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Tropical Cyclone Intensity Estimation Using RVM and DADI Based on Infrared Brightness Temperature

CHANG-JIANG ZHANG AND JIN-FANG QIAN College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China

LEI-MING MA AND XIAO-QIN LU Shanghai Typhoon Institute, Shanghai, China

(Manuscript received 6 August 2015, in final form 3 August 2016)

ABSTRACT

An objective technique is presented to estimate tropical cyclone intensity using the relevance vector machine (RVM) and deviation angle distribution inhomogeneity (DADI) based on infrared satellite images of the northwest Pacific Ocean basin from China’s FY-2C geostationary satellite. Using this technique, structures of a deviation-angle gradient co-occurrence matrix, which include 15 statistical parameters nonlinearly related to tropical cyclone intensity, were derived from infrared satellite imagery. RVM was then used to relate these statistical parameters to tropical cyclone intensity. Twenty-two tropical cyclones occurred in the northwest Pacific during 2005–09 and were selected to verify the performance of the proposed technique. The results show that, in comparison with the traditional linear regression method, the proposed technique can significantly improve the accuracy of tropical cyclone intensity estimation. The average absolute error of intensity estimation 2 using the linear regression method is between 15 and 29 m s 1. Compared to the linear regression method, the 2 average absolute error of the intensity estimation using RVM is between 3 and 10 m s 1.

1. Introduction 1995; Velden et al. 2006). In the late 1980s, the World Meteorological Organization (WMO) recommended In recent decades, tropical cyclone track prediction the Dvorak technique as the world’s primary intensity has been greatly improved. However, because of the forecasting tool. But the technique is both subjective difficulties in estimating tropical cyclone intensity, ad- and time intensive. Particularly, its intensity estimation vances in intensity prediction are not quite evident. accuracy mainly depends on the experience of the user. Currently, tropical cyclone intensity estimation Based on the original Dvorak technique, Velden et al. mainly depends on satellite observations. Polar-orbiting (1998) and Olander et al. (2002), respectively, proposed weather satellites and geostationary weather satellites the objective Dvorak technique (ODT) and the ad- were launched in the 1960s and 1970s. Since then, re- vanced objective Dvorak technique (AODT). Although searchers have attempted to use satellite data to esti- these two techniques reduce manual intervention, they mate tropical cyclone intensity (Fett 1964; Sadler 1964; are not suitable for intensity estimation of weak tropical Fritz et al. 1966; Erickson 1967), and, currently, the cyclones. Since then, AODT has been further improved. Dvorak technique is most widely used for estimating After considering how the cloud-top height of the tro- intensity (Dvorak 1972, 1975). The Dvorak technique posphere decreases with latitude (Kossin and Velden estimates tropical cyclone intensity using tropical cy- 2004), the estimation error of intensity of the Dvorak clone cloud structures derived from visible and infrared technique was reduced by 10% compared with AODT satellite images (Dvorak 1984; Dvorak and Smigielski (Olander et al. 2004). The latest ODT is the advanced Dvorak technique (ADT; Olander and Velden 2007). This scheme expands both ODT and AODT and relaxes Corresponding author address: Chang-Jiang Zhang, College of Mathematics, Physics and Information Engineering, Zhejiang their restrictions. The accuracy of ADT estimation de- Normal University, 688 Yingbin Avenue, Jinhua 321004, China. pends on tropical cyclone center positioning based on a E-mail: [email protected] single-channel infrared satellite image. When the eye

