High-Resolution Hurricane Vector Winds from C-Band Dual-Polarization SAR Observations

Home , Hurricane Bertha (2008)

272 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 31

BIAO ZHANG School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China

WILLIAM PERRIE Fisheries and Oceans Canada, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada

JUN A. ZHANG Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

ERIC W. UHLHORN NOAA/AOML/Hurricane Research Division, Miami, Florida

YIJUN HE School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China

(Manuscript received 21 December 2012, in ﬁnal form 1 November 2013)

ABSTRACT

This study presents a new approach for retrieving hurricane surface wind vectors utilizing C-band dual- polarization (VV, VH) synthetic aperture radar (SAR) observations. The copolarized geophysical model function [C-band model 5.N (CMOD5.N)] and a new cross-polarized wind speed retrieval model for dual polarization [C-band cross-polarized ocean surface wind retrieval model for dual-polarization SAR (C-2POD)] are employed to construct a cost function. Minimization of the cost function allows optimum estimates for the wind speeds and directions. The wind direction ambiguities are removed using a parametric two-dimensional sea surface inﬂow angle model. To evaluate the accuracy of the proposed method, two RADARSAT-2 SAR images of Hurricanes Bill and Bertha are analyzed. The retrieved wind speeds and directions are compared with collocated Quick Scatterometer (QuikSCAT) winds, showing good consistency. Results suggest that the proposed method has good potential to retrieve hurricane surface wind vectors from dual-polarization SAR observations.

1. Introduction tracks and intensities, particularly for the protection of coastal residents and infrastructure. Better under- Large tropical storms form as typhoons in the Pacific standing of the hurricane surface wind fields is also Ocean and hurricanes in the Atlantic Ocean. Recent essential. hurricanes such as ‘‘Superstorm’’ Sandy (2012) caused The first applications of microwave remote sensing significant damage with intense rainfall and storm surges, technology to hurricanes involved an airborne active as well as serious flooding. At least 286 people were scatterometer and passive radiometer during Hurri- killed along Sandy’s path in seven countries. Therefore, it cane Allen, demonstrating their potential for reliable is important to accurately forecast and monitor hurricane measurements (Jones et al. 1981). Although scatterometers and radiometers can also observe the ocean surface by day or night, they can only provide coarse- Corresponding author address: Dr. William Perrie, Bedford In- stitute of Oceanography, 1 Challenger Drive, P.O. Box 1006, resolution measurements, and thus their observations Dartmouth NS B2Y 4A2, Canada. are not very suitable to probe high-resolution wind gra- E-mail: [email protected] dient variations between the hurricane eye and eyewall.

