TC best-track data were collected from the Japan Meteorological Agency (JMA) RSMC Tokyo-Typhoon Centre and China National Meteorological Center (NMC). The JMA dataset contained 27,611 sample points of TCs from 1977 to 2023, including variables of the time, typhoon category, LON (longitude), LAT (latitude), Pres (pressure), V_max (maximum wind speed), and R₃₀ (the maximum and minimum radius of 30-knot winds). The NMC dataset contained the variables of time, TC category, LON, LAT, Pres, V_max , and mean R₃₀ from 2015 to 2023. The Multiplatform Tropical Cyclone Surface Winds Analysis (MTCSWA) dataset provided by NOAA (National Oceanic and Atmospheric Administration) was also used. The MTCSWA dataset contained 4,383 sample points in the Northwest Pacific region from 2022 to 2023, including time, LON, LAT, Pres, V_max , R₃₄ (the radius corresponding to the four quadrants of 34 knot winds), and R_max .

Super typhoon Mangkhut (WP262018), Saola (WP092023), and severe typhoon Hato (WP152017), were selected in this study, as they directly influenced the Pearl River Estuary ( Figure 1 ). Figure 2 shows the statistics of TC intensity and R₃₀ of the JMA dataset. Figure 1 shows the model domain and tidal gauge station. Hong Kong and Da Wan Shan were used for Hato and Mangkhut, and Hong Kong and She Kou were used for Saola.

Three represented wind fields, including (1) parametric, (2) reanalysis (3) and numerical wind fields, were implemented to evaluate the storm tide simulation, and to provide data for LSTM training. In the following sections, the three wind fields are described in detail.

The root mean square error (RMSE), correlation coefficient (CC), peak error, and trough error were used to evaluate the simulation performance (Equations 3–5). Smaller values of RMSE and peak/trough error and higher values of r indicated better agreement. These metrics are defined as follows:

where X_mod is the model value, X_obs is the observation value, and f is Earth’s rotation parameter. The superscript of “t_obs” represents the observation time.

The Advanced Circulation (ADCIRC) model was applied to establish a storm tide forecasting model. Our model domain covered the Pearl River Estuary, the Guangdong coast, and the adjacent shallow continental shelf ( Figure 1 ). The model consisted of 272,632 triangular grids and 155,219 nodes, and was locally refined around the estuary. The water depths were merged by the General Bathymetric Chart of the Ocean (GEBCO) 2023 dataset and nautical charts in the Pearl River Estuary. The open boundary conditions including eight major tidal components (K₁, O₁, P₁, S₁, M₂, N₂, K₂, and S₂) were extracted from the TPXO9 tidal dataset (Egbert and Erofeeva, 2002). The tidal simulations were validated against the observations at the Hong Kong, Da Wan Shan and She Kou gauge station ( Figure 3 ). The RMSEs at the three stations were 4.2, 3.9, and 8.68 cm, respectively, and all CCs were greater than 0.99. The good tidal results obtained serve as a strong foundation for further storm tide simulating.

Big-data-driven statistics and machine learning have been applied to forecast storm tides in recent years (Ramos-Valle et al., 2021; Lockwood et al., 2022; Tian et al., 2024). LSTM is a special neural network that addresses gradient explosion and vanishing problems in conventional RNNs (Gers et al., 2000; Pascanu et al., 2013). Unlike typical feedforward neural networks, LSTM particularly suits time-series prediction. LSTM contains four units: memory cell state C_t , input gate i_t , forget gate f_t , and output gate o_t (Equation 6), which are defined as:

where x t , h t , C t ˜ , W , and σ represent the input data, hidden state, temporary cell state, weight matrices, and sigmoid activation function, respectively.

The Random Forest (RF) uses decision trees as estimators based on a bagging algorithm. By combining multiple decision trees, the dataset features are randomly selected or returned with replacements for training (Brownlee, 2020). Here, the dataset was divided into training and testing parts. The training data were split into n samples. Then a bag and an out-of-bag set were constructed for each sample. A decision tree was constructed for each sample, and the predictions were recorded. All generated decision trees were combined to obtain the final RF model.

R_max is an important parameter when constructing the Holland wind field. In addition to Wil, we incorporated a large wind radius into the R_max calculation. Considering the TC as a rotating background, the circulation system of the boundary layer air flowed radially from the outer side to the centre (Riehl, 1954; Wing et al., 2016). In this scenario, the equation for absolute angular momentum (M) is as follows (Equations 7, 8):

R₃₄ is related to M₃₄ and M_max . R_max can be further determined with known V_max and LAT. Thus, R₃₄ links to R_max . A nonlinear regression proposed by Chavas and Knaff (2022), known as Fcha, was used to solve the C15 model (Equation 9). Here, we applied MTCSWA data to determine the appropriate coefficients in the Northwest Pacific region. An additional V_max weighting coefficient µ was introduced to improve the calculation of R_max during strong TCs (Equation 10). Equation 11 (referred to as F34 hereafter) is the modified formula.

Compared with MTCSWA data, CC is 0.77 and RMSE is 17.7 km ( Figure 4 ). The calculation fits well with the dataset practically in the high-wind-speed range.

Some Asian agencies provide a 30-knot wind radius (15.5 m/s, JMA), or a category-7 wind radius (13.9–17.1 m/s, CMA) equivalent to the 30-knot wind radius. Therefore, R₃₀ needs to be converted to R₃₄ based on certain functional relationships. Here, we implemented the Rankine vortex scheme to determine the proportional relationship between R₃₀ and R₃₄ (Equations 12–14). The scheme consists of a solid rotating region with constant vorticity or angular momentum at its centre surrounded by zero-vorticity circulation. The angular momentum loss due to surface friction during typhoons can be assumed to be less than one (Riehl, 1954). The values were set to 0.5 after the typhoon landfall and 0.8 in the open sea.

