Novel Approach to Wind Retrieval from Sentinel-1 SAR in Tropical Cyclones

Abstract The strong winds in tropical cyclones (TCs) are commonly retrieved from cross-polarized SAR images using a geophysical model function (GMF). However, the accuracy of wind retrieval in cross-polarization is significantly reduced at the edges of sub-swaths. In this study, a novel approach to TC wind retrieval from VV polarized SAR images is proposed based on using the azimuthal cutoff wavelength to represent the effect of velocity bunching. A total of 12 dual-polarized (VV and VH) Sentinel-1 (S-1) images acquired in the interferometric wide (IW) mode were used, five of which were collocated with measurements taken by the Stepped-Frequency Microwave Radiometer (SFMR) on board an NOAA aircraft. The SAR-based azimuthal cutoff wavelengths were found to be linearly related to the SFMR wind speeds. Based on this finding, an empirical GMF for TC wind speed retrieval from VV S-1 images was constructed. The inversion results from seven images using this approach were validated against the wind products from the Advanced Scatterometer and the European Center for Medium-Range Weather Forecasts. The RMSE of the wind speed was 2.15 m s−1 and the correlation coefficient (COR) was 0.83 at wind speeds of less than 25 m s−1, while the RMSE was 2.66 m s−1 and the COR was 0.97 when compared with wind retrieval using the VH-polarized GMF S1IW.NR at wind speeds greater than 25 m s−1. The proposed algorithm performs well and has two advantages: (1) it is not subject to the saturation problem of the VV backscattering signal and (2) the discontinuity of the retrieval results obtained using VH GMF at the edges of sub-swaths is improved.

Les vents forts dans les cyclones tropicaux (TC) sont g en eralement r ecup er es a partir d'images RSO en polarisation crois ee a l'aide d'une fonction d'un mod ele g eophysique (GMF).Cependant, la pr ecision de l'extraction du vent en polarisation crois ee est consid erablement r eduite sur les bords des fauch ees.Dans cette etude, une nouvelle approche d'extraction du vent TC a partir d'images SAR en polarisation VV est propos ee bas ee sur l'utilisation de la longueur d'onde de coupure azimutale pour repr esenter l'effet du regroupement de vitesse.Au total, 12 images Sentinel-1 (S-1) a double polarisation (VV et VH) acquises en mode interf erom etrique large (IW) ont et e utilis ees, dont cinq ont et e colocalis ees avec des mesures prises par le radiom etre a micro-ondes a fr equence echelonn ee (SFMR) a bord d'un avion de la NOAA.Les longueurs d'onde de coupure azimutales bas ees sur le RSO se sont av er ees lin eairement li ees aux vitesses du vent SFMR.Sur la base de cette d ecouverte, un GMF empirique pour l'extraction de la vitesse du vent TC a partir d'images S-1 VV a et e construit.Les r esultats d'inversion de sept images utilisant cette approche ont et e valid es par rapport aux produits eoliens du diffusom etre avanc e et ceux du Centre europ een pour les pr evisions m et eorologiques a moyen terme.Le RMSE de la vitesse du vent etait de 2.15 m s À1 et le coefficient de corr elation (COR) etait de 0.83 a des vitesses de vent inf erieures a 25 m s À1 , tandis que le RMSE etait de 2.66 m s À1 et le COR etait de 0.97 par rapport a la r ecup eration du vent a l'aide du GMF en polarisation VH S1IW.NR a des vitesses de vent sup erieures a 25 m s À1 .L'algorithme propos e fonctionne bien et pr esente deux avantages : (1) il n'est pas soumis au probl eme de saturation du signal en bande VV et (2) la discontinuit e des r esultats de r ecup eration obtenus en utilisant le GMF en bande VH sur les bords des fauch ees est r eduite.