DOI: 10.1175/JTECH-D-13-00006.1

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Yueh et al. (2003) examined the collocated Quick Scat- without the 1808 ambiguity (Zecchetto and De Biasio terometer (QuikSCAT) winds and Special Sensor Mi- 2002, 2008). crowave Imager (SSM/I) rain rates, and showed that the There can be alias features, such as oceanic or atmo- 2 regions of high rain rate (.20 mm h 1)havealower spheric internal waves, that produce similar linear fea- normalized radar cross section (NRCS) than the neigh- tures on the same spatial scales as wind rows. These boring areas, indicative of the attenuation effects of nonwind streak features are not generally aligned with rain. Compared to these sensors, C-band synthetic ap- the local wind vectors and can therefore contaminate erture radar (SAR) is not only able to contribute fine- wind direction retrievals inferred directly from the resolution sea surface wind field information but also SAR image. In hurricane wind regimes, although the is much less influenced by rain perturbations resulting wind direction dependence of the NRCS for CMOD5 from volume scattering and attenuation by raindrops is much weaker than that of CMOD4 (Horstmann et al. in the atmosphere than the Ku-band sensors men- 2005), inaccurate wind directions are still able to cause tioned above (Tournadre and Quilfen 2003; Weissman serious errors in wind speed retrievals. To avoid the and Bourassa 2011). Although SAR images of typhoons influence of inaccurate wind directions on wind speed and hurricanes occasionally show dark spiral-shaped retrieval, Shen et al. (2006) proposed an approach to features due to extreme precipitation events (Reppucci determine hurricane wind vectors, assuming constant et al. 2008, 2010), the advantages of C-band SAR make wind speeds and equal-distant wind directions in three it a potentially excellent instrument to investigate meso- neighboring subimage blocks of any specific concentric scale hurricane intensity and structure. circle around the hurricane eye. However, this method Great efforts have been devoted to extract hurri- needs to be modified in some circumstances, for ex- cane surface wind fields using spaceborne SAR mea- ample, for degraded hurricanes, which tend to gradu- surements. Horstmann et al. (2005) used a C-band ally lose their circular structure, and for SAR images RADARSAT-1 HH-polarized SAR image of Hurri- not containing the hurricane eye. cane Ivan to investigate the feasibility of hurricane sur- Saturation of the VV-polarized NRCS can be a prob- face wind retrieval using conventional VV-polarized lem for high wind retrieval from SAR. As wind speed geophysical model functions (GMFs), such as C-band increases, VV-polarized NRCS values also increase, even- models 4 and 5 (CMOD4 and CMOD5, respectively). tually reaching a maximum and then starting to decrease However, studies have shown that CMOD4 is inaccurate for higher values of wind speeds. Thus, the VV-polarized for high wind speed retrieval under extreme weather NRCS experiences saturation under high wind condi- conditions (Migliaccio et al. 2003; Horstmann et al. 2005; tions, which creates a wind speed ambiguity problem Signell et al. 2010). In any case, whether CMOD4 or (multiple solutions) for SAR wind speed retrieval CMOD5 is used, ultimately, wind direction has to be (Shen et al. 2009). Investigations from global positioning determined prior to wind speed retrieval from SAR. system (GPS) dropwindsonde observations and labo- In Seasat imagery, linear features were first observed ratory experiments, as well as airborne scatterometer to be aligned with the direction of the wind on the measurements, suggest that sea surface roughness, and scale of a few kilometers (Gerling 1986). Moreover, the air–water drag coefficient, approaches limiting values, marine atmosphere boundary layer (MABL) rolls are and also suggest that the NRCS acquired at VV polari- frequently observed in SAR images as linear streaks zation does not continue to increase as winds increase (Alpers and Brummer 1994). These steaks are caused beyond marginal hurricane strength (Powell et al. 2003; by the convergence or divergence of MABL rolls in Donelan et al. 2004; Fernandez et al. 2006; Black et al. the planetary boundary (Brown 2000). Therefore, wind 2007). Bubble annulus experiments suggest that the direction can be estimated using the linear features bubble layer in saltwater impedes the transfer of mo- associated with wind streaks, in combination with spec- mentum from the wind (Lundquist 1999). Altimeter tral analysis of the SAR image through a discrete Fourier observations also showed that the reflectivity is strongly transform (Vachon and Dobson 1996), or measurement impacted by foam layer and whitecap coverage (Quilfen of SAR image streaks via wavelet transform methods et al. 2010; Toffoli et al. 2011). In addition to the pos- (Du et al. 2002), or by acquisition of the orthogonal of sible effects of foam, sea spray is hypothesized to sig- the most frequent gradient direction using the local nificantly influence the transfer of momentum, heat, gradient method (Koch 2004). However, these methods and moisture in tropical cyclones (Kepert et al. 1999; all produce wind direction with inherent 1808 ambigu- Perrie et al. 2004a,b). A significant weakness of the ities, which can be resolved using the two-dimensional wind speed retrieval using VV-polarized SAR images continuous wavelet transform technique to isolate wind- of hurricanes or typhoons is the CMOD5 saturation related cells and features, and to extract wind direction under high wind conditions. Shen et al. (2009) developed