DOI: 10.1175/WAF-D-15-0100.1

Ó 2016 American Meteorological Society Unauthenticated | Downloaded 09/24/21 05:45 AM UTC 1644 WEATHER AND FORECASTING VOLUME 31 of a tropical cyclone or spiral rainband is shielded by techniques and current nonlinear models have some cirrus clouds, it is difficult to automatically locate the disadvantages in intensity estimation, we need to center position (Olander and Velden 2009). There- consider more efficient indicating factors that can be fore, Olander and Velden (2009) modified ADT once used to describe tropical cyclone intensity. Recently, again by comparing the differences between the ge- more and more researchers have identified the po- ostationary satellite infrared window (IRW) and tential use of cloud-top brightness temperatures water vapor channel (WV) brightness temperature (Piñeros et al. 2011; Ritchie et al. 2012; Jiang 2012; values in the strong convective regions of a tropical Sanabia et al. 2014) in tropical cyclone intensity cyclone. This allows for the estimation of tropical estimation. cyclone intensity by using a linear regression In fact, tropical cyclone intensity estimation can be technique (IRWV). intrinsically considered as data fitting. There are In addition to the Dvorak-type techniques, re- many methods for data fitting, in which a black-box searchers have explored other tropical cyclone in- method is often used. Black-box methods are used to tensity estimation techniques based on geostationary find the relationship between the input variables and satellite data. For example, Kossin et al. (2007) esti- output variables gradually through analyzing limited mated the maximum wind speed radius and critical samples and fitting the unknown function. The most wind radius using linear regression techniques based on common black-box methods involve the use of arti- infrared satellite image data. In recent years, the de- ficial neural networks, such as a back propagation viation angle variance (DAV) technique, based on in- neural network (BPNN; McCulloch and Pitts 1943) frared brightness temperature data, has been used and a radical basis function neural network (RBFNN; (Piñeros et al. 2008, 2011). However, this technique Moody and Darken 1989). Because the network node performs poorly when there is strong wind shear is similar to a human’s brain nerve cells, a neural (Piñeros et al. 2011). Best-track data from the National network can simulate the brain’s incentive function Hurricane Center (NHC) have been used to improve to perform complex data analyses. The basic re- the original DAV technique (Ritchie et al. 2012, 2014). quirement of data fitting is that it has high accuracy Fetanat and Homaifar (2013) have used the k-nearest in prediction, which depends on large amounts neighbor technique to estimate intensity via geosta- of sample data. More sample data leads to better tionary satellite azimuth brightness temperature pro- predictions. However, the amount of sample data file data from historical tropical cyclones. As the cannot increase indefinitely under normal circum- infrared brightness temperature slopes in the tropical stances. To get better predictive results with limited cyclone eyewall, there is significant negative correlation sample data, a new machine learning method called with tropical cyclone intensity. Sanabia et al. (2014) support vector machine (SVM) was proposed by have also estimated tropical cyclone intensity by Vapnik et al. (1997) and widely used for classifica- computing the multipoint cloud-top slopes of the tion, fitting, and pattern recognition. Recently, a new inner core of tropical cyclones with infrared bright- machine learning algorithm, relevance vector ma- ness temperature. chine (RVM), was put forward. Compared with As mentioned above, the current tropical cyclone SVM, RVM can reduce the calculation burden of the intensity estimation techniques are improvements kernel function and relaxes the conditions required over the original Dvorak technique, but deficiencies for selecting the kernel function. RVM can also remain. Some researchers use linear regression tech- avoid subjective operation in the parameter adjust- niques to estimate tropical cyclone intensity (Kossin ment process. et al. 2007; Olander and Velden 2009). However, this In this paper, deviation angle distribution inhomo- may result in significant error when the sample size is geneity (DADI) is used as the indicating factor for not big enough. Recently, some researchers have tropical cyclone intensity (maximum surface wind found that nonlinear models seem promising in esti- speed). DADI is computed using the geostationary mating tropical cyclone intensity (Piñeros et al. 2011; infrared satellite brightness temperatures of the inner Ritchie et al. 2012; Jiang 2012; Sanabia et al. 2014). core of a tropical cyclone. The RVM, which has excel- Numerous studies show that intensity changes in a lent nonlinear modeling ability even for small samples, tropical cyclone have nonlinear physical relationships was used to relate DADI to the intensity of different with vertical wind shear (DeMaria 1996; Zehr 2003). types of tropical cyclones. DADI and tropical cyclone These nonlinear models often require some subjec- intensity are, respectively, used as the input and output tive experience to determine the optimal parame- of RVM. Certain numbers of samples with information ters within the models. As both linear regression about DADI and tropical cyclone intensity are used to

