A Multiple Linear Regression Model for Tropical Cyclone Intensity Estimation from Satellite Infrared Images

atmosphere

Article A Multiple Linear Regression Model for Tropical Cyclone Intensity Estimation from Satellite Infrared Images

Yong Zhao 1,2, Chaofang Zhao 1,2,*, Ruyao Sun 1 and Zhixiong Wang 2

1 Department of Marine Technology, College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China; [email protected] (Y.Z.); [email protected] (R.S.) 2 Ocean Remote Sensing Institute, Ocean University of China, Qingdao 266100, China; [email protected] * Correspondence: [email protected]; Tel.: +86-532-6678-2949

Academic Editor: Jong-Jin Baik Received: 22 January 2016; Accepted: 7 March 2016; Published: 11 March 2016

Abstract: An objectively trained model for tropical cyclone intensity estimation from routine satellite infrared images over the Northwestern Pacific Ocean is presented in this paper. The intensity is correlated to some critical signals extracted from the satellite infrared images, by training the 325 tropical cyclone cases from 1996 to 2007 typhoon seasons. To begin with, deviation angles and radial profiles of infrared images are calculated to extract as much potential predicators for intensity as possible. These predicators are examined strictly and included into (or excluded from) the initial predicator pool for regression manually. Then, the “thinned” potential predicators are regressed to the intensity by performing a stepwise regression procedure, according to their accumulated variance contribution rates to the model. Finally, the regressed model is verified using 52 cases from 2008 to 2009 typhoon seasons. The R2 and Root Mean Square Error are 0.77 and 12.01 knot in the independent validation tests, respectively. Analysis results demonstrate that this model performs well for strong typhoons, but produces relatively large errors for weak tropical cyclones.

Keywords: tropical cyclone; intensity; satellite infrared image; northwestern paciﬁc; linear regression

1. Introduction Tropical Cyclones (TCs) are some of the most damaging natural hazards [1]. The intensity (here refers to the maximum sustained wind) is generally used as a main indicator for quantifying the damage potential of TCs. Because it is difﬁcult to obtain direct in-situ measurements of TC intensity [2], satellite remote sensing, especially geostationary meteorological satellite (GMS) remote sensing, has been heavily relied upon in related studies and operational forecasts. On the one hand, GMS has higher temporal and spatial resolution compared to polar satellite microwave remote sensing [3–5] and air reconnaissance [6–8]. On the other hand, GMS could cover the vast tropical ocean continually, and thereby provide valuable datasets concerning the genesis, track, intensity and other well-concerned information about TCs throughout their life cycles. The Northwestern Paciﬁc Ocean (NWP), which is characterized with frequent cyclone activities, is heavily dependent on GMS for TC intensity estimation and forecast [3,9,10]. During the beginning years (1970s) of satellites, Dvorak summarized previous research [11,12] and proposed a comprehensive pattern recognition technique for tropical cyclone (TC) intensity estimation from satellite imagery, which is known as Dvorak Technique (DT) [13,14]. However, DT depends on experts’ experience, and therefore is subjective and time intensive. Several revisions of the DT technique were developed during the later decades. The Objective Dvorak Technique (ODT) [15]

Atmosphere 2016, 7, 40; doi:10.3390/atmos7030040 www.mdpi.com/journal/atmosphere Atmosphere 2016, 7, 40 2 of 17 recognized patterns in satellite imagery using computer-based algorithm, and created a look-up table. The shortcoming of ODT is that centers of TCs are determined either manually or with the aid of external resources [16]. The more recently developed Advanced Dvorak technique (ADT), which is regarded as the latest version of DT method, advances the original Dvorak technique through modifications based on rigorous statistical and empirical analysis [17,18]. Despite the continual development of the DT method, all versions of DT technique (except for ADT) estimate TC intensity based on cloud features and patterns recognition. Apart from the DT method, some other techniques have also been developed. Mueller (2006) used geostationary IR data to estimate wind field structure of TCs through estimates of radius of maximum wind (RMAX)and wind at 182 km (V182) with 405 cases from the 1995–2003 Atlantic and Eastern Pacific typhoon seasons [19]. Chao (2011) made use of both IR and visible satellite images to estimate TC rotation speed and then sought to predict TC wind intensity using estimated rotation speeds at the 130–260 km ring [10]. Fetanat (2013) proposed a new technique for TC intensity estimation using the spatial feature analogs in satellite imagery. The technique was testified as on par with other objective techniques [20]. Zhuge (2015) combined information from geostationary satellite infrared window (IR) and water vapor (WV) imagery, and proposed a WV-IRW-to-IRW ratio (WIRa)-based indicator to estimate TC intensity over NWP [3]. The results showed that the WIRa-based indicator gives a more accurate estimation of TC intensities. Another approach for characterizing TC cloud dynamics was initially discussed by Piñeros (2008) [21]. In that study, the deviation angle variance (DAV) was used to describe the degree of asymmetry and “organization” of TC cloud. This was then developed into the Deviation Angle Technique (DAV-T) which was applied into many aspects of TC related research [16,22–24]. In particular, it has been proved that DAV-T can be a reliable tool in hurricane intensity estimation [16,22]. The DAV-T was lately applied into estimating TC intensity over NWP. Results showed an accurate estimation with a Root Mean Square Error (RMSE) of 14.3 knot in the 2007–2011 NWP typhoon seasons [25]. More recently, a non-dimensional TC intensity (TI) index was proposed by combining some statistical parameters of DAVs [26]. The TI index was reported to be more suitable for TCs with axisymmetric, non-sheared cloud systems. Despite the aforementioned new techniques for TC intensity estimation, each with its strengths and drawbacks, there is still need to improve the precision and accuracy of TC intensity estimation technique making use of satellite images for the aim of better forecast. Therefore, in this research, we seek to extract the most significant signals and parameters from IR images so as to develop an objective technique to estimate current intensity of TCs. The objective of this paper is to provide another reference for improving our capability of TC intensity estimation. The remaining parts of this paper are organized as follows. Data collection and preprocessing are discussed in Section2. Section3 describes the procedures for developing the model. The model is tested and discussed in Section4. The main conclusions are summarized in Section5.

2. Data Collection and Preprocessing To date, a wide breadth of scientific measurements from in-situ, aircraft, and satellite instruments are readily available for TC related research [27]. However, it is still difficult to gather all information (including both images and data) that pertain to a particular TC or an ocean basin [28]. The JPL Tropical Cyclone Information System (TCIS) includes a comprehensive set of multi-parameter observations and model outputs that are relevant to both large-scale and storm-scale processes in the atmosphere and in the ocean. The TCIS data archive, including AIRS, CloudSAT, MLS, AMSU-B, QuikSCAT, Argo floats, GPS, and many others, pertains to the thermodynamic and microphysical structure of the storms, the air-sea interaction processes and the larger-scale environment over the globe from 1999 to 2010. Storm data are subsetted to a 2000 ˆ 2000 km2 window around the hurricane track for six geographic regions [29]. Atmosphere 2016, 7, 40 3 of 17

The region of interest in this paper covers the NWP basin from 5˝ to 45˝N and from 100˝ to 165˝E (Figure1). The inputs include digital brightness temperatures (BTs) of the IR (10.3–11.3 um) and waterAtmosphere vapor (WV,2016, 7,6.5–7.0 40 um) channel images with spatial and temporal resolution of 8 km3 of and 16 3 h, respectively. It was noted that the TCIS satellite images are actually produced by Hurricane satellite respectively. It was noted that the TCIS satellite images are actually produced by Hurricane satellite data (HURSAT-B1, version 05) [30]. While the HURSAT-B1 covers TCs in Western Pacific Ocean from data (HURSAT-B1, version 05) [30]. While the HURSAT-B1 covers TCs in Western Pacific Ocean from 1978 to 2009, the earliest WV data provider for NWP is GMS-5 from 1996. Therefore, satellite images 1978 to 2009, the earliest WV data provider for NWP is GMS-5 from 1996. Therefore, satellite images fromfrom 1996 1996 to 2009 to 2009 are are used. used. The The HURSAT-B1 HURSAT-B1 images images were downloaded downloaded from from HURSAT HURSAT and andTCIS TCIS for for the yearsthe years 1996–1998 1996–1998 and and 1999–2009, 1999–2009, respectively. respectively. All All im imagesages were were filtered filtered using using a low-pass a low-pass filter filterin in orderorder to exclude to exclude unreasonable unreasonable increment increment or or decrementdecrement in in BTs. BTs. In In addition, addition, the the images images were were screened screened and preprocessedand preprocessed carefully carefully to to avoid avoid introducing introducing uncertainuncertain errors. errors. For For example, example, images images with with “missing “missing belt”belt” are cubic are cubic interpolated. interpolated.

o 45 N 160

140

o 35 N 120

100

o 25 N 80

60 Latitude (DEG)

o /Knot TC intensity 15 N 40

o 5 N 0 105oE 115oE 125oE 135oE 145oE 155oE 165oE Longitude (DEG) FigureFigure 1. The 1. The region region of interestof interest in in this this paper, paper, andand trac tracksks of of the the 325 325 cases cases adopted adopted in training in training the model. the model.