Unauthenticated | Downloaded 10/06/21 05:33 AM UTC 274 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 31 a technique to remove the wind speed ambiguity based wind speed, one NRCS is associated with four rela- on the dominant hurricane wind structure. Reppucci tive wind directions over the range (08;3608). In princi- et al. (2010) proposed a method to overcome the prob- ple, wind directions can be acquired from the wind lem of saturation in the tropical cyclone wind regime, streaks and standard image processing techniques basing the technique on the combined use of SAR mea- (Vachon and Dobson 1996; Du et al. 2002; Koch 2004; 2 surements for areas of wind speed of 20 m s 1 or less, Zecchetto and De Biasio 2002, 2008). Though often and a parametric hurricane profile model (Holland successful, there are some errors that exist in wind di- 1980). However, hurricane vector wind retrievals from rections from these methods. Moreover, the linear fea- single-polarization SAR data are still a challenge, with- tures from which wind directions are inferred from the out assumptions on hurricane wind structure or external SAR images are not always present, and they can some- auxiliary wind information. times be confused with oceanographic features on the C-band cross-polarized ocean backscatter from same spatial scales (Monaldo et al. 2004). Scatterometers RADARSAT-2 fine quad-polarization SAR data has can provide wind direction observations over the open been documented as being insensitive to the wind di- ocean but are contaminated by land signals near coastal rection or the radar incidence angle, and quite linear regions (Yang et al. 2011b). Meteorological forecast 2 with respect to the wind speed (8–26 m s 1), and thus can models tend to produce physically reasonable wind be used to directly retrieve wind speeds (Vachon and direction estimates, but the disadvantage is that their Wolfe 2011; Zhang et al. 2011). The dependence of spatial resolutions are generally limited to be far less cross-polarization returns on high wind measurements than the SAR resolution. Moreover, global weather suggests that it may be ideal for hurricane surface wind models do not necessarily include sufficient aspects of retrievals (Hwang et al. 2010a,b). Recently, Zhang marine atmospheric boundary layer physics to resolve and Perrie (2012) proposed an empirical C-band cross- the finescale features observed by SAR (Li et al. 2011). polarization ocean backscatter model (C-2PO) to re- Compared to single-polarization SAR, dual-polarization trieve high wind speeds, based on quad-polarization SAR can measure ocean backscatters with different SAR measurements and collocated buoy observations. scattering characteristics, which provides an opportunity Although the C-2PO model is established from fine to investigate hurricane wind vector retrievals. There- quad-polarization mode SAR data with a low noise fore, the motivation of this study is to seek a feasible floor, it may possibly apply to other imaging modes, for methodology to simultaneously acquire wind speed and example, ScanSAR Wide. However, the user should direction using dual-polarization SAR observations. exercise care when using this model to retrieve high The retrieved wind fields need to be evaluated using winds from dual-polarization SAR imagery, because available data, from buoys, scatterometer measurements, the noise floors for dual- and quad-polarization data and airborne stepped-frequency microwave radiometer are different. It is therefore necessary to develop a wind (SFMR) data (Uhlhorn and Black 2003; Uhlhorn et al. speed retrieval model based on dual-polarization SAR 2007), and compared to winds from the National Oceanic observations. and Atmospheric Administration’s (NOAA’s) Hurri- For hurricanes, wind speed and wind direction are of cane Wind Analysis System (H*Wind) data (Powell special interest to marine weather forecasters. Scatter- et al. 1998). ometers can illuminate the sea surface at three differ- In this study, we aim to 1) present a new cross-polarized ent azimuth angles via three antennas, and thus the wind speed retrieval model based on observations, in- unique surface wind vector field can be obtained through cluding SFMR and H*Wind data; 2) develop an ap- multiangle observations. However, SAR has one an- proach to simultaneously retrieve wind speed and wind tenna that only provides observations at one azimuth direction from two dual-polarization SAR images of angle. It is difficult to acquire wind speed and direction Hurricanes Bill and Bertha; 3) remove wind direction without ambiguities, by means of individual angle mea- ambiguities utilizing a parametric sea surface inflow surements from SAR. Although fully polarimetric SAR angle model; and 4) assess the accuracy of the proposed measurements provide complementary directional infor- hurricane wind vector retrieval method with collocated mation for the ocean surface wind fields (Zhang et al. QuikSCAT winds. 2012), the observed swaths are very small (25 km 3 25 km or 50 km 3 50 km), which are not suitable for moni- 2. Dataset toring hurricanes from space. In VV polarization, the SAR-measured NRCS is a RADARSAT-2 SAR has capability of provide single- nonlinear cosine function with respect to wind speed (HH or VV or HV or VH), dual- (VV, VH or HH, HV), and direction. For a given radar incidence angle and and quad-polarization (HH, HV, VH, VV) imaging

