Deep learning approach for detecting tropical cyclones and their precursors in the simulation by a cloud-resolving global nonhydrostatic atmospheric model

Abstract

We propose a deep learning approach for identifying tropical cyclones (TCs) and their precursors. Twenty year simulated outgoing longwave radiation (OLR) calculated using a cloud-resolving global atmospheric simulation is used for training two-dimensional deep convolutional neural networks (CNNs). The CNNs are trained with 50,000 TCs and their precursors and 500,000 non-TC data for binary classification. Ensemble CNN classifiers are applied to 10 year independent global OLR data for detecting precursors and TCs. The performance of the CNNs is investigated for various basins, seasons, and lead times. The CNN model successfully detects TCs and their precursors in the western North Pacific in the period from July to November with a probability of detection (POD) of 79.9–89.1% and a false alarm ratio (FAR) of 32.8–53.4%. Detection results include 91.2%, 77.8%, and 74.8% of precursors 2, 5, and 7 days before their formation, respectively, in the western North Pacific. Furthermore, although the detection performance is correlated with the amount of training data and TC lifetimes, it is possible to achieve high detectability with a POD exceeding 70% and a FAR below 50% during TC season for several ocean basins, such as the North Atlantic, with a limited sample size and short lifetime.

Introduction

Tropical cyclones (TCs), also referred to as typhoons, cyclones, and hurricanes, cause significant damage to human life, agriculture, forestry, fisheries, and infrastructure. For example, Typhoon Lionrock in 2016 caused record-breaking heavy rainfall, which resulted in severe floods and the loss of 23 lives in Japan. Moreover, TCs occasionally form very close to and approach countries at low latitudes (e.g., the Philippines) with rapid intensification. Therefore, accurate prediction of TC track and intensity is necessary. Early prediction of TC formation is important not only from an academic but also from a disaster mitigation perspective.

TCs form from convective disturbances in the tropics (Riehl 1954). Dynamic environmental conditions (e.g., small vertical wind shear, low-level cyclonic vorticity, and non-zero planetary vorticity) and thermodynamically favorable environmental conditions (e.g., sea surface temperature > 26 °C, existence of convective instability, and mid-tropospheric moisture) necessary for TC formation were proposed in the pioneering work of Gray (1968, 1975). However, because only a small percentage of convective disturbances in the tropics develop into TCs under favorable environmental conditions (Emanuel 1989), accurate and early prediction of TC formation is still a developing area of research. The Japan Meteorological Agency (JMA) extended the Dvorak method (Dvorak 1975; Dvorak 1984), which estimates TC intensity based on satellite infrared imagery (IR), to tropical depressions (maximum sustained surface wind speed < 17.5 m s⁻¹). This extension, known as early-stage Dvorak analysis (EDA), has been utilized in operational forecasts since 2001 (Tsuchiya et al. 2001), and the JMA issues early warnings on typhoon occurrence 1 day before its formation based on EDA. The National Hurricane Center (NHC) and Central Pacific Hurricane Center (CPHC) also use the advanced Dvorak method for predicting TC genesis with lead time and accuracies of 48 h and 15–57%, respectively (Cossuth et al. 2013). Yamaguchi and Koide (2017) demonstrated that that the predictability of TC genesis could be improved to 35–79% by combining the Dvorak method and multi-model ensemble forecasts. On the other hand, with recent advancements in high-performance computing and numerical weather prediction, TC formation could be simulated 2 weeks in advance in case studies of eight typhoons in August 2004 (Nakano et al. 2015), Hurricane Sandy in 2012, and Super Typhoon Haiyan in 2013 (Xiang et al. 2015).

In recent years, deep learning, a machine learning method based on neural networks, has been receiving increasing attention and is being applied to various pattern recognition tasks (Krizhevsky et al. 2012; Simonyan and Zisserman 2015). In meteorology, several studies have proposed applying deep neural networks to existing TC detection (Liu et al. 2016; Kim et al. 2017), tornado prediction (Trafalis et al. 2014), hurricane pathway prediction (Kordmahalleh et al. 2015), and extreme rain fall prediction (Gope et al. 2016). Although several studies have used deep learning approaches for TCs after their formation, no research has considered this approach for detecting TCs before their formation.

