Wind field reconstruction based on dual-polarized synthetic aperture radar during a tropical cyclone

ABSTRACT A wind field reconstruction method for dual-polarized (vertical-vertical [VV] and vertical-horizontal [VH]) Sentinel-1 (S-1) synthetic aperture radar (SAR) images collected during tropical cyclones (TCs) that does not require external information is proposed. Forty S-1 images acquired in interferometric-wide (IW) and extra-wide (EW) modes during the Satellite Hurricane Observation Campaign in 2015–2022 were collected. Stepped-frequency microwave radiometer (SFMR) observations made onboard the National Oceanic and Atmospheric Administration’s hurricane aircraft are available for 13 images. The geophysical model functions, namely VV-polarized C-SARMOD and cross-polarized S-1 IW/EW mode wind speed retrieval model after noise removal (S1IW.NR/S1EW.NR), were employed to invert the wind fields from the collected images. TC wind fields were reconstructed based on SAR-derived winds, enhancing TC intensity representation in the VV-polarized SAR retrievals and minimizing the error of the VH-polarized SAR retrievals at the sub-swath edge. The wind speeds retrieved from the SAR IW image were validated against the remote-sensing products from the soil moisture active passive (SMAP) radiometer, yielding a root mean squared error (RMSE) of approximately 4.3 m s−1, which is slightly smaller than the RMSE (4.4 m s−1) for the operational CyclObs wind product provided by the French Research Institute for Exploitation of the Sea (IFREMER). However, the CyclObs wind product has better performance than the approach proposed in this paper for the S-1 EW mode. Moreover, the RMSE of the wind speed between SAR-derived wind speed obtained using the proposed approach and the CyclObs wind product is within 3 m s−1 in all flow directions clockwise relative to north centered on the TC’s eye. This study provides an alternative method for TC wind retrieval from dual-polarized S-1 images without suffering saturation problem and external information; however, the pattern of the wind field around the TC’s eye needs to be further improved, especially at the head and back of the TC’s eye.


Introduction
A tropical cyclone (TC) is an essential phenomenon that plays an important role in heat and energy exchanges between low-and middle-latitude regions.It is commonly recognized that a TC associated with a storm surge is a serious disaster before and after it makes landfall.Traditionally, the sea surface wind is observed by moored buoys in real-time, such as in the open-access National Data Buoy Center (NDBC) data provided by the National Oceanic and Atmospheric Administration (NOAA).However, buoy-based measurements are unsuitable for analyses requiring wide coverage in global and regional seas.Moreover, buoy data are not commonly available for TCs due to the damage caused by strong winds and extreme sea states (Hu et al., 2020;Sheng et al., 2019).
Remote sensing techniques operating at optical and microwave frequencies provide valuable resources for research on oceanography.Recently, operational products have been officially released with a delay of only a few days, i.e. scatterometer data for wind (Shao et al., 2021) and altimeter data for significant wave height (SWH) (Ye et al., 2015).The spatial resolution of scatterometer wind is up to 12.5 km, and the temporal resolution is limited to twice per day (Anderson et al., 2017).Sea surface waves are only measured by the altimeter following the satellite's footprint (approximately 10 km).The advanced Chinese-French oceanography satellite (CFOSAT) jointly developed by the Chinese National Space Agency (CNSA) and the Centre National d'Etudes Spatiales (CNES) of France carries a wave spectrometer (surface wave investigation and monitoring, SWIM) (Hao et al., 2023) and a rotating fan-beam wind scatterometer (RFSCAT) (Xu et al., 2019), which allows for the measurement of the wave spectrum with an 18 km × 18 km coverage.However, these products do not meet the requirement in coastal waters where wind data with a fine spatial resolution are necessary.
At present, cross-polarized GMFs are being developed for various SARs in the C-band, including the cross-polarization coupled-parameters ocean (C-3PO) model for RADARSAT-2 (R-2) (Zhang et al., 2017) and the S-1 IW/EW mode wind speed retrieval model after noise removal (S1IW.NR/S1EW.NR) for S-1 (Gao et al., 2021(Gao et al., , 2021)).To cover the range of a TC as much as possible, SAR images in the IW and EW modes consist of several sub-swaths.The limitation is the discontinuity of the retrieval results obtained using a cross-polarized GMF (Shao et al., 2018), which is caused by the low NESZ at the edge of the sub-swaths.In contrast, the discontinuity of the co-polarized wind speed is significantly reduced because the co-polarized backscattering signals on the sea surface are stronger than in cross-polarization (Zhong et al., 2023).Furthermore, the accuracy of wind retrieval at low-tomoderate winds (< 30 m s −1 ) (Shao et al., 2019) is higher in co-polarization than in cross-polarization (Shao et al., 2022).Collectively, the two types of inverted wind from co-and cross-polarization SAR images have advantages and limitations.
In this paper, 40 dual-polarized (VV and VH) S-1 SAR images are collected during TCs.These images are collocated with the measurements from a steppedfrequency microwave radiometer (SFMR) and remote sensing products from the soil moisture active passive (SMAP) radiometer.The winds are inverted from VVand VH-polarized images using existing GMFs.An approach for reconstructing the wind profile in TCs is proposed to improve the accuracy, and the results are validated against SFMR and SMAP data.The remainder of this paper is organized as follows: the SAR images and auxiliary data are described in Section 2. Section 3 presents the methodology of the SAR wind retrieval and wind reconstruction.The results are discussed in Section 4, and the conclusions are summarized in Section 5.