Introduction
During the cyclone season, tropical cyclones (TCs) are a common phenomenon in coastal areas.A TC is an essential dynamic process in the air-sea layer that plays an important role in energy and heat exchange.Moreover, strong winds, large waves, and heavy rainfall are the main marine disasters around China's seas.Nowcasting and hindcasting research on TCs is commonly conducted using atmospheric (Sun et al. 2014) and oceanic modeling (Sheng et al. 2019;Hu et al. 2020) due to the difficulty of real-time observation of TCs.
At present, remote-sensing data from space-borne satellites are valuable sources for oceanographic research, especially for research on TCs (Katsaros et al. 2002).Optical satellites, such as the Moderate Resolution Imaging Spectroradiometer (MODIS) (Kitabatake and Bessho 2008), Fengyun (FY) series (Jin et al. 2020), and Global Navigation Satellite System (GNSS) (Li et al. 2015), have been used to study various aspects of TCs, including their cloud structure, path, and intensity.However, the sea surface is undetectable by optical satellites because light cannot pass through the heavy clouds during TCs.Satellites that operate at microwave frequencies are useful for monitoring sea surface dynamics, i.e., scatterometers for wind (Stoffelen et al. 2017) and altimeters for waves (Shao et al. 2021a).Although microwave remote-sensing wind and wave products are available for TCs, their spatial resolutions are relatively coarse, i.e., 12.5 km for scatterometers and 10km footprints for altimeters, which still meet the requirements for TCs.Synthetic aperture radar (SAR) is an advanced technology that can operate under allweather and all-day conditions, and it has wide-swath coverage and fine spatial resolution, with a pixel size of up to 1 m for the Chinese Gaofen-3 (GF-3) (Shao et al. 2019;Zhu et al. 2020;Hu et al. 2023) and the German TerraSAR-X (TS-X) (Zhong et al. 2023).
Recent studies utilizing SAR measurements have developed SAR wind retrieval geophysical model functions (GMFs) in the C-band, i.e., C-SARMOD (Mouche and Chapron 2016;Lu et al. 2018) for RADARSAT-2 (R-2) and CSARMOD-GF (Shao et al. 2021b) for recalibrated GF-3, which relate a wind vector to the co-polarized (vertical-vertical [VV] and horizontal-horizontal [HH]) backscattering signals represented by the normalized radar cross section (NRCS) and incidence angle.When applying a GMF, the wind direction has to be obtained from the pattern at the spatial scale of a kilometer on the SAR image (Du, Vachon, and Wolfe 2002;Guo et al. 2022); this is called the wind streak (Alpers and Br€ ummer 1994).Without the distortion caused by other marine phenomena (Xu et al. 2018;Jiang et al. 2023), it has been proven that these GMFs perform well for wind retrieval from co-polarized SAR images under low-to-moderate wind speeds (<30 m s À1 ), yielding a 2 m s À1 error in wind speed (Shao et al. 2014;Yang et al. 2011;Yao et al. 2022).However, the strong winds during TCs could be inverted in crosspolarized SAR images due to saturation problems resulting from the co-polarization of the NRCS at high wind speeds (Hwang et al. 2010).Volumetric scattering occurs in the TC's inner zone, making the backscattering of a TC more complicated (Liu et al. 2020;Liu et al. 2021), which in turn makes scatterometer-based GMFs difficult to apply there.Moreover, wind information is necessary for SAR wave retrieval (Shao et al. 2022).In particular, TC wind speeds are used in theory-based (Ding et al. 2019) and empirical wave retrieval algorithms (Shao et al. 2018).It has been discovered (Vachon and Wolfe 2011) that wind speed has a linear relationship with the NRCS in vertical-horizontal (VH) polarization, which is sensitive to wind speeds of up to 55 m s À1 (Zhang and Perrie 2012).Based on these findings, VH-polarized GMFs for TC wind retrieval from Sentinel-1 (Gao et al. 2020) and R-2 (Zhang et al. 2017) SAR images have been developed.The performance of a VH-polarized GMF relies on a high-quality estimate of the noiseequivalent sigma zero (NESZ).In addition, the SAR image is usually a composite of several sub-swaths in order to obtain wide coverage of the TC area; for example, there are three and five sub-swaths for the S-1 interferometric wide (IW) and extra wide (EW) imaging modes, respectively (Gao et al. 2021a).The reason for this is that the wind speed retrieval is significantly contaminated by the noise along the subswaths.
In the literature, the wave mapping mechanism of SAR mainly includes the tilt (Zhang et al. 2021), hydrodynamic modulation (Valenzuela 1978), and non-linear velocity bunching (Alpers and Bruening 1986).Velocity bunching is the unique modulation of SAR caused by the relative motion between the satellite and sea surface, and it is proportional to the distribution of the orbital wave velocity (Beal et al. 1986).Velocity bunching results in sea surface waves with lengths shorter than a specific value being undetectable along the flight direction; this is called the azimuthal cutoff wavelength.The azimuthal cutoff wavelength is the second moment of the wave spectrum (Stopa et al. 2015), and it is inherently correlated with the significant wave height (SWH).In other words, the SWH can be directly retrieved from the SAR-based azimuthal cutoff wavelength (Shao et al. 2016;Shao et al. 2023).Under cyclonic conditions, the wind and waves are associated through the limited growth of wind-generated ocean surface waves during a TC (Hwang 2016).Following this rationale, recent studies have attempted to retrieve the TC wind based on the azimuthal cutoff wavelength from X-band SAR images under fully developed sea states (Corcione et al. 2019;Migliaccio et al. 2019).
In this study, the dependence of the wind speed on the azimuthal cutoff wavelength was studied using several dual-polarized (VV and VH) S-1 IW images acquired during the Satellite Hurricane Observation Campaign (SHOC).Then, a VV-polarized GMF was empirically constructed from the SAR-based azimuthal cutoff wavelength and measurements from the Stepped-Frequency Microwave Radiometer (SFMR) onboard an aircraft from the US National Oceanic and Atmospheric Administration (NOAA).The retrieval results from all of the VV-polarized images using the developed GMF were compared with the wind speeds inverted from VH-polarized images using an existing GMF S-1 IW mode wind speed retrieval model after noise removal (S1IW.NR) (Gao et al. 2021b) and the wind products from the Advanced Scatterometer (ASCAT).
The remainder of this paper is organized as follows.The S-1 SAR images, SFMR measurements, and ASCAT wind products are introduced in Section 2. The VV-polarized GMF based on the azimuthal cutoff wavelength is described in Section 3. Section 4 presents the accuracy of the wind speeds retrieved using the proposed algorithm through a comparison with the results from VH-polarized images, ECMWF and ASCAT winds.The conclusions are presented in Section 5.

