1. Introduction

Understanding tropical cyclone (TC) intensity change, especially rapid intensification (RI), is one of the most significant challenges for the scientific community. In the past few decades, although the TC track forecast has been improved steadily, TC intensity forecasting only improved little until around 2010 (Cangialosi et al. 2020). According to DeMaria et al. (2021), RI forecast skill has improved 20%–25% between 2016 and 2020 relative to the 2015–17 baseline period. However, predicting TC intensity change remains one of the greatest challenges due to a lack of a complete understanding of the physical processes associated with TC intensification, especially RI.

Since the beginning of the satellite era, several advances have been achieved in recognizing patterns that help estimate TC current intensity and predict future intensity from remote sensing observations (Dvorak 1975; Glass and Felde 1992; Rao and MacArthur 1994; Rodgers and Pierce 1995; Velden et al. 2006; Ritchie et al. 2012; Fischer et al. 2018). The Dvorak technique and other recent geostationary satellite-based methods have been using infrared brightness temperatures to estimate TC intensity (Dvorak 1975; Velden et al. 2006; Ritchie et al. 2012). The advent of microwave techniques has particularly contributed to the retrieval of distinct precipitation features useful for TC intensity studies. For instance, a very good correlation between TC intensity and the TC inner-core variables associated with the rain rate and 85-GHz polarization-corrected brightness temperature (PCT₈₅; Spencer et al. 1989; Cecil et al. 2002) as measured by low-Earth orbiting satellite has been found in previous studies (Glass and Felde 1992; Rao and MacArthur 1994; Rodgers and Pierce 1995). Using different ice-scattering signature variables from 85-GHz observations, Cecil and Zipser (1999) found a strong linear correlation when they compared the current and 24-h future TC intensity with the inner-core mean PCT₈₅. Using the relationship between satellite microwave observations and TC intensity, Jiang et al. (2019) derived three regression models using 85-GHz variables, rain rate variables, and combined 85-GHz and rain variables to predict TC 6-h future maximum sustained surface wind (V_max). Among these three models, they found that the model that combined 85-GHz with rain rate variables performed better than the model using only 85-GHz or rain rate variables. The combined model was skillful when applied to the Atlantic and east Pacific TCs with a mean absolute error of 9.6 kt (1 kt ≈ 0.51 m s⁻¹) for 6-h future V_max prediction. Fischer et al. (2018) found that 37-GHz brightness temperatures also display a strong relationship to TC intensity.

The role of symmetric versus asymmetric processes in TC intensification has been a subject of long-standing debate in the field. Among the subsynoptic-scale contributors to TC intensification, convective-scale processes within the TC inner-core region are widely recognized as crucial. Previous modeling studies have emphasized the significance of rotating, asymmetric deep convection in the inner core (i.e., vortical hot towers), in driving TC intensification (Hendricks et al. 2004; Montgomery et al. 2006; Nguyen et al. 2008; Bui et al. 2009; Persing et al. 2013; Ryglicki et al. 2019, 2021). In contrast, early theoretical studies indicated that symmetric convection/heating played a primary role in initiating the spin-up of inner-core winds (Ooyama 1969; Smith 1981; Shapiro and Willoughby 1982). Nolan and Grasso (2003) and Nolan et al. (2007) revisited this issue by analyzing the evolution of a symmetric, balanced vortex perturbed by asymmetric, unbalanced heat sources. Using an enhanced linearized primitive equation model, they indicated that the intensity of the vortex changes in a symmetric manner, responding to the azimuthally averaged release of latent heat.

For RI in particular, observational case studies (Reasor et al. 2009; Guimond et al. 2010; Molinari and Vollaro 2010; Nguyen and Molinari 2012; Reasor and Eastin 2012; Stevenson et al. 2014; Rogers et al. 2015; Susca-Lopata et al. 2015; Callaghan 2017) have emphasized the role of horizontally small-scale, asymmetric very deep convection (such as convective bursts and hot towers) within the TC inner-core region during RI, particularly when the storm was experiencing moderate-to-high vertical wind shear. For example, Hurricane Guillermo (1997) underwent RI under a moderate shear environment with a cyclonic vortex of strong convective bursts (Reasor et al. 2009; Reasor and Eastin 2012). Several observational studies on Hurricane Earl (2010) (Stevenson et al. 2014; Rogers et al. 2015; Susca-Lopata et al. 2015) indicated deep and vigorous convections played a significant role in extending the cyclonic vortex over a deep layer before RI underwent in Earl.

On the other hand, many satellite-based statistical studies (Jiang 2012; Kieper and Jiang 2012; Jiang and Ramirez 2013; Zagrodnik and Jiang 2014; Alvey et al. 2015; Tao and Jiang 2015; Harnos and Nesbitt 2016; Xu et al. 2017) implied that the presence of symmetric widespread precipitation, with or without a very low percentage of asymmetric deep convection, is important in initiating RI in the following 24 h. Storms with higher intensification rates have a greater overall areal precipitation coverage and more symmetric rainfall distribution (Kieper and Jiang 2012; Zagrodnik and Jiang 2014; Alvey et al. 2015; Tao and Jiang 2015). RI storms tend to have a larger raining area, total volumetric rain, increased stratiform precipitation, and weaker lightning activities in the inner core (Jiang 2012; DeMaria et al. 2012; Jiang and Ramirez 2013; Xu et al. 2017). For example, Jiang (2012) pointed out that using convective parameters, including minimum 11-μm infrared brightness temperature, upper-level maximum radar reflectivity, and maximum 20-dBZ radar echo height, the prediction of RI could be improved to some extent, but hot towers were found to be neither necessary nor sufficient condition of RI. This indicates that RI could be achieved without very deep convection. Using a 14-year Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) dataset, Tao and Jiang (2015) indicated that the inner-core shallow to moderate precipitation increases significantly after RI onset. A 37-GHz precipitation-type classification method was proposed by Jiang et al. (2018). Based on different precipitation and convection types classified by this method, they found that the coverage of stratiform rainfall and shallow precipitation/convection within the TC inner core significantly increases between 3 and 21 h before RI onset time.