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FIG. 1. (a) An axisymmetric graph. (b) A diagram of the deviation angle. train RVM in order to build a tropical cyclone intensity quasi-axisymmetric structure of the inner core of a estimation model. typical tropical cyclone. The deviation angle u (see This paper is structured as follows. Our methodology Fig. 1b) is the angle between the radial line l and the and data are introduced in section 2. Results and veri- gradient direction of a point (x, y). fication of the proposed technique are presented in The life cycle of a tropical cyclone can be divided section 3. Finally, the conclusions of this study are pre- into three stages: early, mature, and dissipation. The sented in section 4. cloud structure of a cyclone is usually shaped from disorganized to axially symmetric with increasing intensity. For example, the infrared satellite images 2. Methodology and data of different development stages of Typhoon Talim (2005) are shown in Figs. 2a–c. They reveal that Ta- a. Methodology lim’s cloud structure during its mature stage ap- proaches an axisymmetric circle, but in other stages 1) TROPICAL CYCLONE STRUCTURE DESCRIPTION the cloud structure is disorganized. We calculated the BASED ON DEVIATION ANGLE tropical cyclone deviation angle matrix with the Figure 1a shows an axisymmetric graph whose gra- above method based on infrared satellite imagery, dient direction and tangent direction are mutually andthenusedadeviationanglehistogramtodescribe perpendicular. This can be used to investigate the the structure of the tropical cyclone.

FIG. 2. Infrared satellite images of TP Talim (2005) during different development stages: (a) early stage (0400 UTC 27 Aug), (b) mature stage (1300 UTC 29 Aug), and (c) dissipation stage (0200 UTC 1 Sep).

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2) RVM AND DAGCOM the tropical cyclone intensity is called the intensity indicating factor. Current tropical cyclone intensity estimation models Tropical cyclones are divided into two categories in are mainly built on traditional linear regression methods this study: eyed tropical cyclones (ETCs) and noneyed and asymptotic theory, which leads to significant errors tropical cyclones (NTCs). ETCs are those with a when the numbers of samples are small. Nonlinear mod- higher intensity grade and that have an obvious eye in eling techniques show promise because the relationship the mature stage. NTCs are those without an obvious between tropical cyclone intensity and its influencing eye and include tropical storms. By calculating the factors is usually nonlinear. RVM is divided into a re- DAGCOM within a radius of 65 pixels (;325 km), gression model and a classification model (Tipping 2001). experiment results indicate that the average absolute This paper uses a regression model and the Matlab error of the tropical cyclone intensity estimation is toolbox (http://www.Miketipping.com/sparsebayes.htm) almost the same as that within a radius of 40 pixels to estimate tropical cyclone intensity (Tipping 2001). (;200 km). Therefore, the DAGCOM within a radius In this paper, the gray gradient co-occurrence matrix of 40 pixels (;200 km) was calculated in order to re- (Hong 1984) was generalized to the deviation angle duce computation time. gradient co-occurrence matrix (DAGCOM). It is called DAGCOM because we replace the gray gra- (i) Intensity estimation for an NTC dient with the deviation angle gradient in the original For NTCs including tropical storms (TSs), we referred gray gradient co-occurrence matrix. A total of 15 to the technique used by Piñeros et al. (2008), which statistical parameters (small gradient advantage, big considers each pixel point to be the reference point used gradient advantage, deviation angle distribution in- to calculate the deviation angle between the reference homogeneity, gradient distribution inhomogeneity, point and each point in the infrared satellite image, re- energy, mean deviation angle value, mean gradient spectively. First, for a NTC infrared satellite image value, deviation angle standard deviation, gradient whose size is N 3 N pixels, we get N 3 N deviation angle standard deviation, correlation, deviation angle en- matrixes. Then, 15 parameters (Table 2) of each de- tropy, gradient entropy, mixed entropy, differential viation angle matrix were calculated, to get N 3 N 3 15 distance, and opposite differential distance) in Table 1 deviation angle gradient co-occurrence matrix pa- related to tropical cyclone intensity were calculated by rameter matrixes. Finally, the median, minimum, and DAGCOM. An element H(x, y) in a DAGCOM is mean of the parameter matrices were calculated. defined as the number of pixels whose deviation angle Models between the above three values and maximum value and deviation angle gradient value are, respec- surface wind speed were built by RVM to estimate tively, x and y in a normalized deviation angle image NTC intensity. F(i, j) and a normalized deviation angle gradient image G(i, j). The deviation angle image F(i, j) can be ob- (ii) Intensity estimation for an ETC tained by employing the method outlined in section 2a We adopted two schemes to estimate the intensity of (1). Based on a deviation angle image F(i, j), the de- ETCs. First, because the eye area is obvious, we used viation angle gradient image G(i, j) can be obtained by the eye area center point as the reference point. The qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi deviation angle between the reference point and each 2 2 G(i, j) 5 [F(i, j 1 1) 2 F(i, j)] 1 [F(i 1 1, j) 2 F(i, j)] . point in the infrared satellite image were calculated in turn. We get N 3 N deviation-angle matrixes from The origin of the DAGCOM is shown in the top- N 3 N eyed tropical cyclone satellite images, and then left corner of the matrix. Gradient values increase computed 15 parameters (Table 1) of the deviation toward the right and the deviation angle values in- angle matrix. Finally, a nonlinear model between the 15 crease downward. Normalized DAGCOM is shown by parameters and the maximum surface wind speed was ^ 5 L L H(x, y) H(x, y)/åx51åy51H(x, y). built based on RVM to estimate the ETC intensity, which is the same intensity estimation scheme we ap- 3) TROPICAL CYCLONE INTENSITY ESTIMATION pliedtoNTCs. WITH RVM AND DAGCOM (iii) Intensity estimation for mixed types of tropical Based on the calculation of parameters for the cyclones tropical cyclone structure, RVM is used to build models between these parameters and tropical For mixed types (NTC and ETC) of tropical cyclones, cyclone intensity (maximum surface wind speed). A we used the intensity estimation scheme of NTCs to parameter of DAGCOM most closely correlated to estimate intensity.