Unauthenticated | Downloaded 10/06/21 05:33 AM UTC FEBRUARY 2014 Z H A N G E T A L . 275 modes with different coverages. In this study, we focus with SAR images of Hurricanes Earl and Ike ac- on measurements from the dual-polarization (VV, VH) quired at 2259 UTC 2 September 2010 and 2356 UTC ScanSAR narrow and wide modes, because they provide 10 September 2008, respectively. SFMR measurements wide swath (300 or 500 km) images, and are suitable over Hurricane Earl were obtained during 2230; for hurricane monitoring with large area coverage from 2330 UTC 2 September 2010. SFMR can potentially pro- space. The entire range of incidence angles for dual- vide along-track mapping of surface wind speeds at rela- polarization ScanSAR mode data is between 208 and tively high spatial (1.5 km) resolution. For Hurricane Ike, 498. For ScanSAR narrow mode, the pixel spacing H*Wind data were acquired at 0130 UTC 11 September is 25 m 3 25 m, the resolution is 79.9;37.7 m 3 2008. The spatial resolution of H*Wind data is 6 km. In 60 m (range by azimuth), while for ScanSAR wide total, the dataset consists of 1845 collocated pairs (buoy: mode, the pixel spacing is 50 m 3 50 m, the resolution 884, SFMR: 348, H*Wind: 613) of NRCS in VH polari- is 160;72.1 m 3 100 m (range by azimuth). The noise zation and wind speeds, which were used to develop the floor of the two modes is about 28 6 2 dB (Slade 2009). wind speed retrieval model for dual-polarization SAR. We remove the speckle noise in the SAR image using Moreover, we collocated two RADARSAT-2 dual- a polarimetric SAR speckle filtering approach (Lee polarization SAR images of Hurricanes Bill (2226 UTC et al. 1999) with a nonoverlapping 7 pixel 3 7 pixel moving 22 August 2009) and Bertha (1014 UTC 12 July 2008), window. This approach emphasizes the preserving of with QuikSCAT wind data of these two hurricanes, polarimetric properties, and statistical correlation be- acquired at 2254 UTC 22 August 2009 and 0942 UTC tween channels, not introducing cross talk, and not 12 July 2008, respectively. For Hurricanes Bill and degrading the image quality. Bertha, the time difference between SAR observations We collected 648 RADARSAT-2 dual-polarization and QuikSCAT data are only 28 and 32 min, respec- (VV, VH) SAR images for the time interval November tively. The collocation is based on the nearest distance 2008–March 2011, with 39 in situ National Data Buoy criteria. We only choose those points where the dis- Center (NDBC) buoy observations in the Gulf of Alaska, tances between SAR retrievals and QuikSCAT mea- and off the East and West Coasts of the United States. surements are smaller than 0.18 to validate the proposed These buoys measured wind speed and direction, aver- dual-polarization SAR hurricane wind vector retrieval aged over 8-min periods, and reported hourly wave pa- methodology. rameters (significant wave height, dominant wave period In this study, QuikSCAT surface wind fields are ob- and direction) and surface meteorological parameters tained from the Remote Sensing Systems (RSS) website (air temperature, sea surface temperature, dewpoint (ftp://ftp.ssmi.com/qscat/). QuikSCAT level 3 (L3) data temperature, sea surface pressure). All buoy wind speeds consists of global grid values of meridional and zonal measured at different anemometer heights were ad- components of winds, measured twice a day in an ap- justed to a reference level of 10 m following Atlas et al. proximately 0.25830.258 resolution, which is suitable (2011). The spatial and temporal windows for the col- for scientific applications (Dunbar and Perry 2001; locations are required to be less than 10 km and 30 min, Callahan 2006). QuikSCAT level 2B (L2B) provides respectively. 12.5-km-swath winds. This kind of data is possibly asso- Buoys can measure ocean surface winds under low to ciated with potential applications in coastal regions. The moderate sea states, but they lose observational capa- mission requirements for QuikSCAT have an accuracy 2 2 bilities when wind speed approaches hurricane force. of 2 m s 1 rms in wind speed for the range 3–20 m s 1, 2 Hurricane surface winds have been estimated remotely 10% rms for the range 20–30 m s 1,and208 rms in wind 2 using SFMR on board the NOAA hurricane research direction for wind speeds ranging from 3 to 30 m s 1 aircraft (Uhlhorn and Black 2003; Uhlhorn et al. 2007). (Dunbar et al. 2006). The original Ku-band GMF, The NOAA Hurricane Research Division’s H*Wind Ku-2001, was developed for QuikSCAT wind vector (Powell et al. 1998) produces a gridded analysis by in- retrieval (Wentz et al. 2001); validation data for winds 2 terpolating and smoothing wind speed observations higher than 20 m s 1 were extremely limited. Analyses from a vast array of marine, land, aircraft, and satellite showed that high winds derived using the Ku-2001 platforms. H*Wind assimilates all of the available wind GMF were significantly overestimated (Smith and Wentz observations from a specific time period into a moving 2003). Therefore, QuikSCAT ocean wind vectors were ‘‘storm relative’’ coordinate system that allows for the completely reprocessed based on the new GMF referred production of an objectively blended wind field. to as Ku-2011, which improves wind speed retrievals at In addition to collocations between SAR images high wind speeds (Ricciardulli and Wentz 2011). The and buoy observations mentioned above, we also col- Ku-2011 GMF was developed using wind speed data from lected SFMR and H*Wind data, which were collocated the ‘‘WindSat’’ sensor with cross-calibrated multiplatform

