Kexin Chen , Guanghua Chen , Chenhong Rao , Ziqing Wang

a Key Laboratory of Cloud-Precipitation Physics and Severe Storms, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

b Shanghai Typhoon Institute, China Meteorological Administration, Shanghai, China

c University of Chinese Academy of Sciences, Beijing, China

Keywords:Tropical cyclone size change rate Multiplatform Tropical Cyclone Surface Wind Analysis data correlation analysis

ABSTRACT In this study, the relationship of tropical cyclone (TC) size change rate (SCR), within 24 hours, with size, intensity,and intensity change rate (ICR) are explored over the western North Pacific. TC size is defined as the azimuthally averaged radius of gale-force wind of 17 m s?1 (R17) based on the Multiplatform Tropical Cyclone Surface Winds Analysis data. The majority of SCRs are mainly distributed in the range from ? 20 to 80 km d?1 . The correlation coefficients between SCR and size (SCR-R17), intensity, and ICR (SCR-ICR) are ? 0.43, ? 0.12, and 0.25, respectively. The sensitivity of the SCR-R17 and SCR-ICR relationships to size, intensity, and evolution stage are further examined. Results show that the SCR-R17 relationship is more sensitive to variations of size and evolution stage than that of intensity. The relationship of SCR-ICR is largely modulated by the evolution stage. The correlation coefficient of SCR-ICR can increase from 0.25 to 0.40 when only considering the lifetime stages concurrently before and after the lifetime maximum size (LMS) and lifetime maximum intensity. This demonstrates that ICR is a potential factor in predicting SCR during these evolution stages. Besides, the TC size expansion (shrinkage) is more likely to occur for TCs with smaller (larger) size and weaker (stronger) intensity.The complexity of size change during a TC’s lifetime can be attributed to the fact that shrinkage or expansion could occur both before and after LMS.

1. Introduction

Tropical cyclones (TCs) forming over the western North Pacific(WNP) have taken an enormous toll on lives and property along the coastline. Since most TC-related disasters are closely associated with wind fields, such as storm surges and torrential precipitation, the study of TC size, which provides information on wind coverage and wind field structure, has been a hot topic and attracted much attention in the TC community.

So far, there is no universal consensus regarding TC size. A variety of definitions have been proposed in previous studies, such as the radius of outermost closed isobar (ROCI) ( Merrill, 1984 ), the radius of maximum wind ( Irish et al., 2008 ; Needham and Keim, 2014 ), and the azimuthally averaged radius of some certain wind speeds, such as vanishings winds, or speeds of 15 or 17 m s( Dean et al., 2009 ; Chavas and Emanuel, 2010 ; Lee et al., 2010 ; Knaffet al., 2014 ). Among these definitions, the azimuthally averaged radius of gale-force winds of 17 m s, or R17, has been extensively adopted ( Kimball and Mulekar, 2004 ;Chan and Chan 2012 , 2015a ; Knaffand Sampson, 2015 ; Chen et al.,2018 ). The relationship between TC size and intensity has been explored in many previous studies. Merrill (1984) found a weak correlation between the ROCI and the maximum sustained winds (

V

) with a correlation coefficient (

R

) of 0.28. Chavas and Emanuel (2010) confirmed this result, showing that the correlation between the radius of vanishing winds and

V

is 0.36. Guo and Tan (2017) also examined the relationship between R17 and

V

max using the extended best-track data, revealing a weak correlation of

R

= 0.29. Recently, Song et al. (2020) revisited the statistical relationship between size and intensity over the WNP that appears to be nonlinear and is affected by the track and evolution type of TCs.

Since R17 is of operational importance in forecasting and decisionmaking, its climatology has been widely studied. In tandem with technological advances, numerous objective wind radii estimates and highresolution numerical models are now available, which have the potential to improve our understanding of TC size change. The effect of TC size change on TC destructive potential has been emphasized in a recent study ( Xu et al., 2020 ). An example of the importance of estimating TC size change can be seen in Typhoon Chan-Hom (2015), which suddenly doubled its size within 24 h when approaching Okinawa and caused heavy losses. Therefore, in contrast to TC size, it would make more sense to focus on TC size change.

In previous studies, the TC size change was found to be affected by the environmental moisture ( Hill and Lackmann 2009 ), angular momentum transports ( Chan and Chan, 2013 ), boundary layer mixing and cloud-radiative forcing ( Bu et al., 2017 ), low-level flow orientation and vertical wind shear ( Chen et al., 2018 ), the spatial pattern of precipitation ( Tsuji and Nakajima 2019 ), and topography ( Lin and Chou, 2018 ),amongst other factors. Despite the complexity, it is quite practical to advance knowledge of TC gale-force wind structure changes. So far,the statistics of TC size change over the WNP and their relationships with other key metrics (i.e., intensity, size) have not yet been comprehensively unraveled. With the aid of the Multiplatform Tropical Cyclone Surface Wind Analysis (MTCSWA) data created based on credible satellite-based estimates of TC near-surface wind ( Knaffet al., 2011 )from 2007—16, this study discusses the statistical relationship between TC size change and other TC parameters, such as size and intensity.