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TABLE 1. Parameters used for the DAGCOM.

No. Parameter Formula L L 1 Small gradient advantage å å H(x, y) 2 x51 y51 y T 5 1 L L å å H(x, y) x51 y51 L L å å H(x, y)y2 x51 y51 2 Big gradient advantage T 5 2 L L å å H(x, y) 5 5 x 1 y 1   L L 2 å å H(x, y) x51 y51 3 DADI T 5 3 L L å å H(x, y) 5 5  x 1 y 1   L L 2 å å H(x, y) y51 x51 4 Gradient distribution inhomogeneity T 5 4 L L å å H(x, y) x51 y51 L L ^ 2 5 Energy T5 5 å å [H(x, y)] x51 y51   L L ^ 6 Mean deviation angle value T6 5 å x Á å H(x, y) x51  y51  L L ^ 7 Mean gradient value T7 5 å y Á å H(x, y) y51 x51   L L 1/2 2 ^ 8 Deviation angle std dev T8 5 å (x 2 T6) å H(x, y)  x51  y51  L L 1/2 2 ^ 9 Gradient std dev T9 5 å (y 2 T7) å H(x, y) y51 x51 1 L L ^ 10 Correlation T10 5 å å (x 2 T6)(y 2 T7)H(x, y) T T 5 5 8 9 x 1 y 1    L L ^ L ^ 11 Deviation angle entropy T11 52 å å H(x, y) Á log å H(x, y)  x51  y51   y51  L L ^ L ^ 12 Gradient entropy T12 52 å å H(x, y) Á log å H(x, y) y51 x51 x51 L L ^ ^ 13 Mixed entropy T13 52 å å H(x, y) Á logH(x, y) x51 y51 L L 2 ^ 14 Differential distance T14 5 å å (x 2 y) H(x, y) x51 y51 L L ^ 5 å å H(x, y) 15 Opposite differential distance T15 2 x51 y51 1 1 (x 2 y) b. Implementation of the proposed tropical cyclone Step 2—DAGCOM is obtained as in section 2a(2),and intensity estimation technique 15 statistic parameters are calculated by DAGCOM and Table 1. The proposed technique is implemented as follows. Step 3—Noneyed typhoon data (2367 infrared satel- Step 1—Based on infrared satellite imagery that lite images) are used to choose the optimal in- contains a tropical cyclone, the corresponding de- tensity, indicating the factor from the DAGCOM. viation angle matrix is calculated as in section 2a(1). DADI is chosen as the optimal intensity indicating For NTCs, each pixel point is used as the reference point factor by the above method. to calculate the corresponding deviation angle matrix. Step 4—RVM is used to relate the tropical cyclone For ETCs, each pixel point and eye area center intensity (maximum surface wind speed) to DADI point are, respectively, used as reference points to for eyed typhoons (ETPs), noneyed typhoons (NTPs), calculate the corresponding deviation angle matrices. TSs, and mixed tropical cyclones (MTCs), respectively.