Datasets
A total of twelve dual-polarized S-1 IW images acquired during the SHOC with clearly observable TC eyes were available for use in this study.Table 1 presents detailed information about the images and the corresponding TCs.The pixel size is 10 m in both the azimuth and range directions, with a swath coverage of approximately 200 km and incidence angles of 30.7-46.1 .Moreover, five images of TCs Irma, Dorian, Isaias, and Delta were treated as a training dataset and collocated with the SFMR onboard the NOAA aircraft, which provided wind speed and rain rate observations within and around the TCs in nearly real-time (Sapp et al. 2019).To date, SFMR data have been a valuable resource for comprehensive TC studies using SAR (Combot et al. 2020) and have been used to develop wind and rain retrieval algorithms from dual-polarized S-1 images (Gao et al. 2021b;Zhao et al. 2023).Furthermore, independent datasets consisting of seven images were used to validate the proposed wind retrieval method.As examples, the VV-polarized and VH-polarized images of TC Delta at 00:07 UTC on October 8, 2020, are shown in Figures 1a and 1b, respectively, in which the red line represents the track of the aircraft carrying the SFMR.
Since February 2007, ASCAT wind products have been operationally released for use by investigators worldwide.Systematic validation against moored buoys monitored by the Meteorological Archival and Retrieval System has shown that the error of the ASCAT wind speed is less than 1 m s À1 (Vogelzang and Stoffelen 2017).Scatterometer-based wind products have been commonly used for SAR oceanography research, including in the development of C-band model 5 (CMOD5) (Hersbach, Stoffelen, and Haan 2007) and the validation of CSARMOD-GF (Shao et al. 2021b) under low-to-moderate wind speed conditions; however, the ASCAT winds also suffer from saturation at detectable wind speeds of >25 m s À1 .In addition to the ASCAT winds, wind products from the European Center for Medium-Range Weather Forecasts (ECMWF) are also widely used to validate SAR wind retrieval (Hersbach et al. 2007).In this study, the official wind products from ASCAT for 0.25 grids and an 1800-km-wide swath were collected to validate the wind speed retrieval using the proposed algorithm.The ASCAT wind map for 02:54 UTC on October 8, 2020 is shown in Figure 2a, and Figure 2b shows the ECMWF wind map for 03:00 UTC on October 8, 2020, in which the black rectangles represent the spatial coverage of the image in Figure 1.