The paper is organized as follows: Section 2 introduces the data used in this study. Section 3 presents the results of the statistical relationship between TC size change within 24 h and TC size and intensity, and the sensitivity of the relationship variations to the different classifications of size, intensity, and lifetime evolution stage. A summary and discussion are given in section 4 .

2. Data

The six-hourly information on the TC center and the Vare from the U.S. Joint Typhoon Warning Center (JTWC). The Vdata are used to reflect the intensity. Data filtration is carried out based on the following criteria: (1) TC records with intensity less than 35 kt are excluded.(2) To eliminate possible topographic effects and remove TCs experiencing extratropical transition, TC records whose centers are located within 500 km from land or with storm status labeled as “extratropical systems ”are also ruled out. (3) TCs with fewer than four records during their lifetime are removed. As a result, a total of 759 samples are chosen to explore TC size change within 24 h from January to December during 2007—16 in this study.

Although the JTWC has also provided wind radii of 34 kt (1 kt ≈0.514 m s) in four quadrants since 2001, these estimates to a large degree rely on operational forecasters lacking objective post-processing analysis. In contrast, the MTCSWA is a global objective estimation of surface wind fields around active TCs released from 2007 through 2016( Knaffet al., 2011 ). This six-hourly storm-centered product has a horizontal resolution of 0.1° latitude. The wind field for each TC is created based on a variety of satellite-based winds and wind proxies, which is of comparable quality to the Hurricane Wind Analysis System ( Knaffet al.,2011 ). The products were also verified by Tian et al. (2016) , showing that the quality of MTCSWA over the East China Sea compares well to that over the Atlantic. Although underestimation may occur in highwind regions (e.g., the destructive winds in the eyewall), the MTCSWA data provide a good representation of wind structure in the outer-core region, especially where R17 is usually located. Together with numerical prediction products, the MTCSWA data have been used to construct an objective estimation for TC structure parameters, which can forecast the wind radii of interest ( Knaffet al., 2004 ; Xiang et al., 2016 ). Therefore, the credibility of the MTCSWA data assures that they can be used for the statistical study of the size change rate (SCR) as described in the following section.

3. Results

3.1. Relationship of SCR with size and intensity

To discuss changes in TC size within 24 h, the SCR is defined as

where R17( T 24 ) and R17( T 0 ) represent the R17 at the future 24 h and 0 h, respectively.

A weak correlation of TC size with intensity has been shown in previous studies. Considering the importance of forecasting the change in TC size that could be affected by other structure parameters, explorations of the relationships between SCR and intensity as well as intensity change rate (ICR) within 24 hours are expected. Fig. 1 illustrates the correlation of SCR with size, intensity, and ICR, respectively, which are abbreviated to SCR-R17, SCR- V, and SCR-ICR hereafter. The SCR is mainly distributed in the range of ? 20 to 80 km d. The R of SCR-R17 is ? 0.43,showing that smaller (larger) TCs tend to expand (shrink) more pronouncedly than larger (smaller) ones. The weak correlation ( R = ? 0.12)of SCR- V max indicates that the change in TC size within 24 h bears a weak relationship with intensity. In contrast, the R of SCR-ICR is 0.25,twice as much as that of SCR- V, suggesting that ICR has more potential as a predictor of SCR than V max . The rapid intensification of a TC has long been one of the greatest concerns. The SCR-ICR relationship portrayed in Fig. 1 (c) also implies that a TC experiencing rapid intensification tends to expand considerably in its size. This finding agrees with the result of Chan and Chan (2013) , who found that the sample size in the category of both increasing intensity and size is substantially larger than the counterparts in other categories, and the large size growth in tandem with the inner-core intensification was observed in their latter numerical model experiments ( Chan and Chan, 2015b ), indicating that ICR is a potential factor governing SCR.