In general, there are two approaches to detecting extreme events such as TCs: the model-driven approach (deductive approach), including numerical simulation, and the data-driven approach (inductive approach), including machine learning. The model-driven approach has the limitation that the prediction error increases with lead time because numerical models are inherently dependent on initial values. On the other hand, machine learning, as a data-driven approach, requires a large amount of high-quality training data. Most related works use reanalysis data and/or satellite observational data and labeled data as TCs or precursors based on the best track data provided by meteorological agencies. However, best track data for a TC’s occurrence well ahead of its formation is limited because the best track data is basically generated using the EDA technique and are limited in accuracy and elapsed time. For example, the best track data from the Regional Specialized Meteorological Center (RSMC), Tokyo, captures precursors 60 h before TC formation, on average, whereas simulation data from cloud-resolving global atmospheric models (Kodama et al. 2015) and TC tracking algorithms capture TC formation 107 h ahead, on average.

In this work, we adopted the deep learning approach to detect precursors of TCs before their formation using only two-dimensional (2D) Outgoing Longwave Radiation (OLR) data, which is equivalent to IR and is a good proxy of atmospheric deep convection and cloud cover. In our 2D deep convolutional neural networks (CNNs), we use 30 year cloud-resolving global atmospheric simulation data (20 year data for training and 10 year data for verification) and a TC tracking algorithm for automatic labeling. Although the basic concept, simulation data, and TC tracking algorithm of this work are the same as those in our previous conference paper (Matsuoka et al. 2017), the present study improves the deep learning architecture and investigates predictive ability for various basins, seasons, and elapsed times.

The manuscript is organized as follows. The “Data” section presents the climate simulation data and TC tracking algorithm. The “Method” section explains the training data preparation, deep convolutional neural networks, and evaluation metrics of prediction results. The “Results and discussion” section examines the detection results, including detectability for each ocean basin, spatial detectability, seasonal detectability, and long-term detectability. The “Conclusions” section provides a summary of the main conclusions of the present work.

Data

Climate simulation data

Thirty year atmospheric simulation data were produced by the Nonhydrostatic Icosahedral Atmospheric Model (NICAM) with a 14 km horizontal resolution (Kodama et al. 2015). This model employs fully compressible nonhydrostatic equations and guarantees the conservation of mass and energy. Equations were discretized by the finite volume method. One characteristic feature of this model is that it explicitly calculates deep convective circulations without using any cumulus parameterizations. Moist processes are calculated using a single-moment bulk cloud microphysics scheme (NSW6) (Tomita 2008). HadISST (Rayner et al. 2003) is used for lower boundary condition. The seasonal march of TC genesis, TC track, and TC intensity in each basin is well simulated, as described in Kodama et al. (2015). The dataset includes simulated OLR, precipitation, wind velocity, pressure, temperature, water vapor, and cloud (liquid, ice, rain, snow, and graupel) for 30 years since January 1979. OLR and precipitation are output every hour, and other physical quantities are output every 6 h. An example of simulation results of OLR is depicted in Fig. 1a. Three TCs and three precursors are reproduced at 0:00:00 08/17/2008 UTC.

Fig. 1

a An example of the simulated OLR. Blue and red squares show TCs and their precursors, respectively. Numeric values next to the squares represent elapsed time (positive numbers: TCs, negative numbers: precursors). b Detection results of TCs (blue dots) and their precursors (red dots) during 1979–2008 from NICAM. The definition of basins is based on Fudeyasu et al. (2014)

This model is suitable for reproduction of tropical phenomena such as TCs (Nakano et al. 2015; Nakano et al. 2017a; Nakano et al. 2017b) and the Madden–Julian oscillation (MJO) (Miura et al. 2007). For additional details on this model, please see the original and review papers (Tomita and Satoh 2004; Satoh et al. 2014).

