Rainband‐Occurrence Probability in Northern Hemisphere Tropical Cyclones by Synthetic Aperture Radar Imagery

Rainbands are essential to tropical cyclones (TCs), significantly affecting TC structure and intensity change. High‐resolution synthetic aperture radar (SAR) imagery can capture the footprints of rainbands caused by rain‐induced sea surface roughness modification. Using 464 SAR TC images, we investigated the rainband‐occurrence probability of TCs under different hemispheres, local times (LTs), intensities, and ocean basins. Results show that the rainband‐occurrence probability is highest in the downshear‐left quadrant for Northern Hemisphere TCs (downshear‐right quadrant for Southern Hemisphere TCs). For Northern Hemisphere TCs, the rainband‐occurrence probability is overall higher in the early morning (LT), and the peak region of rainband‐occurrence probability appears farther from the TC center in the evening (LT). Compared with weak TCs, the rainband‐occurrence probability becomes higher for strong TCs in the Northern Hemisphere. Furthermore, TCs have a higher rainband‐occurrence probability in the Northwest Pacific than in the North Atlantic and Northeast Pacific.


Introduction
Tropical cyclones (TCs) are strong low-pressure vortexes occurring over the tropical or subtropical ocean.A TC typically consists of an eye, an eyewall, and spiral rainbands.Among these features, rainbands have a significant effect on TC structure and intensity change (Houze et al., 2006;Wang, 2009).The diurnal variation has already been proven to be an essential feature of the TC system (J.D. Lee et al., 2020;Wu et al., 2015;Zhang & Xu, 2021;Zhang et al., 2020).The numerical simulation results show that the rainbands display quasi-diurnal behavior (Li & Wang, 2012;Zhou et al., 2016).
Traditional observations of TC rainbands are mainly based on ground-based or airborne Doppler radars (Didlake & Houze, 2013;Hence & Houze, 2008;May 1996;Yu et al., 2018), which have limitations in spatial coverage.Compared with traditional methods, satellite remote sensing has the advantage of extensive coverage and has already become a common means of global TC observation (Hoque et al., 2017;J. Lee et al., 2019;Velden et al., 2006).Early satellite remote sensing observations of TCs primarily utilized visible (VIS) and infrared (IR) • The sea surface imprint of tropical cyclone (TC) rainbands in many synthetic aperture radar images reveals their occurrence probability • The rainband-occurrence probability is overall higher in the early morning than in the evening.The feature is more obvious in strong TCs • The peak region of the probability appears farther from the TC center in the evening than in the early morning Supporting Information: Supporting Information may be found in the online version of this article.
sensors.VIS and IR imagery can reflect the cloud structures and motions of TCs (Hu & Zou, 2022;Jaiswal & Kishtawal, 2016;Liu et al., 2019;Piñeros et al., 2008;Zheng et al., 2019).With spaceborne microwave remote sensing development, microwave sensors are also used extensively for TC observation.The advantage of microwave sensors is that they can penetrate most clouds and provide excellent all-weather views of TC rainband organization and inner core structure (Hence & Houze, 2012;Jiang et al., 2013;Moradi et al., 2020;Yang et al., 2014).
Recently, synthetic aperture radar (SAR) has been used to study TCs (Cheng et al., 2012;Jin et al., 2014;I. K. Lee et al., 2016;Zheng et al., 2016).Compared to other microwave sensors, SAR has a higher resolution and can capture the fine structure of TCs (Wang et al., 2022;Zheng et al., 2016Zheng et al., , 2018;;Zhou et al., 2022).SAR measures the normalized radar cross section (NRCS), which is affected by the sea surface roughness (Zheng et al., 2016).NRCS of rainbands differs from surrounding areas due to the changes in sea surface roughness caused by the rainfall in the rainbands (Xu et al., 2014;Zhang et al., 2016).Thus, the SAR image can show the sea surface imprint of rainbands, which offers a novel methodology for studying TC rainbands.However, to the authors' knowledge, there is little research on TC rainbands based on hundreds of SAR images.
In this study, we collected 464 SAR TC images and annotated the rainbands on the images.The rainbandannotated data were mapped to grid nodes spaced at 0.027 times the radius of max winds (RMW) in a coordinate system with the origin at the TC center and the y-axis (vertical axis) in the vertical wind shear direction.Then, the rainband-annotated data were further composited under different hemispheres, local times (LTs), TC intensities, and ocean basins, and the so-acquired rainband-occurrence probability was systematically investigated.

