Abstract

This study proposes a statistical regression scheme to forecast tropical cyclone (TC) intensity at 12, 24, 36, 48, 60, and 72 h in the northwestern Pacific region. This study utilizes best track data from the Shanghai Typhoon Institute (STI), China, and the Joint Typhoon Warning Center (JTWC), United States, from 2000 to 2015. In addition to conventional factors involving climatology and persistence, this study pays close attention to the land effect on TC intensity change by considering a new factor involving the ratio of seawater area to land area (SL ratio) in the statistical regression model. TC intensity changes are investigated over the entire life-span, over the open ocean, near the coast, and after landfall. Data from 2000 to 2011 are used for model calibration, and data from 2012 to 2015 are used for model validation. The results show that the intensity change during the previous 12 h (DVMAX), the potential future intensity change (POT), and the area-averaged (200–800 km) wind shear at 1000–300 hPa (SHRD) are the most significant predictors of the intensity change for TCs over the open ocean and near the coast. Intensity forecasting for TCs near the coast and over land is improved with the addition of the SL ratio compared with that of the models that do not consider the SL ratio. As this study has considered the TC intensity change over the entire TC life-span, the proposed models are valuable and practical for forecasting TC intensity change over the open ocean, near the coast, and after landfall.

1. Introduction

Timely and accurately predicting the track and intensity of a tropical cyclone (TC) is crucial for disaster prevention, especially for coastal regions that are very vulnerable to TCs. With the application of weather satellites in the last three decades and the popularity of ensemble forecasting for TC tracking, there has been considerable improvement in TC track prediction (Zhang and Krishnamurti 1997; Goerss 2000; Fraedrich et al. 2003; Langmack et al. 2012; Cangialosi and Franklin 2015; Jun et al. 2017). Although it is reported that TC intensity forecast models improved from 1989 to 2012 at a rate that is statistically significant (DeMaria et al. 2014), forecasting TC intensity remains a challenging task around the world (DeMaria and Kaplan 1999; DeMaria et al. 2005; Knaff et al. 2005; Cangialosi and Franklin 2012; Qian et al. 2012; DeMaria et al. 2014; Duan et al. 2014).

For decades, scientists have been making efforts to improve the skill of TC intensity prediction. Dvorak (1975) provided a technique, which contained some subjectivity, to estimate TC intensity over open oceanic areas by using satellite images. Jarvinen and Neumann (1979) proposed statistical regression equations for the prediction of TC intensity change out to 72 h over the North Atlantic basin by using predictors derived from climatology and persistence (SHIFOR). It is believed by meteorologists that the environment affects the intensity change of TCs. Pike (1985) tried to add synoptic information of geopotential heights and thicknesses as predictors of TC intensity change, in addition to the predictors of climatology and persistence. The addition of synoptic information did not prove to be a fruitful improvement for the prediction of TC intensity change. Merrill (1987) considered a wide range of synoptic predictors, such as the land effect and sea surface temperature (SST), to predict TC intensity change. Although no significant increase in prediction skill was found, Merrill’s (1987) study supported that TC intensity change was influenced by environmental conditions. Based on the work of Merrill (1987) and Jarvinen and Neumann (1979), DeMaria and Kaplan (1994a) proposed a Statistical Hurricane Intensity Prediction Scheme (SHIPS) to predict the TC intensity change over the Atlantic Ocean basin. More synoptic predictors were considered in SHIPS. The results showed that the average errors are 10%–15% smaller than the errors from a model that uses only SHIFOR. Evans (1993) and DeMaria and Kaplan (1994b) explored the relationship between SST and the maximum intensity of tropical cyclones and found that there was an empirical curve of maximum potential intensity (MPI), which few TCs could reach. An equation for TC potential future intensity change (POT) was derived as well (DeMaria and Kaplan 1994a). Generally, as SST increases, the MPI increases nonlinearly. For the 1997 hurricane season, SHIPS incorporated synoptic predictors from forecast fields, so the version of SHIPS was a “statistical–dynamical” model. After the modification, the model showed significant skill to forecast the intensity of TCs over the ocean basin (DeMaria and Kaplan 1999). SHIPS was further improved by considering storm decay over land (DeMaria et al. 2005). The updated model extended the forecast from 3 to 5 days and used an operational global model for the evaluation of atmospheric predictions instead of a simple dry-adiabatic model (DeMaria et al. 2005). Wang et al. (2015) found that the commonly used vertical wind shear measure between 200 and 850 hPa was less representative of the attenuating deep-layer shear effect than that between 300 and 1000 hPa. Moreover, TCs had a better chance to intensify than to decay when the deep-layer shear was less than 7–9 m s−1 and the low-level shear [between 850 (or 700) and 1000 hPa] was less than 2.5 m s−1 (Wang et al. 2015). The probability of rapid intensification (RI) became lower than that of rapid decay when the translational speed was greater than 8 m s−1. Most TCs tended to decay when the translational speed was greater than 12 m s−1, regardless of the shear condition (Wang et al. 2015).