TC tracking

To detect TCs and precursors, we employed a TC tracking algorithm for six-hourly outputs of the horizontal components of wind, temperature, and sea level pressure (SLP). This algorithm was originally proposed by Sugi et al. (2002) and optimized for NICAM data by Nakano et al. (2015) and Yamada et al. (2017). In the first step, grid points at which the SLP was 0.5 hPa less than the mean of its surrounding area (eight-neighbor grids) were selected as candidate TC centers. In this step, grid points that met the following criteria were considered as “TCs”: (i) the maximum wind speed at 10 m is greater than 17.5 m/s, (ii) the maximum relative vorticity at 850 hPa is greater than 1.0 × 10⁻³ s⁻¹, (iii) the sum of temperature deviations at 300, 500, and 700 hPa is greater than 2 K, (iv) the wind speed at 850 hPa is greater than that at 300 hPa, (v) the duration of each detected storm is greater than 36 h, and (vi) the TC is formed within a limited range of latitudes (30° S–30° N). In the second step, these grid points were connected with nearest neighbors in time, and tracks of “precursors” (before becoming TCs), “TCs,” and “extratropical cyclones” were subsequently obtained.

Figure 1b shows the result of applying the above algorithm to the 30 year NICAM data. TCs and precursors are represented by blue and red dots. In 30 years, 2532 TCs were detected (72–103 TCs per year). The numbers of TC tracks, detected samples, positive samples in training data, and average lifetime in each ocean basin (North Indian Ocean, western North Pacific, eastern North Pacific, North Atlantic, South Indian Ocean, South Pacific, and South Atlantic) are listed in Table 1. The definition of basins is taken from Fudeyasu et al. (2014) and illustrated in Fig. 1b. Detected TCs and precursors were used not only for labeling data, but also for ground truth. Ground truth was provided beforehand as the center point of TCs and precursors to evaluate identification results.

Table 1 The numbers of TC tracks, detected samples, positive samples in training data, and average lifetime in each basin

Methods/Experimental

Training data preparation

In this work, we performed a CNN-based binary classification that categorizes 2D cloud data (OLR) into “developing TCs and their precursors” or “non-developing depressions.” Binary classification is the task of categorizing (or classifying) objects into two groups (positive examples and negative examples) on the basis of classification rules. Before classification, it is necessary to prepare a labeled training data set, which is a series of sample data with the labels (positive or negative).

In the present work, at first glance, it appears natural to categorize the data into the following three classes: TCs, precursors, and non-developing depressions. However, since they are defined by the threshold value of maximum wind speed, it is difficult to identify them from cloud images. Figure 2a indicates a 2D histogram of cloud cover and elapsed time of all detected TCs including precursors by using the TC tracking algorithm. Here, we define cloud cover as (OLR_max − OLR_mean)/(OLR_max − OLR_min), where OLR_mean is the mean value of OLR in 64 × 64 grids, and OLR_max = 300.0 W/m² and OLR_min = 100.0 W/m². Figure 2a shows the developing phase and dissipation phase in which the cloud cover increases and decreases over time, respectively. All precursors (elapsed time < 0) were in the developing phase; therefore, we could identify both precursors and TCs in the developing phase (inside yellow dotted line) under the same category “developing TCs and their precursors” (referred to here as “TCs”) for labeling supervised data. The range was 30.0–95.0% for cloud cover and was from 10 days before to 7 days after formation, which could cover 97.0% of all precursors of TCs (in Matsuoka et al. 2017, the cloud cover range was 30.0–90.0% and covered 92.0% of all precursors of TCs). The other category, “non-developing depressions” (hereinafter referred as “non-TCs”), are low pressure clouds that were candidates for TCs but did not satisfy criteria (i)–(vi). For the binary classification, we labeled “TCs” and “non-TCs” data as “positive” and “negative” examples, respectively.