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s0 s0 FIG. 1. Mean VH from RADARSAT-2 dual-polarization SAR FIG. 2. Mean VH from RADARSAT-2 ﬁne quad-polarization vs in situ–measured U10 from buoys, SFMR data, and H*Wind; SAR vs in situ–measured U10 from buoys (from Zhang and Perrie s0 the correlation coefﬁcient between SAR-observed VH and simu- 2012). s0 lated VH with Eq. (1) is 0.93.

characteristic is very similar to that of the C-2PO model data for wind direction (Atlas et al. 2011). WindSat is derived from ﬁne quad-polarization SAR data (see designed to demonstrate the capability of polarimetric Fig. 2, following Zhang and Perrie 2012). The inter- microwave radiometry to observe ocean surface wind cepts of solid lines in Figs. 1 and 2 are different, which speeds. Meissner and Wentz (2009) developed a new reveal that s0 from dual- and quad-polarization data algorithm for the WindSat winds and demonstrated that VH have different relationships with U . Previous studies it has validity even in rain and storm conditions. The 10 have shown that the wind direction dependence on WindSat retrieval algorithms were trained with NOAA NRCSinVVpolarization(s0 ) under high winds be- Hurricane Research Division (HRD) data, which are VV came weaker than the dependence in moderate winds, used as the optimum calibration for QuikSCAT wind 2 but not for radar incidence angles (Horstmann et al. speeds up to about 35 m s 1 (Ricciardulli and Wentz 2005). Moreover, s0 levels off as the wind speeds in- 2011). The Physical Oceanography Distributed Active VH crease above hurricane force as shown in Fig. 1, which is Archive Center (PO.DAAC) provides both QuikSCAT possibly associated with s0 attenuation due to intense L3 and L2B wind products, but these two kinds of data VH rainfall and related high sea-state processes. It should be are processed with the Ku-2001 GMF. Although RSS noted that the C-2PO model is based on a dataset that only provides QuikSCAT L3 data, they are produced 2 includes only a few wind speeds above 20 m s 1,with using the new Ku-2011 GMF. They are therefore more 2 a maximum wind of 26 m s 1. Although C-2PO has the suitable for our study on high winds than those from potential for retrieval of high wind speeds, it needs fur- PO.DAAC. Thus, we use QuikSCAT L3 winds instead ther improvement by investigation of higher wind speed of L2B winds to validate the proposed dual-polarization observations. SAR vector wind retrieval algorithm. Airborne C-band dual-polarization (HH, VV) SAR observations over the ocean under moderate and high 3. Methodology, retrieved winds, and validation winds have exhibited the essential backscatter features of NRCS in copolarizations (Mouche et al. 2005; Sapp a. Dual-polarization SAR wind vector retrieval et al. 2013). However, the behavior of cross-polarized Figure 1 shows the relation between RADARSAT-2- NRCS from spaceborne dual-polarization (VV, VH) s0 measured VH-polarized NRCS ( VH) and collocated SAR was not reported. Thus, we need to study cross- observed 10-m neural wind speed (U10), from buoys, polarized SAR ocean surface backscatter character- SFMR measurements, and H*Winds data. We ﬁnd that istics especially under extreme weather conditions and s0 VH is not sensitive to the radar incidence angle or to develop a wind vector retrieval algorithm for dual- wind direction, but it is dependent on wind speed. This polarization SAR.