However, the influences of TC intensity on the storm’s convective structure can mask the relationship between TC precipitation/convection parameters and intensity change. With the increase of TC intensification rate from weakening (W) to neutral (N), slow intensification (SI), and finally RI, the TC inner-core precipitation/convection parameters were not always found to be consistently getting stronger (Jiang and Ramirez 2013; Zagrodnik and Jiang 2014; Alvey et al. 2015; Tao and Jiang 2015; Tao et al. 2017). Jiang and Ramirez (2013) indicated that many convective intensity parameters did not have consistently positive relationships with TC intensification rate. For example, they presented that the median radar echo top height within the inner core of W TCs is the same as in RI TCs, although it increases from N to SI to RI storms. The main reason is that they did not remove the impact of current TC intensity on these inner-core parameters. To eliminate this problem, several studies (Zagrodnik and Jiang 2014; Tao and Jiang 2015; Tao et al. 2017) intentionally removed tropical depressions and major hurricanes to study RI, but this problem still existed in their results. For example, Tao and Jiang (2015) found that the smallest percentage occurrence of moderate precipitation appeared in N TCs rather than in W TCs.

Using a normalization technique, the dependency of precipitation parameters on TC current intensity was first removed by Fischer et al. (2018), and they found that the normalized brightness temperature could be a good indicator for RI. However, they only studied storms in North Atlantic and eastern North Pacific and did not identify specific precipitation or convection types, such as stratiform rainfall, shallow precipitation/convection, or deep convection. By grouping TCs into various detailed intensity change-intensity categories, Su et al. (2020) found a linear relationship between the TC 24-h intensity change and inner-core rainfall using the multisatellite 3B42 dataset with a spatial resolution of 25 km × 25 km. However, they did not consider the impact of the vertical wind shear. Su et al. (2020) did not include the relationship between the TC intensification rate and the strength or the symmetry of different types of convection/precipitation, such as shallow convection, deep convection, and stratiform precipitation within the TC inner core.

With a 16-yr (1998–2013) TRMM Microwave Imager (TMI) dataset for global TCs, this paper examines the relationship between TC intensification rate and TC inner-core precipitation and convective parameters, as well as the relationship between TC intensification rate and the symmetry of these parameters. The relative importance of different precipitation and convection types on TC intensity change is also studied. This study distinguishes itself from previous satellite-based statistical studies (Zagrodnik and Jiang 2014; Tao and Jiang 2015; Tao et al. 2017) by decoupling the dependency of precipitation and convection features on TC intensity and that on TC intensification rate. This is achieved by classifying samples into one of 16 intensity change–intensity categories. Furthermore, tropical depressions and major hurricanes, which were removed by the three satellite-based studies mentioned above, are included. Three research questions to be addressed are: “How do different precipitation/convective parameters distribute for different intensity change–intensity categories? How do axisymmetric indices of different precipitation/convective parameters distribute for these categories? How do averaged precipitation/convective parameters change in different intensity change–intensity categories under different vertical wind shear intensity?” This paper is organized as follows. Section 2 describes the data and methods used in this study. Section 3 compares the distribution and magnitude of the composites of different precipitation/convection parameters and their axisymmetric indices for different intensity change–intensity categories. Section 4 discusses the impact of vertical wind shear magnitude on the relationship between precipitation and convection parameters and TC intensification. The conclusions of this paper are presented in section 5.

2. Data and methodology

a. Selection of TC intensity and intensity change categories

Six-hourly best track data from Joint Typhoon Warning Center (Chu et al. 2002) and the National Hurricane Center (Landsea and Franklin 2013) are used in this study. Based on Saffir–Simpson wind scale, seven intensity categories including tropical depression (TD, V_max ≤ 33 kt), tropical storm (TS, 33 kt < V_max ≤ 63 kt), category-1 hurricane (CAT1, 63 kt < V_max ≤ 82 kt), category-2 hurricane (CAT2, 82 kt < V_max ≤ 95 kt), category-3 hurricane (CAT3, 95 kt < V_max ≤ 112 kt), category-4 hurricane (CAT4, 112 kt < V_max ≤ 136 kt), and category-5 hurricane (CAT5, V_max > 136 kt) are classified. To have more samples in each intensity category, CAT1 and CAT2 hurricane are combined into one minor hurricane category (H12), and CAT3–CAT5 hurricanes are into one major hurricane category (H35). Then, each of the four TC intensity categories (TD, TS, H12, and H35) is further partitioned into four 24-h intensity change (DV_max24 = V_max24 − V_max, where V_max24 is the 24-h future TC intensity) stages: RI (DV_max24 ≥ 30 kt), SI (10 kt ≤ DV_max24 < 30 kt), N (−10 kt ≤ DV_max24 < 10 kt), and W (DV_max24 ≤ −10 kt) by following Jiang and Ramirez (2013). Here, we chose −10 and 10 kt as thresholds to define the group of W, N, and SI stages, which differs from Su et al. (2020). Therefore, 16 intensity change–intensity groups are classified in the study. The group names are shown in the caption of Table 1.

Table 1.

Number of TMI overpasses for 16 different intensity change–intensity categories. These categories are weakening tropical depression (W-TD), neutral tropical depression (N-TD), slowly intensifying tropical depression (SI-TD), rapidly intensifying tropical depression (RI-TD), weakening tropical storm (W-TS), neutral tropical storm (N-TS), slowly intensifying tropical storm (SI-TS), rapidly intensifying tropical storm (RI-TS), weakening minor hurricane (W-H12), neutral minor hurricane (N-H12), slowly intensifying minor hurricane (SI-H12), rapidly intensifying minor hurricane (RI-H12), weakening major hurricane (W-H35), neutral major hurricane (N-H35), slowly intensifying major hurricane (SI-H35), and rapidly intensifying major hurricane (RI-H35).