SAR Data
This study collected 464 1 km-resolution SAR TC images for rainband annotation from CyclObs, a project led by Institut français de recherche pour l'exploitation de la mer (IFREMER).The images are acquired by Radarsat-2 and Sentinel-1 satellites from 2012 to 2022.CyclObs also provides TC intensity level (Tropical Storm and Categories 1-5 on the Saffir-Simpson Hurricane Wind Scale) at the imaging time.Thus, we only used images of TCs with sustained maximum wind speed above 34 kt at the imaging time.Figure 1a displays TC center positions and intensity levels at the imaging time.The number of images at each TC intensity level is shown in Figure 1e.In addition, we calculated the LT corresponding to the coordinated universal time (UTC) of each image acquisition.The LTs are concentrated from 05:00 to 07:00 or 17:00 to 19:00.

Auxiliary Data
Some of the SAR images in the study have collocated rain rate data measured by stepped-frequency microwave radiometers (SFMR).The SFMR is onboard the hurricane research aircraft operated by the National Oceanic and Atmospheric Administration and US Air Force.We selected the collocated data pairs with a time difference between SAR and SFMR observations smaller than 30 min.Finally, we obtained 88 data pairs.Then, the collocated data pairs were used to assist in determining the rainband occurrence and help us clarify the rainband features in SAR TC images.Rainbands are considered to occur when spiral features are present in the SAR TC images, and SFMR data demonstrate higher rain rates within the spiral features.
The rainband-annotated data were composited according to the vertical wind shear direction.The wind vector data at 200 and 850 hPa required for the vertical wind shear calculation are from the European Centre for Medium-Range Weather Forecasts' fifth-generation global atmospheric reanalysis (ERA5) data set (Hersbach et al., 2020).ERA5 provides 1 hr-interval wind vector data with a grid size of 0.25°× 0.25°at 37 pressure levels.We temporally interpolated the ERA5 wind vector data to calculate the vertical wind shear at the acquisition time of each image.
The study needed the TC center positions for compositing the rainband-annotated data.We visually identified the TC center positions (TC eyes' geometric center positions) for the SAR images covering TC eyes.For those not covering TC eyes, we temporally interpolated the 3 hr-interval TC position records in the best track (BT) data set of the International Best Track Archive for Climate Stewardship (IBTrACS) (Knapp et al., 2010).IBTrACS merges recent and historical TC BT data from multiple agencies.In this study, we uniformly used the entries registered by the USA agency (e.g., the Joint Typhoon Warning Center and the National Hurricane Center).The difference between the BT-interpolated and manually recognized TC center positions is slight to the considered radius range of two to 10 times the RMW (see Text S1 Supporting Information S1).In addition, the study required the RMW data to normalize the radial distance from the TC center.Therefore, the RMW data were also temporally interpolated from the RMW records in the BT data set.

