OCTOBER 2016 Z H A N G E T A L . 1643 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 Unauthenticated | Downloaded 09/24/21 05:45 AM UTC OCTOBER 2016 Z H A N G E T A L . 1645 FIG. 1. (a) An axisymmetric graph. (b) A diagram of the deviation angle. train RVM in order