Fig. 2

a Histogram of cloud cover and elapsed time for developing TCs and their precursors. Positive and negative values of elapsed time indicate before formation (precursors) and after formation (TCs), respectively. b, c Examples of training data for binary classification of b developing TCs and precursors (positive examples) and c non-TCs (negative examples)

Examples of “TCs” and “non-TCs” are shown in Fig. 2b, c. Although these figures are visualized images of OLR, the actual training and test data are single-precision floating point numbers. Their horizontal sizes were approximately 1000 km × 1000 km (64 × 64 grids). For training, 20 year data (1979–1998) were used, and the remaining 10 year data (1999–2008) were used for prediction tests. The numbers of positive data (TCs and precursors) and negative data (non-TCs) for training were approximately 50,000 and 1000,000, respectively (the numbers of positive data in training data in each basin are listed in Table 1). Generally, the numbers of positive and negative data are often set to same number in binary classification. In this work, in order to train the CNN with a vast number of negative data, ten training data sets including the same 50,000 positive data and 50,000 randomly chosen negative data were generated for ten deep CNNs. By combining multiple CNNs, the influence of initial value dependence becomes smaller than when only single CNN is used (Freund and Schapire, 1997; Kearns and Valiant 1989; Breiman 1996; Breiman 2001).

Training and prediction using deep convolutional neural networks

We used a 2D deep CNN for binary classification (Table 2). CNNs are algorithms of neural networks used for image recognition and classification and for directly learning visual patterns from images. CNNs usually consist of convolutional layers, pooling layers, and fully connected layers (LeCun et al. 1999; Krizhevsky et al. 2012). Convolutional layers extract local features (feature maps) of input images, pooling layers allow spatial invariance by reducing the resolution of the image, and fully connected layers determine which features most correlate to a particular class. Dropout is a regularization technique where randomly selected neurons are ignored during training for preventing overfitting in a neural network.

Table 2 The architecture of our deep CNN. The parameters of the input layer, convolutional layers, pooling layers, and fully connected layers are denoted as [input data size] (e.g., 64 × 64), [filter size]@[number of feature maps] (e.g., 3 × 3@32), [pooling window size] (e.g., 2 × 2), and [number of units] (e.g., 2048), respectively

Our CNN architecture comprises four convolutional layers, three pooling layers, and three fully connected layers. Input data were 64 × 64 grids of OLR data consisting of single-precision real numbers, and output was generated in two classes (1 or positive: TCs; 0 or negative: non-TCs). Hyper parameters were optimized on the basis of the cross-validation test, which was conducted to evaluate the performance of the CNN using a random part of the training data. We examined the validation accuracy of 216 combinations of architecture settings: the number of convolutional (1–5) and pooling layers (1–5), the number of parameters in the fully connected layer (128, 256, 512, 1024, 2048), drop out ratio (0.2, 0.3, 0.4, 0.5), size of the convolutional filter (3 × 3, 5 × 5, 7 × 7), and number of feature maps (16, 32, 64, 128). Accordingly, the architecture with the highest level of performance was adopted, as shown in Table 2. The Adam optimizer (Kingma and Ba 2015) was applied to the CNN to update the network parameter to minimize the loss function called binary cross entropy. Batch normalization (Ioffe and Szegedy, 2015) was also applied to the CNN to minimize the initial-value dependence of the parameters.

The source code for deep learning was implemented in Python 3.6.3 with Keras (TensorFlow backend) (Chollet 2015), running on an NVIDIA Tesla P100 (1 node). Training 100,000 data over one epoch consumed approximately 3 min.

The accuracy of ten CNN classifiers using 100,000 data (50,000 for each of the two classes) for training and 5000 data for cross-validation is shown in Table 3. The maximum, minimum, and average values were 90.99%, 89.58%, and 90.30%, respectively (the number of epochs ranged over 19–46). The metric “Accuracy” is defined as follows:

$$ \mathrm{Accuracy}=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}} $$

(1)

Table 3 Accuracy values (also used as weights) of the ten classifiers

Here, TP (true positive), TN (true negative), FP (false positive), and FN (false negative) correspond to “correctly predicted positive example as positive,” “correctly predicted negative examples as negative,” “incorrectly predicted negative example as positive,” and “incorrectly predicted positive examples as negative,” respectively. Compared with the average accuracy of ten classifiers in Matsuoka et al. (2017), which was 86.60%, the average accuracy increased by 3.7 percentage point. Note that, although simulation data and the TC tracking algorithm were the same as in Matsuoka et al. 2017, in this study, the target range of cloud cover was expanded from 30.0–80.0% to 30.0–95.0%.