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TABLE 2. List of tropical cyclones discussed in this paper, ordered by CMA best-track number. Dates and times of the China FY-2C geostationary satellite observations for TS, ETP, and NTP intensities along with the total number of observations are given. Observations range from 2005 to 2009.

No. of TS No. of ETP No. of NTP Total 2 2 2 TC No. Name First obs Final obs Type (17.2–32.6 m s 1) (32.7 1 ms 1) (32.7 1 ms 1) No. of obs 0507 Banyan 1800 UTC 0000 UTC TS 175 0 0 175 21 Jul 2005 28 Jul 2005 0509 Matsa 1200 UTC 0000 UTC TP 0 32 204 236 31 Jul 2005 9 Aug 2005 0513 Talim 0000 UTC 0000 UTC TP 0 66 94 160 27 Aug 2005 2 Sep 2005 0515 Khanun 0000 UTC 0900 UTC TP 0 42 115 157 7 Sep 2005 13 Sep 2005 0522 Tembin 0000 UTC 0600 UTC TS 29 0 0 29 10 Nov 2005 11 Nov 2005 0601 Chanchu 1200 UTC 1200 UTC STP 0 0 117 117 9 May 2006 18 May 2006 0604 Bilis 0600 UTC 0900 UTC TS 249 0 0 249 9 Jul 2006 15 Jul 2006 0605 Kaemi 0600 UTC 0300 UTC TP 0 0 318 318 19 Jul 2006 26 Jul 2006 0608 Saomai 1200 UTC 0600 UTC SUT 0 71 198 269 5 Aug 2006 11 Aug 2006 0610 Wukong 0600 UTC 1800 UTC TS 301 0 0 301 13 Aug 2006 19 Aug 2006 0620 Cimaron 0600 UTC 1200 UTC SUT 0 59 171 230 27 Oct 2006 4 Nov 2006 0621 Chebi 1200 UTC 0600 UTC SUT 0 17 117 134 9 Nov 2006 14 Nov 2006 0622 Durain 0600 UTC 0600 UTC SUT 0 46 207 253 26 Nov 2006 5 Dec 2006 0709 Sepat 0000 UTC 0600 UTC SUT 0 131 207 338 12 Aug 2007 24 Aug 2007 0711 Danas 0000 UTC 0600 UTC TS 157 0 0 157 6 Sep 2007 12 Sep 2007 0713 Wipha 0000 UTC 1200 UTC SUT 0 29 67 96 15 Sep 2007 20 Sep 2007 0716 Krosa 0600 UTC 0000 UTC SUT 0 101 77 178 1 Oct 2007 10 Oct 2007 0718 Podul 0000 UTC 1200 UTC TS 113 0 0 113 3 Oct 2007 7 Oct 2007 0812 Nuri 0600 UTC 0600 UTC TP 0 15 256 271 17 Aug 2008 23 Aug 2008 0814 Hagupit 1200 UTC 1800 UTC STP 0 56 107 163 17 Sep 2008 25 Sep 2008 0815 Jiangmi 1800 UTC 0000 UTC SUT 0 34 112 146 23 Sep 2008 5 Oct 2008 0912 Dujuan 2000 UTC 0600 UTC TS 185 0 0 185 2 Sep 2009 10 Sep 2009 Total 22 1209 699 2367 4275