The selected dataset comprises 18,108 three-hourly satellite images of 377 tropical cyclone cases Thefrom selected1996 to 2009 dataset NWP comprises typhoon season. 18,108 Of three-hourly the 377 cases, satellite 118 are tropical images depression, of 377 tropical 53 are cyclone tropical cases fromstorm, 1996 to54 2009 are typhoons, NWP typhoon 36 are mo season.derate Of typhoons, the 377 cases,26 are severe 118 are typhoons, tropical depression,57 are super typhoons, 53 are tropical storm,and 54 33 are are typhoons, extreme 36typhoons. are moderate The 377 typhoons, cases are 26divided are severe into two typhoons, groups. 57 They are superare, 325 typhoons, (16,126 and 33 areimages) extreme from typhoons. 1996 to 2007 The and 377 52 cases (1982are images) divided from into 2008 two to 2009 groups. typhoon They seasons, are, 325 performing (16,126 images)as fromtraining 1996 to and 2007 validation and 52 (1982datasets, images) respectively. from More 2008 specifically, to 2009 typhoon of all the seasons, 16,126 training performing images, as 4752 training and validationare tropical depression datasets, respectively. (29.47%), 5513 Moreare tropical speciﬁcally, storms (34.19%), of all the 2444 16,126 are typhoons training (15.16%), images, 1522 4752 are tropicalare depressionmoderate typhoons (29.47%), (7.70%), 5513 910 are are tropical severe storms typhoons (34.19%), (5.64%), 2444 1041 are are typhoonssuper typhoons (15.16%), (6.46%), 1522 are and 252 are extreme typhoons (1.39%), as shown in Figure 1 and Table 1. moderate typhoons (7.70%), 910 are severe typhoons (5.64%), 1041 are super typhoons (6.46%), and

252 are extremeTable 1.typhoons Number and (1.39%), percent as ofshown images inin Figureeach category1 and Tableof tropical1. cyclones for training and validating the model. The terminologies of the typhoon categories are included in the brackets behind Tablethe 1. categoryNumber number. and percent of images in each category of tropical cyclones for training and validating the model. The terminologies of the typhoon categories are included in the brackets behind the No. and Percent of Images No. and Percent of Images category number.Bins in Training Dataset in Validation Dataset Tropical Depression 4752 (29.47%) 581 (29.31%) No. and Percent of Images in No. and Percent of Images in Bins Tropical Storm Training 5513 (34.19%) Dataset Validation 707 (35.67%) Dataset C1 (Typhoon) 2444 (15.16%) 214 (10.80%) TropicalC2 (Moderate Depression Typhoon) 4752 1522 (29.47%) (7.70%) 142 581 (7.16%) (29.31%) Tropical Storm 5513 (34.19%) 707 (35.67%) C3 (Severe Typhoon) 910 (5.64%) 325 (5.75%) C1 (Typhoon) 2444 (15.16%) 214 (10.80%) C4 (Super Typhoon) 1041 ( 6.46%) 160 (8.07%) C2 (Moderate Typhoon) 1522 (7.70%) 142 (7.16%) C3C5 (Severe (Extreme Typhoon) Typhoon) 910 252 (5.64%) (1.39%) 46 325(2.32%) (5.75%) C4 (Super Typhoon)Overall 1041 16,126 ( 6.46%) (100%) 1982 160 (100%) (8.07%) C5 (Extreme Typhoon) 252 (1.39%) 46 (2.32%) AmongOverall TC best-track information 16,126archives, (100%) the dataset from Joint Typhoon 1982 (100%) Warning Center (JTWC) is one of the most broadly used ones [31], and has been proved to be more reliable compared

Atmosphere 2016, 7, 40 4 of 17

Among TC best-track information archives, the dataset from Joint Typhoon Warning Center (JTWC) is one of the most broadly used ones [31], and has been proved to be more reliable compared to other best-track datasets available for NWP basin [32–34]. JTWC best-track dataset is thus adopted as veriﬁcation. To match the three-hourly satellite images, the 6-h interval archived best-track data are interpolated using the linear interpolation method.