Methodology
In this section, the VH-polarized GMF for S-1 IW wind retrieval is briefly introduced.Then, the dependence of the SFMR wind speed on the SAR-based azimuthal cutoff wavelength in VV-polarization is examined.Based on the results, an empirical GMF for TC wind retrieval is constructed considering the VV-polarized azimuthal cutoff wavelength and incidence angle.
VH-polarized SAR wind retrieval GMF Saturation of the backscattering signal leads to the inapplicability of VV-polarized GMFs to TCs.As mentioned by Zhang and Perrie (2012), a VH-polarized NRCS is linearly correlated with strong wind speeds and is independent of the wind direction.The primary deficiency of VH-polarized algorithms is the inevitable discontinuity in wind retrieval caused by the signal-to-noise floor of each sub-swath.The sea surface backscattering signal is relatively weak compared with the noise at low-to-moderate wind speeds.
The formulation of S1IW.NR (Gao et al. 2021b) is expressed by the polynomial function of the incidence angle h and wind speed U 10 ( 30 m s À1 ) at a height of 10 m above the sea surface: (1) where r 0 is the VH-polarized NRCS (dB).At high wind speeds (U 10 > 30m s À 1), the function is corrected by removing the incidence angle term because the sea surface backscattering is sufficiently strong.(2) Existing VV-polarized GMFs, i.e., CMOD and the C-SARMOD family, have been shown to have good performances in regions far from the eye of the TC, but they require prior wind direction information.In this study, the prior wind direction is obtained from the ECMWF direction data through the interpolation method (Shao et al. 2019).The inverted wind maps obtained using the GMF CMOD5 and S1IW.NR, which correspond to the VV-and VH-polarized images in Figure 1, are presented in Figures 3a and  3b, respectively.It can be observed from the VHpolarized wind map that the maximum wind speed is 60 m s À1 , whereas the maximum wind speed is only 30 m s À1 for the VV-polarized wind map.However, the sharp gradient between the sub-swaths of the VHpolarized wind map is more apparent than that for the VV-polarized wind map.This phenomenon is relatively weak in the VV-polarized wind map because the VV-polarized backscattering signal is more sensitive to the sea surface, especially at low wind speeds.It was found that the validation of the retrieved wind speed through comparison with the SFMR measurements yielded a root mean square error (RMSE) of 2.96 m s À1 at U 10 25 m s À1 and an RMSE of 5.21 m s À1 at U 10 > 25 m s À1 (Figure 4).Therefore, we can conclude that the wind retrievals from the VH-polarized S-1 images of the TCs can be used to confirm the applicability of the proposed algorithm, especially for high winds.

