A Kernel Density Estimation Approach and Statistical Generalized Additive Model of Western North Pacific Typhoon Activities

Abstract

This paper presents a development of a statistical model of typhoon genesis, tracks based on kernel density estimation and a generalized additive model (GAM). Modeling of typhoon activity is ultimately beneficial to the people living in coastal zones, insurance/re-insurance companies, policy, planning and decision departments. A 50-year record (1972–2021) of typhoon track observations from the International Best Track Archive Climate Stewardship have been used to observe the distribution of typhoon genesis by kernel density estimation. The tracks are simulated through the development of a GAM. It reproduces the observation well. A distance calculation approach between observed and simulated tracks’ landfall have been used to validate the model and the model shows a very good skill (approximately 75%).

1. Introduction

The Western North Pacific (WNP) basin is most active for typhoons during boreal summer, although typhoons can be observed all year round. Typhoons forming in the main development region often impact on the compactly occupied littoral regions of eastern (e.g., Japan, Korean, China) and south-eastern Asia (e.g., Philippines and Vietnam) due to a mean westward steering flow [1]. Typhoons forming nearer the equator and west of 130°E generally show the “straight-moving” west-northwestward trajectories and impact to Southeast Asia and southern China [2], while typhoon systems occurring more centrally in the basin tend to have curving trajectories [3], often impacting the eastern Asian countries such as Japan and Korea with high intensity [2].

In comparison to typhoon frequency projections, there is currently a low confidence in projected changes of typhoon tracks in a warming climate around the globe. Typhoon track properties define “activity regions” which have received attention [4] but investigations into projected changes isolating typhoon tracks themselves and how they contribute to overall typhoon activity are limited across the globe. A record on typhoon frequency, genesis location and track projection results are observed highly in WNP typhoon basin through a number of numerous climate projection. Generally, climate projection utilizes one of three approaches to examine typhoon behaviors in climate models: (i) direct simulation, (ii) downscaling, or (iii) use of large-scale genesis indices. In direct simulation, algorithms are put in place to detect typhoons in model data using a tracking scheme and in downscaling, less computer-intensive coarse resolution models which detect typhoons that are fed into a finer resolution regional model to solve typhoon intensities. In genesis indices, typhoon genesis climatologies are directly implied from large scale environmental conditions. An advantage of direct simulation is the detection algorithm, and no additional assumptions are required [5] when compared to the other two methods. For the direct simulation of typhoon in the WNP, both fine (~20–50 km) and coarse (~100–300 km) resolution climate models have been used [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. They can have relatively good representations of the large-scale processes that affect typhoon characteristics such as genesis locations and tracks [21,22], though typhoon intensities are poorly resolved in coarse resolution models. The coarse resolution models are readily available for the climate projection studies and therefore, models can be used as a key tool for delivering valuable evidence on future projections of typhoon genesis and tracks.

All models have strengths and limitations and can generate very diverse results when compared to the observation [23,24] and so we argue the WNP basin is worth revisiting with a necessarily different methodology. The algorithm in [25] uses a threshold within the model which is objectively defined and shows an advantage between model and detector error which is helpful to mask model errors [26,27,28,29,30,31] partly. This is principally problematic for low-resolution models and weak storms [23] which are typical of typhoons directly simulated in models.

A generalized additive model (GAM) is a powerful and simple technique and easy to interpret based on the flexibility and regularization of prediction functions [32,33,34,35,36,37] Modeling studies will be a great societal value when the risk-mitigation policies are considered and future planning efforts are focused to the most high-risk areas [38,39,40,41,42]. In the present study, we have used a kernel density estimation approach and GAM to observe the typhoon characteristics in the WNP basin.

2. Data and Methods

2.1. Typhoon Observation

The International Best Track Archive for Climate Stewardship-World Meteorological Organization version (IBTrACS-WMO) is a widespread compilation of quality controlled global typhoon best-track data, available at 3 h intervals and sourced from several meteorological organizations and agencies around the world. Typhoon tracks from this database are taken 3-hourly over the 50-year period 1972 to 2021. Data in this period are consistent with the era after which routine satellite observations became available. Globally, a good alternative to IBTrACS-WMO can be achieved by combining data from the Joint Typhoon Warning Centre (JTWC) and National Hurricane Centre (NHC).

2.2. Kernel Density Estimation

In a nonparametric way, KDE is a process to estimate the probability density function (PDF) of a random variable. The KDE distribution is defined by a smoothing function and a bandwidth value that reins the smoothness. More formally, kernel estimators convolve each data point with a kernel function K to produce a smooth estimate $\widehat{f}$ of the density,

$$\widehat{f}\left(x\right)=\frac{1}{n}{\displaystyle \sum }_{i=1}^{n}K\left(\frac{x-x\left(i\right)}{h}\right)$$

(1)

The degree of this involvement is conditional upon the shape of the kernel function and h, the chosen bandwidth. A higher bandwidth increases the region influenced by each xi, resulting in a smoother estimate. The kernel K must satisfy the constraint and is a common choice.

$$K\left(x\right)={\left(2 \pi \right)}^{-1}\exp \left(-\frac{x^2}{2}\right)$$

(2)

The distribution of genesis points as a function of season is approximated by KDE. In the plug-in analysis, the kernel bandwidth is calculated as hopt = 1.06σn − 0.2, here σ, n denote the standard deviation and number of observations, respectively.