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c. Examining precipitation and convective parameters

The TRMM TMI is a passive microwave radiometer with five frequencies at 10, 19, 21, 37, and 85 GHz. All frequencies have both horizontal (H) and vertical (V) polarizations except the frequency of 21 GHz, which only has the V channel. Because the TRMM’s altitude increased from 350 to 402 km during the satellite boost in August 2001, the swath width of TMI increased from 760 to 878 km. This study uses the TMI 2A12 rain rate and 37- and 85-GHz brightness temperatures. The footprint sizes of 37 and 85 GHz are 16 km × 9 km (18 km × 10 km after boost) and 7 km × 5 km (8 km × 6 km after boost), respectively. The 2A12 rainfall product used the Goddard Profiling algorithm to retrieve surface rain rate from TMI brightness temperatures from all frequencies (Kummerow et al. 1998). It has the same spatial resolution as the 85-GHz channel.

In this study, six TMI-derived precipitation and convective parameters are analyzed for each intensity change-intensity group. These parameters include TMI 2A12 rain rate, PCT₈₅, stratiform rainfall occurrence, shallow convection occurrence, deep convection occurrence, and inner-core size. The PCT₈₅ is defined by Spencer et al. (1989) in order to distinguish low brightness temperature values caused by ice scattering from deep convection over ocean, from those due to radiometrically cold sea surface:

${\text{PCT}}_{85}=1.82V_{85}-0.82H_{85},$(1)

where V₈₅ and H₈₅ represent the vertically polarized and horizontally polarized brightness temperatures, respectively. PCT₈₅ parameters have been used as proxies for convective intensity (Spencer et al. 1989; Mohr and Zipser 1996; Nesbitt and Zipser 2003; Alvey et al. 2015). For example, Alvey et al. (2015) classified pixels with PCT₈₅ < 190 K as strong convection, 190 ≤ PCT₈₅ < 220 K as moderate convection, and 220 ≤ PCT₈₅ < 250 K as moderate rain. In this study, three precipitation types, including stratiform precipitation, shallow convection, and deep convection, are defined using a method developed by Jiang et al. (2018) using three 37-GHz brightness temperatures including vertically polarized (V₃₇) and horizontally polarized brightness temperature (H₃₇) and PCT₃₇. The PCT₃₇ is defined by Grody (1993) as

${\text{PCT}}_{37}=2.18\times V_{37}-1.18\times H_{37}=V_{37}+1.18\times (V_{37}-H_{37}).$(2)

The thresholds of brightness temperature for the classification of the three precipitation types are shown in Table 2. Jiang et al. (2018) validated and justified their partition scheme using TRMM PR reflectivity profiles collocated with each 37-GHz pixel. Please refer to Jiang et al. (2018) for the detailed description of this classification method. Using these three precipitation types, frequency of each precipitation type is calculated and examined in this study, including stratiform precipitation occurrence, shallow convection occurrence, and deep convection occurrence.

Table 2.

Definition of precipitation types (taken from Jiang et al. 2018).

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This study examines the shear-relative composites of five precipitation and convection parameters (including TMI 2A12 rain rate, PCT₈₅, stratiform rainfall occurrence, shallow convection occurrence, and deep convection occurrence, as shown in Figs. 3–7 below) for each intensity change–intensity group. The environmental vertical wind shear is calculated by the difference of wind vectors between 200 and 850 hPa. The wind vectors are averaged within a 500–750-km ring surrounding the TC center to minimize the impact of the storm’s circulation, following the approach of Hence and Houze (2011). The wind field data are derived from the 0.75° × 0.75° resolution European Centre for Medium-Range Weather Forecasts interim reanalysis dataset (Simmons et al. 2007). Each 2D composite is generated by rotating the field with the direction of vertical wind shear pointing upward and the TC center positioned in the center of the image by following Tao and Jiang (2015). Following Chen et al. (2006) and Wingo and Cecil (2010), the shear-relative pixels of Southern Hemisphere overpasses are flipped 180° before compositing them with Northern Hemisphere cases.

This study also quantifies the degree of symmetry of above 5 precipitation and convection parameters using an axisymmetric index (γ) defined by Miyamoto and Takemi (2013) as follow. Any parameter Φ can be divided into the azimuthal mean $\overline{\text{Φ}}$ and the deviation Φ′ from the azimuthal mean:

$\text{Φ}(r,\lambda )=\overline{\text{Φ}}(r)+{\text{Φ}}^{\prime }(r,\lambda ),$(3)

where r and λ are the radial and tangential directions, respectively. Then the axisymmetric index is defined as

$\gamma (r)\equiv \frac{\overline{\text{Φ}}{(r)}^2}{\overline{\text{Φ}}{(r)}^2+{{\displaystyle \int }}_0^{2\pi }{\text{Φ}}^{\prime }{(r,\lambda )}^{2}d\lambda /2\pi }.$(4)

The range of γ value is between 0 and 1, with higher values indicating more symmetry. In this study, the axisymmetric index is calculated for every 10-km annulus from the TC center. Then the inner-core mean axisymmetric index is derived by averaging all values within the TC inner-core (see definition below). Another TMI-derived parameter to be examined in this study is the inner-core size. The radius of maximum azimuthally mean rain rate (RMR) within 200-km radius from the TC center is used as the TC inner-core size parameter. To illustrate how RMR is calculated, Fig. 1 shows the radial distribution of the azimuthal mean rain rate averaged in each 10-km-wide annulus around the TC center within 200-km radius for each intensity change-intensity group. Ideally, the TC inner-core region is defined according to the radius of maximum wind (RMW). However, RMW data are only available for a small subset of TCs from the extended best track dataset (Demuth et al. 2006) for the Atlantic and east and central Pacific basins and the best track data for other basins. There are a large portion of TMI overpasses used in this study without a corresponding RMW value. Thus, RMR is used here as an alternate measure of RMW, similar to previous studies (Shimada et al. 2018; Guzman and Jiang 2021). To link RMR with RMW, Fig. 2 shows the comparison between mean values of RMR and RMW as a function of TC intensity. We can see that both RMR and RMW decrease with TC intensity, while the RMR value is about 10–20 km larger than RMW for each TC intensity category.