Intensity forecast research for TCs in the Pacific Ocean was carried out as well. Elsberry et al. (1975) developed a statistical forecast scheme for tropical cyclone intensity change over the open ocean in the western North Pacific. The statistical equations were derived from climatology and persistence conditions (Elsberry et al. 1975). This scheme was updated in 1988 by including environmental information represented by the empirical orthogonal functions of the operationally analyzed wind fields at 700, 400, and 250 hPa and the vertical wind shear between these levels (Elsberry et al. 1988). This updated statistical scheme considered only storms with intensity over 18 m s−1 (35 kt) over the ocean basin. Ten predictors were selected for the proposed statistical regression equations for the prediction of TC intensity 24, 48, and 72 h into the future in the western North Pacific region. The smallest mean absolute intensity errors were 10.4 m s−1 for the 48-h forecast and 11.3 m s−1 for the 72-h forecast. Chu (1994) found that the relationship between intensities and other predictors such as Julian day, the latitude of the TC location, the longitude of the TC location, the past 12-h zonal component of tropical cyclone motion, the past 12-h meridional component of the TC motion, the current intensity, and the past 12-h change of the TC intensity was not linear. Fitzpatrick (1997) proposed a new intensity prediction scheme, Typhoon Intensity Prediction Scheme (TIPS), for storms over open water in the western North Pacific. TIPS utilized digitized satellite data as a new predictor, combined with other predictors from climatology and persistence, and the synoptic conditions. However, TIPS considered only TCs that achieved tropical storm strength (VMAX ≥ 35 kt) over the ocean basin. The TCs over land and TCs close to coastal areas were not applied to TIPS. Tropical depressions were not included in the scheme either (Fitzpatrick 1997).

A modification of the operational Statistical Hurricane Intensity Prediction Scheme was also applied to the eastern and central North Pacific (DeMaria and Kaplan 1999; DeMaria et al. 2005). The evolution of storm intensity was remarkably similar in the Atlantic and western North Pacific basins, with average intensification and decay rates of approximately 12 m s−1 day−1 and 8 m s−1 day−1, respectively (Emanuel 2000). The performance of the 5-day TC intensity forecast models derived from climatology and persistence for the Atlantic, eastern North Pacific, and western North Pacific Oceans were similar, and these models possessed similar bias characteristics (Knaff et al. 2003). In addition to the above statistical and statistical–dynamic models to forecast TC intensity, Tsai and Elsberry (2014, 2015) developed a weighted analog technique for 5-day intensity and intensity spread predictions for TCs in the western North Pacific and Atlantic, based on the rankings of the 10 best historical track analogs to match the official track forecast and current intensity.

Previous studies mainly considered TC intensity change over open water. However, TCs that make landfall or move close to the coast are usually responsible for most loss of life and damage. Therefore, forecasting the intensity of offshore TCs and TCs over land should be more important than the forecasting of TC intensity over the open ocean. To account for the influence of the land effect on the TC intensity change, Merrill (1987) defined “distance to land” as the distance at the point of the closest approach (PCA) in a 12-h period, measured at 3-h intervals. However, with the same PCA, the land shapes might vary from a sharp-tip coast to a flat long coast, which might have a differing influence on the TC intensity change. Therefore, this land consideration was too simple. Kaplan and DeMaria (1995) developed a simple empirical model for predicting the decay of TC wind after TC landfall by using the parameters of wind speed at landfall and time since landfall. However, the decay of a TC over land is also influenced by the background environment. Predicting a TC’s intensity decay without considering any environmental factors might be unreasonable.

In this study, a statistical regression method is proposed to forecast future TC intensity at 12, 24, 36, 48, 60, and 72 h in the northwestern Pacific region. In addition to the conventional factors of climatology and persistence, this study pays special attention to the land effect on TC intensity change by adding a new factor of “ratio of sea area to land area” into the statistical regression model. The paper is arranged as follows. An overview of the data and methodology is presented in section 2. Section 3 contains the results and discussion. Summaries are given in the final section.