In the present study, in order to effectively train imbalanced data (positive 50,000, negative 1000,000), ten classifiers (Classifier 1, 2, …, 10) were generated by training ten sets of 100,000 data on the same neural network, as shown in Fig. 3a. Each classifier was trained with the same 50,000 positive data and randomly selected 50,000 negative data. In this manner, our CNNs could train 50,000 positive examples and 500,000 negative examples simultaneously.

Fig. 3

The flow charts of the proposed ensemble CNNs: a training and cross-validation phase and b prediction phase. Hyper parameters of the CNN architecture are listed in Table 2

To verify the model’s performance, classifiers trained using the 20 year data were applied to the test data (untrained 10 year simulation data). Candidate regions in the test data to be predicted by applying trained classifiers were clipped with a sliding window, which is widely used for object detection (Kumar 2013). We slid a rectangular area (approximately 1000 × 1000 km) with a 125 km (eight-grid) stride and continued sliding the window over the whole data within latitudes of 30° N to 30° S because three pooling layers of our CNN assumed eight grids of horizontal shift. Furthermore, in order to reduce the number of candidate regions, we set a limit to the cloud cover in the range of 30.0 to 95.0% and 50% or more over sea areas. In this manner, 97.0% of precursors of TCs in the simulation data could be covered.

Our ensemble CNNs output the ensemble average using the weight value of each trained classifier, as shown in Fig. 3b. The weight value given by the accuracy of the ten classifiers is listed in Table 3. The final probability p for detecting the presence of developing TCs and precursors in an arbitrary region is defined as follows:

$$ p=\frac{1}{10}\sum \limits_{i=1}^{10}\frac{w_i{x}_i}{w_i} $$

(2)

where w_i is the weight value of classifier i, and x_i is the output value obtained by Classifier i (0: non-TCs, 1: TC). When the threshold value p_th is given, arbitrary candidate areas that satisfy p ≥ p_th are regarded as positive. Although we adopt binary classification to facilitate the evaluation of prediction results, we can also output detection results as probabilistic information using p.

Evaluation metrics of prediction results

The false alarm ratio (FAR) and the probability of detection (POD) are often used as evaluation metrics of prediction results in weather forecasting (Jolliffe and Stephenson, 2003; Wilks 2006; Barnes et al. 2007). FAR, incorrectness of positive prediction, is defined using “correctly predicted positive examples as positive (TP, true positive)” and “incorrectly predicted negative examples as positive (FP false positive)” as follows:

$$ FAR=\frac{FP}{TP+ FP} $$

(3)

As shown in Fig. 4a, when a positive predicted area captures the ground truth, the area is TP. Similarly, when a positive predicted area does not capture the ground truth, the area is FP. In the example of Fig. 4a, TP is 3, FP is 1, and FAR is 25.0%. Although FAR is closely related to Precision = TP/(TP + FP), which is widely used in computer vision and pattern recognition (Forsyth 2011), Precision is one minus FAR and means correctness of positive prediction.

Fig. 4

Conceptual diagram explaining our evaluation metrics: a accuracy and FAR and b POD

POD is another important metric in prediction; it indicates the amount of ground truth that can be correctly predicted. POD is conceptually the same as Recall = TP/(TP + FN) used in computer vision except for cases in which multiple positive predicted areas overlap, as shown in Fig. 4b. This is because the denominator of POD is the value of the ground truth, whereas the denominator of Recall is the number of predicted areas corresponding to the ground truth. Therefore, TP is given to TCs instead of prediction area, and we define the POD at multiple areas with the same detected ground truth as follows:

$$ POD=\frac{\mathrm{number}\ \mathrm{of}\ \mathrm{correctly}\ \mathrm{predicted}\ \mathrm{TCs}}{\mathrm{number}\ \mathrm{of}\ \mathrm{TCs}} $$

(4)

Here, the numbers of both TCs and correctly predicted TCs include precursors as mentioned above.