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The radial distribution of the azimuthal mean rain rate within 200 km from the TC center for 16 intensity change–intensity categories.

Citation: Weather and Forecasting 39, 2; 10.1175/WAF-D-23-0155.1

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Comparison between mean values of RMR and RMW as a function of TC intensity. The mean values of RMR are calculated from TMI overpasses used in this study (1998–2013), while the mean values of RMW for TCs during 1998–2013 are derived from the extended best track dataset for the Atlantic and east and central Pacific basins and the best track data for other basins.

Citation: Weather and Forecasting 39, 2; 10.1175/WAF-D-23-0155.1

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The averaged values of the first five precipitation and convection parameters and the mean axisymmetric indices of these parameters are calculated within the TC inner-core region (as shown in Tables 5 and 6 below). A sensitivity test has been done to define the inner-core size as 1.0 × RMR, 1.3 × RMR, 1.7 × RMR, or 2.0 × RMR. The results of this study do not change significantly by varying the inner-core size like this. A final selection of 1.7 × RMR is determined to be the outer bound of the inner-core size (the inner-core domain starts at the TC center) because it includes most of the heavy rainfall and convection in the TC core region and excludes rains from outer rainbands. Student’s t tests are conducted to evaluate the statistical significance of the differences of these inner-core mean values between W and N, between N and SI, and between SI and RI groups for each intensity category.

3. Results

Table 3 shows the averaged RMR in each intensity change–intensity category. The RMR ranges from 41 to 98 km on average. For each TC intensity change category, the RMR decreases with TC intensity, consistent with previous studies (Lonfat et al. 2004; Guzman and Jiang 2021), which showed that the RMR decreases with TC intensity from TD to category-5 hurricane. The RMR for each TC intensity category also generally decreases with the TC intensification rate. This result for RMR is similar to RMW, which was found to be contracting simultaneously with TC intensification (Willoughby et al. 1982; Willoughby 1990). From Table 3, we can see that RI overpasses have significantly smaller RMR than SI overpasses for TCs with initial intensity in TS and H12 categories. This is consistent with the finding by Carrasco et al. (2014) that TCs that undergo RI are more likely to be smaller initially than those that do not. However, a Student’s t test shows that the difference of RMR between RI and SI overpasses with a current intensity of H35 is not significantly different. This seems consistent with Stern et al. (2015), who found that the most eyewall contraction stops prior to the end of the intensification period for H35. This also could be due to the small sample size of RI-H35 category.

Table 3.

Mean values of RMR for 16 different TC intensity change–intensity categories and the mean value differences of RMRs between W and N, between N and SI, and between SI and RI groups in each intensity category. Asterisks represent the statistical significance of the difference at the 95% (*), 99% (**), and 99.9% (***) confidence levels.

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Figure 3 presents the 2D composite shear-relative distribution of TMI 2A12 rain rate for each intensity change–intensity group. Table 4 shows the averaged vertical wind shear in each group. The maximum rain rate is located at the downshear-left quadrant for each group. This downshear-left dominance of TC rainfall is consistent with many previous studies (Rogers et al. 2003; Chen et al. 2006; Cecil 2007; Ueno 2007; Wingo and Cecil 2010; Pei and Jiang 2018). In terms of rainfall magnitude, the mean inner-core rain rate increases with the TC intensification rate for each TC intensity group (Table 5). All the differences of rain rate between each intensity change group in the four different intensity categories are statistically significant at the 99% confidence level or above, except for the H35 category, in which the difference between the SI and N groups is not statistically significant. This is generally consistent with Su et al. (2020)’s result.

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Composite shear-relative distribution of rain rate (mm h⁻¹) in each of the 16 different TC intensity change–intensity categories: (a) W-TD, (b) N-TD, (c) SI-TD, (d) RI-TD, (e) W-TS, (f) N-TS, (g) SI-TS, (h) RI-TS, (i) W-H12, (j) N-H12, (k) SI-H12, (l) RI-H12, (m) W-H35, (n) N-H35, (o) SI-H35, and (p) RI-H35. The unit of both the x and y axes in each panel is kilometers. The shear vector points upward, shown by the black arrow at the top of each panel.

Citation: Weather and Forecasting 39, 2; 10.1175/WAF-D-23-0155.1

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Table 4.

Averaged vertical wind shear intensity for 16 different TC intensity change–intensity categories and the mean value differences of RMRs between W and N, between N and SI, and between SI and RI groups in each intensity category. Asterisks represent the statistical significance of the difference at the 95% (*), 99% (**), and 99.9% (***) confidence levels.

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Table 5.

Inner-core (within 1.7 × RMR) mean rain rate, PCT₈₅, stratiform rainfall occurrence, shallow precipitation/convection occurrence, and deep convection occurrence for each intensity change–intensity category and the differences of the inner-core mean values between W and N, between N and SI, and between SI and RI in each intensity category. Symbols represent the statistical significance of the difference at the 90% (^) 95% (*), 99% (**), and 99.9% (***) confidence levels.