Method
Due to the influence of rainfall on electromagnetic wave propagation and sea surface roughness, the NRCS of rainbands is different from the surrounding areas.Therefore, the rainbands are visible in the SAR images (Figures 1b-1d).Rainbands are spirally distributed around the TC center and have four types of signatures (dark, bright, inner rainbands dark and outer rainbands bright, and half dark and half bright (Li et al., 2013)).The collocated results of SFMR rain rate data and SAR images also show that the higher rain rate regions are brighter or darker than the surrounding regions, and the spiral features are evident (Figure S1 in Supporting Information S1).Hence, the criteria for identifying rainbands can be summarized as the following two items: (a) spiralshaped distribution features around the TC center and (b) brighter or darker than the surrounding regions.Following the above two criteria, we annotated the rainbands in SAR TC images.Figure S2 in Supporting Information S1 displays various types of rainbands presented in SAR TC images.The rainband annotation results of the four SAR TC images in Figure S2 in Supporting Information S1 are shown in Figure S3 in Supporting Information S1.Then, we made the rainband-annotated data corresponding to each SAR image.The spacing between the grid nodes is 1 km.Each grid node may have a zero, one, or nan value in the rainband-annotated data.Zero and one mean SAR observations, while one means rainband occurrences.Nan means no SAR observations.Then, we estimated the rainband-occurrence probability by compositing the rainband-annotated data with the following three steps (Figure S4 in Supporting Information S1).
Step 1: The vertical wind shear was calculated as the difference between the 200 and 850 hPa (V 200 -V 850 ) mean wind vectors within an annulus between 200 and 800 km from the TC center (Harnos & Nesbitt, 2011).Based on the vertical wind shear direction and TC center position, the rainband-annotated data were mapped to grid nodes spaced at 1 km in a rotated coordinate system with the origin at the TC center and the y-axis in the vertical wind shear direction (Figure S5 in Supporting Information S1).
The mapping was accomplished by resampling with nearest-neighbor interpolation.
Step 2: The rainband-annotated data were further mapped to grid nodes spaced at 0.027 times the RMW in a normalized coordinate system with the origin at the TC center and the y-axis in the vertical wind shear direction (Figure S5 in Supporting Information S1).The grid node spacing was computed by dividing the grid node spacing (1 km) in the rotated coordinate system by the median (37 km) of the RMWs of the TCs in the SAR images.Thus, for a specific TC case, the grid nodes' coordinates in the rotated coordinate system were calculated by multiplying the grid nodes' coordinates in the normalized coordinate system by 0.027 times the RMW of the TC.Nearest-neighbor interpolation was also used to complete resampling.
Step 3: All rainband-annotated data were processed according to Steps 1 and 2.Then, the rainband-annotated data are composited to obtain the number of rainband occurrences and the number of SAR observations at each grid node.The rainband-occurrence probability is calculated by dividing the number of rainband occurrences by the number of SAR observations.In addition, we only retained the estimated probabilities at the grid nodes with more than 20 SAR observations outside twice the RMW and inside 10 times the RMW.

Results and Discussions
According to the method presented in Section 3, we estimated the rainband-occurrence probability of TCs under different hemispheres, LTs, TC intensities, and ocean basins by dividing the rainband-annotated data.
First, the data were divided according to the Northern and Southern Hemispheres.The numbers of data are 383 and 81 in the Northern and Southern Hemispheres, respectively.
Second, the data in the Northern Hemisphere were further divided according to LTs and TC intensities.The data were divided into two classes based on LTs: early morning (05-07 LT) and evening (17-19 LT).Meanwhile, the data were divided into two intensity classes: weak TCs (Tropical Storm and Category 1) and strong TCs (Categories 2-5).Finally, the data of the two intensity classes were divided a second time according to LTs to investigate the rainband-occurrence probability in the early morning and evening under different TC intensities.
Third, the data were divided according to ocean basins.However, we only investigated the rainband-occurrence probability of TCs in the Northwest Pacific (NWP), North Atlantic (NA), and Northeast Pacific (NEP) due to the small sample size in other ocean basins (Table S1a in Supporting Information S1).Therefore, the data in the three ocean basins were also divided a second time according to LTs to investigate the rainband-occurrence probability in the early morning and evening under different ocean basins.

Rainband-Occurrence Probability of TCs in Northern and Southern Hemispheres
Figure 2 shows the rainband-occurrence probability of TCs in the Northern and Southern Hemispheres.Rainbands have the highest occurrence probability in the downshear, while downshear-left quadrant in Northern Hemisphere TCs and downsheer-right quadrant in Southern Hemisphere TCs.Furthermore, the rainbandoccurrence probability suggests that the distribution of rainbands is asymmetrical.The vertical wind shear likely determines the azimuthal placement of rainbands.