3. Methodologies

3.1. Estimation and Development of DAV As aforementioned in the introduction section, DAV-T is another reliable approach for TC intensity estimation by quantifying the degree of axisymmetry and “organization” of IR brightness temperatures. In this paper, gradient vectors of BTs are computed by performing the sobel template. For each pixel within 300-km radius from the center pixel, the deviation angle between the gradient vector and corresponding radial extending from the TC center is calculated, and the DAV is then determined. Ritchie (2014) [25] relates the DAV to TC intensity via a sigmoid model. We tested that model using the 325 cases in the training datasets. However, the R2 is only 0.36. Therefore, we endeavor to develop the DAV-T through adding some statistical parameters. Since the interpolated best-track information, especially the locations might be inconsistent with satellite images, we here adopt a center region, which is assumed as the nine pixels surrounding corresponding JTWC best-track center location on each image. The deviation angles and all undermentioned parameters are hence computed upon the center region. Accordingly, the average values of the center regions are determined as optimal ones in order to minimize errors caused by inaccurate TC center positions. The first statistical parameter, the probability density of mean deviation angle (P_MDA) proposed by Liu (2015) [26] is included. Liu found that P_MDA is positively related with intensity. Nevertheless, the P_MDA here is derived using accumulating probability densities between DAs ´ 2 RMSE pDAsq ` p q and DAs 2 RMSE DAs , where DAs denote deviation angles. Because this coulda take most of significant peaksa in the histogram of the deviation angles into account, which means that the P_MDA would not be decided solely by the probability density at the mean deviation angle which might be an uncertain noise, and hence reduce uncertain errors. The second statistical parameter is the interquartile range (IQR) of deviation angles. The advantage of IQR is that this could effectively exclude unreasonable extremums and some possible noises derived from BTs. After obtaining parameters DAV, P_MDA and IQR, we concentrate on developing a new index by combining effects of these three. According to previous studies, a weak cyclone system is featured with disorganized and asymmetrical cloud cluster. Therefore, gradient vectors of the brightness temperatures would be extremely disorganized, and thereby the higher the DAV. Accordingly, the stronger the TC, the larger the P_MDA and the smaller the IQR. That being said, we are not going to build proportional (or reciprocal) relationships between the intensity and the three parameters, but try to seek a mode that could improve the explanatory power of these parameters to intensity as large as possible. After times of tests (not shown here), the new index DAO is eventually determined as follows: 100 10 P_MDA DAO “ ˆ p q (1) IQR log pDAVq where the amplification factor 100 is added to raise the order of the magnitude of DAO while it does not influence DAO’s behaviors. Here we take a weak TC as an example to clarify the mechanism of DAO, for such a case, the DAV would be relatively large compared with those strong TC. According to Figure3 in Ritchie (2013) [ 25], large increment of DAV corresponds to small intensity change for weak TCs, and vice versa. Therefore, the Logarithmic operation is performed on DAV to compress changes in large DAVs and expand changes in small DAVs. The P_MDA acts as an exponent. That is, for cases with differing intensities but possibly the same DAV, the power function distinguish the Atmosphere 2016, 7, 40 5 of 17 intensity based on the mechanism that for weaker TCs, much fewer peak deviation angles would distribute within the vicinity of the mean deviation angle, and therefore the smaller the DAO. The performance of DAO and the three parameters are tested individually. Results prove that the DAO performs better than using any of the three parameters alone on the 325 cases. Specifically, by testing the 16,126 images, the correlation coefficient between DAO and TC intensity is proved to be higher Atmosphere 2016, 7, 40 5 of 16 (0.74) compared with DAV (´0.62), P_MDA (0.60) and IQR (´0.63). performs better than using any of the three parameters alone on the 325 cases. Specifically, by testing 3.2. Potentialthe 16,126 Predicators images, the Extraction correlation coefficient between DAO and TC intensity is proved to be higher Radial(0.74) profiles compared of with theIR DAV brightness (−0.62), P_MDA temperature (0.60) and (IRBT IQR for(−0.63). short) form the other basis for extracting possible3.2. predicators Potential Predicators for TC Extraction intensity. This is achieved by converting the Cartesian latitude and longitude gridded data into a polar coordinate system. Then, the BT data are azimuthally averaged at Radial profiles of the IR brightness temperature (IRBT for short) form the other basis for 4 km intervalsextracting from possible the TCpredicators center. Notefor TC that intensity. the radial This is profiles achieved may by converting differ slightly the Cartesian if they latitude are calculated accordingand to longitude different gridded TC center data locations.into a polar This coordina couldte introducesystem. Then, uncertain the BT errorsdata are in azimuthally computing radial profilesaveraged of the IRBTs. at 4 km Therefore, intervals from as the down TC center. in calculating Note that the DAVs, radial a profiles mine-pixel may differ center slightly region if they is taken to create theare azimuthallycalculated according averaged to different IRBT profiles. TC center The locations. mean of This the could nine introduce profiles obtaineduncertain inerrors this in region is finally adoptedcomputing as radial the optimalprofiles of one. the IRBTs. The Empirical Therefore, as orthogonal down in calculating function DAVs, (EOF) a mine-pixel analysis iscenter commonly region is taken to create the azimuthally averaged IRBT profiles. The mean of the nine profiles used to extract crucial information from IRBT [7,19,35]. However, here we do not correlate TC intensity obtained in this region is finally adopted as the optimal one. The Empirical orthogonal function (EOF) directlyanalysis to IRBT is profiles, commonly because used to byextract testing crucial the information 325 cases wefrom found IRBT that[7,19,35]. taking However, the EOFs here as we predicators do for intensitynot correlate contributes TC intensity very little directly to improving to IRBT profil thees, regression. because by Instead,testing the we 325 extract cases we critical found signals that from the profilestaking to the represent EOFs as characters predicators of for satellite intensity images. contributes very little to improving the regression. AsInstead, defined we by extract [36– critical38], the signals core from region the profiles of TC couldto represent be divided characters into of satellite inner coreimages. and outer core regions (fromAs 0defined˝ to 1˝ andby [36–38], from 1the˝ to core 2.5 ˝regionradially of TC respectively). could be divided Thus, into the inner inner core core and average outer core BT (ICBT) regions (from 0° to 1° and from 1° to 2.5° radially respectively). Thus, the inner core average BT (ICBT) and theand outer the core outer average core average BT (OCBT) BT (OCBT) are are estimated. estimated. In In addition, addition, the the minimum minimum and and the themaximum maximum BT within theBT outerwithin corethe outer region core are region also derived are also (hereinafter derived (hereinafter denoted denoted as MIBT as andMIBT MABT, and MABT, respectively). Figure2respectively). shows the SchematicFigure 2 shows diagram the ofSchematic the distribution diagram ofof aforementionedthe distribution parameters.of aforementioned In Figure 2, the solidparameters. curve represents In Figure the2, the mean solid ofcurve the repres 16,126ents IRBT the mean profiles. of the 16,126 IRBT profiles.

240 L45 to U45 : Inner Eyewall L45 to FOT: Lower Eyewall MABT L45 to CCT: Total Eyewall FOT to U45: Middle Eyewall 230 FOT to CCT: Mid-upper Eyewall U45 to CCT: Upper Eyewall

220 L45 FOT MIBT CCT 210 U45 Infrared Brightness Temperature (K) Temperature Brightness Infrared Inner Core Outer Core 0 50 100 150 200 250 Distance From Typhoon Center (km) Figure 2.FigureSchematic 2. Schematic diagram diagram of of the the radial radial profileprofile (solid curve, curve, calculated calculated by averaging by averaging the radial the radial profilesprofiles of the 16,126of the 16,126 images) images) of theof the IR IR brightness brightness temperature.temperature. The The vertical vertical gray graydashed dashed line divides line divides the core region into inner and outer core, respectively. the core region into inner and outer core, respectively. According to Sanabia (2014) [39], IR profiles in the TC inner core could be represented by four Accordingcritical points to Sanabiawhich locate (2014) mainly [39 within], IR profiles100 km from in thethe TC TC center. inner The core first could critical be point represented is the by four criticalradial points location which of the coldest locate cloud mainly top within (CCT) within 100 km 200 from km from the the TC TC center. center. The Note first that criticalhere thepoint is CCT differs from the location of MIBT. The second critical point, the radial location of the first the radial location of the coldest cloud top (CCT) within 200 km from the TC center. Note that here overshooting top (FOT hereinafter), is defined using the BT difference (TWV-IR) between water vapor the CCT(WV) differs and IR from brightness the location temperature of MIBT. [40]. The The third second and fourth critical critical point, points the are radial selected location to define of a the first overshootinglower and top upper (FOT extent hereinafter), (hereinafter is defineddenoted as using L45 and the U45) BT differenceof the inner (Teyewall,WV-IR) respectively. between water The vapor (WV) andL45 IRin this brightness paper is identified temperature as the [first40]. 45° The downtu thirdrn and inflection fourth point, critical which points is the location are selected at which to define a lowerthe and orientation upper extentof the IR (hereinafter profile changes denoted from vertical as L45 to the and horizontal, U45) of and the vice inner versa eyewall,the U45,because respectively.

Atmosphere 2016, 7, 40 6 of 17

The L45 in this paper is identified as the first 45˝ downturn inflection point, which is the location at which the orientation of the IR profile changes from vertical to the horizontal, and vice versa the U45, because we adopted normal cartesian coordinate system without inverting the y axis as did in Sanabia (2014). The mean location of the four critical points are plotted in Figure2. One of the premises for locating L45 and U45 is that the CCTs do not locate in TC centers. However, not all images meet this criterium. Therefore, for such cases, we subjectively define L45, U45 and CCT as the mean of those whose L45 and U45 could be identified. The other obstacle for identifying L45 and U45 is, for some cases, it is inevitable that the eye and eyewall do not exist, and therefore the radial profile do not slope to register a 45˝ angle. For such occasions, we adjust the threshold angle to a smaller one iteratively until finding the point where the profile changes from vertical to horizontal, and from horizontal to vertical.Nevertheless, the minimum threshold angle for L45 and U45 cannot be less than 35˝. As shown in Figure2, six slopes of the IR brightness temperature between the four critical points are calculated. These six slopes can be regarded as proxies for inner-core convections. For example, SL45-FOT represents the slope between the locations of L45 and FOT, which is obtained by dividing the change in IRBT between L45 and FOT by the radial distance. Finally, the mean brightness temperature between every two critical points are calculated. Table2 lists all the potential predicators. All these predicators are probably relevant to TC intensity, while the significance of each one is not determined. Note that in Table2, all terms of the eyewall follow previous studies [39,41].

Table 2. Potential predicator pool for intensity estimation from the IR images.