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Figure 3 also indicates that, as TC intensity and intensification rate increase, the rainfall distribution exhibits a greater azimuthal coverage of relatively high rain rates from downshear and left-shear quadrants to upshear and right-shear quadrants. This is in line with the result of Table 6, which shows that the inner-core mean axisymmetric index of rain rate increases significantly (at the 99.9% confidence level) with the increase of TC intensification rate for each intensity category, except from SI to RI in the H35 category. The RI-H35 storms have significantly more asymmetric rainfall distribution than that of SI-H35 storms (at the 90% confidence level). This is associated with the very strong down-shear-left rainfall enhancement as seen in Fig. 3p. In general, the rain pattern of major hurricanes tends to be highly symmetric, with an axisymmetric index greater than 55% for each intensity change group (Table 6). Previous satellite studies indicated that RI storms have more symmetric rainfall patterns than SI storms (Zagrodnik and Jiang 2014; Tao and Jiang 2015; Tao et al. 2017). However, these studies only included TCs with initial intensity in TS and H12 categories. Our result here is consistent with these previous studies for TCs with initial intensity in TD, TS, and H12 categories. However, our new finding is that, for TCs with initial intensity in the H35 category, RI storms have more asymmetric rainfall pattern than SI storms. As mentioned in section 2b, one needs to be cautious on this considering the small sample size of RI-H35.

Table 6.

Inner-core (within 1.7 × RMR) mean axisymmetric indices of rain rate, PCT₈₅, stratiform rainfall occurrence, shallow precipitation/convection occurrence, and deep convection occurrence for each intensity change–intensity category and the differences of these inner-core mean axisymmetric indices between W and N, between N and SI, and between SI and RI in each intensity category. Symbols represent the statistical significance of the difference at the 90% (^), 95% (*), 99% (**), and 99.9% (***) confidence levels.

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Figure 4 presents the 2D composite shear-relative distribution of PCT₈₅ for each intensity change-intensity group. As mentioned in section 2c above, colder PCT₈₅ values indicated stronger convective intensity. For each intensity change-intensity group, the coldest PCT₈₅ is located in the downshear-left quadrant. This downshear-left dominance of TC convective intensity is consistent with previous lightning studies in TCs (Corbosiero and Molinari 2002, 2003; Stevenson et al. 2016). The inner-core mean PCT₈₅ decreases with the TC intensification rate for each TC intensity group (Table 5). The W-TD and N-TD groups have the highest mean PCT₈₅ value (214 K) in TC inner core, while the RI-H35 has the lowest mean PCT₈₅ value (179 K). All the differences of mean PCT₈₅ values between each intensity change group in four different intensity categories are statistically significant at 99.9% confidence level, except for the TD category, in which the difference between the W and N groups is not statistically significant. This result is consistent with many previous satellite-based studies indicating that inner-core convective intensity is stronger for RI than non-RI, especially SI storms (Jiang 2012; Jiang and Ramirez 2013; Zagrodnik and Jiang 2014; Alvey et al. 2015; Tao and Jiang 2015; Harnos and Nesbitt 2016). However, all of these previous studies did not remove the dependence on TC intensity so that they showed that convective intensity in weakening TCs is stronger than SI or RI TCs (e.g., Fig. 3 of Alvey et al. 2015). Instead, our study updated the current understanding and indicated that the positive relationship between inner core convective intensity and TC intensification rate is valid for all TC intensity and intensity change categories.

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As in Fig. 3, but for PCT₈₅ (K).

Citation: Weather and Forecasting 39, 2; 10.1175/WAF-D-23-0155.1

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Similar to the rainfall distribution in Fig. 3, Fig. 4 shows that as TC intensity and intensification rate increase, the PCT₈₅ distribution gets exhibits a greater azimuthal coverage of relatively cold PCT₈₅ from the downshear-left quadrant to upshear and right-shear quadrants. As shown in Table 6, the degree of symmetry of the TC inner core PCT₈₅ increases significantly with 24-h future intensification rate for all TC intensity categories. The most asymmetric PCT₈₅ pattern appears in the W-TD category with an axisymmetric index of 78%, while the most symmetric PCT₈₅ pattern appears in the RI-H35 category with an axisymmetric index of 87% (Table 6). All the differences of axisymmetric indices of PCT₈₅ between each intensity change group in four different intensity categories are statistically significant at he 95% confidence level or above. Again, this finding is consistent with many previous satellite-based studies suggesting that the degree of symmetry of TC inner-core precipitation and convection is higher for RI than SI storms (Kieper and Jiang 2012; Zagrodnik and Jiang 2014; Alvey et al. 2015; Tao and Jiang 2015; Fischer et al. 2018). However, this study advances the current knowledge by extending this positive relationship between the rate of symmetrization of inner core convection and TC intensification rate to all TC intensity change categories (including from W to N and from N to SI).

Figure 5 presents the 2D shear-relative distribution of stratiform rainfall occurrence for each intensity change–intensity group. The overall pattern of stratiform rainfall occurrence is similar to the total rain pattern in Fig. 3, with the maximum value located at the downshear-left quadrant. The inner-core mean stratiform rainfall occurrence increases with the TC intensification rate for each TC intensity group (Table 5). In the inner core, the W-TD group has the lowest mean stratiform rainfall occurrence (5.29%), while the RI-H35 group has the highest (72.94%). All the differences of mean stratiform rainfall occurrence between each intensity change group in four different intensity categories are statistically significant at 99.9% confidence level, except for the H35 category, in which the difference between the SI and N groups is not statistically significant. Tao et al. (2017) found a much higher percent occurrence of stratiform rain within the inner core for RI storms than SI storms, which is consistent with what is found here. But their result was only for TCs with initial intensity in TS and H12 categories, while our result is for all TC intensity categories. The stratiform rain defined here is similar to the “moderate precipitation” defined by Tao and Jiang (2015) using the TRMM PR 20-dBZ echo height between 6 and 10 km and “moderate rain” defined by Alvey et al. (2015) using PCT₈₅ between 220 and 250 K. Tao and Jiang (2015)’s finding of increasing frequency of TC inner-core “moderate precipitation” with intensification rate is consistent with our result here, although their result was only for TCs with initial intensity in TS and H12 categories. Alvey et al. (2015) found that the frequency of TC inner-core “moderate rain” increases from SI to RI, but decreases from W to N because they did not remove the dependence on TC intensity.