Results and discussion

Detection results

This section first introduces one of the best cases of detection results under the condition that the number of TCs and precursors is larger than eight and POD is larger than 80.0%. Similarly, one of the worst cases under the condition that the number of TCs and precursors is larger than five is also introduced.

Figure 5 shows the best case of detection results during the 10 year period (October 21, 2003, 18:00:00 UTC) for (a) p_th = 1.0 and (b) p_th = 0.6. Red and white boxes represent positive predicted areas (TCs) and negative predicted areas (non-TCs), respectively. Furthermore, blue and red dots represent the central points of actual TCs and precursors (as ground truth) calculated by the TC tracking algorithm, respectively. In Fig. 5a, five developing TCs and three precursors of nine ground truths can be correctly predicted; hence POD is 88.9% (= 8/9). Furthermore, 74 of 82 positive prediction areas could be correctly predicted; hence, FAR is 9.8% (= 1–74/82). Figure 5b shows the prediction results after decreasing the threshold p_th to 0.6. In this case, the correctly predicted area (true positive) increases (POD is 100.0%) because the positive predicted area is expanded. However, the false alarm rate also increases (FAR is 34.1%).

Fig. 5

Detection results at 18:00:00 UTC 10/21/2003 with a p_th = 1.0 (POD = 88.9% and FAR = 9.8%), and b p_th = 0.6 (POD = 100% and FAR = 34.1%). Numbers next to the blue or red letters indicate the elapsed time of the ground truth of TC or pre-TC, respectively

Representing the worst case, prediction results of August 17, 2006 18:00:00 UTC are shown in Fig. 6, in which many TCs and precursors with less cloud cover were missed and there are numerous false alarms. While the PODs range from 20 to 60%, the FARs were high (72.7 to 78.3%).

Fig. 6

Detection results at 18:00:00 UTC 08/17/2006 with a p_th = 1.0 (POD = 20.0% and FAR = 72.7%) and b p_th = 0.6 (POD = 60% and FAR = 78.3%). Numbers next to the blue or red letters indicate the elapsed time of the ground truth of the TC or pre-TC, respectively

Detectability for each basin

The performance for various p_th was evaluated on each basin. Figure 8 shows the relationship between POD and FAR when p_th was varied from 10 to 100% in 10% increments. It represents the average value over 10 years (1999–2008) for each basin. The South Atlantic was not considered in this study because the number of TCs that occur in that area is extremely small. Although there are differences in values of detection performance depending on the basin, POD and FAR exhibited a trade-off relationship for all cases. When p_th is increased, the positive prediction area is narrowed down, and both FAR and POD decrease. In contrast, if p_th is decreased, the positive predicted area becomes wider, and both FAR and POD increase because dropout is reduced.

There are several reasons for the variation in detection performance for different basins. First, it is known that the pattern of TC genesis is different for each basin (Holland 2008), and the detectability for each pattern may differ (as will be described in the “Conclusion” section, investigation of the detectability for each generation pattern will be undertaken in future studies). Second, in general, the performance of supervised machine learning depends on the number of training data for each pattern. In our results, the correlation coefficient between POD and the number of training data is 0.749, and that between the FAR and the number of training data is − 0.756. Lastly, since the cloud pattern of TCs is broken over time in the dissipation phase, their detectability should decrease. In other words, the detectability should be high for TCs with long lifetimes. The correlation coefficient between POD and average TC lifetime in each basin is 0.821 and that between FAR and average lifetime is − 0.802.

For example, as seen in Fig. 7, it was found that the basin with the best detection performance was the western North Pacific and that with the worst detection performance was the North Indian Ocean. In the western North Pacific, the number of training data was the largest (TCs 9549, pre-TCs 8023) and the average lifetime was also the longest (6.8 days). On the other hand, in the North Indian Ocean, the number of training data was relatively small (TCs 1422, pre-TCs 1184) and the average lifetime was also relatively short (4.6 days).