Potential Predictors Description ICBT Average BT within the inner core (0˝–1˝ radially) OCBT Average BT within the outer core (1˝–2.5˝ radially) MIBT Azimuthally averaged minimum BT within the outer core MABT Azimuthally averaged maximum BT within the outer core SL45-FOT The slope of the lower eyewall SL45-U45 The slope of the inner eyewall SL45-CCT The slope of the total eyewall SFOT-U45 The slope of the middle eyewall SFOT-CCT The slope of the mid-upper eyewall SU45-CCT The slope of the upper eyewall AL45-FOT The average BT within the lower eyewall AL45-U45 The average BT within the inner eyewall AL45-CCT The average BT within the total eyewall AFOT-U45 The average BT within the middle eyewall AFOT-CCT The average BT within the mid-upper eyewall AU45-CCT The average BT within the upper eyewall

3.3. Multiple Linear Regression Model Development Although it is encouraged to seek potential predicators as much as possible, it is unadvisable to take all the potential predicators into the final regression, because some of them may mutually correlated and thus provide redundant information. Therefore, it is necessary to “thin” the initial pool of the potential predictors. Note that for the aim of training an objective method of TC intensity estimation without knowing any information of the TC in advance, any variables that represent TC itself are not included, they had been testified as significant in estimating TC wind structure though [7,8,19,35]. For DAV-T related parameters, the new index DAO and the square of the DAV (DAV2) are selected. For predicators extracted from IRBT profiles, we manually exclude those which are weakly related to the TC intensity by testing the 325 cases. After this, the potential predicator pool initially contains 2 12 predicators: DAV . DAO, ICBT, OCBT, MIBT, SL45-U45,SL45-CCT,SFOT-U45,AL45-U45,AL45-CCT, AFOT-U45 and AU45-CCT. For ICBT and OCBT, we divide them by AL45-U45,AL45-CCT,AFOT-U45 and AU45-CCT, respectively and introduce eight new parameters into the pool. Atmosphere 2016, 7, 40 7 of 17

The regression is performed using a stepwise regression method. In the selection procedure, predicators are either added or removed from the multilinear model according to their statistical significance. The initial model contains no predicators other than the constant term. From then on, the model compares the explanatory power of incrementally larger and smaller models. At each step, the p-value of an F-statistic is computed to test models with and without a potential predicator. If a predicator is not currently in the model, the null hypothesis is that the predicator would have a zero coefficient if added to the model. If there is sufficient evidence to reject the null hypothesis, the predicator is added to the model. Conversely, if a predicator is currently in the model, the null hypothesis is that the predicator has a zero coefficient. If there is insufficient evidence to reject the null hypothesis, the predicator is removed from the model. The model terminates when no single inputting predicator improves the model. Here, we set the lowest confidence level as 99.99%. That is, we require the maximum p-value for a predicator to be added as 0.0005, and the minimum p-value for a predicator to be removed as 0.0001. After selection by the stepwise regression procedure, eventually, seven predicators are 2 involved into regression. They are DAV , DAO, ICBT/AFOT-U45, ICBT/AL45-U45, OCBT/AU45-CCT, 2 OCBT/AL45-FOT and SL45-U45. The DAV is included as the first as previous studies have proved its significance. The order by which the remaining predicators are input (Column 2 in Table3) are decided according to their contribution rates to the accumulated variance. Table3 lists some statistics produced while training the model. In order to quantify the relative contributions of all predictors to the model, all these predicators were normalized, and the stepwise regression was performed again. As shown in the last two columns in Table3, the predicators ICBT/A L45-U45 and ICBT/AFOT-U45 dominate the regression (41.92% and 40.31%, respectively). This is then followed by SL45-U45 (6.28%) and OCBT/AL45-FOT (4.26%). It is obvious that the inputting predicators in this model improves the accuracy of the regression considerably (with a net difference of 18.42 knot and a net improvement of 59.21%).

Table 3. Statistics related to the regression model.

RMSE after Coefﬁcients for Relative Added Predicators Coefﬁcients p-Value Addition of the Normalized Contribution Order Predicator (Knot) Predicators (%) DAV2 1st ´6.04 ˆ 10´6 3.39 ˆ 10´61 31.11 ´22.37 1.66 DAO 2nd 44.64 4.35 ˆ 10´115 19.41 43.69 3.24 ICBT/AL45-U45 3rd ´2703.25 0 17.22 ´565.05 41.92 ICBT/AFOT-U45 4th 2730.51 0 16.46 543.39 40.31 ´112 SL45-U45 5th 12.81 4.90 ˆ 10 15.46 84.61 6.28 ´33 OCBT/AL45-FOT 6th ´201.98 3.46 ˆ 10 13.16 ´57.45 4.26 ´16 OCBT/AU45-CCT 7th 126.48 1.42 ˆ 10 12.69 31.34 2.32

4. Results and Discussions

4.1. Dependent Tests and Results The ﬁnal regressed model is as following:

ICBT ICBT TCI “ ´6.04 ˆ 10´6 ˆ DAV2 ` 44.64 ˆ DA0 ` 2730.51 ´ 2703.25 AFOTÚ45 AU45´L45 OCBT OCBT (2) `126.48 ´ 201.98 ` 12.81 ˆ Sl45ú45 ` 69.11 AU45ĆCT AL45´FOT where TCI represents TC intensity estimated using the trained model. Figure3a shows the scatterplot of the model estimated vs. interpolated best-track intensities. It can be seen that for weak Tcs, the model overestimates intensities noticeably. Figure3b plots the distribution of the errors, which fitted a Gauss model well (the black solid curve). From the curve, 68.26% of the errors lie within the region between ´14.69 knot and 11.69 knot, and 95.44% lie within the region between ´27.38 knot and 23.38 knot. Atmosphere 2016, 7, 40 8 of 17 Atmosphere 2016, 7, 40 8 of 16

Atmosphere 2016, 7, 40 8 of 16

FigureFigure 3. (a )3. Scatterplot (a) Scatterplot of modelof model regressed regressedvs. vs. interpolatedinterpolated best-track best-track intensities intensities in the in thedependent dependent test. The solid line was derived by a linear regression procedure using least square method. (b) The test. The solid line was derived by a linear regression procedure using least square method; distribution of the errors. The solid curve represents a Gaussian model which was derived by fitting (b) The distribution of the errors. The solid curve represents a Gaussian model which was derived by Figurethe error 3. distribution.(a) Scatterplot of model regressed vs. interpolated best-track intensities in the dependent ﬁtting the error distribution. test. The solid line was derived by a linear regression procedure using least square method. (b) The distributionThe model ofis thevalidated errors. The several solid timescurve representsto justify aits Gaussian accuracy. model First which of all, was we derived adopted by fittingthe n -fold Thecross modelthe validation erroris distribution. validated method to several examine times the accuracy to justify of the its model accuracy. for individual First of all, TCs. we To adopted begin with, the then-fold cross16,126 validation images method are divided to examineinto mutually the accuracyexclusive 325 of theindividual model TC for groups. individual Then, the TCs. validation To begin are with, the 16,126performedThe images model 325 are times. is dividedvalidated For each into several ti mutuallyme, timeswe leave to exclusive justify one case its 325 outaccuracy. individual and train First the TCof model all, groups. we using adopted Then, the remaining the n validation-fold cross validation method to examine the accuracy of the model for individual TCs. To begin with, the are performed324 cases iteratively. 325 times. After For eachthat, time,the trained we leave model one is validated case out andusing train the one the modelwhich was using not the included remaining 16,126into training images the are model. divided Note into althoughmutually thisexclusive produced 325 individual 325 models, TC the groups. differences Then, theamong validation these 325are 324 cases iteratively. After that, the trained model is validated using the one which was not included performedmodels are 325 quite times. small For (not each shown time, wehere leave for oneavoiding case out redundancy) and train the and model are similar using thewith remaining the one into training the model. Note although this produced 325 models, the differences among these 324showed cases above. iteratively. In each After validation that, the process,trained model the di isstribution validated of using the mean the one absolute which waserror not (MAE), included the 325 modelsintoRMSE training and are the quitethe mean model. small absolute Note (not although relative shown errorthis here pr (MARE) foroduced avoiding 325are calculated(Figuremodels, redundancy) the differences and4). Figure areamong similar 4a theseplots with 325the the one showedmodelsdistribution are above. quiteof the In smallerrors each (notwhich validation shown is obtained here process, forby anavoiding theaccumulating distribution redundancy) procedure of theand of meanare the similar 16,126 absolute images.with error the It onecan (MAE), the RMSEshowedbe seen and thatabove. the 50%, mean In 75% each absolute and validation 90% relativeof theprocess, model error the estima (MARE) distributionted intensities are calculatedof the aremean with (Figure absolute the MAE4). error Figure less (MAE), than4a plots7, the13, the distributionRMSEand 20 andknot, of the the respectively. errors mean whichabsolute Figure is relative obtained 4b shows error by the an(MARE) aver accumulatingage ofare RMSE calculated(Figure procedurefor individual of 4). TCs. the Figure16,126 For the4a images. 325plots cases the It can be seendistributionin the that dependent 50%, of 75%the test, errors and well 90%which over of is75% the obtained of model their by intensities estimated an accumulating are intensities estimated procedure arewith with ofa meanthe the 16,126 RMSE MAE images. less less than thanIt can 127, 13, be seen that 50%, 75% and 90% of the model estimated intensities are with the MAE less than 7, 13, and 20knot, knot, while respectively. only 18 TCs Figure over 415b showsknot. The the averaged average ofRMSE RMSE is 18.52 for individual knot for the TCs. overall For 325 the cases. 325 cases and 20 knot, respectively. Figure 4b shows the average of RMSE for individual TCs. For the 325 cases in theFigure dependent 4c,d plots test, the well averaged over MARE 75% of and their averaged intensities bias (defined are estimated as the average with a differences mean RMSE between less than inthe the estimated dependent intensity test, well and over the best-track75% of their intensity) intensities for arethe estimated 325 cases, with respectively. a mean RMSE The mean less thanMARE 12 12 knot, while only 18 TCs over 15 knot. The averaged RMSE is 18.52 knot for the overall 325 cases. knot,is 19.91% while and only the 18mean TCs bias over is 15−0.56 knot. knot The (while averaged the mean RMSE absolute is 18.52 bias knot is 4.47 for knot).the overall 325 cases. FigureFigure4c,d plots4c,d plots the averagedthe averaged MARE MARE and and averaged averaged biasbias (deﬁned(defined as as the the average average differences differences between between 60 25 the estimatedthe estimated intensity intensity and and the the best-track best-track intensity) intensity)(a) for forMean: the the 8.52 325325 cases,cases, respectively. respectively.(b) The The mean mean MARE MARE is 20 19.91%is 19.91% and the and mean the mean bias40 is bias´0.56 is −0.56 knot knot (while (while the the mean mean absolute absolute biasbias is 4.47 4.47 knot). knot). 15 10 6020 25