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In the present study, we incorporate SFMR-measured requiring that the partial derivatives with respect to surface winds and H*Wind data. In total, there are 633 wind speed and wind direction be zero. We thus ob- 2 wind speeds above 20 m s 1, and the highest wind speed tain optimum estimates for wind speed, and direc- 2 is 39.7 m s 1 as shown in Fig. 1, providing an opportunity tion, with associated ambiguities (multisolutions; e.g., to develop a high wind speed retrieval model for dual- u, p 2 u, p 1 u,2p 2 u). polarization SAR observations. We use nonlinear least s0 b. Wind direction ambiguity removal squares to derive a model relating VH to U10 as follows: Because of the friction between hurricanes and the s0 5 : 3 2 : VH 0 332 U10 30 143. (1) ocean surface, the winds inside the hurricane rotate counterclockwise and the inflow angle is toward the s0 In Eq. (1), the units of VH and U10 are decibels and storm’s center in the Northern Hemisphere. The aver- meters per second, respectively. The correlation co- age inflow angle is approximately 208 (Powell et al. 1996). s0 s0 efficient between observed VH and simulated VH with Recent investigation by Zhang and Uhlhorn (2012) has Eq. (1) is 0.93, and the relation is independent of ex- shown that the mean inflow angle in hurricanes is in the ternal wind direction or radar incidence angles. There- range 222:6862:28 with 95% confidence. This result is fore, we have developed a C-band cross-polarized ocean obtained from analysis of near-surface (10 m) inflow surface wind retrieval model for dual-polarization SAR angles using wind vector data from over 1600 quality- (C-2POD). controlled global positioning system dropwindsondes The wind speed range of the fit for C-2POD is 3.7– deployed by aircraft on 187 flights in 18 hurricanes. 2 2 39.7 m s 1, whereas for C-2PO, the range is 2.0–26.0 m s 1. They proposed an analytical parametric model for the In addition to differences in the intercepts, between surface inflow angle aSR, which requires, as inputs, the C-2POD and C-2PO models, as addressed previously, storm motion speed, maximum wind speed, and radius the slopes (angular coefficients) for the two models are of maximum wind, according to the relationship different. They are 0.332 and 0.580, respectively. For a u 5 1 example, if we assume the VH-polarized NRCS from SR(r*, , Vmax, Vs) Aa0(r*, Vmax) Aa1(r*, Vs) dual-polarization SAR observation is 224 dB, and in- 3 u 2 1 « cos[ Pa1(r*, Vs)] , (3) put this value into both the C-2POD and C-2PO models, 21 the resulting wind speeds are 18.5 and 20.1 m s ,re- where Vmax and Vs are maximum wind speed and storm spectively. It is evident that the C-2PO model over- motion speed, respectively. The normalized radial dis- estimates wind speed. Thus, it is important to use tance r* has a radius of maximum wind speed (r* 5 C-2POD, instead of C-2PO, to retrieve wind speeds r/Rmax); « is model error; and Aa0, Aa1,andPa1 are from dual-polarization SAR images. functions that are described by Zhang and Uhlhorn Because dual-polarization SAR provides simulta- (2012). neous co- and cross-polarized ocean backscatter with In this study, the model-estimated inflow angle can different scattering characteristics, we can potentially be used to select the ‘‘optimum wind direction’’ from the retrieve wind vectors. Therefore, to simultaneously multiple of possible wind direction solutions. At each retrieve wind speed and direction, we construct a cost pixel location, the wind alias nearest to the counter- function involving both the copolarized geophysical clockwise tangential direction, less than the estimated model function [C-band model 5.N (CMOD5.N)] and inflow angle (toward the storm center), is chosen as the C-2POD. The cost function is correct wind direction. To obtain the tangential direction at each pixel location, we use the approach of 5 sm 2 so 2 1 sm 2 so 2 J(i, j) [ VV(i, j) VV(i, j)] [ VH(i, j) VH(i, j)] , Du and Vachon (2003) to determine the location of (2) the center of the hurricane eye. The maximum wind speed (Vmax) is directly obtained from the C-2POD sm sm so so where VV and VH are simulated and VV and VH are model. The maximum wind speed Vmax can also be es- observed NRCS in VV and VH polarizations, respec- timated via fitting of a parametric model for the trop- tively. Here, i and j are the line and column pixel loca- ical cyclone wind speed (Holland 1980) to the SAR tions, respectively, in the SAR image. For each pixel, measurements in the lower wind speed regime (Reppucci sm sm we estimate VV and VH with the observed radar in- et al. 2010). Thus, the radius of maximum wind can be cidence angle and assumed wind direction and speed. obtained by estimating the distance between the hurricane Using a nonlinear least squares technique, along with eye center and the maximum wind speed location. The simulated and observed NRCS in VV and VH polari- storm motion speed can be acquired from National Hur- zations, we minimize the cost function at each pixel by ricane Center (NHC) 6-hourly best-track data. Therefore,

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FIG.3.RADARSAT-2 dual-polarization SAR image acquired over Hurricane Bill at 2226 UTC 22 Aug 2009 s so showing (a) VV polarization and (b) VH polarization, where the color bar shows 0 (dB) in VV polarization ( VV) so 21 andinVHpolarization( VH), respectively. (c) SAR-retrieved wind speeds. Color bar shows wind speeds (m s ) at U10, and (d) SAR-retrieved wind directions without ambiguities. (RADARSAT-2 data and product 2009 MacDonald, Dettwiler and Associates Ltd., All Rights Reserved.) The locations of HEC and Vmax are indicated by the black plus sign (1) in panel (c). the inflow angle is easily calculated using hurricane in- respectively. The cost function uses co- and cross- tensity and the motion parameters, using the parametric polarized wind speed retrieval models (CMOD5.N and inflow angle model. SAR wind direction determination, C-2POD), as well as NRCS in VV and VH polariza- among the possible aliases, is therefore easily accom- tions and radar incidence angles, to obtain the wind plished, making use of the inflow angle at each pixel speed and direction, with ambiguities. Figure 3c shows location. the optimum wind speeds associated with the minimum cost function. Figure 4 shows wind speeds from c. Retrieved winds the CMOD5.N model with overlaid interpolated wind Figures 3a and 3b show a RADARSAT-2 SAR im- directions from QuikSCAT. The wind speed resolutions age of Hurricane Bill in VV and VH polarizations, for Figs. 3c and 4 are 1 km. Compared to scatterometer

