1. Introduction
Tropical cyclones (TCs) can cause severe socioeconomic damage to coastal areas worldwide. According to the World Meteorological Organization, 1942 TCs have occurred over the past 50 years, killing 779 324 people and causing economic losses of over U.S. $1.4 trillion. The locations of TC lifetime maximum intensities (LMI) are continuing to migrate poleward, in line with the expansion of the tropical zones caused by global warming (Kossin et al. 2014; Knutson et al. 2019). Consequently, LMI locations are migrating toward coastlines by 30 km decade−1, particularly in the western North Pacific region (Wang and Toumi 2021). Some studies suggest that the overall TC intensity will increase, with slower weakening of landfalling TCs due to the increased atmospheric saturated water vapor in a warmer climate (Knutson et al. 2020; Li and Chakraborty 2020). The socioeconomic damage caused by TCs in coastal areas is only likely to increase in the future (Peduzzi et al. 2012; Mendelsohn et al. 2012), which suggests the importance of improving the abilities of communities to forecast the locations and the intensity of TCs.
While the ability to accurately predict the path of TCs has improved markedly over the past few decades (Elsberry 2014; Peng et al. 2017), predicting TC intensity remains a challenging problem (DeMaria et al. 2014; Huang et al. 2021; Jiang et al. 2022). For example, the National Hurricane Center (NHC) uses two different types of models (i.e., dynamical models and statistical–dynamical models) to forecast TC intensity changes over 24 h but has only managed to reduce the mean absolute error (MAE) by 11% from the 1990s to 2010s over the Atlantic region [9.8 and 8.5 kt (1 kt ≈ 0.51 m s−1) for the 1990s and 2010s, respectively]. By contrast, MAE for forecasting 24-h TC tracks was reduced by 53% (Cangialosi et al. 2020).
Similarly, in the western North Pacific, the China Meteorological Association (CMA), the Joint Typhoon Warning Center (JTWC), and Regional Specialized Meteorological Center (RSMC) Tokyo–Typhoon Center managed to improve their 24-h intensity forecasts to a significantly less extent than the tracking forecasts (i.e., improvement rates in MAE from 2005 to 2018 are 1.16% and 2.88% yr−1 for the intensity and track forecast, respectively) (Huang et al. 2021).
To some extent, the relative lack of success in accurately forecasting TC intensity can be attributed to the difficulties in predicting extreme intensity changes. Extreme intensity changes of TC can be categorized as rapid intensification (RI) and rapid weakening (RW). RI (RW) is commonly defined as an increase (decrease) in TC intensity of 30 kt or more within a 24-h period (Fudeyasu et al. 2018; Na et al. 2018; Trabing and Bell 2020; DeMaria et al. 2021). In this study, we follow these definitions, as do the RIs and RWs referred to hereafter. Trabing and Bell (2020) and DeMaria et al. (2021) showed that annually averaged forecast errors tended to be greater in years with more frequent RI occurrences. Similarly, Trabing and Bell (2020) revealed that the year-to-year variations in the number of RI and RW occurrences are significantly correlated with the overall TC intensity errors in the Atlantic and eastern Pacific regions. They showed that when RI and RW events were removed from the error calculations, the 24-h lead intensity forecast errors were reduced by 16% and 22% in the Atlantic and eastern Pacific regions, respectively. This implies that the difficulty in predicting extreme intensity changes contributes significantly to the total intensity forecast errors, even though they rarely (<10%) occur.
DeMaria et al. (2021) evaluated the performance of the NHC’s dynamical and statistical–dynamical forecast models for RI over the Atlantic and eastern Pacific. Between 2016 and 2020, the hit rates for RI of the models’ 24-h lead forecasts were 1%–21% in the Atlantic and 7%–31% in the eastern Pacific. In the western North Pacific, the hit rates of the RI occurrence for the CMA, JTWC, and RSMC-Tokyo’s 24-h lead forecasts were only 4%, 6%, and 4%, respectively between 2005 and 2018 (Huang et al. 2021). Given their severe impacts, successfully forecasting the extreme TC intensity changes, as well as the overall intensity changes, remains a high priority (Elsberry et al. 2007; Na et al. 2018; Trabing and Bell 2020).
TC intensification involves multiscale interactions between convective clouds within and outside the inner core area (i.e., inside the radius of maximum wind), TC-scale circulation, and the large-scale environmental conditions such as sea surface temperature (SST), moisture, and vertical wind shear (Chang and Wu 2017; Hendricks et al. 2010; Fudeyasu et al. 2018; Wu et al. 2015). Hong et al. (2000) and Shay et al. (2000) revealed that warm-core eddies within the inner core could contribute to TC development by reducing the SST cooling due to the upwelling. Kossin and Schubert (2001) showed that the development of eyewall mesovortices could induce RI when the vorticity of the parent vortex is initially sufficiently large. Zagrodnik and Jiang (2014) found that rapidly intensified TCs show more symmetric rainfall distribution in the inner core region compared with TCs that intensify slower. In addition, observational and numerical studies have shown that the presence of hot towers or convective bursts inside a storm can also facilitate RI (Reasor et al. 2009; Guimond et al. 2010; Rogers et al. 2013).