Development of the VV-polarized SAR wind retrieval GMF
The two-dimensional SAR spectrum is integrated in the azimuth direction to obtain a one-dimensional spectrum.The maximum value of this one-dimensional spectrum is located at zero, and fitting the onedimensional spectrum using a Gaussian function is reasonable.Therefore, the azimuthal cutoff wavelength can be calculated by minimizing the standard error of a Gaussian function G(k x ) fitted to the normalized one-dimensional spectrum along the flight orientation, as stated in Equation (3): in which k x is the wavenumber in the azimuthal direction and k c is inversely proportional to the azimuthal cutoff wavelength k (k c ¼ 2p/k) (Sun and Kawamura 2009).As an example, Figure 5 shows a map of the azimuthal cutoff wavelength k from a VV-polarized S-1 image during TC Delta acquired at 00:07 UTC on October 8, 2020.The relationship between the SFMR wind U 10 and SAR-based k under VV-polarization at a distance >30 km away from the TC's eye is shown in Figure 6a, in which the data pairs are grouped in 5 incidence angle intervals ranging from 31 to 46 and the colorful solid lines represent the regression curves for each incidence angle bin.The error bar represents the standard deviation of the wind speed for a bin of 2 m s À1 .It can be clearly observed that k is linearly correlated with U 10 during TCs with wind speeds that are consistent with backscattering theory.It is observed that azimuthal cutoff wavelength oscillates with incidence angle due to the complex scattering variability (i.e., volumetric scattering).As revealed in a previous study (Corcione et al. 2019), the azimuthal cutoff wavelength is related to the wind speed in a fully developed sea state.In fact, the wind-sea was dominant during the TCs (Shao et al. 2017), indicating that the growth of the waves was continuously promoted by strong winds.Considering the fetch and duration-limited feature inside a TC, the wind speed and SWH are explicitly related (Hwang 2016), as expressed by: in which H s is the SWH and x gx is the fetch parameter represented by the distance from the TC's eye.
The azimuthal cutoff wavelength is determined by the   SWH (Shao et al. 2016).For this reason, the exponential relation between TC wind speed and the azimuthal cutoff wavelength is as shown in Figure 6a.This behavior is the foundation of TC wind retrieval from VV-polarized SAR images.In contrast, the winds around the eyes of the TCs were weak, and swells dominated in these regions (Black et al. 2007).Moreover, in this study it was found that most of the azimuthal cutoff wavelengths were outliers.Thus, the proposed algorithm was not adopted for the inner TC (i.e., a distance < 30 km away from TC eye).As mentioned in Equation ( 4), the TC wind speed is exponentially related to the SWH.The polynomial function referred to as the empirical model for SWH retrieval (i.e., CWAVE) was used for the TC wind retrieval in this study, denoted as TCWIND_S1: The coefficient matrix a was fitted using more than 2000 matchups and least square regression (Table 2).Due to the lack of matchups with extreme wind speeds (>40 m s À1 ), the proposed algorithm may be unable to be verified at high wind speeds.Figure 7 compares the values simulated using TCWIND_S1 with the SFMR wind speeds of up to 40 m s À1 with bins of 2 m s À1 , yielding an RMSE of 3.26 m s À1 , a correlation coefficient (COR) of 0.82, and a scatter index (SI) of 0.80.Under these circumstances, we conclude that the TCWIND_S1 algorithm can be applied to TC wind retrieval from VV-polarized SAR images without suffering from saturation.

Results
It is well known that the wind speed is weak around the eye of a TC, indicating that the wind-sea interaction produced by the wind is very weak and swells are dominant.Thus, the azimuthal cutoff wavelength around the eye of a TC is caused by swells rather than the windsea interaction (Shao et al. 2017).The relationship between the azimuthal cutoff wavelength and wind speed around TC eyes (i.e., the area defined by a radius of <30 km from the TC's eye) is distorted; therefore, the proposed algorithm is not implemented in these regions.As a retrieval example, a quick-look of the VV-polarized S-1 image of Typhoon Hermine is shown in Figure 8a, and the inversion wind map obtained using the GMF TCWIND_S1 and the azimuthal cutoff wavelength is  shown in Figure 8b.The TC wind pattern can be clearly observed.In particular, the saturation problem in the retrieval results when using a traditional CMOD is solved.In addition, prior wind direction information is not required to use the proposed algorithm.
The ASCAT swath and ECMWF winds covering the SAR scenes were collected, and the temporal difference between the ASCAT, ECMWF, and SAR retrieval was less than 1 hour; these were used in the error analysis.The proposed algorithm was applied to seven images in the validation dataset, and the more than 4000 retrieved wind speeds were compared with the ASCAT and ECMWF measurements (U 10 25 m s À1 ) and the VH-polarized wind speeds (U 10 > 25 m s À1 ).The results of the statistical analysis are shown in Figure 9, yielding an RMSE of 2.15 m s À1 , a COR of 0.83, and an SI of 0.13 for low-to-moderate wind speeds and an RMSE of 2.66 m s À1 , a COR of 0.97, and an SI of 0.06 for high wind speeds.As a result, the proposed algorithm and the CMOD have good performances at lowto-moderate wind speeds.At high wind speeds, the accuracy should be confirmed; that is, it should be validated against observations, although the retrieval results obtained using the GMF TCWIND_S1 are close to those achieved for VH-polarization.It was determined that the discontinuity of the retrieval results obtained using a VH-polarized GMF at the edges of the subswaths is removed by the TCWIND_S1; however, the limitation of the GMF TCWIND_S1 is its inapplicability around the eye of a TC.
At present, the French Research Institute for Exploitation of the Oceans provides SAR retrieval products for TCs, denoted as the Level-2 CyclObs wind product (Mouche et al. 2019).It is important to note that the external wind field (i.e., ECMWF) is necessary for it be treated as "first-guess" information in the retrieval process for the CyclObs wind product.In this study, we compared the retrievals of the proposed algorithm with the CyclObs wind product.Figure 10a shows the CyclObs wind map of Typhoon  Hermine.It can be seen that the TC cyclonic structure obtained by the GMF TCWIND_S1 is similar to that of the CyclObs wind product.Figure 10b compares the results of the retrievals of the GMF TCWIND_S1 and the CyclObs wind product, yielding an RMSE of 2.73 m s À1 , a COR of 0.96, and an SI of 0.13.This indicates that the GMF TCWIND_S1 is suitable for TC wind speed retrieval from co-polarized SAR images without external information.