MAE (knot) (a) Mean: 8.52 (b) 13 RMSE (knot) 5 7 20 400 0 0 25 50 75 90 100 150 50 100 150 200 250 300 Percent (%) Typhoon No 10 20 Mean: 19.91 (c) Mean: 0.56 (d)

MAE (knot) 10 1340 RMSE (knot) 5 7 300 0 0 25 50 75 90 100 00 50 100 150 200 250 300 20 Percent (%) Typhoon No MARE (%) (c) (knot) BIAS -10 10 Mean: 19.91 10 Mean: 0.56 (d) 40 0 300 50 100 150 200 250 300 0 50 100 150 200 250 300 Typhoon No 0 Typhoon No 20 MARE (%) BIAS (knot) BIAS -10 Figure 4. N-fold10 cross validation of the model using the 325 cases in the northwestern pacific Ocean 0 during the time period0 50 from100 1996150 to 2002007.250 (a) The300 cumulative0 50 distribution100 150 200 of the250 absolute300 errors. (b) Typhoon No Typhoon No The root mean square error for each left out case. (c) The absolute relative error for each left out case. FigureFigure(d) 4. TheN-fold 4.bias N-fold crossfor eachcross validation left validation out case. of of the the model model usingusing the 325 325 cases cases in in the the northwestern northwestern pacific paciﬁc Ocean Ocean during during the timethe time period period from from 1996 1996 toto 2007. (a ()a The) The cumulative cumulative distribution distribution of the ofabsolute the absolute errors. (b errors;) The root mean square error for each left out case. (c) The absolute relative error for each left out case. (b) The root mean square error for each left out case; (c) The absolute relative error for each left out (d) The bias for each left out case. case; (d) The bias for each left out case.

Atmosphere 2016, 7, 40 9 of 17 Atmosphere 2016, 7, 40 9 of 16

InIn orderorder toto examineexamine whetherwhether thethe performanceperformance ofof thethe modelmodel reliesrelies onon thethe categorycategory ofof thethe TCTC intensity,intensity, the the 16,126 16,126 images images are are divided divided into into every every 5 5 knot knot bins. bins. FigureFigure5 a5a shows shows the the counts counts of of TCs TCs in in eacheach intensityintensity binsbins inin thethe dependentdependent tests.tests. FigureFigure5 b5b shows shows that that the the mean mean RMSE RMSE generally generally increases increases withwith intensityintensity butbut forfor intense intense typhoons typhoons ( ě(≥130130 Knot).Knot). However, fromfrom FigureFigure5 5c,c, the the MARE, MARE, it it can can be be foundfound thatthat thethe absolute absolute relative relative error error is is not not signiﬁcant significant ( ď(≤15%)15%) forfor TCsTCs strongerstronger thanthan 6060 knot,knot, whichwhich meansmeans thatthat althoughalthough moremore errorserrors couldcould bebe expectedexpected forfor intenseintense typhoons,typhoons, thethe relativerelative errorerror isis quitequite small.small. FromFrom FigureFigure5 d,5d, the the model model generates generates noticeable noticeable (absolute (absolute bias bias > > 10 10 Knot) Knot) overestimation overestimation in in casescases ofof weakweak systemssystems ( ď(≤25 knot) and underestimation inin casescases ofof intenseintense ((ě≥150150 knot). knot).

20 (a) Mean: 11.81 Knot (b) 2000 15

Count 1000 10 RMSE (knot)

0 5 20 45 70 95 120 145 20 45 70 95 120 145 Intensity Bin (knot) Intensity Bin (knot) Mean: 15.45 % (c) Mean: -4.17 Knot (d) 50 10 40 30 0 20 MARE (%) BIAS (knot) BIAS -10 10 20 45 70 95 120 145 20 45 70 95 120 145 Intensity Bin (knot) Intensity Bin (knot)

FigureFigure 5.5. ResultsResults ofof thethe dependentdependent teststests byby intensitiesintensities bins.bins. ((aa)) TheThe frequencyfrequency distributiondistribution ofof thethe cyclonescyclones byby intensityintensity inin thethe dependentdependent tests;tests; TheThe average:average: ((bb)) rootroot meanmean squaresquare error;error; (c(c)) absoluteabsolute relativerelative error; error; and and (d) ( biasd) bias for eachfor each intensity intensity bin. bin.

ToTo facilitate facilitate further further analysis, analysis, thethe 16,12616,126 imagesimages areare thenthen divideddivided intointo sevenseven groupsaccordinggroupsaccording toto Safﬁr–SimpsonSaffir–Simpson Scale. Scale. TheThe RMSERMSE andand MAREMARE areare calculatedcalculated forfor eacheach group.group. Table4 4 shows shows the the results. results. InIn general, general, the the error error increases increases with with intensity, intensity, with with the the RMSE RMSE 10.52, 10.52, 12.94, 12.94, 15.68, 15.68, 17.49 17.49 and and 18.93 18.93 knot knot for categoryfor category 1–5 typhoons,1–5 typhoons, respectively. respectively. However, However, from thefrom MARE the MARE (last column (last column in Table in4 ),Table it can 4), be it foundcan be thatfound the that model the performsmodel performs well but well for but tropical for tropical depressions depressions and storms and storms (also see (also Figures see Figures3 and5) 3 which and 5) haswhich the highesthas the proportionhighest proportion of samples of (63.66%). samples The(63.66%). MARE The between MARE the between regressed the and regressed the interpolated and the best-trackinterpolated intensities best-track for tropicalintensities depressions for tropical is asdepres highsions as 30.35% is as althoughhigh as 30.35% the RMSE although is relatively the RMSE small is (7.77relatively knot). small Figures (7.773a andknot).5d, Figures Table4 all3a and suggest 5d, Table that this 4 all is suggest due to an that overestimate this is due (96.74%)to an overestimate for this category,(96.74%) whilefor this for categorycategory, 1–5 while typhoons, for thecatego modelry 1–5 tends typhoons, to produce the underestimations. model tends Asto aproduce whole, forunderestimations. all the 16,126 images, As a whole, 57.76% for (9314) all the are 16,126 overestimated images, 57.76% while 42.24% (9314) are (6812) overestimated are underestimated. while 42.24% The overall(6812) RMSEare underestimated. is 12.69 knot (also The see overall Table 4 RMSEand Figure is 12.693a). Meanwhile,knot (also see the overallTable 4 MARE and Figure is 19.78% 3a). whichMeanwhile, is resulted the primarilyoverall MARE from tropicalis 19.78% storms which and is depressions,resulted primarily when theyfrom are tropical removed storms from theand dependentdepressions, tests, when the they overall are MAREremoved deceases from the to depend 12.55%ent for alltests, category the overall 1–5 typhoons.MARE deceases to 12.55% for all category 1–5 typhoons.