The extent to which the external environmental factors, which are commonly defined as domain averages centered at the TC core region (e.g., 10° × 10° box averages), control TC intensification is relatively well known. Although it is well known that TCs often intensify in environments with weaker vertical wind shear, higher sea surface/upper-ocean temperatures, stronger upper-level divergence, and high low- and midlevel relative humidity (RH) (Kaplan and DeMaria 2003; Hendricks et al. 2010; Rozoff and Kossin 2011; Kaplan et al. 2015; Fudeyasu et al. 2018), the relative contributions of these various environmental factors on TC intensity forecasts are not currently well quantified.
In addition to the environmental variables, the detailed horizontal structure of environmental variables is also known to affect TC intensification as well as the potential occurrence of an RI event. Shu and Wu (2009) showed that the intrusion of a dry Saharan air layer from the front quadrant (i.e., the front side in TC motion-based coordinate) of the TC tends to lead to intensifications. On the other hand, when dry air is present in the rear quadrants, the TC tends to be weakened. In addition, satellite observation found that azimuthal asymmetry of the environmental RH was more substantial during RI with relatively dry front and moist rear quadrants (Wu et al. 2012). Idealized simulations made with the Weather Research and Forecasting (WRF) Model confirmed these relationships (Ge et al. 2013; Wu et al. 2015).
The aforementioned studies show that both the domain-averaged environmental factors and their horizontal structure must be considered when making accurate TC intensity predictions. However, the horizontal structures of environmental variables are not accounted for in the inputs to the current statistical models for TC intensity prediction (DeMaria et al. 2005; DeMaria 2009; Knaff et al. 2018). For instance, the Statistical Hurricane Intensity Prediction Scheme (SHIPS), which has been used by the NHC for operational intensity guidance since 1991 (DeMaria and Kaplan 1994; DeMaria et al. 2005), uses only radial or annular averaged predictors such as initial maximum winds, 200-hPa divergence, 200-hPa temperature, and vertical shear, without considering the horizontal structure of environmental factors. Incorporating the horizontal structure of environmental variables may improve the performance of the statistical TC intensity prediction models.
Recently, the rapid advances and notable scalability of deep learning have prompted its application in the field of climate research; deep learning techniques have been successfully applied to weather forecasting (Bi et al. 2023), El Niño–Southern Oscillation prediction (Ham et al. 2019), and Madden–Julian oscillation prediction (Kim et al. 2021), to enhance the forecast accuracy. Additionally, deep learning has been instrumental in the identification of climate phenomena and the detection of signals associated with global warming (Son et al. 2022; Ham et al. 2023), thereby facilitating new discoveries in the climate science. Upon this trend, scientists have been actively attempting to improve TC intensity prediction performance by utilizing various deep learning techniques such as multilayer perceptron (MLP), long short-term memory (LSTM), convolutional neural network (CNN), or a generative adversarial network (GAN) (Chaudhuri et al. 2013; Pan et al. 2019; Wang et al. 2020; Xu et al. 2021). For example, Xu et al. (2021) proposed a TC intensity forecasting model based on the MLP with two hidden layers and 2048 nodes per layer. They optimized the number of hidden layers and nodes using the Bayesian optimization method and achieved a 24-h lead intensity prediction performance comparable with the state-of-the-art operational dynamical model from Hurricane Weather Research and Forecasting (HWFI) and the NHC’s official forecasts. Rüttgers et al. (2022) performed TC intensity forecasts using GAN with satellite images and reanalysis as input and demonstrated a comparable hit rate for each intensity category with those from operational agencies. Although the deep learning–based models have shown promising results, their performance has not surpassed that of the operational forecast products.
Jiang et al. (2022) developed a TC intensity forecasting model for the western North Pacific based on CNN using two- and three-dimensional convolution and showed a 6.5% improvement compared with the official guidance of the agencies in an indirect comparison (i.e., did not perform direct comparisons with the same sample). It is worth noting that Jiang et al. (2022) used various two- and three-dimensional best track information and atmospheric and oceanic variables as inputs to consider the spatial and temporal complexity of the TC, while other models did not use any specific dimensional data as predictors. This suggests that using multidimensional data as a predictor may improve prediction performance for TC intensity.
While the accuracy of overall TC intensity forecasts can be improved using deep learning–based models to a certain extent, their ability to correctly predict RI occurrence still remains at an abstract level (Pan et al. 2019; Xu et al. 2021). This is because the forecasted amplitude tends to be systematically underestimated, meaning that the current deep learning–based models are not sufficiently trained for the extreme intensity change events even though the overall forecast error is reduced. To overcome this weakness, a classification model is developed (Su et al. 2020; Bai et al. 2020). The classification model generates probabilities for each category. Even though the hit rate for RI of the machine learning–based model is improved to some extent, the classification model may have a problem by defining the relationship between predictors and predictands based on the artificial discretization. For example, with a classification of the RI with a threshold of 30 kt, an intensity change of 29 kt is classified as a different category despite their similarity. In this respect, regression models (i.e., this refers to models that produce scalar values as output) would be optimal for predicting both moderate and extreme intensity changes.
This study aims to develop a deep learning model to successfully predict both moderate and rapid intensification events for TCs in the western North Pacific region. To achieve this goal, we apply the concept of focal loss (Lin et al. 2017) in formulating a CNN-based, 24-h lead TC intensity change forecast model that considers samples for RI events as well as samples with moderate intensity changes. We set the prediction target lead time to 24 h, which allows a largest number of samples compared to other lead times. Note that, in the JTWC best track dataset, 4234 samples are available for 24-h forecasts, but only 3171, and 2249 samples are available for 48- and 72-h forecasts, respectively. Additionally, forecasts with lead times shorter than 24 h (e.g., 6 and 12 h) are too much dependent on its autocorrelation; therefore, it may not be adequate to examine the relationship between TC intensity change and the physical variables. We will show that our deep learning model, which will be referred to as the DeepTC model, outperforms the operational TC intensity forecasts from the CMA and other agencies. With the aid of a deep learning interpretation method, we will also identify the source of the predictive performance of the DeepTC model.