Dataset
Forty S-1 images acquired in interferometric wide (IW) mode with a pixel size of 10 m and in extra wide (EW) mode with a pixel size of 40 m during the Satellite Hurricane Observation Campaign (SHOC) in 2016-2021 were available for this research.The incidence angle ranges from 20° to 51°, and the swath coverage is greater than 200 km.Information about the images and TCs from the National Hurricane Center (NHC) is presented in Table 1.The SFMR onboard the hurricane research aircraft measures the sea surface brightness temperature at six C-band frequencies (Uhlhorn et al., 2007).SFMR observations with a spatial resolution of 0.01°, i.e. wind vector and rain rate, have been commonly used in research on SAR oceanography in TCs (Zhao et al., 2023) due to a comparable accuracy (root mean squared error (RMSE) of ~3.9 m s −1 ) of the SFMR-measured wind speed (Klotz & Uhlhorn, 2014).Among these images, the NOAA hurricane aircraft passed over the spatial coverages of 13 images.Administration (NASA).In particular, the accuracy of the SMAP-measured wind in TCs is not affected by strong rainfall.A standard deviation of approximately 3 m s −1 was calculated for wind speeds greater than 25 m s −1 by comparing the SFMR with the SMAP during 20 TCs imaged in 2015 and 2016 (Meissner et al., 2017).The wind products from SMAP for TCs along the tracks in the ascending/descending directions are collected.The spatial resolution of SMAP data is 0.25° grid, and the swath is 1000 km.For example, the SMAP wind map over TC Michael at 23:39 UTC on 9 October 2018 is shown in Figure 3.The black rectangle in Figure 3 denotes the spatial coverage of the image in Figure 2. The French Research Institute for Exploitation of the Sea (IFREMER) team developed a SAR ocean surface wind gridded Level-2 product based on R-2, S-1A, and S-1B measurements, denoted as the Level-2 CyclObs wind product.This product combines the measurements in the VV-and VH-polarization channels with a priori information from the European Centre for Medium-Range Weather Forecasts (ECMWF) (Mouche et al., 2017).In this paper, the CyclObs wind product is also used to validate the proposed wind retrieval method.As examples, the CyclObs wind maps over TC Hermine and TC Michael are presented in Figure 4(a,b), respectively, in which the black rectangle represents the spatial coverage of the image in Figure 1.The entire SAR image is divided into several sub-scenes, i.e. 256 × 256 pixels (~3 km) for the IW mode and 128 × 128 pixels (~5 km) for the EW mode.The reconstruction method is implemented for all of the sub-scenes.In the matchups chosen for validation, the spatial distance between the SFMR and the SAR sub-scenes or CyclObs wind products is 0.01°, and the difference in the temporal resolution is less than 30 minutes.Similarly, the spatial distance between the SMAP product and the SAR sub-scenes or CyclObs wind products is 0.2°, and the difference in the temporal resolution is less than 1 hour.

Methodology
In this section, the VV-polarized and VH-polarized GMFs for wind retrieval from S-1 SAR images are introduced.Subsequently, a TC wind field reconstruction method is described.