2.3. Generalised Additive Model

Generalized additive model (GAM) is an extension of the generalized linear model in which the function considers both the linearity and non-linearity nature of the datasets using the smooth transformations of the predictors.

In case of regression, the mean, can be modeled as a linear combination of predictor variables,

$$\mu =E(Y|X_1,X_2,\dots ,X_p)={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\dots {\beta }_p{X}_p$$

(3)

where, ${\beta }_0-{\beta }_p$ are the regression coefficients to be estimated.

The generalized linear model spreads the linear model in two key ways. First, the consideration of any distribution from any exponential family of distributions (including the Poisson, Binomial, and Normal families). Secondly, the predictors enter the model through the linear predictor.

The generalized additive model uses a number of smooth transformations expressed in the form:

$$\mu =E(Y|X_1,X_2,\dots ,X_p)={\beta }_0+f_1\left(X_1\right)+f_2\left(X_2\right)+\dots f_p\left(X_p\right).$$

(4)

where the regression model seeks to estimate the regression coefficients β₀, β₁… β_p, the additive model seeks to estimate these smooth transformations f₁, f₂… fp.

2.4. Outline of Simulation

The outlines of the simulation are:

• The month corresponding to typhoon genesis and the track, are calculated. Then, the GAM is fitted to the track increments by calculating the track velocities.
• A GAM is fitted to the velocity for the prediction. Each velocity is considered as a smooth function of location in each month.
• KDE approximates the distribution of genesis points, and the kernel bandwidth is considered automatically using a standard plug-in estimator.
• Samples are drawn using a Gaussian mixture. Random samples of 200 genesis points are chosen from each of the densities.
• The trajectories take a matrix of initial points, and an array of stochastic innovations is applied at each time step. A 7-day life span is considered.

2.5. Skill and Validation

The distance between the observed and simulated landfall points is calculated and validated. We compute the landfall for the observed tracks and then measured the distance of the true landfall from the simulated landfall. We can see that the majority of simulated TC landfall occurrences (approximately 75% which is calculated through distance between observation and simulation) occur within 0–1000 km of the observed track locations which is the spatial scale of typhoon O (1000 km).

3. Results and Discussion

We have considered a 50-year record of storms from JTWC database for the period of 1972–2021. The observed genesis locations (left) and tracks (right) are shown in Figure 1. Most typhoons initially move towards the westward and later on in their lifetime, they are seen to recurve towards the northeast. Month-wise typhoon tracks are shown in Figure A1a–l in Appendix A, consistent with earlier studies [1,42]. Most typhoons move towards the westward in January (See Figure A1a in Appendix A). The same characteristics are seen from February to May (See Figure A1b–e in Appendix A). In June, two cluster types of tracks are seen. One cluster moves westward and the other one initially moves westward and then recurves towards the northeast (See Figure A1f in Appendix A). The same characteristics are seen from July to December (See Figure A1g–l in Appendix A). This is consistent with an earlier study by Camargo et al. [2] where they showed typhoons that formed close to the equator and west of 130E, moved to westward direction and impacted southeast Asia and southern China.

The observed genesis points are shown in Figure 2. Using the kernel density estimation, the modeled distribution of genesis points is shown in Figure 3. The highest density is found in August followed by September and July which is consistent with the observed genesis locations.

For each season like July to September, we have fitted the GAM to the observed typhoon tracks. The GAM estimates the typhoon velocities (Figure 4) as a function of each season. In June–July, we can see the westward or northward movement of the fitted typhoon tracks whereas, in the August–September season, it shows a tendency for typhoons to move towards the north, and then recurve towards the northeast.

Simulations of typhoon genesis (Figure 5) and tracks (Figure 6) indicate how the modeled storms tend to move. In June–July, the typhoon track indicates a westward or northward movement and in the August–September season, it shows a tendency to move towards the north, and then recurve towards the northeast. It is clear that typical changes in TC activity were due to ENSO variability. This includes north-westward displacement of TCs in the WNP during La Niña (e.g., Chan [43,44]).

We have calculated the distance between the observed and simulated track points across all simulated tracks and the distribution histogram is presented in Figure 7. We can see the highest percentage (approximately 75%) of simulated TC landfall within 0–1000 km of the observed track locations. As we are aware of the spatial scale of typhoon, modeled tracks’ occurrences within ~1000 km of the observations would suggest very good model performance.

4. Summary

The WNP basin is most active during the boreal summer though typhoons can be observed all year round. This study has described a new climatological statistical model of typhoon genesis, tracks and landfall for the WNP basin. The main findings are as follows:

• Kernel density estimation is an effective method to estimate the distribution of typhoon genesis points. Using the kernel density estimation, the modeled genesis distribution can reproduce the observed genesis.
• A novel generalized additive model (GAM) has skill to reproduce the track in each season by creating a velocity field.
• The highest percentage of typhoon genesis is seen in July–September among all twelve months and the modeled genesis distributions are consistent with observations.
• The model shows 75% skill using a distance calculation approach between observed and simulated track locations.

Overall, this work has provided an in-depth look at typhoon activities over the WNP basin, and it is expected that the work will contribute in decreasing the uncertainty and move towards a consensus in the arena of typhoon forecasts. This work will also benefit both the scientific community and the society at a large scale.