2. Data and methods
a. Best track data
The data for the location of the TC center in latitude and longitude (°) and maximum 1-min average sustained wind speed (kt) were obtained from the U.S. Navy’s JTWC best track archive. We used JTWC best track data with 6-h intervals when analyzing 274 TCs occurring in the western North Pacific region between 2000 and 2018. Note that a typhoon event is defined from the time that its intensity categorized it as a tropical storm (intensity ≥ 35 kt) to the time that it became a tropical depression (intensity < 35 kt). Intensity change is defined as the current intensity minus the intensity of the previous 24 h. We used latitude, longitude, intensity, and intensity change during the previous 24 h (IC0) as scalar types of predictors to consider developmental conditions of TCs and used 24-h lead intensity change [i.e., 24-h lead intensity minus current intensity (IC24)] as a predictand. The number of samples which span the entire lifetime of all the TCs is 4234, and the number of samples for RI is 366.
b. NCEP FNL data
The six-hourly SST (K), three-dimensional (3D) RH (%), zonal and meridional wind speed (m s−1), vertical velocity (Pa s−1), temperature (K), and geopotential height (gpm) data were derived from the NCEP Final Analysis (FNL) operational global data at a 1° × 1° resolution (National Centers for Environmental Prediction/National Weather Service/NOAA/U.S. Department of Commerce 2000). Given the potential utilization for real-time forecasts, the FNL dataset, which updates relatively quickly (i.e., a 6–10-h latency), is more suitable than other reanalysis datasets such as NCEP-1 (2–3-day latency) or ERA5 (5-day latency). We cropped all the analysis data with the size of 11° × 11° around the TC center location according to the best track data.
c. Operational forecasts
We used operational forecasts for TC intensity from the Korea Meteorological Administration (KMA) and CMA to compare the forecast performance of our DeepTC model. The KMA provided 2195 TC intensity forecasts from 2004 to 2018, while the CMA provided 3619 samples from 2002 to 2018. Both sets of forecasts covered the western North Pacific region. To compare the reference data from JTWC, which uses a 1-min average wind speed measured in knots, we standardized the TC intensity of the KMA and CMA. The KMA provides a 10-min average forecast in meters per second, and the CMA provides a 2-min average forecast in meters per second. We converted these values to a 1-min average value in knots using linear fitting and Huang et al.’s conversion table (Huang et al. 2021).
d. Input data preparation
Four of the seven zero-dimensional input datasets were obtained from the best track (longitude, latitude, intensity, and IC0), while the other three were obtained from analysis [SST, RH, and 850–200-hPa vertical wind shear (SHR)]. All one-, two-, and three-dimensional variables were obtained from the analysis dataset (Table 1). The one- and two-dimensional data comprised two variables (the vertical profile of wind speed and temperature) and one variable (SST), respectively. The three-dimensional data included six variables: zonal and meridional wind speed, vertical velocity, temperature, RH, and geopotential height.
Predictors used in the DeepTC model.
All two- and three-dimensional variables were centered at the TC center with a size of 11° × 11°. For the two-dimensional variable SST, with dimensions of 11° (longitudinal) × 11° (latitudinal), we conducted a horizontal standardization for each variable and each sample. This process involved subtracting the horizontal mean and dividing by the horizontal standard deviation. The three-dimensional variables (e.g., zonal and meridional wind and RH) have a size of 11 (longitudinal) × 11 (latitudinal) × 21 (vertical; from 1000 to 100 hPa). For the three-dimensional variables, we conducted a horizontal standardization for each variable, each vertical level, and each sample.
The reason why the values of two- or three-dimensional variables are separated into two components (domain-averaged value as a form of zero- or one-dimensional variables and its deviations as a form of two- or three-dimensional variables) is in order to easily separate the influence of the domain-averaged environmental conditions and its detailed horizontal structures on forecasting the TC intensity and RI. For example, through the model sensitivity test with no zero- or one-dimensional components, one would assess the impact of detailed structural information on TC intensity forecasts. In addition, this approach allows the DeepTC model to better detect detailed structural features of the TCs.
e. DeepTC model for 24-h TC intensity change forecast
Figure 1 shows the architecture of our DeepTC model, which is a CNN-based 24-h TC intensity change prediction model. The DeepTC consists of the 2D module, the 3D module, and three fully connected (FC) layers. The DeepTC takes various zero-, one-, two-, and three-dimensional predictors (Table 1) as input and produces a 24-h TC intensity change as an output. We applied three-dimensional (3D) convolution for 3D input variables to reduce the number of parameters, as 3D convolution reduces the overall number of parameters by sharing them between the horizontal and vertical axes.
The architecture of the deep learning–based IC24 prediction model (DeepTC). The red, blue, black, and green boxes denote the 3D module, 2D module, dense, and concatenate processes, respectively. The parentheses in the white boxes of the 3D and 2D modules denote an activation function and the number of convolutional filters in the convolutional layer. The parentheses in the black boxes denote an activation function and the number of neurons in the dense layer. The square brackets indicate the dimensions of each layer. Here, tanh and h_sig refer to tangent hyperbolic function and hard sigmoid function, respectively.