Table 4. Dependent tests of the model by dividing the cyclones into seven groups according to Saffir–Simpson Scale. The number and ratio of underestimated or overestimated images are listed in the table.

No. of No. of No. of RMSE MARE Bins Samples (%) Overestimated (%) Underestimated (%) (Knot) (%) Tropical Depression 4752 (29.47) 4597(96.74) 155 (3.26) 7.77 30.35 Tropical Storm 5513 (34.19) 3575 (64.85) 1938 (35.15) 9.95 18.46 C1 (Typhoon) 2444 (15.16) 766 (31.34) 1678 (68.66) 10.52 12.71 C2 (Moderate Typhoon) 1242 (7.70) 397 (31.96) 845 (68.04) 12.94 14.79

Atmosphere 2016, 7, 40 10 of 17

Table 4. Dependent tests of the model by dividing the cyclones into seven groups according to Safﬁr–Simpson Scale. The number and ratio of underestimated or overestimated images are listed in the table.

No. of No. of No. of RMSE Bins MARE (%) Samples (%) Overestimated (%) Underestimated (%) (Knot) Tropical Depression 4752 (29.47) 4597(96.74) 155 (3.26) 7.77 30.35 Tropical Storm 5513 (34.19) 3575 (64.85) 1938 (35.15) 9.95 18.46 C1 (Typhoon) 2444 (15.16) 766 (31.34) 1678 (68.66) 10.52 12.71 C2 (Moderate Typhoon) 1242 (7.70) 397 (31.96) 845 (68.04) 12.94 14.79 C3 (Severe Typhoon) 910 (5.64) 247 (27.14) 663 (72.86) 15.68 14.26 C4Atmosphere (Super Typhoon) 2016, 7, 40 1041 (6.46) 391 (37.56) 650 (62.44) 17.4910 11.82 of 16 C5 (Extreme Typhoon) 224 (1.39) 107 (47.76) 117 (52.24) 18.93 10.69 C3Overall (Severe Typhoon) 16,126 910 (100) (5.64) 9314 247 (57.76) (27.14) 6812 663 (42.24) (72.86) 12.69 15.68 14.26 19.78 C4 (Super Typhoon) 1041 (6.46) 391 (37.56) 650 (62.44) 17.49 11.82 C5 (Extreme Typhoon) 224 (1.39) 107 (47.76) 117 (52.24) 18.93 10.69 4.2. IndependentOverall Tests Results 16,126 (100) 9314 (57.76) 6812 (42.24) 12.69 19.78 The developed model is run on 52 cases (see Figure6 and Table1 for detail number and percent 4.2. Independent Tests Results of images in each group) from the 2008 to 2009 typhoon season for validation. Of the 52 cases, five are tropicalThe developed depressions, model is 23 run are on tropical 52 cases storms,(see Figure five 6 and are Table typhoons, 1 for detail six arenumber moderate and percent typhoons, threeof are images severe in typhoons, each group) five from are the super 2008 typhoons, to 2009 ty andphoon fvie season are extreme for validation typhoons.. Of the Because 52 cases, this five 52 cases are notare included tropical depressions, in training 23 the are model, tropical the storms, results five of are the typhoons, independent six are tests moderate are indicative typhoons, of three what we are severe typhoons, five are super typhoons, and fvie are extreme typhoons. Because this 52 cases can expect when this model is applied into real-time estimation process. For the aim of comparison are not included in training the model, the results of the independent tests are indicative of what we amongcan groups expect withwhen approximately this model is applied same size.into real-time The 52 cases estimation are divided process. into For threethe aim groups of comparison by thresholds <60 knot,among 60 groups to 120 knotwith andapproximatelyě120 to <100 same knot, size. and The 100 52 to cases 130 knotare divided and ě130 into knot, three according groups by to their maximumthresholds intensity <60 knot, (hereinafter 60 to 120 denotedknot andas ≥120 G1, to G2 <100 and knot, G3, and respectively), 100 to 130 producingknot and ≥130 690, knot, 689 and 603 imagesaccording in eachto their group, maximum respectively. intensity After (hereinafter that, validations denoted are as performedG1, G2 and independently. G3, respectively), Figure 7 showsproducing the accuracy 690, 689 of and the 603 model images in estimatingin each group, intensity respectively. of the After 52 cases that, validations in three groups. are performed Comparing to best-trackindependently. intensities, Figure the7 shows results the indicateaccuracy aof high the model accuracy, in estimating especially intensity for intense of the typhoons52 cases in (G3). As shown,three groups. for G1 Comparing (Figure7a), to more best-track errors intensities, exist as there the results are more indicate images a high on accuracy, which TCs especially are weak for and the modelintense tends typhoons to overestimate (G3). As shown, their for intensities. G1 (Figure For7a), G2more (Figure errors7 existb), the as modelthere are performs more images better on with which TCs are weak and the model tends to overestimate their intensities. For G2 (Figure 7b), the an R2 of 0.66, while for G3 (Figure7c), in which the typhoons are quite strong, the model can estimate model performs better with an R2 of 0.66, while for G3 (Figure 7c), in which the typhoons are quite R2 intensitiesstrong, with the amodel much can higher estimate accuracy intensities ( of with 0.84). a Tablemuch5 higher lists statistics accuracy produced (R2 of 0.84).Table in testing 5 thelists three 2 groups.statistics The mean produced of RMSE, in testing MAE, the bias, three MARE groups. and TheR meanare 12.01 of RMSE, knot, MAE, 9.50 knot,bias, 2.00MARE knot, and 21.67%, R2 are and 0.77 for12.01 the knot, overall 9.50 cases,knot, 2.00 respectively. knot, 21.67%, and 0.77 for the overall cases, respectively.

o 160 45 N 2008/17w 2009/krovanh2009/melor 2008/vongfong 2008/16w 2009/dujuan 140 2008/kalmaegi 2008/11w 2009/lupit 2009/etau o 120 35 N 2009/choi-wan2008/bavi2008/sinlaku 2008/rammasun 2009/nepartak 2008/jangmi 2008/nakri 2009/kujira 100 2008/haishen 2008/fung-wong 2009/linfa 2008/halong 2009/06w 2009/28w o 2009/chan-hom2008/matmo 80 25 N 2008/fengshen2009/nangka 2008/hagupit2009/koppu2008/nuri2009/molave2008/neoguri2008/higos 2008/dolphin 2008/kammuri 2009/nida 2009/soudelor 2008/14w 2009/mujigae 2009/25w 60 2008/22w

Latitude (DEG) 2008/mekkhala2009/goni TC intensity /Knot TC intensity o 2009/ketsana 40 15 N 2009/24w 2008/maysak 2008/noul2009/mirinae 2009/18w 2009/27w 20

o 2008/01w 5 N 0 105oE 115oE 125oE 135oE 145oE 155oE 165oE Longotude (DEG)

FigureFigure 6. Same 6. Same as Figureas Figure1 but 1 but for for cases cases from from 2008 2008 toto 20092009 typhoon typhoon season season used used in the in the independent independent tests. The green boxes represents the name of the cyclones. tests. The green boxes represents the name of the cyclones.

Table 5. Statistics produced in the independent tests.

<60 Knot 60–120 Knot ≥120 Knot Overall RMSE (knot) 6.47 11.22 12.29 12.01 MAE (knot) 8.30 8.92 9.47 9.50 Mean Bias (knot) 7.30 0.01 0.73 2.00 MARE (%) 26.34 18.76 15.16 21.67 R2 0.47 0.66 0.84 0.77

Atmosphere 2016, 7, 40 11 of 17 Atmosphere 2016, 7, 40 11 of 16

60 120 (a) y=0.86*x+-1.17 (b) y=1.09*x-4.9 (c) y=0.99*x-0.25 150 100 50

80 40 100 Atmosphere 2016, 7, 40 60 11 of 16

30 60 12040 50 (a) y=0.86*x+-1.17 (b) y=1.09*x-4.9 (c) y=0.99*x-0.25 Best-track IntensitiesBest-track (Knot) R-Squae=0.47 R-Squae=0.66 150 R-Squae=0.84 20 10020 5020 40 60 20 40 60 80 100 120 50 100 150 Model80 Estimated Intensities (Knot) 40 100 Figure 7. ScatterplotsScatterplots of the modelmodel estimatedestimated60 vs. best-trackbest-track intensities for groups in which the maximum intensity: (a) <60 knot; (b) 60–120; and (c) >120 knot in the independent tests. The solid lines indicates intensity30 : (a) <60 knot; (b) 60–120; and (c) >120 knot in the independent tests. The solid lines indicates the thegoodness goodness of the of regression the regression of the of scatterplot, the scatterplot,40 which whichare obtained are obtained using the using least50 the square least method. square method.