Discussion
Although the k-based algorithm is a potential technique for TC wind retrieval, the GMF TCWIND_S1 could be further improved according to the conducted error analysis.The variation in the difference in the wind speed, i.e., TCWIND_S1 minus ASCAT U 10 25 m s À1 and TCWIND_S1 minus S1IW.NR at U 10 > 25 m s À1 , with respect to the wind speed, incidence angle, and azimuthal cutoff wavelength is presented in Figure 11.It can be observed that the differences remain within ±5 m s À1 as the azimuthal cutoff wavelength increases.It is not surprising that the bias significantly increases with increasing wind speed, especially with a difference of >5 m s À1 at U 10 > 50 m s À1 , and the bias oscillates with the incidence angle due to the insufficient number of samples in the regression dataset.Collectively, the enhancement of  the retrieval accuracy of the GMF TCWIND_S1 is due to its applicability to extreme winds and a wide range of incidence angles.

Conclusions
At present, strong wind retrieval during TCs is an interesting topic in SAR research.Due to the saturation of the backscattering signal in co-polarization, the TC wind field is usually inverted from cross-polarized (mainly VH) SAR images.Several cross-polarized GMFs in the C-band (Zhang et al. 2017) have been developed based on the linear relation between the cross-polarized NRCS and the wind speed (Vachon and Wolfe 2011).However, a discontinuity in the cross-polarized retrieval results caused by the low NESZ in the sub-swaths is inevitably observed.This discontinuity is reduced in co-polarized images.
The azimuthal cutoff wavelength is also related to the wind speed.Based on this principle, the TC wind can be retrieved from the X-band TS-X without a crosspolarization channel (Corcione et al. 2019).In this study, the dependence of the wind speed on the azimuthal cutoff wavelength estimated from VV-polarized S-1 images acquired during TCs was studied, after which an empirical approach to TC wind retrieval was developed.
Twelve dual-polarized (VV and VH) S-1 IW images were acquired during the SHOC.Of these, five images that were acquired during TCs Irma, Dorian, Isaias, and Delta were collocated with the observations from the SFMR operated by NOAA.The winds were retrieved from VH-polarized images using the VHpolarized GMF S1IW.NR, and the results were compared with the SFMR-measured wind speeds, yielding an RMSE of 2.96 m s À1 at wind speeds of less than 25 m s À1 and an RMSE of 5.21 m s À1 at wind speeds of greater than 25 m s À1 .The VH-polarized SAR winds were reliable at high winds; however, the accuracy was worse, with an error of 2 m s À1 for the copolarized GMF (Shao et al. 2019) at low-to-moderate winds.It was found that the SAR-derived azimuthal cutoff wavelength was linearly correlated with the SFMR wind speeds.Following this rationale, a TC wind retrieval GMF based on the azimuthal cutoff wavelength (TCWIND_S1) was developed.The validation of the SAR-derived wind against the ASCAT and ECMWF wind speed ( 25 m s À1 ) based on seven images yielded an RMSE of 2.15 m s À1 ; however, the difference in the wind speed (i.e., 2.66 m s À1 RMSE) was greater for high wind speeds (> 25 m s À1 ), as determined based on a comparison of the wind speeds inverted using the GMF TCWIND_S1 and the GMF S1IW.NR.The variation in the difference in the wind speed showed that the accuracy of the SAR retrieval results obtained using the GMF TCWIND_S1 was significantly reduced at high winds (> 50 m s À1 ) and that the difference oscillated with the incidence angle.It was concluded that the proposed algorithm is a promising approach to TC wind retrieval from VV-polarized SAR images without the negative effect of the saturation of the backscattering signal.
In the future, more SAR images in the C-band, i.e., R-2, S-1, and GF-3, acquired during TCs will be collected, and the GMF TCWIND_S1 will be further developed under extreme winds at a wide range of incidence angles.