To evaluate the performance on storm tide simulation, we conducted simulations based on new F34 and previous Fcha data. During Hato and Mangkhut, F34 yielded better results for peak errors ( Figure 5 ). The maximum error eliminated was up to 20 cm, which indicates that the modified R_max calculation can conduct better simulations.

In the previous sections, we described four ways to construct a wind field during strong typhoons. Parametric wind fields based on F34 and Wil, numerical wind fields using WRF, and reanalysis wind fields from ERA5 were then implemented into ADCIRC to carry out the storm tide simulations. ERA5 and WRF wind data were provided at hourly intervals. To avoid specific time errors caused by different minute–averaging methods among JMA, C15, and other dataset, Wil and F34 data, which have a longer time interval, were provided every 6 h. To adjust tidal elevation, the simulations ran for three days from a cold start. Subsequently, the storm tides during super typhoon Mangkhut (15–18 September 2018) and severe typhoon Hato (22–25 August 2017) were simulated based on well-adjusted tide data.

Figure 6 shows the simulated results and Table 2 shows the performance metrics. During super typhoon Mangkhut, the CCs between F34 and the observation both exceeded 0.94. F34 also shows the smallest peak error (1.7 cm at Hong Kong and -3.46 cm at Da Wan Shan) and trough error (13.31 cm at Hong Kong and 5.9 cm at Da Wan Shan). Conversely, the simulation based on WRF wind shows a higher water level than the observation, with peak errors of -22.6 and -25.7 cm at the two stations, respectively. The simulation based on Wil wind resulted in a lower water level, with peak errors reaching 27.7 and 14.15 cm at the two stations, respectively. Additionally, both WRF and Wil showed poor performance during the receding period, with much higher trough errors ( Table 2 ).

During the severe typhoon Hato period, the performances of F34 and Wil were similar. Both accurately simulated the water level surge and recession closely matching the observations. In contrast, WRF simulated relatively larger peaks and trough errors ( Table 2 ). Additionally, the simulation based on ERA5 showed poor performance for both TCs, indicating that it is not suitable for storm tide forecasting during strong TCs.

According to the metrics, F34 effectively reproduced the storm tides during the two TC events. It not only outperformed other wind fields (WRF and ERA5), but it also reduced the simulation error compared to the commonly used Wil model. Although the results for Hato showed good agreement with the observations, the simulated results for F34 and Wil were almost identical.

Figure 7 shows spatial distributions of peak and trough water levels. The water level at Hong Kong changed approximately 2 h faster than that at Da Wan Shan during Mangkhut. The time of the extreme water level at Hong Kong was used as time reference. The peak water level order is WRF > F34 ≈ Obs > Wil, and the trough water level order is WRF< Wil< F34 ≈ Obs. This further proves that F34 yields a more reasonable simulation. Therefore, the introduction of large wind radius to calculate R_max in strong TCs is necessary to simulate storm tides using parametric wind fields.

Due to the better constraint on R_max calculation provided by the C15 model, the Holland wind field using F34 exhibited the highest performance. We calculated R_max for TCs at 6-h intervals from 1977 to 2023 in the Northwest Pacific region using the F34 formula. These calculated data were then used to train an LSTM network and forecast R_max for the next 6, 12, 24, 36, and 48 h separately ( Figure 8 ). The training data span from 1977 to 2014, comprising 22,655 samples. The validation data covered the period from 2015 to 2021 with 4,127 samples. The testing data included 903 samples from 2022 to 2023.

The specific settings of our LSTM model were as follows:

The input layer included six parameters: LAT, LON, Pres, V_max , averaged R₃₀ , and R_max . The outputs were R_max for the next 6, 12, 24, 36, and 48 h. The hidden layer contained 128 neurons. The number of epochs was set to 200, the activation function was ‘Relu’, the initial learning rate was 0.005, the dropout value was 0.1, and the training algorithm was the ‘Adam’ optimisation. Each network was trained 10 times. The output of the LSTM model was compared with testing data ( Figure 9 ). The CCs were 0.994, 0.913, 0.740, 0.577, and 0.434, respectively. The RMSEs were 3.64, 10.02, 16.17, 19.68, and 21.75 km, respectively. These results indicate that the neural network can accurately capture the patterns of R_max and forecast its future values.

To further test the applicability of our neural network, we conducted a forecast experiment using JMA data during super typhoon Saola. The forecasted R_max was compared with F34, Wil, and the ATCF Tropical Cyclone Database ( Figure 10 ). At 6 and 12 h, the forecasted R_max matched F34 very well, with only slight differences observed at 24 and 36 h. However, the trend and magnitude at 24 and 36 h fit well with ATCF. Although the bias increased at 48 h, the values remained within a reasonable range.

We then simulated the storm tide during Saola based on the forecasted R_max . Figure 11 and Table 3 show the simulation results. Compared with the observations, F34 still shows the best performance, followed by the 6, 12, 24, 36, and 48-h forecasts, with Wil showing the worst performance. For the 6-h forecast, the CCs were 0.96 and 0.94 at the two stations, respectively, while the RMSEs were 18.1 and 22.4 cm, respectively. The peak errors were 14.4 and 26.4 cm, respectively. As the forecasting hours increased, the errors grew. For the 48-h forecast, the CCs were 0.87 and 0.86, the RMSEs were 32.05 and 39.80 cm, and the peak errors were 29.39 and 41.59 cm. This result not only confirms the improvement of using the F34 method in simulating storm tide during strong TCs, but also demonstrates that constraining the neural network with the C15 model for prediction is feasible.