3.2. Correlation variations in the different size, intensity, and evolution type categories

It is intriguing to what extent the above-mentioned relationship is dependent on the different classifications of size and intensity. Therefore, we further examine the variations of the relatively high correlation of SCR-R17 and SCR-ICR among different size and intensity categories at 0 h. In addition, several previous studies have revealed that, during a TC’s lifetime, the size—intensity relationship turned out to be nonlinear, and accentuated the need to separately examine correlation variations during different development stages defined by the time of the lifetime maximum size (LMS) and lifetime maximum intensity (LMI)( Wu et al., 2015 ; Wang et al., 2017 ; Song et al., 2020 ). For instance,Song et al. (2020) emphasized the variant size—intensity relationships due to the different lag between the times at which a TC reaches its LMS and LMI. Therefore, another classification criterion is adopted to distinguish the different evolution stages: Type A (concurrently before LMS and LMI); Type B (before LMI while after LMS); Type C (before LMS while after LMI); Type D (concurrently after LMS and LMI). The criteria and the number of the sample size of each category are summarized in Table 1 .

Fig. 2 (a—c) shows that, except for the typhoon (TY) and Type B groups, the negative correlations of SCR-R17 in most of the categories are weaker than that calculated from the whole data ( R = ? 0.43). The peak negative correlations occur in the 100—200-km ( R = ? 0.30), TY intensity ( R = ? 0.52), and Type B ( R = ? 0.51) categories. Note that the positive correlation of SCR-R17 in the 0—100-km category is primarily due to the small sample size of only 63 cases, and the correlation coeffi-cient fails to pass the Student’s

t

-test at 99% confidence level ( Fig. 2 (a)).Except for the TY category, the SCR-R17 correlations in other categories change less than those of the size and evolution stage, reflecting that the SCR-R17 relationship is less sensitive to intensity than size and the evolution stage ( Fig. 2 (b)).

Fig. 1. Distribution of size change rate for (a) size (R17), (b) intensity ( Vmax ), and (c) intensity change rate (ICR). The number in each box is the number of sample sizes. The vertical red dashed lines with labels RS and RE represent the threshold values of rapid shrinkage and rapid expansion, respectively. The number at the top-right of each panel is the Pearson’s correlation coefficient (all have confidence levels exceeding 99% based on the Student’s t -test).

Table 1 The criteria and the number of the sample size of each size, intensity, and evolution stage category, where the number in the brackets is the percentage of the sample size in each category to the total sample size.

Fig. 2 (d—f) portrays the variations of the SCR-ICR relationship among different size, intensity, and evolution stages. The

R

among the different size categories is maximized in the 0—100-km category (

R

= 0.52),and then decreases with increasing size ( Fig. 2 (d)). The significantly positive SCR-ICR correlations only exhibit in the severe tropical storm(STS) and TY categories ( Fig. 2 (e)). In terms of the evolution stage, the distinctly positive correlations of SCR-ICR are present in Types A and D ( Fig. 2 (f)). The negative SCR-ICR in Type C differs from the counterparts in other types, which is in good agreement with the result reported by Wang et al. (2017) that size and intensity take on an opposite change trend during the mature stage, defined as the period from the time of LMI to the time of LMS. It is noteworthy that the positive SCRICR relationship found in Type B conflicts with the results reported by Wu et al. (2015) that, after LMS, size slowly decreases while the TC further intensifies, which may be attributable to the small size sample (46 cases) in Type B with a non-significant correlation in this study.Because of the change in the signs of the SCR-ICR correlation, especially in Types B and C, that can partly impair relationship coherence, the evolution stage should be taken into consideration when discussing the SCR-ICR relationship. The percentages of four types of evolution stage in the different size and intensity categories are displayed in Fig. 3 (a). As the size grows, the percentages of Types B and C increase,thus leading to a decrease in

R

of SCR-ICR presented in Fig. 2 (d). Similarly, the relatively large percentages of Types B and C in the TS and super typhoon (STY) categories contribute to the almost uncorrelated SCR-ICR relationship shown in Fig. 2 (e). If excluding the samples in Type B and C, the overall SCR-ICR correlation increases from 0.25 to 0.40. Only considering the samples in Types A and D, the correlation between SCR and ICR becomes less sensitive to the size and intensity variations ( Fig. 3 (b, c)) compared to those presented in Fig. 2 (d, e).Besides, the overall decreasing trends of SCR-ICR correlation with increasing size and intensity in Fig. 3 (b, c) can be explained as follows:For TCs with lower intensity or smaller size, SCR would be sensitive to ICR because the R17 is likely to be found near the radius of

V

. After a TC intensifying and becoming larger, the R17 usually expands radially outward, and thus SCR becomes less ICR-dependent ( Chavas et al.,2010 ).