VV-polarized GMFs
Utilizing commonly available datasets, including Envisat-advanced SAR (ASAR), R-2, and S-1 images collocated with moored buoys, the C-SARMOD was developed (Mouche & Chapron, 2016).It has been concluded that it has a good performance in wind retrieval from VV-polarized images in the C-band (Lin et al., 2017).The basic equation is as follows: σ 0 ¼B 0 ð1þB 1 cosφþB 2 cos2φÞ; (1) where σ 0 is the linear NRCS in VV-polarization, φ is the wind direction relative to the satellite's flight path, and matrix B is a function of the 10-m wind speed above the sea surface U 10 and the incidence angle θ.When applying the above GMF, the wind direction has to be known.The wind streaks for wavelengths of 800-3000 m on the two-dimensional SAR image spectrum are parallel to the wind direction with a 180° ambiguity (Alpers & Brümmer, 1994).Thus, the preliminary information about the wind direction with a coarse resolution is used to remove the 180° ambiguity by utilizing a reanalysis dataset from the ECMWF or a scatterometer product.
In the Northern Hemisphere, TC winds rotate counterclockwise.Therefore, the true wind directions are obtained using the spectrum transformation method and the nature of the TC winds.Figure 5(b) presents an example of the SAR intensity spectrum corresponding to the sub-scene in Figure 5(a) which was extracted from the image in Figure 1(a).In Figure 5, the red line represents the wind direction.The inverted wind maps obtained from the VV-polarized images over TC Hermine and TC Michael are presented in Figure 6(a,b), respectively.It should be noted that the discontinuity of the wind retrieval from the EW image is more apparent than that of the wind retrieval from the IE image.Figure 7 compares the inverted wind speeds from 13 images with SFMR observations with a 5 m s −1 bin size, in which the errorbar represents the standard deviation at each bin.It can be seen that there is significant underestimation in the high wind range, with an RMSE of 9.86 m s −1 , a correlation coefficient (COR) of 0.59, and a scatter index (SI) of 0.35.It is well known that the VV-polarized SAR wind speed has a comparable accuracy under lowto-moderate meteorological conditions.

VH-polarized GMFs
As mentioned above, the saturation problem exists when applying VV-polarized GMFs, resulting in the extreme winds in TCs being undetectable.As discussed by (Vachon & Wolfe, 2011), the crosspolarized NRCS is linearly correlated with the wind speed and is independent of the wind direction under a regular sea state.This behavior has also been confirmed in TCs (Zhang & Perrie, 2012).The SAR images acquired in the IW and EW modes consist of several sub-swaths.Thus, the    different signal-to-noise floors of the sub-swaths inevitably lead to discontinuity of the wind retrieval in VH-polarization.Moreover, the wind retrieval accuracy is low due to the weak backscattering signal compared to the noise at low-to-moderate wind speeds.Under these conditions, VHpolarized GMFs have been specifically developed for S-1 in the IW and EW modes, i.e.S1IW.NR and S1EW.NR.

Reconstruction method
Since the ECMWF winds significantly underestimate the maximum wind speed in TCs, an effective wind reconstruction method has been proposed to enhance the TC intensity representation in the ECMWF winds (Li et al., 2022).The validation against SFMR observations for 94 TC cases shows that the bias is reduced from −6.06 m s −1 for the ECMWF winds to −0.19 m s −1 after reconstruction.In this study, we applied the wind reconstruction method to SAR wind retrieval.The center of the TC is identified according to the SAR-derived wind field from the VH-polarized images.In addition, two TC parameters are calculated from the SAR wind retrievals: 1) the maximum wind, denoted as Maxwind_VV in VV-polarization and Maxwind_VH in VH-polarization, and 2) the radius of the maximum wind R max _VH in VH-polarization.The wind profile is reconstructed based on the VVpolarized SAR wind U 10 , which has less distortion at the edges of the sub-swaths and a high accuracy at low-to-moderate wind speeds, and the distance correction parameter r from the TC's eye, as shown in the following equations: where The construction method developed by (Li et al., 2022) needs to be improved in regards to the maximum wind speed because SAR has a higher spatial resolution than the ECMWF winds.A flowchart of our SAR wind reconstruction method is presented in Figure 10.