2. Study area, data, and methodology

a. Study area and data

There is uncertainty in the TC intensity from the best track data when there is no direct intensity observation from aircraft (Torn and Snyder 2012; Manion et al. 2015). To account for the uncertainty, two different TC datasets are used in this study: the best track data from the Joint Typhoon Warning Center (JTWC 2016) and the best track data from Shanghai Typhoon Institute (STI 2016) for the period from 2000 to 2015 in the northwestern Pacific region, covering the area with latitude north of 0°N and longitude west of 180°. The TCs’ full life-spans are included in the data, including the pretropical storm stage, tropical intensification, tropical decay, extratropical transition, and occlusion. JTWC data are widely used in intensity forecast studies in the northwestern Pacific (Knaff et al. 2005; Tsai and Elsberry 2015). For TCs that affect China, the best track data from China might have obvious advantages such as more complete and more accurate information (Ren et al. 2011). The best track datasets include the TC time (year, month, day, hour), position (latitude and longitude of the TC center), TC central pressure, and the maximum sustained wind speed near the TC center. From the technical report of the World Meteorological Organization (WMO 2017), the criterion that different organizations (i.e., China and the United States) use for the TC classification is different. China uses the maximum sustained 2-min-average wind to classify TC intensity in the northwestern Pacific, while the United States uses the maximum sustained 1-min-average wind. Figure 1 shows the tracks of the TCs in the northwestern Pacific from 2000 to 2015 using the best track data from STI.

Fig. 1.

Tracks of the TCs in the northwestern Pacific from 2000 to 2015 (best track data from STI, 6-h interval).

Fig. 1.

Tracks of the TCs in the northwestern Pacific from 2000 to 2015 (best track data from STI, 6-h interval).

In addition to the TC data, this study uses the National Centers for Environmental Prediction (NCEP) Final (FNL) Operational Global Analysis data to reflect the environmental background (NCEP 2016). NCEP FNL data are on 1° × 1° grids at intervals of 6 h, that is, 0000, 0600, 1200, and 1800 UTC every day. The analyses are available at the surface and 26 mandatory levels from 1000 to 10 hPa. The parameters include sea level pressure, geopotential height, temperature, relative humidity, u and υ winds, and vertical motion. Furthermore, this study employs global weekly means of SST provided by NOAA (NOAA 2016), as the warm seawater is the energy source for TCs. The data from 2000 to 2011 are used for model calibration, and the data from 2012 to 2015 are used for model validation.

b. Method

1) Multiple linear regression model

Similar to SHIPS (DeMaria and Kaplan 1994a), multiple linear regression (Hill and Lewicki 2007) is used in this study to explore the statistical prediction model for TC intensity. The TC intensity changes are used as predictands, and the climatological, persistence, and synoptic variables are used as predictors. Only the statistically significant predictors at 95% confidence level based on the F-statistic test are chosen in the prediction model.

2) Sea–land ratio

Warm ocean water is the main source of energy for TCs (Simpson and Riehl 1981). A change in the underlying surface from ocean water to land will have great impact on TC intensity. TCs will generally weaken quite rapidly over land (Chen et al. 2004; Chen 2012). Therefore, the ratio of water area to land area will be of great importance to the intensity change of TCs.

In this study, a new factor called sea–land ratio (SL ratio) is proposed to account for the ratio of water over a certain area. A similar concept was proposed by DeMaria et al. (2006) in a TC wind decay model for storms moving over narrow landmasses. SL ratio is defined in Eq. (1). Taking any TC position as the center, a circle is drawn with a radius of a certain distance, for example, 500 km (Fig. 2). The SL ratio is defined as the ratio of the water surface area within the circle over the whole circle area:

 
formula
Fig. 2.

Diagram of the SL ratio.

Fig. 2.

Diagram of the SL ratio.