Citation: Artificial Intelligence for the Earth Systems 3, 2; 10.1175/AIES-D-23-0052.1
To extract the features of three-dimensional variables, which have a dimension of 11 (longitudinal) × 11 (latitudinal) × 21 (vertical) × 6 (variables), the 3D convolution module consists of three 3D convolutions, two average poolings, and a maximum pooling process, which generates a final feature map with dimensions of 6 × 6 × 2 × 8. Let 3D_Cf[i, j, k] denote an i × j × k 3D convolution, where i, j, k, and f denote the kernel size for x, y, and z dimensions and the number of 3D filters, respectively. The 3D module for the first, second, and third convolution processes has the architecture 3D_C64[3, 3, 3], 3D_C8[3, 3, 3], and 3D_C8[3, 3, 3], respectively. Note that the outputs of all convolution processes (i.e., both 2D and 3D convolution) were zero-padded to preserve their original dimensionality. The stride of all pooling processes is equal to their window size.
The 2D module is used for the two-dimensional variables, with dimensions of 11 (longitudinal) × 11 (latitudinal). The model consists of three 2D convolution processes and a maximum pooling process, which generates a feature map with dimensions of 6 × 6 × 2, where 2D_Cf[i, j] denotes an i × j 2D convolution with f number of 2D filters. The first, second, and third convolution processes have the architecture of 2D_C2[3, 3], 2D_C2[3, 3], and 2D_C2[3, 3], respectively.
Subsequently, the feature maps generated by the 3D and 2D modules are flattened and concatenated and then processed by dense, which generates the first FC layer with eight nodes. Meanwhile, the zero- and one-dimensional variables are concatenated and then directly connected to another FC layer with 64 nodes. The FC layers with eight nodes for two- and three-dimensional variables and 64 nodes for zero- and one-dimensional variables are concatenated and then processed by a second dense layer with 32 nodes. Finally, an FC layer is embedded by dense with a single neuron to generate output (i.e., 24-h TC intensity change). Thus, the DeepTC model consists of 34 874 weights and 191 biases (total: 35 065 parameters).
Note that the number of convolutional filters and nodes in the FC layer is determined using the Bayesian optimization method (Shahriari et al. 2016), as implemented in the KerasTuner Python package (O’Mally et al. 2019). The deep learning library TensorFlow (https://www.tensorflow.org/) was used to build the CNN-based 24-h TC intensity change prediction model. We generated seven ensemble members with different random initial weights, and the predicted 24-h TC intensity change value was ensemble-averaged to derive the final forecast results.
The type of activation functions, the learning rate, and the dropout rate are also determined using the Bayesian optimization method (Shahriari et al. 2016). The hard sigmoid was used for the second convolutional layer of the 3D module and the second dense layer, and the hyperbolic tangent was chosen as an activation function for the remaining layers. The learning rate and dropout rates were set to 0.01 and 0.1, respectively. Additionally, we employed the Adam optimization algorithm, one of the gradient descent techniques (Kingma and Ba 2015). To mitigate overfitting, we implemented early stopping by stopping the training process if the validation loss did not exhibit a decrease within the preceding 100 epochs. Subsequently, we selected the model version characterized by the lowest validation loss for our final analysis. Consequently, on average, across all cross-validation experiments and ensemble members, the training conducted approximately 436.4 epochs.
Similarly, by multiplying the absolute value of the label (y), samples with large amplitudes strongly affected the total loss (
To evaluate the forecast skill without any overfitting issues, we performed a leave-1-yr-out cross-validation experiment. In this study, we did not fix the random initial parameters for each cross-validation window. We utilized seven ensemble members to reduce the uncertainty associated with the random initial parameters. We utilized cases for 2 years close to the testing year as validation samples, while the samples for the remaining years (except for the testing year) were used as training samples. For example, for testing the cases in 2018, samples taken between 2000 and 2015 were used for training, and those from 2016 to 2017 were used for validation.
To assess the forecast performance of the DeepTC model for IC24, we conducted a comparative evaluation with the KMA, CMA, and persistence (PER) forecasts. The PER forecast utilizes the same dataset as DeepTC, which is the JTWC best track dataset; hence, its evaluation period spans from 2000 to 2018. However, due to the availability of forecast data, we limited the comparison between the DeepTC, KMA, and CMA to the period between 2004 and 2018. During this time frame, the KMA began forecasting in 2004, while the CMA started in 2002. This allows us to analyze and compare the forecast results of the DeepTC, KMA, and CMA for the selected period of 2004–18.
f. Forecast evaluation
3. Results
a. Skill evaluation of TC intensity forecasts in the DeepTC
Figures 2a and 2b show the MAE and coefficient of determination r2, respectively, of IC24 forecasts for all cases (see methods for the detailed forecast evaluation metrics). The DeepTC model’s forecast performance was better than that of the KMA, CMA, and persistence forecasts (i.e., previous 24-h intensity change, hereafter referred to as PER). The MAE for the DeepTC was the lowest among the four forecast models (12.9, 14.2, 14.4, and 22.0 kt for the DeepTC, KMA, CMA, and PER, respectively), while r2 for the DeepTC was the highest (0.54, 0.41, 0.41, and 0.05 for the DeepTC, KMA, CMA, and PER, respectively). This indicates that the DeepTC is more accurate than the KMA, CMA, and PER in predicting overall TC intensity changes.