3.3. Analysis of SCR based on the classification of expansion and shrinkage

For the sake of discussion, all samples are categorized into rapid shrinkage (RS), slow shrinkage (SS), normal (N), slow expansion (SE),and rapid expansion (RE). The threshold for RS and RE is the 90th percentile of the cumulative distribution function of the absolute SCR for shrinkage and expansion samples, and the classification of SS, N, and SE are bounded by the 30th and 60th percentiles. The threshold values are ? 85, ? 20, 25, and 125 km d, and the numbers of samples in each category are 18, 127, 170, 344, and 68, respectively. Fig. 4 exhibits the mean SCR (line) and percentage (bar) of RS, SS, SE, and RE in each category. As size grows ( Fig. 4 (a)), the percentage of expansion decreases while that of shrinkage increases, which indicates that smaller (larger)TCs have more tendency to expand (shrink). The trend of decrease (increase) in the mean SCR of RE (RS) and SE (SS) with the increasing size is consistent with the above-mentioned negative SCR-R17 correlation.For intensity classification ( Fig. 4 (b)), the percentage variations in RE and SE imply that TCs are likely to expand rapidly during the TS stage and then incline to expand slowly afterward. After reaching the intensity of STS, shrinkage becomes more likely to happen but with no monotonical change in the mean SCR. The relatively larger percentages of RS and SS in the TS category might be contributed by the TS at higher latitude with larger size due to the interactions with midlatitude systems.In terms of evolution stage ( Fig. 4 (c)), Types A and C (Types B and D)are the preferred stages for size expansion (shrinkage) during which TCs evolve before (after) its LMS. Therefore, the complexity of size changes can be attributed to the fact that size could shrink before attaining LMS(SS and RS in Types A and C) or expand after reaching LMS (SE and RE in Types B and D).

Fig. 2. Linear regressions of size change rate with size and intensity change rate corresponding to the different size (a, d), intensity (b, e), and evolution stage (c, f).The blue, green, yellow, and red lines represent the 0—100-, 100—200-, 200—300-, and 300—500-km size categories in (a, d); TS (tropical storm), STS (severe tropical storm), TY (typhoon), and STY (super typhoon) intensity categories in (b, e); and evolution stages of Types A, B, C, and D in (c, f). The number in brackets is the correlation coefficient, and the asterisk indicates the correlation coefficient has a confidence level exceeding 99% based on the Student’s t -test.

4. Summary and discussion

In this study, the statistical relationships of TC size (defined by R17)change within 24 h with size and intensity are analyzed. In addition, the details of the correlation variations are presented in terms of different sizes, intensities, and evolution stages.

The SCR is mainly distributed in the range from ? 20 to 80 km d.The correlation coefficients of SCR-R17, SCR- V, and SCR-ICR are? 0.43, ? 0.12, and 0.25, respectively. The results suggest that the relationships of SCR with size and ICR are quite different because the latter is more modulated by the evolution stage. The SCR-R17 variations are more sensitive to the classification of size and evolution stage than that of intensity. The negative correlation of SCR-R17 is largely contributed by TCs with size 100—200 km, TY intensity, and evolution stage Type B. In terms of the SCR-ICR relationship, after excluding Type B and C during which size and intensity may change in an opposite trend, the correlation of SCR-ICR increases from 0.25 to 0.40.Therefore, ICR can be regarded as one of the potential factors in predicting SCR during the stages of Type A and D. Variations in the percentage of SCR demonstrate that the expansion (shrinkage) is more likely to occur for TCs with smaller (larger) size and weaker (stronger)intensity. Discussion on the different evolution stages can help understand the complicated relationship of size change during a TC’s lifetime.

The findings of this study motivate us to shed light on the underlying mechanisms from thermodynamic and dynamic viewpoints in our ongoing research. Other factors, such as the environmental vertical wind shear and synoptic circulation patterns ( Merrill, 1984 ; Cocks and Gray, 2002 ; Knaffet al., 2004 ; Reasor et al., 2013 ; Chen et al., 2018 ), as well as sea surface temperature, humidity and inner-core precipitation( Hill and Lackmann, 2009 ; Tsuji and Nakajima, 2019 ; Ma et al., 2019 ),all play vital roles in affecting the change in TC size. Insightful examination of how these factors affect the size change will help us to improve TC size forecasting, which is being undertaken and will be reported in the future.

Funding

This study was supported by the National Natural Science Foundation of China [grant numbers 41975071 and 41775063].

Fig. 3. (a) The percentage of different evolution stages in different size and intensity categories, where the red, green, blue, and yellow columns represent the evolution stage of Types A, B, C, and D. (b, c) The linear regression of size change rate with intensity change rate as in Fig. 2 (d, e), but with the exclusion of samples in Types B and C.

Fig. 4. The mean size change rate (lines, right ordinate) and percentage (bars, left ordinate) of the SE (slow expansion, yellow), RE (rapid expansion, red), SS (slow shrinkage, green), and RS (rapid shrinkage, blue) in each category corresponding to the different (a) sizes, (b) intensities, and (c) evolution stages.

Acknowledgments

The authors thank the two anonymous reviewers for their valuable comments that helped improve the quality of the manuscript.