Taiwan region, where large red areas indicate substantial prediction errors. This could be due to the complex topography and diverse track changes in the longitudinal direction, leading to greater errors as the model processes these variations.

Regarding Bias², both the line charts and scatter plots (Figure 10 and Figure 12) indicate that Bias² values are generally higher in the longitudinal direction than in the latitudinal direction, reflecting greater systematic errors in longitude tracks. The BiLSTM + ConvGRU + WDL model (A) consistently shows Bias² values close to zero across all forecast times, especially in the 24-h latitude forecast, demonstrating stable performance with well-controlled bias. In contrast, the Kalman Filter (E) and BiLSTM + ConvLSTM + xDeepFM (D) models exhibit peak Bias² values in the 72-h forecast, indicating significant systematic bias in long-term forecasts. In the Bias²-Latitude and Bias²-Longitude scatter plots (Figure 12), the BiLSTM + ConvLSTM + WDL model shows balanced performance in both latitude and longitude, with consistently low Bias² values across all time scales. In contrast, the Bias² values of the BiLSTM + ConvGRU + WDL model are slightly higher but still reflect relatively low systematic bias. However, the Bias² values of the BiLSTM + ConvLSTM + xDeepFM model are noticeably higher in longitude, especially in the 72-h prediction, where extensive red areas indicate larger errors in longitude.

For Distribution, the line charts and scatter plots (Figure 10 and Figure 13) show that the WRF model (C) consistently exhibits the lowest Distribution values, especially in the 72-h forecast, showcasing excellent data distribution consistency. This suggests that the WRF model can accurately replicate the distribution characteristics of the observed data when forecasting latitude paths, with the predicted path closely aligning with the actual observations. Similarly, the WRF model performs well in the longitudinal direction, maintaining relatively low Distribution values despite slight fluctuations across different forecast times. In contrast, the Kalman Filter (E) and BiLSTM + ConvLSTM + xDeepFM (D) models show significantly higher Distribution values, particularly in the 72-h forecast and in the longitudinal direction. This indicates that these models struggle to maintain consistent data distribution between predictions and observations, leading to a poor match between the forecasted and actual paths, especially in long-term forecasts.

For Sequence, both the line charts and scatter plots (Figure 10 and Figure 14) reflect that Sequence values increase with forecast time, with a more pronounced increase in the longitudinal direction, suggesting poorer temporal consistency when forecasting longitude paths. The LSTM + ConvGRU + WDL model (A) consistently demonstrates the lowest Sequence values across all forecast times, particularly in the 24-h latitude forecast, indicating optimal temporal sequence consistency. In contrast, the Sequence values for the Kalman Filter (E) and BiLSTM + ConvLSTM + xDeepFM (D) models peak in the 72-h longitude forecast, indicating significant shortcomings in temporal sequence consistency for long-term path forecasts. In the Sequence-Latitude and Sequence-Longitude scatter plots (Figure 14), the BiLSTM + ConvLSTM + WDL model shows low temporal sequence errors in both latitude and longitude, particularly in the 24-h prediction, where regions like the southeast coast and southern China exhibit the lowest Sequence errors. This suggests that the model maintains good temporal sequence consistency, with more noticeable correction effects. However, the BiLSTM + ConvLSTM + xDeepFM model exhibits significantly higher Sequence errors in longitude, especially in complex path areas like the South China Sea and Taiwan Strait.

Overall, the models exhibit commonalities and differences in error patterns across latitudinal and longitudinal directions. MSE, Bias², Sequence, and Distribution values are generally higher in the longitudinal direction, indicating that models are more prone to greater errors, systematic bias, poor data distribution consistency, and more pronounced lead or lag issues when forecasting longitude paths. Conversely, the models demonstrate more stable performance in the latitudinal direction, with smaller errors, closer data distribution to observations, and better temporal sequence consistency, especially in short-term forecasts. These differences highlight the need for future path forecast efforts to focus more on optimizing longitudinal processing to enhance overall forecast accuracy and improve model performance in long-term forecasts. Through the above comparative analysis, it is evident that the BiLSTM + ConvLSTM + WDL model outperforms the other models across various metrics, particularly excelling in key indicators such as Bias², MSE, and Sequence. This model demonstrates balanced performance in both longitude and latitude, providing stable predictions, especially along the southeast coast and southern regions of China. As forecast time decreases, all statistical metrics show a downward trend, further confirming the BiLSTM + ConvLSTM + WDL model’s superiority in short timescales, significantly enhancing overall forecast outcomes.