Figure 1 .
Figure 1.The quick-looks of the dual-polarized Sentinel-1 (S-1) synthetic aperture radar (SAR) images during tropical cyclone (TC) Delta at 00:07 UTC on October 8, 2020: (a) vertical-vertical (VV) and (b) vertical-horizontal (VH).The red rectangle represents the track of the Stepped-Frequency Microwave Radiometer (SFMR) onboard on the aircraft of the National Oceanic and Atmospheric Administration (NOAA).

Figure 2 .
Figure 2. (a) The measured wind vectors from the Advanced Scatterometer (ASCAT) at 02:54 UTC on October 8, 2020.(b) The measured wind vectors from the European Center for Medium-Range Weather Forecasts (ECMWF) at 03:00 UTC on October 8, 2020.The black rectangle represents the spatial coverage of the image in Figure 1.

Figure
Figure6bshows relation between SAR-based azimuthal cutoff wavelengths in VV-polarization from all images and incidence angle, which are grouped by times of radius of maximum wind speed, in which the data pairs are grouped in 2 incidence angle intervals.It is observed that azimuthal cutoff wavelength oscillates with incidence angle due to the complex scattering variability (i.e., volumetric scattering).As revealed in a previous study(Corcione et al. 2019), the azimuthal cutoff wavelength is related to the wind speed in a fully developed sea state.In fact, the wind-sea was dominant during the TCs(Shao et al. 2017), indicating that the growth of the waves was continuously promoted by strong winds.Considering the fetch and

Figure 3 .
Figure 3.The inverted wind maps from the dual-polarized S-1 images during tropical TC Delta: (a) VV-polarized retrieval result obtained using the geophysical model function (GMF) CMOD5N and (b) VH-polarized retrieval obtained using GMF S1IW.NR.

Figure 4 .
Figure 4. Comparison of SAR-derived wind speeds from VHpolarized images with SFMR observations.The red points represent wind speeds > 25 m s À1 .The black points represent wind speeds 25 m s À1 .

Figure 6 .
Figure 6.(a) SAR-based azimuthal cutoff wavelengths in VV-polarization versus SFMR wind speeds.The data pairs are grouped in 5 incidence angle intervals between 31 and 46 , and the solid lines represent the regression curves for each incidence angle bin.(b) SAR-based azimuthal cutoff wavelengths in VV-polarization from all images versus incidence angle, which are grouped by times of radius of maximum wind speed in which the data pairs are grouped in 2 incidence angle intervals.

Figure 7 .
Figure 7.The SFMR wind speeds versus the simulated values obtained using the proposed GMF TCWIND_S.The error bar represents the stander deviation of the wind speed for a bin of 2 m s À1 .

Figure 8 .
Figure 8.(a) Quick-look of the VV-polarized S-1 image over.(b) Inverted wind map of Typhoon Hermine obtained using GMF TCWIND_S1.

Figure 9 .
Figure 9.The inverted winds obtained using the proposed algorithm compared to (a) the ASCAT and ECMWF for wind speeds of 25 m s À1 and (b) the VH-polarized SAR-derived results for wind speeds of >25 m s À1 .

Figure 10 .
Figure 10.(a) The wind map from the Level-2 CyclObs wind product and (b) the inverted winds obtained using the proposed algorithm compared to the CyclObs wind product.

Figure 11 .
Figure 11.Variation in the bias in the wind speed (TCWIND_S1 minus ASCAT U 10 25 m s À1 and TCWIND_S1 minus S1IW.NR at U 10 > 25 m s À1 ) with respect to three variables: (a) wind speed, (b) incidence angle, and (c) azimuthal cutoff wavelength.

Table 1 .
Information about the images and the corresponding tropical cyclones (TCs).