The forecast skills of the DeepTC, KMA, CMA, and PER in the western North Pacific region between 2004 and 2018. (a) MAE (kt), (b) coefficient of determination r2 for IC24, and HSS for (c) RI and (d) RW. Error bars indicate 95% confidence intervals, calculated using the bootstrap method with 1000 iterations.
Citation: Artificial Intelligence for the Earth Systems 3, 2; 10.1175/AIES-D-23-0052.1
The predictions for TC rapid intensity change (i.e., RI and RW) in the DeepTC model were also significantly better than the others (Figs. 2c,d). The HSS for the RI (RW) of the DeepTC was 0.48 (0.42), compared with only 0.12 (0.27), 0.13 (0.38), and 0.13 (0.09) for the KMA, CMA, and PER, respectively (Figs. 2c,d). The differences in the forecast skill between the DeepTC and the other three models were statistically significant at the 95% confidence level based on the bootstrap method.
Figure 3 shows the joint probability density function (PDF) between the observed and predicted IC24 values in the DeepTC, KMA, CMA, and PER models. The joint PDF between the observations and the DeepTC forecasts generally follow the one-to-one line relatively closely, even though the forecasted IC24 tends to be underestimated in cases where the observed value was over 60 kt (Fig. 3a). Among the 230 observed RI cases (i.e., IC24 ≥ 30 kt), 124 were correctly predicted by the DeepTC (124 TPs).
The PDFs of IC24 forecasts from different models: (a) DeepTC, (b) KMA, (c) CMA, and (d) PER (y axis), with respect to the observed IC24 (x axis) between 2004 and 2018 for the western North Pacific region. The shading and gray numbers denote the probability (%) and frequency, respectively. The red lines highlight the threshold of RI (30 kt). The TP, TN, FP, and FN denote the true positives, true negatives, false positives, and false negatives of the confusion matrix for RI, respectively. Finally, the red numbers denote the event counts in each confusion matrix category for RI.
Citation: Artificial Intelligence for the Earth Systems 3, 2; 10.1175/AIES-D-23-0052.1
In contrast, the joint PDFs between the observations and other forecasts only loosely follow the one-to-one line well and show relatively broad distributions (Figs. 3b–d). For example, the KMA and CMA forecasts tended to underestimate the occurrence of RI. They had significantly fewer hits (20 and 28 true positives, respectively) and more misses (210 and 202 false negatives, respectively) for RI events than the DeepTC model. Even though the DeepTC model has led to an increase in false positives in the pursuit of achieving more true positives for RI, however, it is noteworthy that the ratio of false positives to true positives was 0.88, which is still lower than that of the KMA or CMA, which have ratios of 0.95 and 1.89, respectively.
Furthermore, both the KMA and CMA forecasts demonstrate a systematic overestimation for the IC24 range from −20 to 20 kt. Unlike the operational forecasts, PER significantly overestimated the occurrence of RI and underestimated the occurrence of RW. It correctly predicted 78 RI cases (78 true positives) and had 324 false alarms for RI (324 false positives), almost triple those of the DeepTC. This shows that the DeepTC model has overcome the limitations of the previous TC intensity forecast models for successfully predicting extreme values (Mercer and Grimes 2017; Bai et al. 2020; DeMaria et al. 2021; Wang et al. 2020; Xu et al. 2021).
b. Physical interpretation of the reliable DeepTC forecasts
In the previous subsection, we showed that the forecast skills of the DeepTC model were systematically superior to other operational forecasts, particularly for RI prediction. To investigate how the DeepTC model was able to achieve this superior RI predictive performance, we first split the RI cases into primary RI cases, which were initially non-RI before developing into RI within 24 h, and successive RI cases, whose intensity change fell into the RI category for both initial and target time, according to their initial conditions (Table 2). The hit rate of the DeepTC for the primary RI cases was 43.8% which was systematically lower than that for the successive RI cases (60.1%).
The event counts in each RI category of the DeepTC forecasts. Primary RI and successive RI denote RI cases that developed within 24 h from initially non-RI and RI status, respectively. The occurrence rate denotes the ratio of RI occurrence under each initial condition in the observational dataset.
One possible reason for the low hit rate for the primary RI cases might be because of the low number of cases, which may have hindered the training. The RI occurrence rate under the initial non-RI conditions was 8.7%, and 17.4% under the initial RI conditions.
More importantly, since the forecast in successive RI cases is made possible by simply relying on the autocorrelation to a greater extent compared with the primary RI cases, it would be easier to predict. In other words, rather than revealing the nonlinear relationship between the IC24 and environmental/structural variables, the forecasts in successive RI cases would simply be dependent on the previous 24-h intensity change (IC0). Since the dependency of the IC24 on the given predictors is likely to be distinct between the primary and successive RI cases, those are analyzed separately.
In this study, we classified predictors into developmental, environmental, and structural factors:
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Developmental factors are defined as zero-dimensional variables associated with storm history information, including longitude, latitude, intensity, and IC0, which are taken from the JTWC best track dataset.
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Environmental factors denote the 11° × 11° box averaged zero- and one-dimensional variables, including SST, RH, SHR, and the vertical profile of wind speed and potential temperature.
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Structural factors are defined as the horizontal-average-removed two- and three-dimensional variables, including SST, zonal and meridional wind speed, pressure vertical velocity, temperature, RH, and geopotential height.