Step 5—The linear regression method and average geostationary satellite over the northwest Pacific absolute error are used to evaluate the performance basin. Tropical cyclone best-track data from the of the proposed technique. Yearbook of Tropical Cyclone [China Meteorologi- cal Administration (CMA) 2007, 2008, 2009, 2010, c. Data 2011], published by the China Meteorological Press, The data presented are derived from infrared (10.3 mm) were used for verification of the estimated tropical cy- satellite images with a spatial resolution of 5 km per clone intensities. These data were archived at 6-h in- pixel, captured at 30-min intervals from the China FY-2C tervals. To match center locations and wind speed

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FIG. 3. Average absolute error curve when using RVM to relate the 15 parameters from a DAGCOM to the tropical cyclone intensity. estimates to the 30-min temporal resolution of the satel- 3. Results lite data, the best-track data were linearly interpolated to a. The relationship between DADI and tropical match the satellite temporal resolution. The northwest cyclone intensity Pacific study uses infrared satellite images that include existing tropical cyclones from the 2005–09 typhoon The results from the model based on DAGCOM and seasons and comprises a total of 4275 unique hourly im- RVM show that DADI (T3;seeTable 1)hasthe ages (Table 2). According to the standard (GB/T 19201– strongest relevance to tropical cyclone intensity 2006) for Chinese tropical cyclones (http://baike.baidu. (Fig. 3). Therefore, the DADI is chosen as the in- com/link?url=pY-lOv_diz-7yvKloFN7xO7xLsdyvEG6 dicating factor to estimate the tropical cyclone in- PxyTAjudVi8wNKcqFuxRhS8n1uXA9JsBg3v5E0QC tensity. Figure 4 shows the original infrared satellite Qyf-iJDz2aHD_K), a tropical cyclone is divided into image, the deviation angle histogram, and a pseudo- 2 six categories: supertyphoon (51 m s 11), severe ty- color map of the DADI for Typhoon Talim in its early, 2 2 phoon (41.5;50.9 m s 1), typhoon (32.7;41.4 m s 1), mature, and dissipation stages. In the deviation angle 2 severe tropical storm (24.5;32.6 m s 1), tropical storm histogram, the X axis shows the deviation angle and the 2 2 (17.2;24.4 m s 1), and tropical depression (10.8;17.1 m s 1). Y axis indicates the probability density. In the pseu- Here, the maximum surface wind speed near the docolor map of the DADI, the X and Y axes represent tropical cyclone center is used as the intensity estima- the width and height of the infrared satellite image, tion for a tropical cyclone. The resulting dataset in- respectively. The size of both the original infrared 2 cluded eight supertyphoons (SUTs; 51 m s 11), two satellite image and the pseudocolor map of the DADI 2 severe typhoons (STPs; 41.5;50.9 m s 1), five typhoons is 130 3 130 pixels (within a radius of 325 km). The bar 2 2 (TPs; 32.7;41.4 m s 1), and seven TSs (17.2;32.6 m s 1). on the right of the pseudocolor map shows the loga- 2 Furthermore, ETPs (32.7 m s 11) consisted of 699 rithm value of the DADI. Taking each point in the 2 images, NTPs (32.7 m s 11) 2367 images, and TSs infrared satellite image as a reference point, the de- 2 (17.2;32.6 m s 1) 1209 images. The above dataset is listed viation angle between each point in the infrared satel- in Table 2. The size of the original infrared satellite image lite image and the reference point were calculated. was 2288 3 2288 pixels, so we cropped a 130 3 130 pixels Then, a deviation angle matrix was obtained, based on image from the original infrared satellite image that in- which the DADI was then obtained. The above oper- cluded tropical cyclone cloud structures as analysis objects. ations were repeated, and a DADI matrix was de- There are 15 statistical parameters in the DAGCOM. In veloped. To distinguish this matrix, we use different the study, we used noneyed typhoon data (2367 infrared colors to represent the values of the DADI in Fig. 4. satellite images) to choose the optimal intensity-indicating The pseudocolor map of the DADI with the same color factor from the DAGCOM. scale is shown in Fig. 5.