Rainband-Occurrence Probability of Northern Hemisphere TCs in Different LTs and TC Intensities
Whether in the early morning or evening, the rainband-occurrence probability of Northern Hemisphere TCs presents a pronounced downshear-left preference (Figures 3b and 3c).However, rainbands show a higher occurrence probability in the early morning.The early morning/evening rainband-occurrence probability difference was computed by subtracting the rainband-occurrence probability in the evening from the rainbandoccurrence probability in the early morning.The result (Figure S6a in Supporting Information S1) displays that most grid nodes (69.42% of all grid nodes with difference values) have a value greater than or equal to zero.The median of the rainband-occurrence probability for all grid nodes is 8.33% in the early morning and 6.45% in the evening.The Mann-Whitney U test can compare the rainband-occurrence probability between two groups of samples (probabilities at grid nodes) with the mean rank and test the significance of the comparison result.The Mann-Whitney U test indicates that the rainband-occurrence probability in the early morning is statistically significantly higher than in the evening, with mean ranks of 478,387 and 349,062 and a p-value of 0.00.Corresponding to the above values of the whole region, those of the downshear region are 70.08%,10.26%, 7.95%, 239,735, 173,398, and 0.00.The variations of rainband-occurrence probability with radial distance (Figures S7b and S7c in Supporting Information S1 for the whole region and Figures S8b and S8c in Supporting Information S1 for the downshear region) and azimuth (Figures S9b and S9c in Supporting Information S1) also indicate that rainbands have a higher occurrence probability in the early morning.
These features suggest that the rainband-occurrence probability of TCs has a strong diurnal oscillation with an early morning maximum and an evening minimum.The diurnal cycle could be due to oscillations in TC clouds associated with the cloud-clear sky differential radiation heating (Gray & Jacobson, 1977) and direct radiationconvection interaction (Kraus, 1963;Xu & Randall, 1995).At night, radiative cooling enhances subsidence in the cloud-clear sky region around TCs and leads to low-level convergence and deeper convection in the cloudy region of the TCs (Gray & Jacobson, 1977).Meanwhile, the nighttime long-wave radiation cooling at cloud tops could also enhance convection and rainfall through increasing local destabilizing (Kraus, 1963;Xu & Randall, 1995).These processes could lead to TC rainfall, characterized by a maximum in the early morning and a minimum in the evening.
Following the diurnal cycle of TC rainfall intensity, the region of TC rainfall shows a similar diurnal cycle.Our finding also suggests this feature.Although the higher rainband-occurrence probability region has a broader distribution in the early morning (Figure 3b), the peak region of rainband-occurrence probability is farther from the TC center in the evening (Figure 3c), similar to the diurnal pulses of coverage of TC cloud tops (Dunion  , 2014).This similarity may be due to rainfall coverage moving away from TC overnight and reaching the most distant areas from the TC center by the following afternoon.
We have also used the deep learning technique to extract rainbands, and the results support the findings on the differences in rainband-occurrence probability and probability peak position between the early morning and evening (see Text S2 Supporting Information S1).
Next, the rainband-occurrence probability of TCs under different intensities was investigated.Compared to weak TCs (Figure 3d), the rainbands-occurrence probability is higher for strong TCs (Figure 3g).The difference (Figure S6g in Supporting Information S1) between the rainband-occurrence probabilities of strong TCs and weak TCs was calculated by subtracting the rainband-occurrence probability of weak TCs from that of strong TCs.62.64% of the grid nodes with values of the difference have values greater than or equal to zero.The median of the rainband-occurrence probability for all grid nodes is 7.89% for strong TCs and 6.56% for weak TCs.The Mann-Whitney U test indicates that the rainband-occurrence probability for strong TCs is statistically significantly higher than for weak TCs, with mean ranks of 463,098-364,351 and a p-value of 0.00.Correspondingly, the numbers of the downshear region are 69.40%,10.34%, 7.50%, 245,831, 167,302, and 0.00.The variations of rainband-occurrence probability with radial distance (Figures S7d and S7g in Supporting Information S1 for the whole region and Figures S8d and S8g in Supporting Information S1 for the downshear region) and azimuth (Figures S9d and S9g in Supporting Information S1) also suggest that the rainband-occurrence probability is higher for strong TCs than for weak TCs.
The early morning/evening rainband-occurrence probability differences were calculated for weak and strong TCs, respectively (Figures S6b and S6c in Supporting Information S1).For weak TCs, 56.32% of the grid nodes with values of the difference have values greater than or equal to zero.For strong TCs, the proportion is 69.06%.The medians of rainband-occurrence probability are 7.14% and 6.45% in the early morning and evening for weak TCs and 8.89% and 6.38% for strong TCs.The Mann-Whitney U test indicates that the rainband-occurrence probability in the early morning is statistically significantly higher than in the evening for both weak and strong TCs.For weak TCs, the mean ranks are 349,198 and 330,099, and the p-value is 0.00; For strong TCs,479,194,348,255, and 0.00.Correspondingly, the numbers of the downshear region are 54.58%,7.69%, 7.69%, 176,969, 175,698, and 0.00 for weak TCs and 70.87%, 11.59%, 8.20%, 244,149, 168,984, and 0.00 for strong TCs.
The difference is slight in the downshear region for weak TCs while statistically significant.Although the TC diurnal cycle increase with increasing intensity is still debatable, the results presented here show a larger diurnal variation for strong TCs than weak TCs.This result is similar to the diurnal cycle of TC rainfall from the Tropical Rainfall Measuring Mission by Bowman and Fowler (2015).
In addition, the rainband-occurrence probability peak (marked in black or magenta ellipse) appears in the region farther from the TC center in the evening for both weak and strong TCs (Figures 3e,3h,and 3i).