SL ratios with a radius of 500 km along the mainland China coastline are computed. The mean and median values for the SL ratios are 49.6% and 49.66%, respectively. Therefore, when (SL ratior=500) < 50%, the TC position is approximately defined as over land. For all historical TC positions, SL ratios with a radius of 500 km are computed. This SL ratio is used to separate TC samples. When (SL ratior=500) ≥ 99.9%, the TC position is defined over the open ocean; when 50% ≤ (SL ratior=500) ≤ 99.9%, the TC position is defined near the coast; when (SL ratior=500) < 50%, the TC is over land. All TC samples can then be separated into samples over open ocean, near the coast, and over land. For example, position A in Fig. 2 is computed to be a point near the coast, while position B is computed to be an open ocean point, and position C is computed to be a land point. The reason for choosing 500 km as a criterion to separate the TC samples is to balance the size of TC samples near the coast and over the open ocean. Choosing 600 km or more will lead to much more TC samples near the coast than samples over the open ocean, while choosing 400 km or less will lead to the opposite situation. The numbers of TC samples over the open ocean, near the coast, and over land based on the radius of 500 km, as well as the total TC samples for future 12-, 24-, 36-, 48-, 60-, and 72-h TC intensity change prediction models are summarized in Table 1. Furthermore, an SL ratio with a smaller radius ranging from 100 to 500 km with increments of 50 km is computed and introduced as a predictor candidate into the multiple linear regression model. The radius of the SL ratio is eventually determined when the minimum mean absolute error (MAE) is obtained for the intensity change forecasting models.

Table 1.

Sample numbers for different TC groups. Cal = calibration; Val = validation.

Sample numbers for different TC groups. Cal = calibration; Val = validation.
Sample numbers for different TC groups. Cal = calibration; Val = validation.

3) Potential predictors

Referring to the SHIFOR model (Jarvinen and Neumann 1979), SHIPS model (DeMaria and Kaplan 1994a, 1999), and TIPS model (Fitzpatrick 1997), the potential predictors used in this study are listed in Table 2. Some of the variables in Table 2 are computed with an area of 200–800 km, while some of the variables are computed with an area of 100–700 km. The area for those variables is chosen based on the computed area relationship with the intensity change. For example, wind shear at 1000–300 hPa (SHRD) computed with an area of 200–800 km is more representative than an area of 100–700 km, so SHRD with an area of 200–800 km is left as the potential predictor in Table 2. Only the statistically significant predictors at the 95% level will be chosen in the TC intensity prediction models.

Table 2.

Potential predictors available for the regression models.

Potential predictors available for the regression models.
Potential predictors available for the regression models.

3. Results and discussion

a. Comparison of the TC intensities from different data sources

The two TC datasets (STI data and JTWC data) are first compared to find their different TC intensity characteristics. As described in section 2a, China uses the maximum sustained 2-min-average wind to classify TC intensity in the northwestern Pacific, while the United States uses the maximum sustained 1-min-average wind. Generally, the value of maximum sustained 1-min-average wind should be greater than the value of maximum sustained 2-min-average wind if these data are from the same data source. In Fig. 3, it can be observed that for most of the time, the TC intensity of JTWC is greater than the TC intensity of STI; however, there are also some cases in which the TC intensity from STI data is greater, especially when the TC intensity is below 50 m s−1.

Fig. 3.

Comparison of the TC intensity between JTWC and STI.

Fig. 3.

Comparison of the TC intensity between JTWC and STI.

b. Computation and selection of the model predictors

For the multiple linear regression model, the dependent variables are the intensity changes from the initial forecast time at 12-h intervals (i.e., intensity change for the future 12, 24, 36, 48, 60, and 72 h). The potential predictors in Table 2 are computed and evaluated for their combined statistical significance for the corresponding models. All multiple linear regression models for the two different datasets are developed. As the sample size (Table 1) for TCs over land is not large enough to develop a reasonable model, this study considers only TC intensity changes within 24 h (including 24 h) after TC landfall. Table 3 shows the selection results of the significant predictors for the prediction models based on the two different datasets. A zero value in the table means the variable is not selected in the prediction models for both datasets; 1 means the variable is selected by the prediction model for the STI dataset; an italic 2 means the variable is selected by the prediction model for the JTWC dataset; an italic bold 3 means the variable is selected by the prediction models for both datasets. The radius of the SL ratio is eventually determined to be 500 km, as the computed MAE for the near-coast TC models and all TC sample models for different time intervals is the smallest for most times when the radius is 500 km, based on both STI and JTWC datasets.

Table 3.

Selection results for the significant variables for TC intensity models for STI and JTWC datasets. A zero value means the variable is not selected in the prediction models for both datasets; 1 means the variable is selected by the prediction model for the STI dataset; an italic 2 means the variable is selected by the prediction model for the JTWC dataset; an italic bold 3 means the variable is selected by the prediction models for both datasets.