Results
As an example, Figure 11(a,b) present maps of the wind fields after the reconstruction over TC Hermine and TC Michael, respectively.Compared with the VV-polarized and VH-polarized SAR wind fields, the structural integrity of the reconstructed wind profile is visible; however, this type of pattern is determined by the VV-polarized SAR retrievals due to the usage of the maximum wind and the radius of the maximum wind R max _VH instead of SAR measurements in VH-polarization.Although it is important to note that the discontinuity of the VH-polarized SAR wind field was improved by our method, the two-  dimensional pattern of the wind profile needs to be further studied.In particular, the reconstructed wind field over TC Michael exhibits some deviations from the CyclObs wind product (Figure 4(b)).
The statistical analysis results are shown in Figure 12, in which the quality control is not specifically performed.Figure 12(a,b) compare the retrieval results and the CyclObs wind product with the SFMR observations for the IW images, respectively.Figure 12  (c,d) compare the retrieval results and the CyclObs wind product with the SMAP products for the IW images, respectively.The spatial distance between the SFMR and SAR is about 0.01°, while the spatial distance between the SMAP and SAR is about 0.2°.The matchmaps are grouped into a 2.5 m s −1 , in which the errorbar represents the standard deviation at each bin.The data illustrate that for the comparison with the SFMR observations for the IW SAR image, the RMSE of the wind speeds after the reconstruction is 4.23 m s −1 and the COR is 0.94, which are slightly smaller than the RMSE of 4.42 m s −1 and the COR of 0.92 for the comparison of the CyclObs wind product and the  SFMR observations.For the comparison of the SFMR observations with the retrievals from the EW image, the CyclObs wind product has a better performance (RMSE = 3.23 m s −1 ; COR = 0.92).This is also demonstrated by the comparisons with the SMAP products (Figure 13), i.e. the comparisons of the retrieval results and the CyclObs wind product with the SMAP products for the EW images and the comparisons of the retrieval results and the CyclObs wind product with the SMAP products for the EW images.We believe this is due to the coarse resolution of the SARretrievals from the EW image obtained using the proposed approach.In order to analyze the spatial difference between the retrieval and CyclObs wind product, the statistical Taylor diagram for the flow direction centered on the TC's eye is presented in Figure 14.The flow directions are discrete at intervals of 45°-Clockwise relative to north.It was found that the maximum RMSE of the wind speed is 3 m s −1 at the head of the TC's eye, i.e. ranges of 0-45° and 315-360°.The RMSE of the wind speed is approximately 2.5 m s −1 at the back of the TC's eye, i.e. ranges of 135-180° and 180-225°.To the right and left of the TC's eye, the RMSE is within 2.0 m s −1 .Accordingly, it is believed that the SAR-derived wind after the reconstruction needs to be further improved at the head and back of the TC's eye.
The applicability of the reconstructed wind fields under various conditions was further analyzed.Plots of the bias (the SAR-reconstructed wind speed minus the combination of the SFMR and SMAP data) versus the distance from the TC's eye and the incidence angle are shown in Figure 15(a,b), respectively.It should be noted that the bin sizes of 3° for the incidence angle and 5 km for the distance are grouped into pairs.It is reasonable that the bias gradually decreases in the regions 250 km away from the TC's eye, where the VVpolarized GMF performs well for low-to-moderate winds.The variation in bias oscillates with the incidence angle.The bias variations, along with the wind speed in the combination of the SFMR and SMAP data for a bin size of 5 m s −1 and the rain rate from the SFMR for a bin size of 2 mm hr −1 , are shown in Figure 15(c,d), respectively.Generally, the SAR-reconstructed wind speed is still slightly underestimated at high wind speeds (<50 m s −1 ).Unsurprisingly, rain cells have a significant   influence on the SAR backscattering signal (Shi et al., 2019;Yuan et al., 2021).That is, the difference increases with increasing rain rate for rain rates of greater than 20 mm hr −1 and further affects the wind (Ye et al., 2016) and wave retrieval (Zhao et al., 2021).This is the most probable explanation for the decrease in accuracy with increasing rain rate, and an improvement is needed to eliminate the impact of rainfall.

Conclusions
Wind field retrieval from SAR images is still an open and challenging topic, especially under extreme conditions.Saturation of the co-polarized SAR backscattering signal leads to a deficiency of strong winds in the wind retrieval.Although cross-polarized SAR does not have this problem, there is a discontinuity in the wind retrieval at the edges of the sub-swaths due to the different NESZ values.In this study, a scheme for wind reconstruction without the use of external information was developed.The newly developed method combines the advantages of the inverted wind from coand cross-polarized SAR images.
In this study, 40 dual-polarized S-1 images acquired during the SHOC in 2016-2021 were collected.SFMR observations were available for 13 cases.The wind fields were inverted from VV-and VH-polarized images using corresponding GMFs.The VV-polarized SAR wind was found to be underestimated.A comparison of the VV-polarized SAR wind speed and SFMR yielded an RMSE of 9.86 m s −1 , a COR of 0.59, and an SI of 0.35.The wind fields were reconstructed to enhance the representation of the TC intensity in the VV-polarized SAR wind and to minimize the error of the VH-polarized SAR wind at the edges of the sub-swaths.A recent study (Li et al., 2022) reported that the TC wind reconstruction based on the ECMWF winds is consistent with SFMR observations and SMAP products.Notably, our reconstruction method is improved to some extent by considering the impact of the radius of the maximum wind speed due to the high spatial resolution of the SAR image.The wind speed reconstructed from an EW SAR image was validated against the collocated samples from the SMAP, yielding an RMSE of 4.30 m s −1 and a COR of 0.94.These results are better than those for the comparison between the CyclObs wind speed product and the SMAP product (RMSE = 4.60 m s −1 , COR = 0.92).This result was also confirmed by comparing the reconstructed wind speeds with SFMR observations.The statistical Taylor diagram for the flow directions of TC eyes revealed that after the reconstruction, the SAR-derived wind was close to the CyclObs wind product.Although GMFs integrated using the approach proposed in this paper are suitable for wind retrieval from dual-polarized SAR in TCs without suffering saturation problem and external information using co-polarized GMFs, the pattern of the wind field around the TC's eye needs to be further improved by using SAR measurements in VV-and VH-polarization.
In the future, the proposed methodology will be tested for X-band SAR in TCs using the corresponding XMOD GMFs.In addition, the SAR wind field in a TC will be fused with other remote sensing wind products, i.e. scatterometer, altimeter, and microwave radiometer products.
Figure 1(a,b) show the VVpolarized and VH-polarized NRCS maps of the IW image over TC Hermine at 23:45 UTC on 1 September 2016.The red rectangles in Figure 1 denote the aircraft tracks.Similarly, the quick looks of the EW image in VV and VH polarization over TC Michael at 23:44 UTC on 9 October 2018 are shown in Figure 2(a,b), respectively.Since 2015, sea surface wind has been operationally retrieved from the brightness temperature measured by the passive L-band radiometer SMAP instrument launched by the National Aeronautics and Space