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As in Fig. 3, but for stratiform rainfall occurrence (%).

Citation: Weather and Forecasting 39, 2; 10.1175/WAF-D-23-0155.1

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Figure 5 also shows that the distribution of stratiform rainfall occurrence generally exhibits a greater azimuthal coverage of relatively high frequencies from downshear and left-shear quadrants to upshear and right-shear quadrants with the increases of TC intensity and intensification rate, similar to the distribution of rain rate and PCT₈₅. As shown in Table 6, RI groups have significantly higher axisymmetric indices than SI groups for the TS and H12 categories (at the 90% confidence level). In contrast, the RI-H35 storms have significantly more asymmetric stratiform rainfall occurrence distribution than that of SI-H35 storms (at the 90% confidence level). This is associated with the very strong downshear-left stratiform rainfall enhancement as seen in Fig. 5p. This suggests that asymmetric latent heating from stratiform rainfall and its projection onto the azimuthal mean may be important for RI in major hurricanes. Previous satellite studies suggested that RI storms have more symmetric moderate or stratiform precipitation than SI storms through 2D shear-relative composite plots similar to this study’s Fig. 5 (Tao and Jiang 2015; Tao et al. 2017). However, these studies only included TCs with an initial intensity in TS and H12 categories and did not quantify the degree of symmetry using an index like this study. Our result here quantitatively confirms their findings for TCs with initial intensity in TS and H12 categories. However, our new finding is that, for TCs with initial intensity in the H35 category, RI storms have more asymmetric stratiform rainfall pattern than SI storms.

Figure 6 presents the 2D shear-relative distribution of shallow precipitation/convection percentage occurrence for each intensity change–intensity group. The maximum value for the shallow precipitation/convection occurrence in the W-TD group is located at the downshear-left quadrant. The distribution rotates gradually clockwise from downshear-left to upshear-right from low intensity and intensification rate categories to high intensity and intensification rate categories. Similarly, Tao and Jiang (2015) found a gradual increase of frequency of shallow precipitation/convection (defined as radar 20-dBZ echo height less than 6 km) in the upshear-right quadrant from W/N to SI, and from SI to RI storms.

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As in Fig. 3, but for shallow precipitation/convection occurrence (%).

Citation: Weather and Forecasting 39, 2; 10.1175/WAF-D-23-0155.1

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Table 5 shows that in general, the inner-core averaged shallow precipitation/convection occurrence increases with TC the intensification rate for TD and TS, and decreases for H12 and H35. Tao and Jiang (2015) found a much higher shallow convection occurrence in the inner core for RI storms than non-RI storms when combining TCs with initial intensity in TS and H12 categories. However, by separating TCs into more detailed intensity change-intensity categories, this study finds that the inner-core mean shallow precipitation/convection occurrence of the RI group is significantly higher than that of the SI group for TCs with initial intensity in TD and TS categories while the inner-core mean shallow precipitation/convection occurrence of the RI group is significantly lower than that of the SI group for TCs with initial intensity in H12 and H35 categories (all at the 99.9% confidence level). In terms of the degree of symmetry of shallow precipitation/convection, Table 6 shows that for TCs with initial intensity in TD, TS, and H35 categories, the RI group has a significantly more asymmetric pattern of shallow convection occurrence than the SI group at the 95% confidence level or above.

Figure 7 presents the 2D shear-relative distribution of deep convection percentage occurrence for each intensity change–intensity group. The maximum deep convection occurrence occurs left of shear for the W-TD group, downshear for the N-TD, SI-TD, and RI-TD groups, and downshear-left for all the rest of the intensity change–intensity groups. As seen from Table 5, the inner-core mean deep convection occurrence is small in general, ranging between 1% and 8%, which is much smaller than the inner-core mean stratiform rainfall occurrence (ranging between 5% and 72%) and the inner-core mean shallow precipitation/convection occurrence (ranging between 12% and 31%). Although the inner-core mean deep convection occurrence increases with TC intensity for each intensity change category, it does not have a clear relationship with TC intensification rate. In particular, comparing RI with SI, the RI groups in both TD and H35 categories have a significantly lower (at the 95% confidence level or above) inner-core mean deep convection occurrence than that of the SI groups, respectively. However, the opposite is true for the H12 category, while there is no significant difference between the SI-TS and RI-TS groups. Similar to this result, Alvey et al. (2015) found that when combining all TC intensity categories together, the differences in percentage contribution from strong convection between different intensification rates were marginal and not statistically significant. In terms of the degree of symmetry of deep convection, Table 6 shows that for TCs with initial intensity in TD, TS, and H35 categories, the RI group has a significantly more symmetric pattern than the SI group at the 95% confidence level or above. By comparing with the distribution of stratiform rain occurrence in Fig. 5 and the distribution of shallow precipitation/convection occurrence in Fig. 6, we conclude that the upshear-right dominance of shallow precipitation/convection occurrence for TCs with a stronger intensity and a greater intensification rate is mainly because the precipitation/convection in the downshear-left quadrant of these types of TCs tends to have a greater frequency of stratiform precipitation and deep convection.

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As in Fig. 3, but for deep convection occurrence (%).

Citation: Weather and Forecasting 39, 2; 10.1175/WAF-D-23-0155.1

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4. Discussion

The environmental vertical wind shear has been long recognized to be closely related to TC formation and intensity change. Many studies have shown that the vertical shear and ventilation can impact the symmetry of developing TCs in not only modeling studies (Hendricks et al. 2004; Nguyen et al. 2008; Tao and Zhang 2014; Fischer et al. 2023) but also observational studies including aircraft observations and satellite observations (DeMaria 1996; Frank and Ritchie 2001; Lawrence et al. 2001; Rogers et al. 2003; Molinari and Vollaro 2010; Moskaitis 2010). A large ambient shear could not only cause a rapidly intensifying storm limited in intensity but also diminish the rate of intensification (Molinari and Vollaro 2010; Lawrence et al. 2001). Our result above shows that the symmetry of rainfall and convective intensity in the inner core increases with TC intensification rate for each of the four different TC intensity categories. However, this result may change if the impact of shear is considered.