Figure 4 shows the top 10 predictors with the highest occlusion sensitivity for primary and successive RI cases. Three developmental factors—namely, latitude, IC0, and intensity—were ranked at a top rate for the high occlusion sensitivity for the primary RI cases (Fig. 4a). Next, several environmental factors such as SHR, SST, and vertical profile of potential temperature were found to be relatively important for RI prediction, which is consistent with previous studies that emphasize the role of those variables for the RI of a TC (Emanuel et al. 2004; Hendricks et al. 2010; Kaplan et al. 2015; Fudeyasu et al. 2018). Among the TC structural factors, three-dimensional RH (3D RH) exhibited the largest occlusion sensitivity.
The absolute error reduction of the top 10 variables for (a) the primary RI and (b) the successive RI derived by occlusion sensitivity analysis. The gray, red, and blue bars denote the developmental, environmental, and TC structural conditions, respectively. The numbers in the parentheses indicate the dimensions of the particular variable. Error bars indicate 95% confidence intervals, calculated using the bootstrap method with 1000 iterations.
Citation: Artificial Intelligence for the Earth Systems 3, 2; 10.1175/AIES-D-23-0052.1
For the successive RI cases, unlike the primary RI, the occlusion sensitivity of IC0 and latitude overwhelmed that of the other variables. The summed absolute error reduction of IC0 and latitude was 10.7 kt, while that of the remaining variables was only 4.4 kt indicating that the reliable RI forecasts for the successive RI cases are mostly dependent on its autocorrelation, as mentioned earlier (Kaplan et al. 2010; Rozoff and Kossin 2011; Wei and Yang 2021).
As the successful forecasts for the successive RI cases rely to a large extent on their autocorrelations, we focused on the variables with the largest occlusion sensitivity for primary RI cases. Therefore, we examined the relationship between IC24 and the five developmental and environmental factors (i.e., latitude, IC0, intensity, SHR, and vertical profile of wind speed) and one structural factor (i.e., 3D RH), which exhibited the highest occlusion sensitivity for the primary RI cases.
In observations, the joint PDF between latitudinal location and IC24 showed a negative relationship (Fig. 5a), which indicates that a low latitude is a favorable condition for an RI event. Previous studies have shown that the onset of RI in the western North Pacific region tends to occur within a few days of the tropical storm formation, with a peak at 12–24 h after its formation (Fudeyasu et al. 2018; Hendricks et al. 2010). Moreover, latitude serves as a direct indicator of planetary vorticity, and it has been demonstrated that lower planetary vorticity accelerates the development of TCs (Li et al. 2012). The DeepTC model accurately simulated this inverse relationship between latitude and IC24 (Fig. 5b). In contrast, the KMA and CMA simulations were weaker, particularly the PDF of the CMA model showed a solid double peak distribution (Figs. 5c,d).
The relationship between the predictand and the key zero-dimensional predictors. The PDFs of IC24 from the (first row) observation, (second row) DeepTC, (third row) KMA, and (last row) CMA with respect to each predictor: (first column) latitude, (second column) intensity, (third column) IC0, and (last column) SHR that was greater than the 90th percentile. Both the shading and colored bars denote probability (%). The asterisk denotes that the regression slope between the predictand and the key zero-dimensional predictors was greater than a 95% confidence level based on the Student’s t test.
Citation: Artificial Intelligence for the Earth Systems 3, 2; 10.1175/AIES-D-23-0052.1
The joint PDF between intensity and IC24 indicates a negative relationship between them in observations (Fig. 5e). The weaker TCs tend to be further away from their maximum potential intensity (Kaplan and DeMaria 2003). Thus, this negative relationship shows that TCs in their early development stages that have a weak intensity may develop a future RI event (Fudeyasu et al. 2018; Hendricks et al. 2010). In addition, TCs tend to be located further south during the early stages of their life cycle, where the environmental conditions, with their increased moisture, are much more favorable. This observed inverse relationship between intensity and IC24 is also accurately simulated by the DeepTC (Fig. 5f) but weakly simulated by the KMA and CMA (Figs. 5g,h). The joint PDF between the IC0 and IC24 is positive in observations, referring to the autocorrelation of the IC (Fig. 5i). This positive autocorrelation of intensity change was well simulated by both the DeepTC and CMA models (Figs. 5j,l) but weakly simulated by the KMA model (Fig. 5k).
Last, it is well known that weak SHR is a favorable condition for the development of a TC (Emanuel et al. 2004; Wang and Wu 2004; Kaplan et al. 2015). This negative relationship is shown in Fig. 5m where the PDF of IC24 is shifted to negative values when SHR is the extremely strong regime (i.e., SHR > 90th percentile). This shift in the PDF to the negative values when SHR is in the positive extreme percentile is generally well simulated in the DeepTC model (Fig. 5n). However, unlike in the observations or DeepTC model, the peak PDF in both the KMA and CMA models was shifted toward positive IC24 values (Figs. 5o,p). This indicates that the negative relationship between IC24 and SHR is oppositely simulated.
Subsequently, we explored the role of the vertical profile of wind speed (WS) (1D in Fig. 4a) in predicting RI. We compared the composites of the cases that developed from initial non-RI status to RI (i.e., primary RI) and those that remained as non-RI (referred to as successive non-RI) (Fig. 6). Interestingly, primary RI cases showed weaker WS across all vertical levels compared to successive non-RI cases, with smaller differences between the upper and lower levels. This suggests that the reduction in WS across vertical levels and the decrease in the WS difference between the upper and lower levels are important information for predicting RI.