Rainband-Occurrence Probability of Northern Hemisphere TCs in Different Ocean Basins
Figure 4 gives the rainband-occurrence probability of TCs in the NWP, NA, and NEP.Figures S6d-S6f in Supporting Information S1 show early morning/evening rainband-occurrence probability differences for the three ocean basins, respectively, and 61.30% (NWP), 56.43% (NA), and 70.21% (NEP) of the grid nodes with values of the difference have values greater than or equal to zero.Table S2a in Supporting Information S1 gives the medians of the rainband-occurrence probability in the early morning and evening for TCs in the three ocean basins.The Mann-Whitney U test indicates that the rainband-occurrence probability in the early morning is statistically significantly higher than in the evening for all three ocean basins.For NWP, the mean ranks are 425,851 and 358,108, and the p-value is 0.00; For NA,195,199,180,398,and 0.00;For NEP,379,358,263,215, and 0.00.
In the downshear region of NWP, NA, and NEP TCs, 66.14%, 50.96%, and 68.06% of the grid nodes with values of the early morning/evening rainband-occurrence probability difference have values greater than or equal to zero.Table S2b in Supporting Information S1 gives the medians of the downshear region's rainband-occurrence probability in the early morning and evening for TCs in the three ocean basins.The Mann-Whitney U test indicates that the downshear region's rainband-occurrence probability in the early morning is statistically significantly higher than in the evening for NWP, with mean ranks of 212,385 and 166,688 and a p-value of 0.00, and for NEP TCs,with 193,446,141,161, and 0.00.However, for NA, the rainband-occurrence probability is higher in the evening according to the mean ranks of 84,380 and 86,863.The conclusion for the downshear region of NA TCs needs to be further checked, as a large part of the downshear region currently has no available data for comparison (see Figures 4e and 4f).The variation of rainband-occurrence probability with radial distance is shown in Figure S10 in Supporting Information S1 for the whole region and Figure S11 in Supporting Information S1 for the downshear region.The variation with azimuth is shown in Figure S12 in Supporting Information S1.
In addition, the peak region of rainband-occurrence probability appears farther from the TC center in the evening for TCs in the three ocean basins.
Furthermore, Figure 4 shows that NWP TCs have a higher rainband-occurrence probability.The median of the rainband-occurrence probability is 7.92% in NWP TCs, while 7.50% and 6.25% in NA and NEP TCs.Correspondingly, the median in the downshear region is 10.91% in NWP TCs, while 8.75% and 7.14% in NA and NEP TCs.Table S3 in Supporting Information S1 gives the result of the Mann-Whitney U test among the three ocean basins, which indicate that the descending order from high to low rainband-occurrence probability is NWP, NA, and NEP in both the whole and downshear regions of TCs.  Lee et al., 2016;Webster et al., 2005), and our study shows that the rainband-occurrence probability in strong TCs is higher than in weak TCs.