To examine the influence of shear magnitude on the relationship between TC intensification rate and the symmetry of inner-core precipitation and convection, here we classify our TMI samples into low- versus high-shear categories. As mentioned in section 2, the shear vector is defined as the difference of the wind vector between 200 and 850 hPa within a 500–750-km ring surrounding the TC center. The averaged magnitude of the vector shear for all the overpasses is 8.2 m s⁻¹. Thus, we use 8 m s⁻¹ as the threshold to separate high versus low shear. Low shear is defined as the magnitude of the shear vector equal to or less than 8 m s⁻¹, while high shear greater than 8 m s⁻¹. Table 7 shows the inner-core mean axisymmetric indices of rain rate and PCT₈₅ for each intensity change–intensity category in low- and high-shear conditions, respectively.

Table 7.

Inner-core (within 1.7 × RMR) mean axisymmetric indices of rain rate and PCT₈₅, for each intensity change–intensity category and the differences of these inner-core mean axisymmetric indices between W and N, between N and SI, and between SI and RI in each intensity category in a low-shear or high-shear environment, respectively. Symbols represent the statistical significance of the difference at the 90% (^), 95% (*), 99% (**), and 99.9% (***) confidence levels.

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Under a high-shear environment, the inner-core mean axisymmetric index of rain rate still increases significantly (at least 95% confidence level) with the increase of TC intensification rate for each intensity category, except for the H35 category. The W-H35 storms have significantly more symmetric rainfall distribution than that of N-H35 storms (at the 90% confidence level), while the difference of axisymmetric index between RI-H35 and SI-H35 storms is not statistically significant. The statistically insignificant result for the symmetry of rain rate between RI-H35 and SI-H35 storms might be due to the very small sample size of RI-H35 under high shear (only three TMI overpasses).

Under a low-shear environment, the inner-core mean axisymmetric index of rain rate also increases significantly (at 99.9% confidence level) with the increase of TC intensification rate for TD, TS, and H12 intensity categories. However, for the H35 category, the differences of axisymmetric indices between each intensity change category are not statistically significant. This suggests that the symmetry of rain rate in major hurricanes are similar among different intensification rates under low shear.

Under high shear, the inner-core mean axisymmetric index of PCT₈₅ mostly increases significantly (at the 99.9% confidence level) with the increase of TC intensification rate. However, there are some exceptions. The differences of PCT₈₅ axisymmetric indices between W-TD and N-TD, between SI-H12 and RI-H12, and between W-H35 and N-H35 are not statistically significant. More surprisingly, the RI-H35 storms have significantly more asymmetric convective intensity distribution than that of SI-H35 storms (at the 90% confidence level). This is similar to the finding in Table 6 for the symmetry of rain rate. Shi and Chen (2021) found that under moderate or strong environmental shear, RI cases tend to have stronger outflow in the upshear flank, which is closely associated with stronger convection in the same location, than the non-RI cases. They argued that intensified outflow blocks the upper-level environmental flow and thus decreases the local shear, building an environment favorable for RI. Although we found the RI-H35 storms have significantly more asymmetric convective intensity distribution than that of SI-H35 storms under high shear, the convective intensity in upshear quadrants is stronger for RI-H35 high-shear composite than that for the SI-H35 high-shear composite (not shown), consistent with Shi and Chen (2021)’s finding. However, the asymmetric deep convection in the downshear-left quadrant (Figs. 3p and 7p) might also play a role for RI in major hurricanes under a high-shear environment. Further studies in this direction are needed.

Under low shear, the inner-core mean axisymmetric index of PCT₈₅ mostly increases significantly (at 99.9% confidence level) with the increase of TC intensification rate. However, similar to the high-shear case, there are some exceptions. The differences of PCT₈₅ axisymmetric indices between W-TD and N-TD, between SI-TD and RI-TD, and between N-H35 and SI-H35 are not statistically significant.

Overall, Table 7 suggests that the symmetry of rainfall and convective intensity in the inner core increases with TC intensification rate still holds under the impact of vertical wind shear, especially for TCs with initial intensity of TD, TS, and H12. There are some exceptions for major hurricanes, especially for rain rate under low shear and PCT₈₅ under high-shear conditions.

5. Conclusions

Using a 16-yr (1998–2013) TMI dataset containing 8195 overpasses from 1518 global TCs, this study examines the relationship between TC intensification rate and inner-core precipitation and convection parameters by decoupling the dependency of these parameters on TC intensity and that on TC intensification rate. Unlikely many previous satellite-based RI studies (Zagrodnik and Jiang 2014; Tao and Jiang 2015; Tao et al. 2017) that only include TCs with intensity in TS to H12 categories, this study includes all TC intensity categories (e.g., TD, TS, H12, and H35). Different from Fischer et al. (2018), this study examines TCs on a global scale, expanding the scope of investigation. In comparison to Su et al. (2020) and Fischer et al. (2018), a more extensive range of precipitation/convection parameters are examined. The analysis not only encompasses various precipitation/convection types but also quantifies the axisymmetric index of them. The study investigates the impact of vertical wind shear magnitude on the relationship between TC intensification and inner-core precipitation and convection parameters, which was not addressed in Fischer et al. (2018) and Su et al. (2020).