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FIG. 5. Storm-relative inﬂow angle (aSR, deg) computed by the 21 parametric model for Hurricane Bill motion speed of Vs 5 9.4 m s , 21 and intensities of Vmax 5 34:8ms . Storm direction is toward the top of the ﬁgure.

21 and radius of maximum wind (Rmax). They are 34.8 m s 2 and 40.1 km for Hurricane Bill, and 31.8 m s 1 and 47.5 km for Hurricane Bertha, respectively. The propa- FIG. 4. SAR-retrieved wind speeds from the CMOD5.N model gation motion speeds (V ) of Hurricanes Bill and Ber- and VV-polarized SAR image of Hurricane Bill as shown in Fig. 3a, s tha, as given by the NHC 6-hourly best-track data, are with external wind directions from QuikSCAT. Color bar shows 2 21 1 wind speeds (m s )atU10. about 9.4 and 2.5 m s , respectively. To remove the ambiguities in the retrieved wind directions, the tangential direction and inflow angle at each pixel location winds, the advantage of high-resolution SAR is that have to be ascertained. The VH-polarized SAR image it can image super hurricanes with very small eyes is used to determine the hurricane eye center (HEC) (;10 km) and analyze the wind gradient variations be- following Du and Vachon (2003). The HEC longitude tween the eye and eyewall regions. Moreover, the Ad- and latitude are 6282201100W and 378310300N for Hurri- vanced Scatterometer (ASCAT) on the Meteorological cane Bill, and 6283102800W and 2984304900N for Hurricane Operation-A (MetOp-A) satellite is able to provide Bertha. Thus, the tangential direction can be deter- ocean surface winds with an enhanced resolution up to mined using a line between HEC and the pixel location. 12.5 km, which is particularly suitable for observing large The locations of HEC and Vmax for Hurricane Bill are storm systems with fast-moving propagation speeds. indicated in Fig. 3c. The storm-relative inflow angles are s0 Figure 3b clearly shows that the smaller values for VH calculated using the hurricane intensity, radius of max- are associated with lower wind speed—for example, imum wind, and storm motion speed, using the para- s0 in the hurricane eye area—while larger VH values are metric model of Zhang and Uhlhorn (2012). Figure 5 related to higher wind speeds in the eyewall region. This shows the estimated inflow angles. The mean value is characteristic demonstrates that the cross-polarized 222.58. SAR observations are not dependent on wind direction As mentioned previously, the wind alias closest to or radar incidence angle, but qualitatively vary linearly the counterclockwise tangential direction, less than the with wind speeds. It should be noted that, as shown in estimated inflow angle (toward the storm center), is se- s0 Fig. 1, VH is not saturated when wind speeds are smaller lected as the optimum wind direction. Thus, we remove 2 than 30 m s 1 but levels off as the wind speeds increase the ambiguity in the solutions and obtain the final above that value, above hurricane force winds, which is unique wind directions, which are shown in Fig. 3d. possibly caused by intense rainfall contamination and Figures 6a and 6b show a corresponding RADARSAT-2 additional effects associated with severe sea states. SAR image of Hurricane Bertha in VV and VH polari- The resultant retrieved winds allow us to easily derive zations, respectively. Figure 6c shows the optimum wind the hurricane intensity (maximum wind speed, Vmax) speeds associated with the minimum cost function, and

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FIG.6.RADARSAT-2 dual-polarization SAR image acquired over Hurricane Bertha at 1014 UTC 12 Jul 2008 s so showing (a) VV polarization and (b) VH polarization, where the color bar shows 0 (db) in VV polarization ( VV) so 21 and in VH polarization ( VH), respectively. (c) SAR-retrieved wind speeds. Color bar shows wind speeds (m s ) at U10, and (d) SAR-retrieved wind directions without ambiguities. (RADARSAT-2 data and product 2009 MacDonald, Dettwiler and Associates Ltd., All Rights Reserved.) The locations of HEC and Vmax are indicated by the black plus sign (1) in panel (c).