Selection results for the significant variables for TC intensity models for STI and JTWC datasets. A zero value means the variable is not selected in the prediction models for both datasets; 1 means the variable is selected by the prediction model for the STI dataset; an italic 2 means the variable is selected by the prediction model for the JTWC dataset; an italic bold 3 means the variable is selected by the prediction models for both datasets.
Selection results for the significant variables for TC intensity models for STI and JTWC datasets. A zero value means the variable is not selected in the prediction models for both datasets; 1 means the variable is selected by the prediction model for the STI dataset; an italic 2 means the variable is selected by the prediction model for the JTWC dataset; an italic bold 3 means the variable is selected by the prediction models for both datasets.

From Table 3, it can be seen that for the STI and JTWC datasets, intensity change during the previous 12 h (DVMAX), POT, and SHRD are the most significant predictors for TCs near the coast and over the open ocean and have been selected as predictors in all models for different time intervals for both STI and JTWC data. After TC landfall, the significant variables become less than the time when TCs are over the open ocean and near the coast. DVMAX is the most important variable after TC landfall.

Analysis of the significant model predictors

From the previous section, it can be seen that DVMAX, POT, and SHRD are the most significant predictors for TCs near the coast and over the open ocean. The following section shows the relationship between the TC intensity change and those significant model predictors. Only the analyses based on STI data are shown here.

(i) DVMAX

Figure 4 shows the frequency distribution of the TC future intensity change relative to DVMAX near the coast and over the open ocean based on STI data. The blue bars in the figure refer to the negative intensity change, while the red bars refer to the positive intensity change, and the black bars represent no intensity change. The left column of Fig. 4 shows the intensity change for TCs near the coast, while the right column shows the intensity change for TCs over the open ocean. From top to bottom, Fig. 4 shows the next 12–72-h TC intensity change relative to DVMAX.

Fig. 4.

Frequency distribution of the intensity change relative to DVMAX for TCs near the coast and over the open ocean based on STI data. (left) TCs near the coast; (right) TCs over the open ocean. (from top to bottom) The next 12–72-h intensity change relative to DVMAX.

Fig. 4.

Frequency distribution of the intensity change relative to DVMAX for TCs near the coast and over the open ocean based on STI data. (left) TCs near the coast; (right) TCs over the open ocean. (from top to bottom) The next 12–72-h intensity change relative to DVMAX.

It can be seen in Fig. 4 that more than 95% of the 12-h intensity change is within 10 m s−1 of zero. There is a relatively high probability that the TC intensity will not change within 12 h. For TCs near the coast, the probabilities of no intensity change for the next 12 h are approximately 25% for negative DVMAX and approximately 11% for positive DVMAX. For TCs over the open ocean, the probabilities of no intensity change for the future 12 h are approximately 21% for negative DVMAX and approximately 13% for positive DVMAX. Over time, this probability of no intensity change decreases evidently. For TCs near the coast with a negative DVMAX, the intensity change over the next 12 to 72 h will most likely decrease. For TCs near the coast with a positive DVMAX, the intensity change over the next 12–24 h will most likely increase; however, the intensity change probability for the next 36–72 h becomes uncertain. For TCs over the open ocean with a negative DVMAX, the probability of a decrease in intensity over the next 12–72 h is almost the same at approximately 20%, while the probability of an increase over the next 12 h is approximately 13%, and the probability of an increase over the next 24–72 h is approximately 19%. In comparison, for TCs over the open ocean with a positive DVMAX, the probability of intensity change over the next 12–72 h is more likely to increase. The shorter the forecast time is, the more certain the tendency is. In conclusion, the future TC short-time (12–24 h) intensity change will be more dominated by the previous 12-h intensity change, while with an increase in time, the TC intensity change becomes uncertain, especially for TCs near the coast with positive DVMAX and for TCs over the open ocean with negative DVMAX.

(ii) POT

POT is the difference between the MPI and the current storm intensity (DeMaria and Kaplan 1994a). Similar to Fig. 4, Fig. 5 shows the frequency distribution of the intensity change relative to POT. It can be seen in Fig. 5 that the probability of no intensity change for the next 12 h is approximately 35% for TCs both near the coast and over the open ocean. Over time, the probability of TC intensity change increases, especially the decreasing tendency for TCs near the coast and the increasing tendency for TCs over the open ocean.

Fig. 5.

As in Fig. 4, but for POT.

Fig. 5.

As in Fig. 4, but for POT.

Generally, it can be seen in Fig. 5 that when POT is small, TC intensity tends to decrease, while when POT is large, TC intensity tends to increase. The threshold for these intensity trend changes is different between the TCs near the coast and TCs over the open ocean. For TCs near the coast, the POT threshold is 50 m s−1, which means when POT is below 50 m s−1, it is more likely that the intensity of TCs near the coast will decrease; when POT is above 50 m s−1, the intensity of TCs near the coast will be more likely to increase. For TCs over the open ocean, this POT threshold is approximately 40 m s−1, smaller than that of TCs near the coast. That means it is easier for TCs over the open ocean to grow stronger than TCs near the coast.