Conclusions
This study systematically investigated the rainband-occurrence probability of TCs based on 464 SAR TC images.The results are summarized below.
First, differences in the rainband-occurrence probability of TCs in the Northern and Southern Hemispheres: The rainband-occurrence probability is highest in the downshear-left quadrant for Northern Hemisphere TCs while downshear-right quadrant for Southern Hemisphere TCs.Second, differences in the rainband-occurrence probability of Northern Hemisphere TCs under different LTs and TC intensities: (a) The rainband-occurrence probability in the early morning and evening exhibits a difference.Rainbands have a higher occurrence probability in the early morning overall.Notably, the difference is more obvious for strong TCs than weak TCs.Furthermore, the difference suggests that rainband-occurrence probability has a diurnal variation.The diurnal variation could result from cloud-clear sky differential radiation heating and direct radiation-convection interaction.And the diurnal variation becomes more obvious for strong TCs.(b) The locations of the peak region of rainband-occurrence probability in the early morning and evening are also different.Compared with the early morning, the peak region appears farther from the TC center in the evening.(c) The rainband-occurrence probability is higher for strong TCs than weak TCs.
Third, differences in the rainband-occurrence probability of TCs in different ocean basins (NWP, NA, and NEP): TC rainbands exhibit a higher occurrence probability in the early morning in the NWP and the NEP, and the peak region appears farther from the TC center in the evening.In addition, TCs have a higher rainband-occurrence probability in the NWP.
This paper demonstrates the potential for studies of TC rainbands based on SAR images.Rainband-occurrence probability can help us understand the distribution of rainbands under different TC conditions.Rainbands have a significant effect on TC structure and intensity change.The relationship between rainbands, TC structure, and intensity may be further investigated using SAR images.

Figure 1 .
Figure 1.(a) Distribution of synthetic aperture radar (SAR) tropical cyclone (TC) images.The annotated results of rainbands (enclosed by red lines) in SAR TC images and the collocated stepped-frequency microwave radiometers rain rate: (b) TC Karl at 22:21:32 UTC on 23 September 2016, (c) TC Ana at 04:44:31 UTC on 19 October 2014, (d) TC Arthur at 11:13:56 UTC on 3 July 2014.(e) The number of images in each TC intensity level.

Figure 2 .
Figure 2. Rainband-occurrence probability within 10 times the radius of max winds (RMW) for Northern Hemisphere tropical cyclones (TCs) (a) and Southern Hemisphere TCs (b).The black dotted circles indicate the locations of four, six, and eight times the RMW.

Figure 3 .
Figure 3. Rainband-occurrence probability of Northern Hemisphere tropical cyclones (TCs) under different local times and tropical cyclone intensities.(a) Northern Hemisphere TCs, (b) Northern Hemisphere TCs in the early morning, (c) Northern Hemisphere TCs in the evening, (d) Northern Hemisphere weak TCs, (e) Northern Hemisphere weak TCs in the early morning, (f) Northern Hemisphere weak TCs in the evening, (g) Northern Hemisphere strong TCs, (h) Northern Hemisphere strong TCs in the early morning, and (i) Northern Hemisphere strong TCs in the evening.The peak region is marked with ellipses.
rainbands occur more frequently in NWP TCs could be relevant to the recent result by Lavender and McBride (2021) that NWP TCs have higher rainfall.The higher rainband-occurrence probability in NWP TCs could be explained by the fact that stronger TCs occur more frequently in the NWP than in the NA and NEP (C.Y.

Figure 4 .
Figure 4. Rainband-occurrence probability of tropical cyclones (TCs) under different local times and ocean basins (a) Northwest Pacific (NWP) TCs, (b) NWP TCs in the early morning, (c) NWP TCs in the evening, (d) North Atlantic (NA) TCs, (e) NA TCs in the early morning, (f) NA TCs in the evening, (g) Northeast Pacific (NEP) TCs, (h) NEP TCs in the early morning, and (i) NEP TCs in the evening.The peak region is also marked.