Figure 3 .
Figure 3. Wind map from soil moisture active passive (SMAP) radiometer over TC Michael at 23:39 UTC on 9 October 2018.The black rectangle represents the spatial coverage of the image in Figure 2.

Figure 4 .
Figure 4. Wind maps from CyclObs over (a) TC Hermine and (b) TC Michael.The black rectangle represents the spatial coverage of the image in Figure 1.

Figure 5 .
Figure 5. (a) sub-scene extracted from the image in Figure 1(a); and (b) the corresponding SAR intensity spectrum.The red line represents the wind direction.

Figure 6 .
Figure 6.(a) inverted wind map from IW images in VV-polarization over TC Hermine; and (b) inverted wind map from EW images in VV-polarization over TC Michael.

Figure 7 .
Figure 7.Comparison of inverted wind speeds from 13 S-1 images and SFMR observations.The data is grouped into a 5 m s −1 , in which the errorbar represents the standard deviation at each bin.

Figure 8 .
Figure 8. Inverted wind maps from VH-polarized images from S1IW.NR and S1EW.NR, i.e.TC Hermine in Figure 1(a) and TC Michael in Figure 2(a).

Figure 9 .Figure 10 .
Figure 9.Comparison of VH-polarized SAR wind retrievals and SFMR observations.The data is grouped into a 5 m s −1 , in which the errorbar represents the standard deviation at each bin.

Figure 11 .
Figure 11.Maps of wind fields after the reconstruction over (a) TC Hermine and (b) TC Michael.

Figure 12 .
Figure 12.Comparisons of (a) the retrieval results and (b) the CyclObs wind product with SFMR observations for IW images; comparisons of (c) the retrieval results and (d) the CyclObs wind product with SMAP products for IW images.The data is grouped into a 2.5 m s −1 , in which the errorbar represents the standard deviation at each bin.

Figure 13 .
Figure 13.Comparisons of (a) the retrieval results and (b) the CyclObs wind product with SFMR observations for EW images; comparisons of (c) the retrieval results and (d) the CyclObs wind product with SMAP products for EW images.The data is grouped into a 2.5 m s −1 , in which the errorbar represents the standard deviation at each bin.

Figure 14 .
Figure 14.The statistical Taylor diagram for the flow direction centered on the TC's eye.The flow directions are discrete at intervals of 45°Clockwise relative to north.

Figure 15 .
Figure 15.Bias (the SAR-reconstructed wind speed minus the combination of SFMR and SMAP data) versus (a) the distance from the TC eye and (b) the incidence angle, in which the incidence angle and distance are grouped into a bin size of 3° and 5 km, respectively.Bias versus (a) the wind speed in the combination of SFMR and SMAP data for a bin size of 5 m s −1 , and (b) rain rate from SFMR for a bin size of 2 mm hr −1 .

Table 1 .
Information about the Sentinel-1 (S-1) synthetic aperture radar (SAR) images and the corresponding tropical cyclones (TCs) collected from the National Hurricane center (NHC).
TC ID Maximum wind speed [m s −1 ] SAR acquisition time [UTC] TC ID Maximum wind speed [m s −1 ] SAR acquisition time [UTC]