(a) The vertical characteristics of WS for each group and (b) their difference from the 850 hPa baseline. The red and blue lines represent the WS vertical profile composites for the primary RI and successive non-RI, respectively. The shading indicates a 95% confidence interval, calculated using the bootstrap method with 1000 iterations.
Citation: Artificial Intelligence for the Earth Systems 3, 2; 10.1175/AIES-D-23-0052.1
Last, we examined the relationship between IC24 and 3D RH, which was the most important structural variable in forecasting the primary RI cases. Wu et al. (2012) revealed the azimuthal asymmetric structure of environmental RH based on satellite observations, with the rear side (in the TC motion-based coordinate) tending to be moister than the front side during RI (Wu et al. 2012). This is further supported by Wu et al. (2015) who performed WRF experiments confirming that TCs were weakened when moist forcing was prescribed in the front and strengthened when moist forcing was prescribed in the rear.
In addition to the azimuthal asymmetric structure, Shu and Wu (2009) and Wu et al. (2012) also found that there was a larger negative radial gradient of upper-tropospheric RH during an RI event, which was particularly significant in the northwest quadrant of the TC. This negative radial gradient of RH is known to be a favorable condition for TC development (Wu et al. 2012) as it strengthens secondary circulation, which can lead to a stronger warm-core structure and a tangential wind of TC (Fritz and Wang 2014).
Focusing on the aforementioned two perspectives, we investigated whether the structural features of 3D RH associated with RI occurrence detected by the DeepTC coincide with the previous findings. In the following results, we compared the composites of the cases that developed from initial non-RI status to RI (i.e., the primary RI) and those that remained as non-RI (i.e., successive non-RI) in order to identify the 3D RH structural characteristics responsible for RI development. Note that, as TCs in the western North Pacific generally move in a northwesterly direction (particularly in their developmental stage), the geographically northwest (southeast) quadrant roughly corresponds to the front (rear) side in TC motion-based coordinate. However, north of 25°N, TCs tend to move to the northeast. To enhance the robustness of our analysis, we have excluded all successive non-RI cases that occurred north of 25°N.
Regarding the first perspective mentioned above (i.e., azimuthal asymmetry in the RH), we examined the normalized RH and horizontal wind anomalies composite at 500 and 850 hPa for each case (Fig. 7). In the middle troposphere, both groups show an asymmetric azimuthal moisture structure with a dry front (northwest quadrant) and a moist rear (southeast quadrant) structure (Figs. 7a,b). In the lower troposphere, this structure still appears in the composited RH anomalies for primary RI cases but is absent for successive non-RI cases (Figs. 7d,e). This dry front and moist rear structure in the outer core region is a significant difference between the two groups, suggesting that this structure is related to the rapid development of TCs (Figs. 7c,f). In the inner core region, the primary RI cases exhibit drier condition than the successive non-RI cases. This is mainly since the primary RI cases have weaker intensity than the successive non-RI cases (Fudeyasu et al. 2018; Hendricks et al. 2010).
The horizontal structural characteristics of normalized RH for each group. The normalized RH and horizontal wind anomaly composite for (left) primary RI, (middle) successive non-RI, and (right) their difference at (top) 500 hPa and (bottom) 850 hPa. The shading and black arrows denote the normalized RH anomaly and the normalized horizontal wind anomaly vector, respectively. Hatching highlights the values, with the RH difference exceeding the 95% confidence level, based on the bootstrap method.
Citation: Artificial Intelligence for the Earth Systems 3, 2; 10.1175/AIES-D-23-0052.1
Ying and Zhang’s (2012) cloud-resolving WRF simulations showed that the dry air in the front of a storm (i.e., the northwest quadrant) reinforces the secondary circulation and the mid- and low-level radial inflows by suppressing convection in the outer core region. Consequently, the inner core spinup process is accelerated, increasing the storm’s intensity. On the other hand, Wu et al. (2015) found that the moist perturbations in the rear area of the storm induce supplementary cyclonic circulation, helping transport additional moisture from the relatively moist southern areas. Subsequently, more symmetrical and powerful convection is induced in the inner core, and diabatic heating increases, strengthening the TC. This suggests that the dry front and moist rear horizontal structure of RH, as detected by the DeepTC, is a physically robust feature that can also strengthen the TC.
Next, to examine the radial characteristics of the upper-tropospheric RH, we compared the 400-hPa RH anomaly composite according to the distance from the center of the TC in the northwest quadrant during the primary RI cases and the successive non-RI cases (Fig. 8a). Both groups showed positive RH anomalies near the TC center as a consequence of the strong low-atmospheric convergences, while the negative RH anomalies are dominant once the distance from the TC center is farther than 350 km. The stronger negative radial gradient of the RH in the primary RI case is confirmed by the horizontal moisture differences between the near (200–300 km) and far environments (500–600 km) (Fig. 8b). The positive RH anomalies led by the strong convergence, in turn, contribute to additional cloud formations, which amplify the cloud-radiative feedbacks maintaining the TC’s intensity (Ruppert et al. 2020). The negative RH anomalies far from the TC center contribute to a stronger radial gradient of RH and strengthen the secondary circulation, which can lead to a stronger warm-core structure and a tangential wind of TC (Fritz and Wang 2014).