Best-track IntensitiesBest-track (Knot) R-Squae=0.47 R-Squae=0.66 R-Squae=0.84 20 Table 5. Statistics20 produced in the independent tests. Figure20 8 shows40 the intensity60 sequences20 40 of60 TCs80 in 100 the 120 three group50s. The 100 model 150 estimated intensities sequence for G3 (Figure 8c) shows high consistence with the best-track over time. <60 KnotModel Estimated 60–120 Intensities Knot (Knot)ě120 Knot Overall Meanwhile, more errors could be found for weak typhoons TCs as expected (top panel in Figure 8 RMSE (knot) 6.47 11.22 12.29 12.01 for G1).Figure Figure 7. Scatterplots 8 also indicates of the model that variations estimated vs. of bestthe -BTstrack in intensities satellite for images groups do in not which necessarily the maximum produ ce changes in intensities.MAE (knot) 8.30 8.92 9.47 9.50 intensityMean: (a) <60 Bias knot (knot); (b) 60–120; and 7.30 (c) >120 knot in 0.01 the independent 0.73 tests. The solid lines 2.00 indicates the goodness ofMARE the regression (%) of the scatterplot, 26.34 which are 18.76 obtained using 15.16 the least square method. 21.67 2 Model EstimatedR Intensities 0.47 0.66 0.84 0.77 Figure60 8Best-track shows Intensities the intensity sequences of TCs in the three groups. The model estimated intensitiesFigure 8 sequence shows the for intensity G3 (Figure sequences 8c) ofshows TCs in high the three consistence groups. with The model the best estimated-track over intensities time. 40 sequenceMeanwhile, for more G3 (Figure errors8 c)could shows be highfound consistence for weak typhoons with the best-trackTCs as expected over time. (top Meanwhile, panel in Figure more 8 for G1). Figure 8 also indicates that variations of the BTs in satellite images do not necessarily produce errors could be found for weak typhoons TCs as expected (top panel in Figure8 for G1). Figure8 also changes20 in intensities. indicates that variations of the BTs in satellite images do not necessarily produce changes in intensities.

0 100 200 300 400 500 600

120 Model Estimated Intensities 60 Best-track Intensities 100 150

Intensity (Knot) Intensity 80 40 100 60 4020 50

20 0 100 200100 300 400200500 600 300700 0 400100 200500 300 400600 500 120 Tropical Cyclone Sequence 100 150

Figure (Knot) Intensity 8. The sequences of the intensity of the 52 typhoons divided into three groups. The gray line 80 indicates the best-track intensities and the black line repre100 sents the model estimated ones. 60 4.3. Case40 Analysis of Extreme Typhoon Melor (No. 202009)50 20 For investigating factors that could be attributed as the source of errors, the extreme typhoon 0 100 200 300 400 500 600 700 0 100 200 300 400 500 Melor—No. 202009—is selected to analyzeTropical further Cyclone as itSequence is the strongest case in the independent validation tests. Typhoon Melor (2009), known as Typhoon Quedan in the Philippines, was the secondFigure category 8. The 5 sequences typhoon ofin the2009. intensity It reached of the 150 52 typhoonstyphoonsknot (central divided pressure into three 911 groups. hPa) at The 12 : gray00 p.m. line UTC 4 October.indicates Figure thethe best-trackbest 9a shows-track intensitiesintensities an image andand of Melor thethe blackblack (2009) lineline reaching representsrepresents the thethe peak modelmodel intensity, estimatedestimated and ones.ones. Figure 9b shows the intensity sequence estimated using the model. In addition, the model estimated intensity curve was 4.3. Case Analysis of Extreme Typhoon Melor (No. 202009) 12-h smoothed (black solid line). The smoothed curve is consistent with the best-track curve (R2 of 0.91). For investigating factors that could be attributed as the source of errors, the extreme typhoon Melor—No. 202009—is selected to analyze further as it is the strongest case in the independent validation tests. Typhoon Melor (2009), known as Typhoon Quedan in the Philippines, was the second category 5 typhoon in 2009. It reached 150 knot (central pressure 911 hPa) at 12:00 p.m. UTC 4 October. Figure 9a shows an image of Melor (2009) reaching the peak intensity, and Figure 9b shows the intensity sequence estimated using the model. In addition, the model estimated intensity curve was 12-h smoothed (black solid line). The smoothed curve is consistent with the best-track curve (R2 of 0.91).

Atmosphere 2016, 7, 40 12 of 17

4.3. Case Analysis of Extreme Typhoon Melor (No. 202009) For investigating factors that could be attributed as the source of errors, the extreme typhoon Melor—No. 202009—is selected to analyze further as it is the strongest case in the independent validation tests. Typhoon Melor (2009), known as Typhoon Quedan in the Philippines, was the second category 5 typhoon in 2009. It reached 150 knot (central pressure 911 hPa) at 12:00 p.m. UTC 4 October. Figure9a shows an image of Melor (2009) reaching the peak intensity, and Figure9b shows the intensity sequence estimated using the model. In addition, the model estimated intensity curve was 12-h smoothed (black solid line). The smoothed curve is consistent with the best-track curve (AtmosphereR2 of 0.91). 2016, 7, 40 12 of 16

(a) 1200 UTC 04 Oct. (b) Best-track 160 150 Knot 911 hPa Unsmoothed 21.7 140 Smoothed

120 18.9 Typhoon Center 100

16.1 80 intensity (knot) intensity Longitue (DEG) Longitue 60 R-Square=0.91 13.3 40 MARE= 15.43% RMSE=12.72 Knot 20 Mean Bias =-3.66 Knot 10.5 135.15 137.95 140.75 143.55 146.35 01/00 03/00 05/00 07/00 09/00 Latitude (DEG) October