From Figure 15, it is evident that the BiLSTM + ConvLSTM + WDL model demonstrates a significant advantage over the BiLSTM + ConvGRU + WDL model in correcting WRF forecast results. The scatter plots show that the BiLSTM + ConvLSTM + WDL model achieves R² values of 0.9726 and 0.9836 for longitude and latitude, respectively, which are both higher than the BiLSTM + ConvGRU + WDL model’s R² values of 0.9242 and 0.9848. This indicates a stronger correlation between the forecast results and actual observation data for the BiLSTM + ConvLSTM + WDL model.

In terms of RMSE, the BiLSTM + ConvLSTM + WDL model records RMSE values of 0.6252° for longitude and 0.5748° for latitude, significantly lower than the BiLSTM + ConvGRU + WDL model’s values of 1.0412° and 0.5534°. This demonstrates that the BiLSTM + ConvLSTM + WDL model more effectively reduces errors when correcting WRF forecast paths, providing more accurate path corrections. Additionally, the MBE for the BiLSTM + ConvLSTM + WDL model is also lower in both longitude and latitude, further emphasizing its superiority in controlling systematic errors.

Figure 16 and Figure 17 further validate these conclusions. The BiLSTM + ConvLSTM + WDL model (green path) shows a higher degree of alignment with historical typhoon paths (black path), especially in complex and variable regions. In contrast, although the BiLSTM + ConvGRU + WDL model (blue path) also exhibits good correction effects, it shows larger deviations in certain segments, particularly in the second path diagram, where the BiLSTM + ConvGRU + WDL model’s predicted path significantly diverges from the historical path.

In summary, the BiLSTM + ConvLSTM + WDL model exhibits higher accuracy and stability when correcting WRF forecast paths, establishing itself as one of the most effective models for typhoon path correction. While the BiLSTM + ConvGRU + WDL model generally performs well, its effectiveness is somewhat lacking in complex paths. Overall, the BiLSTM + ConvLSTM + WDL model more accurately captures subtle changes in typhoon paths, significantly improving prediction accuracy and demonstrating superior performance in the field of typhoon path correction.

5. Discussion

This study systematically compares the performance of various deep learning models, machine learning methods, and traditional approaches in typhoon track correction, highlighting the strengths and weaknesses of the BiLSTM + ConvLSTM + WDL model, BiLSTM + ConvGRU + WDL model, BiLSTM + ConvLSTM + xDeepFM model, and the Kalman Filter. The experimental results demonstrate that the BiLSTM + ConvLSTM + WDL model excels across all evaluation metrics, especially in key indicators such as Bias², MSE, and Sequence. This model exhibits well-balanced performance in both longitude and latitude predictions, particularly in the southeastern coastal and southern regions of China, achieving higher predictive accuracy and stability. Moreover, the BiLSTM + ConvLSTM + WDL model effectively reduces systematic bias and distribution bias in track forecasts, significantly enhancing the accuracy of typhoon track corrections.

In this study, the BiLSTM plays a crucial role in capturing the spatiotemporal features of typhoon tracks. Its bidirectional structure enables the model to consider both past and future information simultaneously, thereby improving the accuracy of track forecasts. The ConvLSTM, by integrating convolutional operations with LSTM’s memory capabilities, better captures local spatial features of typhoon tracks, leading to significantly improved performance in complex track forecasts. The TN layer is essential in eliminating nonlinear trends and noise in time series data, ensuring consistent data processing across different time periods, thus enhancing the model’s generalization ability.

While effective in many cases, the BiLSTM + ConvGRU + WDL model shows some deficiencies in correcting complex tracks. The BiLSTM + ConvLSTM + xDeepFM model exhibits considerable bias in long-term track forecasts, particularly in the longitude direction, where it shows higher errors and distribution bias. Moreover, the Kalman Filter’s performance is markedly inferior to the deep learning models, especially in handling complex tracks.