(a) The normalized RH400 (vertically averaged from 400 to 300 hPa) anomaly composite for primary RI (red line) and successive non-RI (blue line) in the northwest quadrant. The shading indicates a 95% confidence interval, calculated using the bootstrap method with 1000 iterations. (b) The averaged RH400 difference between the near (200–300 km) and far (500–600 km) environments for primary RI (red bar) and successive non-RI (blue bar). Error bars indicate 95% confidence intervals, calculated using the bootstrap method with 1000 iterations.
Citation: Artificial Intelligence for the Earth Systems 3, 2; 10.1175/AIES-D-23-0052.1
c. Enhancement in prediction performance from the application of amplitude focal loss
In this section, we assessed the enhancement in prediction performance resulting from the implementation of amplitude focal loss. To this, we conducted a sensitivity experiment using MAE and mean square error (MSE) as a loss function (Table 3). The application of amplitude focal loss led to a significant improvement in the HSS for both RI and RW. Notably, the HSS for RI saw an increase by more than threefold, even though it exhibits a marginal decrease in the MAE and r2 for the intensity change.
The forecast skill comparison between the (first row) DeepTC model with amplitude focal loss, (second row) DeepTC model with MAE, and (third row) DeepTC model with MSE as a loss function. The table includes (second column) MAE and (third column) coefficient of determination r2 for IC24 and (fourth column) HSS for RI and (last column) RW. The bold values represent the best performing of the three models for each skill score.
This suggests that the application of amplitude focal loss played a key role in improving both RI and RW predictive performance. When conventional MAE and MSE were used as the loss function of the DeepTC model instead of amplitude focal loss, the HSS for RI was only 0.09 and 0.15, which was similar to the CMA (0.13), respectively (Table 3). This clearly demonstrates that amplitude focal loss is more effective than MAE or MSE for training the deep learning–based model to forecast the extreme percentile of the output variable.
4. Summary and discussion
In this study, we developed a deep learning model for 24-h TC intensity forecast. A special focus was on correctly predicting rapid TC development (i.e., RI and RW cases). For this purpose, we developed the amplitude focal loss function that more heavily weights large-magnitude cases and applied it to our deep learning model.
The prediction skills of our DeepTC model were significantly better than the operational forecast from both the KMA and CMA for both IC24 and the RI. The MAE of IC24 in the DeepTC was 12.95 kt, which is 8.9% and 10.2% lower than that of the KMA (14.22 kt) and CMA (14.42 kt), respectively. Additionally, the r2 of the DeepTC is 0.54, which is significantly higher than that of the KMA (0.41) and CMA (0.40). Moreover, the RI prediction skill of the DeepTC was notably greater than the operational forecasts. The HSS of the DeepTC is 0.47, which, again, is significantly higher than the KMA (0.12) and CMA (0.13). The DeepTC was also significantly better at predicting RW occurrence compared with the operational forecasts.
To understand how our DeepTC model achieved its superior RI forecast performance, we quantified the importance of each predictor using occlusion sensitivity. The relationship between the key factors and IC24, which was identified by occlusion sensitivity, was in line with the findings in previous studies that used observational analysis and model experiments (Emanuel et al. 2004; Wang and Wu 2004; Kaplan et al. 2010; Hendricks et al. 2010; Rozoff and Kossin 2011; Kaplan et al. 2015; Wei and Yang 2021; Kaplan and DeMaria 2003). The developmental or environmental features associated with IC24, namely, lower latitude, weaker intensity, greater previous intensity change, and weaker vertical wind shear, were successfully simulated by the DeepTC and were poorly simulated by the KMA and CMA model. In addition, the DeepTC successfully detected RI-related features in 3D RH fields that have been highlighted in previous observational and modeling studies, such as the dry front-moist rear structure (Shu and Wu 2009; Wu et al. 2012; Ge et al. 2013; Wu et al. 2015; Ying and Zhang 2012) and a stronger radial moisture gradient in the upper troposphere. This confirms that the DeepTC managed to learn physically reasonable features, thereby demonstrating that it can be a powerful tool for improving the understanding of the occurrence of RI as well as providing more reliable TC intensity forecasts.
Compared with deep learning models using the MAE or MSE as a loss function, the prediction performance for RI in our model with the amplitude focal loss, designed to focus more on extreme intensity change, was significantly greater, indicating that the amplitude focal loss played an important role in the successful prediction of the DeepTC. This successful implementation of the amplitude focal loss for predicting extreme cases suggests that this loss function can be utilized to predict other extreme weather events.
However, it should be noted that the NCEP FNL dataset used in this study takes between 6 and 10 h to update, meaning that the prediction system of this study can only provide lead time forecasts for 18 h or less applied to near-real-time conditions. Nevertheless, it can provide another independent operational forecast if the DeepTC is trained using analysis fields routinely produced for agencies’ official forecasts.
Acknowledgments.
This study was supported by the Ministry of Science and ICT through the National Research Foundation of Korea (NRF-2022M3K3A1094114), the Korea Environmental Industry and Technology Institute (KEITI) through “Project for developing an observation-based GHG emissions geospatial information map,” funded by the Korea Ministry of Environment (MOE) (Grant RS-2023-00232066), National Natural Science Foundation of China (NSFC) (Grant 42088101), and National Oceanic and Atmospheric Administration (NOAA) (Grant NA18OAR4310298).
Data availability statement.
The data utilized in this study can be downloaded from NCEP final analysis (https://doi.org/10.5065/D6FB50XD), JTWC (https://www.metoc.navy.mil/jtwc/jtwc.html?best-tracks), CMA (https://mtarchive.geol.iastate.edu/), and KMA (https://apihub.kma.go.kr/).
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