(iii) SHRD

Vertical wind shear has been found to be one of the most important dynamic parameters affecting TC intensity change (Gray 1968; McBride and Zehr 1981; DeMaria and Kaplan 1999; Zehr 2003; Wang and Wu 2004; DeMaria et al. 2005; Paterson et al. 2005; Zeng et al. 2010; Riemer et al. 2010; Kaplan et al. 2015; Wang et al. 2015). In Table 3, it can be seen that SHRD is chosen as a significant predictor in all intensity forecast models for TCs near the coast, over the open ocean, and entire TC samples (the last column).

In Fig. 6, it can be seen that more than 90% of SHRD is within the range of 5–20 m s−1. When TCs are over the open ocean, their intensity will be more likely to increase when SHRD is less than 15 m s−1; when SHRD is greater than 20 m s−1, the intensity will definitely decrease over the open ocean, while when SHRD is between 15 and 20 m s−1, it is more likely that the intensity will decrease. By comparison, when TCs are near the coast, the threshold of SHRD for TC intensity change is 10 m s−1. When SHRD is less than 10 m s−1, TC intensity will be more likely to increase for the next 12–36 h. However, for the future time longer than 36 h, the tendency of the intensity change becomes uncertain for SHRD less than 10 m s−1. Under this condition, the probabilities of TC intensity increasing and decreasing are almost the same.

Fig. 6.

As in Fig. 4, but for SHRD.

Fig. 6.

As in Fig. 4, but for SHRD.

(iv) SL ratio

In addition to the conventional parameters, this study introduces a new variable, SL ratio, into the statistical multiple linear regression (MLR) model. This variable is a constant of 1 and should have no influence on TC intensity change when a TC is over open ocean; however, SL ratio will impact a TC’s intensity change when the TC is near the coast or is over land. As TCs will usually decay quickly after they make landfall, this study considers only the TC intensity change within 24 h (including 24 h) after TC landfall. Therefore, Fig. 7 shows only the frequency distribution for the next 12- and 24-h intensity change relative to SL ratio for TCs over land and near the coast. In the figure, it can be seen that only when the SL ratio is greater than 0.9 would the TC intensity be more likely to increase. When a TC is near the coast with SL ratio below 0.9, the intensity is more likely to decrease. The lower the SL ratio, the more possible the TC intensity will decrease. For TCs over land with SL ratio below 0.5, less than 6% of the TC intensity will possibly increase for the next 12 and 24 h.

Fig. 7.

Frequency distribution of the intensity change relative to the SL ratio for TCs over land and near the coast based on STI data. (left) TCs over land; (right) TCs near the coast. The next (a),(b) 12- and (c),(d) 24-h intensity change relative to the SL ratio.

Fig. 7.

Frequency distribution of the intensity change relative to the SL ratio for TCs over land and near the coast based on STI data. (left) TCs over land; (right) TCs near the coast. The next (a),(b) 12- and (c),(d) 24-h intensity change relative to the SL ratio.

c. Evaluation of the prediction model for TC intensity change

As described in section 2, the historical data from 2000 to 2011 are used for model calibration, and the data from 2012 to 2015 are used for model validation. Before the model development, all predictors and predictands are normalized by subtracting the means and dividing by the standard deviations of the corresponding variables (Steel and Torrie 1980; DeMaria and Kaplan 1994a). The performance of the prediction models for both calibration and validation periods can be evaluated in terms of the statistical properties of coefficient of determination R2, MAE, and root-mean-square error (RMSE). Figures 8 and 9 show the comparisons of the prediction models’ performance based on STI data and JTWC data. Particularly, the performance of the prediction models with and without the variable of the SL ratio is compared in Figs. 8 and 9. In the figure, it can be seen that the models’ performance including the variable of the SL ratio for the TCs over land, the TCs near the coast, and all TC samples is generally better than the models’ performance without the variable for both calibration and validation. Generally, R2 will increase by approximately 3%–5% when including the variable of the SL ratio; the MAE and RMSE will decrease by approximately 2% compared to the prediction models without the variable of the SL ratio. The R2 value will increase with the forecasting interval time. For STI (JTWC) data, R2 is approximately 0.47 (0.5) at the 12-h-interval forecast time and is approximately 0.66 (0.64) at the 72-h-interval forecast time for all TC prediction models. MAE and RMSE will also increase with increasing forecast time interval. For all models of STI (JTWC) data, MAE is approximately 2.5 (3) m s−1 at the 12-h forecast time interval and is approximately 8 (10) m s−1 at the 72-h forecast time interval. From the comparison, the best track data from STI might be slightly better than the best track data from JTWC.