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FIG. 4. (left) Infrared satellite image, (middle) deviation angle histogram, and (right) pseudocolor map of the DADI for TP Talim (2005) during different development stages: (a) early stage (0400 UTC 27 Aug), (b) mature stage (1300 UTC 29 Aug), and (c) dissipation stage (0200 UTC 1 Sep).

As shown in Fig. 4, we found that a deviation angle approaches uniformity. The spread of the histogram in histogram can be used to describe the structural Fig. 4c once again increases. The pseudocolor map characteristics of a tropical cyclone during its different (Figs. 4a–c) of the DADI can be used to intuitively development stages. When a tropical cyclone is in its describe the structure of a tropical cyclone across its early stage, the cloud structure is disorganized, and the wholelifecycle.FromFig. 5, we find that the DADI deviation angle histogram is spread out (Fig. 4a). rises to a peak and then gradually descends. What is When a tropical cyclone is in its mature stage (Fig. 4b), more, the peak arrives when a tropical cyclone is in its the corresponding histogram shows a large peak at the mature stage. 08 angle and very little spread. Most of the deviation b. Intensity estimation for tropical cyclones with angles approach or are equal to zero. The probability different intensities density of the deviation angle histogram approaches a normal distribution. The structure of a tropical cy- Four experiments were conducted to estimate the 2 clone during the dissipation stage (Fig. 4c)ismessy, intensity of tropical cyclones: 1) ETPs (32.7 m s 11), 2 2 and the deviation angle probability density distribution 2) NTPs (32.7 m s 11), 3) TSs (17.2;32.6 m s 1), and

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FIG. 5. Pseudocolor map of the DADI with the same color scale for TP Talim during different development stages: (a) early stage (0400 UTC 27Aug), (b) mature stage (1300 UTC 29 Aug), and (c) dissipation stage (0200 UTC 1 Sep).

2 2 2 4) MTCs (17.2 m s 11). Two-thirds of the sample was and it is biggest (30 m s 1) for ETPs (32.7 m s 11). We used to train the RVM and one-third to verify the built noticed that the number of ETP samples is smallest (see intensity estimation model. The average absolute error Table 2). This suggests that the linear regression method of the above tropical cyclone intensity estimation results results in a bigger intensity estimation error. are shown in Table 3.InTable 3, boldfaced values show For the RVM model, the average absolute error for 2 2 the minimum of the average absolute errors. The aver- TSs (17.2;32.6 m s 1) is the least (3 m s 1 or so). The age absolute error, using the mean, median, and mini- average absolute errors for ETPs (taking each point in mum of the DADI separately as intensity-indicating the infrared satellite image as a reference point; 2 2 factors, is similar. Therefore, in the future, only one of 32.7 m s 11)andNTPs(32.7ms11) are similar 2 the mean, median, or minimum of the DADI is sufficient (8 m s 1 or so). The average absolute errors for ETPs to estimate the intensity of a tropical cyclone. Next, we (taking the center point of the tropical cyclone as a 2 2 chose the best result for ETP, NTP, TS, and MTC from reference point; 32.7 m s 11) and MTCs (17.2 m s 11) 2 Table 3. Absolute error histograms are shown in are also similar (10 m s 1). Compared with the linear Figs. 6a–j. The X and Y axes of each histogram, re- regression method, RVM is more efficient for small spectively, represent the absolute error (error interval is samples and greatly improves the tropical cyclone in- 2 1ms 1) and frequency. tensity estimation. Table 3 shows that the average absolute error by Three cases [SUT Sepat (No. 0709), STP Hagupit (No. RVM is smaller than that of linear regression. Figure 6 0814), and TS Dujuan (No. 0912)] were used to verify shows that the error histogram of RVM is concentrated, but the error histogram of linear regression is dispersive. TABLE 3. Average absolute error of tropical cyclone intensity 21 What is more, the error histogram of RVM is closer to estimation (m s ). Boldface values show the minimum of the av- erage absolute errors. zero than is the linear regression. According to Table 3 and Fig. 6, we find that the proposed method, compared No. of samples Indicating factor LR RVM 2 to linear regression, shows an obvious improvement in 1) ETPs (32.7 m s 11) tropical cyclone intensity estimation. The average ab- 699 DADI 29.27 10.64 solute errors for both ETPs (taking each point of the Mean of DADI 29.09 9.70 infrared satellite image as a reference point) and NTPs Median of DADI 29.16 9.40 21 Min of DADI 29.41 8.75 are about 8 m s or so, and the average absolute error 211 21 2) NTPs (32.7 m s ) for TSs is about 3 m s . However, the average absolute 2367 Mean of DADI 15.87 8.32 errors for both ETPs (taking the center of the tropical Median of DADI 15.85 8.39 cyclone as a reference point) and MTCs are about Min of DADI 16.03 8.11 2 21 10 m s 1. For ETP, NTP, TS, and MTC cases, the aver- 3) TSs (17.2;32.6 m s ) age absolute error using the linear regression method is 1209 Mean of DADI 19.78 3.16 Median of DADI 19.78 3.23 inferior to that of RVM. Min of DADI 19.96 3.25 2 With the linear regression method, the average error 4) MTCs (17.2 m s 11) 2 2 for NTPs (32.7 m s 11)is16ms 1 or so. Similarly, the 4275 Mean of DADI 18.61 10.07 2 average absolute error for MTCs (17.2 m s 11)is Median of DADI 18.62 10.07 2 2 2 19 m s 1; for TSs (17.2;32.6 m s 1), it is about 20 m s 1; Min of DADI 18.78 10.10