Fig. 7

Relationship of the POD and FAR with various p_th for different basins. The POD and FAR are 10 year average values from 1999 to 2008 for each basin

Spatial detectability

This section first shows the spatial distribution of detection performance for a threshold value of p_th = 1.0. Figure 8a, b shows the spatial distributions of POD and FAR, respectively. Here, the spatial distributions of POD and FAR are calculated as their 10 year means at each grid point and are defined in a 64 × 64 rectangular area centered on the ground truth. Figure 8c shows the count of ground truths for both TCs and pre-TCs in the training data at each grid point. Figure 8d shows the count of positive prediction areas at each grid point. Areas with many TCs and pre-TCs are represented by a gray and white dotted line in Fig. 8a, b, d.

Fig. 8

Ten year means of a POD and b FAR with p_th = 1.0, respectively. c Spatial distribution of the count of ground truth in the training data of TCs and precursors. d Spatial distribution of the count of positive prediction areas

In most basins, both POD and FAR appeared to be roughly associated with the ground truth count in the training data. Especially in the Indian Ocean and the Pacific, POD was higher and FAR was lower in regions that had higher ground truth counts. As an exception, POD also exceeds 80% and FAR falls to 60% in a part of the North Atlantic, despite limited training data. Previous studies reported that there is a pattern of TC genesis unique to the basin (Ritchie and Holland 1999; Yoshida and Ishikawa 2013; Fudeyasu and Yoshida, 2018). For example, Russell et al. (2017) reported that 72% of TCs in the North Atlantic are caused by African Easterly Waves (AEW). Accordingly, our results may indicate that TCs and pre-TCs caused by the AEW are easy to detect using CNNs.

Next, the detection performance of the TC area and pre-TC area are compared. In each basin, pre-TC areas are located at lower latitudes than the TC area. As shown in Fig. 8b, the FAR of the pre-TC area was higher than that of the TC area. Although there was no significant difference in POD between the TC and pre-TC areas, the count of positive predictions was larger in the pre-TC area than in the TC area. That is, the count of misdetection is larger in the pre-TC area than in the TC area. Intuitively, the pattern of developed TCs is simpler than that before formation, and therefore, it is reasonable that the detectability of TCs is higher than that of pre-TCs.

In the western South Pacific and South Atlantic, although the FAR was close to 100%, there were few positive prediction areas. In other words, the number of misdetections (false positives) was small. In contrast, near the equator of the Indian Ocean and the eastern Pacific, although the FAR was also close to 100%, the number of positive prediction areas was large. That is, the number of misdetections was large in these areas.

Seasonal detectability

Seasonal detectability, monthly mean of POD, and FAR from 1999 to 2008 in each basin are shown in Fig. 9. Monthly variability of the number of training data (positive) and ground truth in each month and each basin are also shown in the same figure. In each basin, monthly changes in POD and FAR almost correspond to the number of training data. In other words, seasonal TCs can be detected without generating numerous false alarms. In particular, seasonal TCs in the western North Pacific (from July to November) could be detected with a POD of 79.0–89.1% and a FAR of 32.8–53.4% (p_th = 1.0). Similarly, seasonal TCs in the South Indian Ocean (from December to March) could be detected with a POD of 76.7–78.0% and a FAR of 31.1–40.3%. Furthermore, seasonal TCs in the North Atlantic (from August to November) could be detected with a POD of 75.0–78.2% and a FAR of 36.7–51.0%.

Fig. 9

POD and FAR (p_th = 1.0 and p_th = 0.6) and the number of data (training and test data) for each month in each basin. Note that the POD cannot be defined when the number of TCs is zero according to Eq. (2). In the same manner, the FAR cannot be calculated when the positive prediction area is zero, according to Eq. (3)

In contrast, numerous false alarms were generated during seasons with a low frequency of TCs. In the western North Pacific, although POD was not very low (65.7–83.0%) during January to May, the FAR was remarkably high (75.4–95.3%). It is noteworthy that POD in the North Pacific is unlikely to decrease even during seasons with a low frequency of TCs, except for months with extremely small numbers of positive ground truth. In the western North Pacific in December, the POD was 78.7% and the FAR was 65.9% (p_th = 1.0). Similarly, in the eastern North Pacific in November, the POD was 72.6% and the FAR was 68.4% (p_th = 1.0).