Fig. 8.

Statistical comparisons of R2, MAE, and RMSE for the intensity prediction models for TCs over land, near the coast, and over the open ocean for STI data: (left) R2, (center) MAE, and (right) RMSE. (a)–(c) TCs over land; (d)–(f) TCs near the coast; (g)–(i) TCs over the open ocean; (j)–(l) all TC samples.

Fig. 8.

Statistical comparisons of R2, MAE, and RMSE for the intensity prediction models for TCs over land, near the coast, and over the open ocean for STI data: (left) R2, (center) MAE, and (right) RMSE. (a)–(c) TCs over land; (d)–(f) TCs near the coast; (g)–(i) TCs over the open ocean; (j)–(l) all TC samples.

Fig. 9.

As in Fig. 8, but for JTWC data.

Fig. 9.

As in Fig. 8, but for JTWC data.

For TCs over land, R2 for the simulation of TC intensity change is approximately 0.7 for the 12-h forecast interval time and is approximately 0.9 for the 24-h forecast interval time. The MAE and RMSE are less than those values for TCs near the coast and TCs over the open ocean. The reason might be that the TC intensity will normally decay quickly after landfall. The number of significant variables affecting TC intensity change is less than the significant variable numbers when TCs are near the coast and over the open ocean; therefore, the TC intensity decay process is not as complicated as for TCs near the coast and over the open ocean, yielding better performance for TC intensity prediction after landfall.

In addition, the MLR model is compared with the simple empirical inland wind decay model (Kaplan and DeMaria 1995) to forecast TC intensity after landfall. The simple empirical wind decay model (EWDM) can be expressed by the following equation (Kaplan and DeMaria 1995):

 
formula

where is the maximum sustained surface wind speed (MSSW) with time; is the decay constant (h−1), and t (h) is the time after landfall; is the MSSW at and is the background wind speed to which the MSSW decays; and R is a reduction factor to account for the rapid wind decrease as the landfalling TC crosses the coastline (Kaplan and DeMaria 1995).

Again, the historical data from 2000 to 2011 are used for model calibration, and the data from 2012 to 2015 are used for model validation. Tables 4 and 5 illustrate the performance comparison based on both datasets and the computed results of the parameters and for the EWDM.

Table 4.

Comparison of the model performance between the simple EWDM and the MLR model in forecasting TC intensity after TC landfall in terms of statistical characteristics of R2, MAE, and RMSE for the STI dataset. The computed coefficients of and for a series of R values are shown in the table as well. Cal = calibration; Val = validation.

Comparison of the model performance between the simple EWDM and the MLR model in forecasting TC intensity after TC landfall in terms of statistical characteristics of R2, MAE, and RMSE for the STI dataset. The computed coefficients of  and  for a series of R values are shown in the table as well. Cal = calibration; Val = validation.
Comparison of the model performance between the simple EWDM and the MLR model in forecasting TC intensity after TC landfall in terms of statistical characteristics of R2, MAE, and RMSE for the STI dataset. The computed coefficients of  and  for a series of R values are shown in the table as well. Cal = calibration; Val = validation.
Table 5.

As in Table 4, but for the JTWC dataset.

As in Table 4, but for the JTWC dataset.
As in Table 4, but for the JTWC dataset.

The computed results of and for the EWDM based on STI data and JTWC data are similar. Comparing the parameter values computed by Kaplan and DeMaria (1995) for TCs landfalling in the United States, the value for TCs landfalling in Asia is smaller, which means that TCs generally decay more slowly in Asia than in America. In Tables 4 and 5, it can be seen that although the statistical parameters of R2, MAE, and RMSE of the EWDM are not bad for the calibration period, the performance of the model is not good for the validation period. By comparison, the MLR model introduced in this study performs well for both calibration and validation periods.

Furthermore, the performance of the above MLR model in forecasting TC intensity over the northwestern Pacific Ocean basin is compared with the forecasting skill of the Statistical Typhoon Intensity Prediction Scheme (STIPS) proposed by Knaff et al. (2005) based on JTWC data. The MAEs are almost the same for the two models, and the R2 value obtained in this study is slightly higher than the R2 obtained by Knaff et al. (2005). Actually, the performance of these two models in forecasting TC intensity over the open ocean is almost the same, as they are based on the same physical regression mechanism; however, the data are from different periods.