Figure 9. (a) IR imageimage of typhoontyphoon Melor (2009) at 12:00 p.m. UTC 4 October, the arrow indicatesindicates the typhoon center derived from JTWC best-track dataset;dataset. (b) The intensity sequence estimated using the model developed in this paper (gray solid curve), the curve that is 12-h smoothed (black solid curve), and that from best-track (black dashed curve).curve). The model underestimates intensity of Melor (mean bias of −3.66 Knot) in most cases while the The model underestimates intensity of Melor (mean bias of ´3.66 Knot) in most cases while the peak intensity and intensities in the following 48 h are slightly overestimated. By examing the images peak intensity and intensities in the following 48 h are slightly overestimated. By examing the images within this 48-h time interval, we found that there is no L45 or U45 points on the radial profiles of within this 48-h time interval, we found that there is no L45 or U45 points on the radial profiles of most most images. We doubt that assuming the location of L45 and U45 as the average values might images. We doubt that assuming the location of L45 and U45 as the average values might introduce introduce errors but further examination is in need. As described in the data section, since the errors but further examination is in need. As described in the data section, since the existence of the existence of the “missing belt” in the Satellite images, which is filled by interpolation, we doubt that “missing belt” in the Satellite images, which is filled by interpolation, we doubt that this also results in this also results in uncertain errors as it produces considerable errors in computing gradient vectors uncertain errors as it produces considerable errors in computing gradient vectors of the brightness of the brightness temperatures. Nonetheless, further improvements are needed to perfect the model temperatures. Nonetheless, further improvements are needed to perfect the model developed in this developed in this study. In addition, the patterns of these images are similar within the core region study. In addition, the patterns of these images are similar within the core region but vary substantially but vary substantially outside the core. Since the fixed radius (300 km) was adopted in computing outside the core. Since the fixed radius (300 km) was adopted in computing deviation angle related deviation angle related parameters, it is possible that errors could be introduced by this fixed radius. parameters, it is possible that errors could be introduced by this fixed radius. From best-track intensity curve, it is clear that typhoon Melor experienced a time period From best-track intensity curve, it is clear that typhoon Melor experienced a time period (approximately from 2 October to 4 October) of stable intensities. However, from the model estimated (approximately from 2 October to 4 October) of stable intensities. However, from the model estimated curve, the intensity see an steadily rising trend. Meanwhile, the intensities within this time period are curve, the intensity see an steadily rising trend. Meanwhile, the intensities within this time period observably underestimated. By examing both the best-track and the model estimated intensities, we are observably underestimated. By examing both the best-track and the model estimated intensities, found the intensity of Melor did remain stable from 0:00 UTC 2 Oct to 6:00 UTC 3 October as recorded we found the intensity of Melor did remain stable from 0:00 UTC 2 Oct to 6:00 UTC 3 October as by the original JTWC best-track, but it increased to 120 knot at 12:00 UTC Oct. 03 and later to 130 recorded by the original JTWC best-track, but it increased to 120 knot at 12:00 UTC Oct. 03 and later knot. Therefore, it is likely that the interpolation process of the best-track data produced such errors. to 130 knot. Therefore, it is likely that the interpolation process of the best-track data produced such To test this, the original best-track intensities and the IR images of corresponding time are used to errors. To test this, the original best-track intensities and the IR images of corresponding time are used perform the regression again. The comparison of statistics of the errors between the model regressed to perform the regression again. The comparison of statistics of the errors between the model regressed using the interpolated best-track and the original intensities are listed in Table 6. It is clear that results using the interpolated best-track and the original intensities are listed in Table6. It is clear that results derived using the original best-track intensities are much better than that using the interpolated ones. derived using the original best-track intensities are much better than that using the interpolated ones. Therefore, we are confident that the accuracy of the model could be improved if accurate and high temporal resolution historical typhoon intensities could be provided.

Table 6. Comparison of the regressed model between using the original and interpolated best-track intensities.

Dependent Tests Independent Tests Interpolated Original Interpolated Original (16,126 Images) (8652 Images) (1982 Images) (931 Images) R2 0.77 0.78 0.77 0.81 RMSE (Knot) 12.69 9.88 12.01 9.48 MARE (%) 19.78 14.93 21.67 15.55

Atmosphere 2016, 7, 40 13 of 17

Therefore, we are conﬁdent that the accuracy of the model could be improved if accurate and high temporal resolution historical typhoon intensities could be provided.

Table 6. Comparison of the regressed model between using the original and interpolated best-track intensities.

Finally, Following Fetanat (2013) [20], a short comparison of statistics produced in validations of existing algorithms for estimating TC intensity was made, the technique introduced by Kossin (2007) [42], the improved DAV-T developed by Ritchie (2014) [25], the feature analogs in satellite imagery (FASI) proposed by Fetanat (2013) [20], and the developed TI index [26] are considered. The overall RMSE produced both in the dependent and independent tests of our models which were developed using the three-hourly interpolated and the original six-hourly archived intensities are used to compare with these techniques, results are listed in Table7. It is noteworthy that in this paper we use the largest set of tropical cyclone cases into developing the model compared with the aforementioned techniques. The accuracy of our model, however, is on par with these techniques. Furthermore, it is obvious that the retrained model using the original three-hourly archived best-track intensities performs even better.

Table 7. Comparison of the model estimated typhoon intensities with previous developed technique using the statistics RMSE.

Technique RMSE (Knot) Kossin et al. (2007) 13.20 Improved DAV-T 12.90 TI index 9.34 FASI 12.70 Interpolated intensity 12.69 Dependent test Original intensity 9.88 Interpolated intensity 12.01 Independent test Original intensity 9.48

5. Conclusions Cloud-top brightness temperatures have long been correlated with surface wind structure of tropical cyclones [7,8,10,19,43]. More recently, several new techniques have been developed to estimate TC intensity from satellite measured brightness temperature in the northwestern pacific basin [3,16,20,25]. This paper presents an objective model for tropical cyclone intensity estimation over northwestern pacific Ocean using geostationary IR data. The final obtained model is developed using tropical cyclone cases (16,126 three-hourly images) from the 1996 to 2009 Northwestern Pacific typhoon seasons, with a multiple linear regression technique. The independent validations are performed on 52 cases from 2008 to 2009 typhoon season. Before regression, significant signals and parameters of satellite IR images are extracted by several steps (as described in Section3). The predicators that are eventually involved in the model include the square of deviation angle variance (DAV2), the new developed index DAO, the inner core mean brightness temperature (ICBT), the outer core brightness temperature (OCBT), the mean brightness Atmosphere 2016, 7, 40 14 of 17

temperature between FOT and U45 (AFOT-U45), the mean brightness temperature between CCT and U45 (AU45-CCT), the mean brightness temperature between L45 and FOT (AFOT-U45), and the slope between L45 and U45 (Sl45-u45). The regressed model is shown in Section 4.1. Various tests are performed to statistically justify the accuracy of the developed model. From the dependent test, the model could perform with a reasonable accuracy (with a mean RMSE of 12.69 knot and mean absolute relative errors of 19.78% for the overall cases). However, the model generally overestimates weak cyclones while underestimates intense typhoons. In the independent tests, it is proven that the model could be regarded as a reference in determining TC intensities in real-time, especially for intense typhoons. By dividing the 52 cases in the independent tests into three groups of approximately equal size, we show that there more errors could be expected when the model is applied into deterring intensities of weak systems. In short, the model can estimate tropical cyclone intensities relatively accurate in the independent tests (a RMSE of 12.01 Knot). In order to quantify the influence of the interpolation of the best-track intensities on the performance of the model, the original best-track intensities are adopted to perform the regression again (results are listed in Tables6 and7). Noticeable improvements could be seen using original best-track intensities. Specifically, this produces a decrease in RMSE of around 2 Knot. Therefore, we have confidence that this model could be improved, providing an accurate and high temporal resolution historical intensity dataset. Many factors may be attributed as error sources and further studies are in need to improve the model. In conclusion, the model developed in this paper provides another reference for tropical cyclone intensity estimation over North Western Pacific Ocean. Future works will focus mainly on the improvement of the model and the application of the model in estimating surface wind structure of typhoons from satellite images.

Acknowledgments: Tropical cyclone best-track data were downloaded from the Joint Typhoon Warning Center. Tropical cyclone satellite images were obtained from HURSAT and the JPL Tropical Cyclone Information System. This work is supported by Shandong Joint Fund for Marine Science Research Center (No. U1406404), the National High Technology Research and Development Program of China (863 Program, No. 2013AA09A505), and the National Basic Research Program of China (973 Program, No. 2012CB955600). Special appreciation is extended to Professor Elizabeth A. Ritchie (University of New South Wales) for explaining the DAV-T and for her insightful comments. The authors are grateful for valuable comments from Kenneth Knapp and other two anonymous reviewers. Author Contributions: Yong Zhao and Chaofang Zhao conceived and designed the framework of this research and wrote the paper. The remaining two authors contributed to the experiments. Conﬂicts of Interest: The authors declare that there are no research conﬂicts to report, but just provide another reference for related research.

Abbreviations The following abbreviations are used in this manuscript:

TC Tropical Cyclone BT Brightness Temperature NWP Northwestern Paciﬁc Ocean TCIS The JPL Tropical Cyclone Information System GMS Geostationary Meteorological Satellite IRBT Infrared Brightness Temperature MSW Maximum Sustained Wind JTWC National Joint Typhoon Warning Center DAV The Variance of Deviation Angles DAV-T The Deviation-Angle Variance Technique P_MDA The Probability Density of Mean Deviation Angle Atmosphere 2016, 7, 40 15 of 17

IQR Interquartile Range of the DAs ICBT The Inner Core Average BT OCBT The Outer Core Average BT MIBT (MABT) Azimuthally Averaged Minimum (Maximum) BT within the Outer Core CCT The Radial Location of the Coldest Cloud FOT The Radial Location of the First Overshooting Top L45 (U45) The Lower (Upper) Extent of the Inner Eyewall MAE Mean Absolute Error RMSE Root Mean Square Error MARE Mean Absolute Relative Error

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