Long-term detectability

Detectability (POD), the number of training data (positive), and ground truth of each elapsed time frame in different basins are shown in Fig. 10. In each basin, the day with the highest POD is the day TCs formed (elapsed time = 0–2 days). One of the reasons for this is that this period is the transition period from the developing phase to the dissipation phase for most TCs, as shown in Fig. 2a. Obviously, fully developed TCs are easy to recognize. Another reason is that the training of the CNNs tends to focus on large samples near this period to reduce errors.

Fig. 10

Average-max-min charts of POD (p_th = 1.0 and p_th = 0.6) and bar graphs of the number of data (training and test data) for each elapsed time frame in each basin

The POD decreases as lead time is increased because it is difficult to detect the precursors many days in advance. For example, 91.2%, 77.8%, and 74.8% of precursors 2, 5, and 7 days before their formation can be detected in the western North Pacific, respectively (Fig. 10b). Similarly, 91.7%, 76.2%, and 70.1% of precursors 2, 5, and 7 days ahead can be detected in the eastern North Pacific, respectively (Fig. 10c). Note that the FAR could not be calculated in each elapsed time frame because TP could not be defined in each elapsed time frame.

In contrast to these basins, long-term detectability decreases rapidly in basins with less training data, such as the North Indian Ocean (Fig. 10a) and the North Atlantic (Fig. 10d). In most basins, the number of ground truth matches of test data is small from 7 to 14 days before the formation of precursors. Therefore, this time frame involves large errors and decreased reliability of POD. Note that these results are reference values because the POD and FAR could not be evaluated simultaneously.

Conclusions

In this work, the detectability of TCs and their precursors for each basin, season, and lead time was investigated based on a deep neural network approach using 20 year simulated OLR by the NICAM. From the results of applying the CNNs to untrained 10 year simulated OLR, the following conclusions can be drawn:

• Particularly in the western North Pacific, we could successfully detect TCs and their precursors during July to November with POD values of 79.0–89.1% and FAR values of 32.8–53.4%. Detection results include 91.2%, 77.8%, and 74.8% of precursors 2, 5, and 7 days before their formation, respectively.

• Although the detection performance was approximately consistent with the number of training data and TC lifetime, the detection performance in the North Atlantic was not relatively low despite limited training data and short lifetimes. In particular, the average POD and FAR values in the North Atlantic during September to October were 74.8% and 40.9%, respectively.

These results suggest the high potential of the data-driven approach for studying tropical cyclogenesis.

In contrast, the limitations of our framework are as follows:

• Since the candidate regions are narrowed down by the threshold value of cloud cover (30–95%), they cannot be detected when the cloud cover is extremely small (< 30%) or extremely large (> 95%).

• Our method considers developing TCs and precursors as one category. To evaluate the detection performance of only pre-TCs, it is necessary to classify them by improving the CNN model.

• Our CNN classifiers may have model-specific biases arising from training using only NICAM data.

In areas with less data such as the North Atlantic, training data from other basins may have a positive influence on prediction results. However, in areas with sufficient data, such as the North Western Pacific, training according to each basin might improve detectability. In order to verify and improve detection performance, it is necessary to analyze the influence of the data in different basins by training the generation patterns and environmental factors in each basin.

This paper describes the preliminary results of detecting precursors of tropical cyclones using only simulated OLR; we plan to use other proxies of convection such as rain rate and mixing ratio of solid water for improving the detection performance. Furthermore, we also plan to apply our ensemble CNNs to reanalysis data and satellite observation data for practical use. For this purpose, data of different spatial resolutions and different variables or satellite channels must be considered. Furthermore, time-sequence data as well as comparative analyses with the results of the Early Dvorak Method are also required.