Finally, the observed and simulated time series of two TCs [Fengshen (200209) and Soudelor (201513)] with 12- and 24-h forecast interval times for the calibration and validation periods, respectively, are compared in Fig. 10. The tracks of these two TCs are shown in Fig. 10a. It can be seen that these two TCs have experienced all three processes: over the open ocean, near the coast, and over land. Figures 10b–e show the TC intensity forecast for Fengshen and Soudelor at 12- and 24-h-interval times based on the two different datasets, respectively. The red color indicates STI data, and the black color indicates JTWC data. The solid lines are the TC intensities from the best track data, and the dashed lines are the intensity forecasts. From the figure, it can be seen that the prediction model can generally capture the TC intensity variation at 12- and 24-h forecast interval times, especially for TCs over the open ocean and after landfall. At these two phases, the underlying surface is relatively simpler than the underlying surface for TCs near the coast. It can also be seen in Fig. 10 that the models’ performance is suboptimal when the TC experiences rapid intensity change.

Fig. 10.

(a) The tracks of Fengshen (200209) and Soudelor (201513); the intensity forecast for TC Fengshen (b) 12 h and (c) 24 h in advance; the intensity forecast for TC Soudelor (d) 12 h and (e) 24 h in advance.

Fig. 10.

(a) The tracks of Fengshen (200209) and Soudelor (201513); the intensity forecast for TC Fengshen (b) 12 h and (c) 24 h in advance; the intensity forecast for TC Soudelor (d) 12 h and (e) 24 h in advance.

4. Conclusions

This study has developed TC intensity prediction models by using TC datasets from STI and JTWC from 2000 to 2015. The TC intensity value defined with the maximum sustained 2-min-average wind by STI is generally smaller than the TC intensity issued by JTWC, which is defined with the maximum sustained 1-min-average wind. By introducing a new parameter of the SL ratio, the TC life-span is divided into three parts: over the open ocean, near the coast, and over land. In contrast to previous studies, this study investigates TC intensity change for the entire life-span. The results show that the intensity change during the previous 12 h (DVMAX), the potential future intensity change (POT), and the area-averaged (200–800 km) wind shear at 1000–300 hPa (SHRD) are the most significant predictors of TC intensity change for TCs over the open ocean and near the coast. The future TC short-time (12–24 h) intensity change will be more dominated by DVMAX, while with the time increase, the TC intensity change becomes uncertain, especially for TCs near the coast with positive DVMAX and for TCs over the open ocean with negative DVMAX. The threshold of POT is 40 m s−1 for TCs over the open ocean and 50 m s−1 for TCs near the coast. When the POT value is above the threshold in the corresponding region, TC intensity is more likely to increase. The threshold of SHRD is 15 m s−1 for TCs over the open ocean and is 10 m s−1 for TCs near the coast. When SHRD is below the threshold in the corresponding region, TC intensity is more likely to increase. The TC prediction models proposed in this study can generally capture TC intensity variation at 12- and 24-h-interval forecast times. The R2 value is approximately 0.47 and 0.5 at a 12-h forecast time for the STI dataset and JTWC dataset, respectively, and is approximately 0.66 and 0.64 at a 72-h forecast time for the two different datasets. The MAE is approximately 2.5 and 3 m s−1 at a 12-h forecast time interval and is approximately 8 and 10 m s−1 at a 72-h forecast time for the two datasets, respectively. Particularly, the performance of the MLR model is compared with the EWDM model in forecasting the TC intensity after landfall. The results show that the MLR model performs better than EWDM.

It is worth noting that all results in the paper are based on the “perfect prog” approach in which analyses are used to estimate the predictors during the forecast period for the model development. Tests with inputs available only in real time are still needed to evaluate the usefulness of the model for operational forecasting. The prediction models proposed in this study consider not only TC intensity over the open ocean but also the intensity change when TCs are near the coast and after they make landfall. Therefore, the prediction models are practically useful and are valuable for operational forecasters.

Acknowledgments

This paper is supported by the Innovation of Science and Technology Commission of Shenzhen Municipality with Grants JCYJ20170413164957461 and JCYJ20150521144320984; the Natural Science Foundation of Guangdong Province with Grant 2015A030313742; and the National Natural Science Foundation of China with Grants 61433012 and U1435215.

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Footnotes

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