By classifying overpasses into one of 16 intensity change–intensity groups, it is found that the TC inner-core (within 1.7 × RMR) mean rain rate increases with TC intensification rate for each TC intensity category, which is consistent with Su et al. (2020). A Student’s t-test result, which was not provided in Su et al. (2020), confirms that that this positive relationship is statistically significant in general. This study further finds that the TC inner-core mean convective intensity (as indicated by PCT₈₅) and stratiform rainfall occurrence also increase with TC intensification rate for each TC intensity category. This updates the findings of previous satellite-based studies that indicated that inner-core convective intensity and stratiform or moderate precipitation occurrence increased from SI to RI (Jiang 2012; Jiang and Ramirez 2013; Zagrodnik and Jiang 2014; Alvey et al. 2015; Tao and Jiang 2015; Harnos and Nesbitt 2016). Without removing the dependence on TC intensity, previous studies showed that convective intensity in weakening TCs is stronger than that in SI or RI TCs (Jiang and Ramirez 2013; Alvey et al. 2015). Instead, this study updates the current understanding and indicates that a statistically significantly positive relationship exists between inner core convective intensity and TC intensification rate for all TC intensity and intensity change categories.

Different from the result of Tao and Jiang (2015) who found a much higher shallow convection occurrence in the inner core for RI storms than non-RI storms when combining TCs with initial intensity in the TS and H12 categories, this study finds that the inner-core mean shallow precipitation/convection occurrence of the RI group is significantly higher than that of the SI group for TCs with initial intensity in either the TD or TS category while the opposite is true for TCs with initial intensity in either the H12 or H35 category. Similar to Alvey et al. (2015) and Tao and Jiang (2015), it is found that the inner-core mean deep convection occurrence is much smaller than the inner-core mean stratiform rainfall occurrence and the inner-core mean shallow precipitation/convection occurrence, and there is no clear relationship between the deep convection occurrence and TC intensification rate.

From 2D shear-relative distributions, the maximum rain rate, convective intensity, and stratiform rainfall occurrence are located at the downshear-left quadrant for each intensity change-intensity category, consistent with many previous studies (Corbosiero and Molinari 2002, 2003; Rogers et al. 2003; Chen et al. 2006; Cecil 2007; Ueno 2007; Wingo and Cecil 2010; Pei and Jiang 2018). As TC intensity and intensification rate increase, the distributions of these parameters get more spread out from the down-shear-left quadrant to the upshear-right quadrant. The inner-core mean axisymmetric index of convective intensity (as indicated by PCT₈₅) increases significantly with 24-h future intensification rate for each TC intensity category. This advances the finding of previous studies showing that the degree of symmetry of TC inner-core precipitation and convection is higher for RI than SI storms (Kieper and Jiang 2012; Zagrodnik and Jiang 2014; Alvey et al. 2015; Tao and Jiang 2015; Fischer et al. 2018) by extending the positive relationship between the rate of symmetrization of inner core convection and TC intensification rate to all TC intensity change categories (including from W to N, from N to SI, and from SI to RI). The inner-core mean axisymmetric indices of rain rate and stratiform rainfall occurrence also increase significantly with the increase of TC intensification rate for each intensity category, except from SI to RI in the H35 category. The RI-H35 storms have significantly more asymmetric rainfall distribution and distribution of stratiform rainfall occurrence than those of SI-H35 storms. This suggests that asymmetric latent heating from rainfall, especially stratiform rainfall, and its projection onto the azimuthal mean may be important for RI in major hurricanes. Previous satellite studies indicated that RI storms have more symmetric rainfall patterns than SI storms only for TCs with initial intensity in TS and H12 categories (Zagrodnik and Jiang 2014; Tao and Jiang 2015; Tao et al. 2017). This study’s result is consistent with these previous studies for TCs with initial intensity in TD, TS, and H12 categories, but different for the H35 category in which RI storms have more asymmetric rainfall pattern than SI storms.

The shear-relative distribution of shallow precipitation/convection occurrence rotates gradually clockwise from downshear-left to upshear-right from low intensity and intensification rate categories to high intensity and intensification rate categories. The upshear-right dominance of shallow precipitation/convection occurrence for TCs with a stronger intensity and a greater intensification rate is mainly because the precipitation/convection in the downshear-left quadrant of these types of TCs tends to have a greater frequency of stratiform precipitation and deep convection. For TCs with initial intensity in TD, TS, and H35 categories, the RI group has a significantly more asymmetric pattern of shallow precipitation/convection occurrence than the SI group. In terms of the degree of symmetry of deep convection, this study shows that for TCs with initial intensity in TD, TS, and H35 categories, the RI group has a significantly more symmetric pattern than the SI group.

It is also found that the inner-core size, as quantified by RMR, decreases with TC intensity for each TC intensity change category and decreases with the TC intensification rate for each TC intensity category. To examine the impact of environmental vertical wind shear on the relationship between TC intensification rate and the symmetry of inner-core precipitation and convection, we classify our TMI samples into low- versus high-shear categories. Overall, our result that the symmetry of rainfall and convective intensity in the inner core increases with TC intensification rate still holds under the impact of vertical wind shear, especially for TCs with initial intensity of TD, TS, and H12. There are some exceptions for major hurricanes. First, the difference of symmetry of rainfall between RI-H35 and SI-H35 is not significant any more, probably due to smaller sample size after separating high- and low-shear conditions. Second, RI-H35 storms have significantly more asymmetric convective intensity distribution than that of SI-H35 storms under high-shear conditions.

The relationships found in this study between TC intensification rate and the intensity and symmetry of TC inner-core precipitation and convection parameters could be used to enhance the current statistical models to predict TC intensification and RI using microwave-based satellite observations (e.g., Fischer et al. 2018; Su et al. 2020). One limitation of this study is that the sample size of the RI-H35 category is only 19 from the TRMM TMI dataset. Future studies using a larger dataset by including Global Precipitation Measurement (GPM) constellations microwave sensors are highly recommended.

Data availability statement.

All data used in this study are publicly available. The best track data can be downloaded from https://www.metoc.navy.mil/jtwc/jtwc.html?best-tracks and https://www.nhc.noaa.gov/data/ websites. The TRMM TMI data are available at https://gpm.nasa.gov/data/directory. The European Centre for Medium-Range Weather Forecasts interim reanalysis dataset is available at https://www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-v5.