In recent years, research on correcting tracks predicted by the WRF model has been limited. A notable study conducted by Kyoungmin Kim [54] et al. in 2023 employed machine learning methods for track correction in the Western North Pacific (WNP) region. The study used data from the typhoon active season between June and November from 2006 to 2018. In their 72-h forecast, the track prediction error (TPE) was reduced from 179.02 km to 171.25 km, an improvement of approximately 4.34%. However, their testing dataset included data only from 2016 to 2018, while the current study uses data from 2018 to 2022. These differences in datasets limit direct comparability, making their results a reference point rather than a direct comparison.

In addition to recent advancements, a related study by Chengfei He [6] et al. in 2015 used the Kalman filter to improve multi-model ensemble track forecasts over the WNP, reducing the TPE to 143.9 km in the 72-h forecast.

Recently, mainstream studies have leaned towards using deep learning methods for direct typhoon track prediction. For example, Jinkai Tan [52] et al. utilized the Gradient Boosting Decision Tree (GBDT) model in WNP tropical cyclone track forecasts, achieving errors of 138 km, 264 km, and 363.5 km for 24-h, 48-h, and 72-h forecasts, respectively. These values are significantly higher than the corrected TPEs obtained in this study, which are 75.31 km, 148.25 km, and 159.23 km after WRF forecast correction. Moreover, Pingping Wang [51] et al. used a 3D Convolutional Neural Network (3D CNN) to predict typhoon tracks in the WNP, achieving a TPE of 112.05 km for the 24-h forecast, which is also higher than the results obtained in this study.

Zili Liu [46] et al. used a Dual-Branched Spatio-Temporal Fusion Network for 24-h predictions in the WNP region, achieving a mean distance error (MDE) of 119.05 km. Similarly, TAO SONG [55] et al. developed a novel deep learning model based on a Bidirectional Gated Recurrent Unit (BiGRU) with an attention mechanism, achieving TPEs of 147.37 km, 164.82 km, and 171.19 km for 24-h, 48-h, and 72-h forecasts, respectively.

Overall, although some studies have explored typhoon track correction, the variability in datasets, methods, and models suggests that these results serve primarily as references. This study significantly reduces track error by leveraging the latest datasets and deep learning techniques for post-processing WRF outputs.

Although this study has achieved significant results in typhoon track correction in the Western North Pacific region, its applicability to other global regions remains unverified. The method’s effectiveness may be limited by differing climatic conditions, ocean dynamics, and atmospheric mechanisms in other regions. Furthermore, this study relies heavily on specific meteorological datasets, which may not fully represent conditions in other regions, potentially limiting the model’s generalization ability. Despite employing deep learning and machine learning methods for track correction, the performance of these methods may still be constrained by the quality and quantity of the input data, particularly when dealing with complex tracks.

6. Conclusions

This study underscores the significant superiority of the BiLSTM + ConvLSTM + WDL model in typhoon track correction and validates the critical role of BiLSTM, ConvLSTM, and the TN layer in enhancing the model’s ability to capture spatiotemporal features and improve track forecast accuracy. As the forecast time shortens, all statistical metrics show a decreasing trend, further confirming the effectiveness of the BiLSTM + ConvLSTM + WDL model in correcting WRF-forecasted tracks over short time scales.

In future research, we plan to validate the current methods across different regions by testing them on global or regional datasets to further assess the generalizability of our findings. Sensitivity analysis will also be a key focus; we intend to adjust the input data and examine the resulting outputs to evaluate the models’ stability and robustness, thereby optimizing their structure. Given the time-intensive nature of this task, it was not completed in the current study but will be prioritized in future research.

To enhance the accuracy of track predictions, we will explore more complex neural network architectures, particularly for long-term forecasts, to improve overall accuracy and stability. Different neural network architectures may be needed for specific geographical regions, as suggested by relevant literature [56]. Future studies could involve clustering paths into types and designing specialized networks for each type or developing distinct networks to correct longitude and latitude separately. In this study, the three-dimensional data primarily used geopotential height; however, future research could consider incorporating additional variables such as relative vorticity, temperature, and cloud cover into the datasets to construct more detailed three-dimensional models, further enhancing the accuracy and reliability of track forecasts.