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FIG. 6. Absolute error histograms for (left) LR and (right) RVM. (a),(b) ETPs when considering DADI as an indicating factor; (c),(d) ETPs when considering the mean of the DADI as an indicating factor; (e),(f) NTPs when considering the minimum of the DADI as an indicating factor; (g),(h) TSs when considering the mean of the DADI as an indicating factor; and (i),(j) MTCs when considering the mean of the DADI as an indicating factor.

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the performance of the proposed technique. The in- tensity estimated by RVM was compared with results from CMA, the Japan Meteorological Agency (JMA), the Joint Typhoon Warning Center (JTWC), and the linear regression (LR) method. From Figs. 7a–c, the intensity estimation performance of RVM is shown to be between JMA and JTWC. It is clear that the intensity estimated by LR changes greatly for every case and performs poorly.

4. Conclusions In this study, based on the DADI, which is calculated through the use of infrared satellite imagery from a tropical cyclone, RVM is used to build intensity estima- tion models for different types of tropical cyclones (ETPs, NTPs, TSs, and MTCs). Experimental results show that, compared with the traditional linear regression method, RVM can greatly improve the accuracy of tropical cy- clone intensity estimation. This implies that the nonlinear relationship between tropical cyclone intensity and its indicating factors should be represented in the intensity estimation model. In this sense, nonlinear modeling techniques can yield higher accuracy than those of linear methods in tropical cyclone intensity estimation. A uni- versal intensity estimation model may result in substantial errors in intensity estimation under some circumstances. Experimental results also show that the accuracy of the intensity estimation of RVM is between that of JMA and JTWC. Although the proposed technique demonstrates a re- markable ability to estimate tropical cyclone intensity, especially in its mature stage, weak tropical cyclones 2 [e.g., tropical depressions (10.8;17.1 m s 1)] are not included in this study. Experimental research on esti- mating the intensity of weak tropical cyclones will be presented in a future publication. In addition, the pro- posed technique only uses infrared geostationary satel- lite observations. Water vapor geostationary satellite observations might prove helpful in improving the tropical cyclone intensity estimation’s precision based on the proposed technique. Finally, the proposed tech- nique will be expanded to the Atlantic basin to verify its performance in the future.

Acknowledgments. This study was supported by the Natural Science Foundation of China (Grants 41575046, 41475059, 40805048, and 11026226), the Project of FIG. 7. Intensity estimation curves for different types of tropical cyclone cases when using different intensity estimation techniques Commonweal Technique and Application Research (RVM, CMA, JMA, JTWC, and LR). of Zhejiang Province of China (Grants 2016C33010 and 2012C23027), the Natural Science Foundation of Zhejiang Province of China (Grant LY13D050001), and the Natural Science Foundation of Shanghai of China

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