the locations of HEC and Vmax.WealsousetheCMOD5.N wind speeds are underestimated, compared to C-2POD model and QuikSCAT-measured wind directions to ob- values, which is possibly caused by saturation of the tain wind speeds, which are shown in Fig. 7. Again, to NRCS in VV polarization, under high wind conditions remove wind direction ambiguities, the inflow angles are and inaccuracy in the external wind direction input. calculated using Vmax and Rmax and the storm motion Figure 9c shows the SAR-retrieved wind directions speed. Figure 8 shows the estimated inflow angles. The versus QuikSCAT measurements. Rain has a signifi- mean value is 221.88. Figure 6d shows the wind di- cant impact on QuikSCAT wind speeds, but not on wind rections without ambiguities. directions, except for very high rain rates (Ricciardulli Since no available SFMR and H*Wind data can be and Wentz 2011). We quantitatively estimate the bias, collocated with SAR images of Hurricanes Bill and and centered root-mean-square error (RMSE), based on Bertha at 2226 UTC 22 August 2009 and 1014 UTC the formula proposed by Koh et al. (2012). Compared 12 July 2008, respectively, we use collocated SAR wind to conventional RMSE, the centered RMSE is not retrievals and QuikSCAT measurements to evaluate the dependent on the bias. We calculate the wind direction 2 accuracy of the proposed hurricane wind vector method. correlation following the vector correlation (ry )ap- 2 2 For Hurricane Bill, we compare the wind speeds from proach (Crosby et al. 1993), where ry 5 2andry 5 0 C-2POD and QuikSCAT in Fig. 9a. They show good are related to perfect correlation and zero correlation, 2 consistency even for high wind speeds (.20 m s 1). respectively. Figure 9b gives the wind speeds from C-2POD versus Figure 10 illustrates the comparisons for Hurricane those from CMOD5.N. It is shown that CMOD5.N Bertha. Overall, the results show that the SAR-retrieved

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FIG. 7. SAR-retrieved wind speeds from the CMOD5.N model and VV-polarized SAR image of Hurricane Bertha as shown in Fig. 6a, with external wind directions from QuikSCAT. Color bar FIG. 8. Term aSR (deg) computed by the parametric model for 21 5 21 shows wind speeds (m s )atU10. Hurricane Bertha motion speed of Vs 2.5 m s , and intensities of 21 Vmax 5 31:8ms . Storm direction is toward the top of the figure. wind vectors are comparable to the QuikSCAT winds. Since wind comparisons are made for SAR and both are involved in the GMF, they can be derived from QuikSCAT operating at different frequencies (C band scatterometer observations at different azimuth angles. and Ku band), apparent differences between SAR re- Compared to scatterometers, SAR only observes the trievals and QuikSCAT measurements can be found at ocean surface in one azimuth angle. Thus, it is difficult individual points. The proposed dual-polarization SAR to simultaneously derive wind speeds and directions, wind vector retrieval method still needs to be vali- combining SAR observations with GMFs, without an- dated using additional SFMR measurements, H*Wind cillary or external wind information. data, and reliable hurricane model results. Saturation of the NRCS in VV polarization, under Although numerical simulations have shown that rain high winds, can cause wind speed ambiguities (multi- attenuation and scattering at the C band are one order of solutions). As shown in Figs. 4 and 7, low wind speeds magnitude lower than at the Ku band (Tournadre and appear to occur in parts of the hurricane eyewall regions, Quilfen 2003), we need to consider the modification of which are caused by NRCS saturation. The comparisons theNRCSbyrain,forhighrainratesandhighwinds. between SAR retrievals and QuikSCAT measurements 2 It was shown that heavy rainfall (35 mm h 1) could showed that high winds derived using CMOD5.N were 2 induce serious wind speed retrieval bias (18.4 m s 1 for underestimated (Figs. 9b and 10b). Moreover, the 2 CMOD5.N and 11.7 m s 1 forC-2PO)betweenSAR CMOD5.N model estimates include both wind speed and and SFMR (Zhang and Perrie 2012). Objectively, nei- direction, and thus one can obtain wind direction before ther C-2POD nor CMOD5.N involve any rain param- deriving wind speed (from the SAR imagery). Wind di- eter because of the lack of collocated high-resolution rection can also be obtained from the SAR image itself, rain-rate data, and thus wind speed retrieval accuracies scatterometer measurements, numerical weather predic- of the two models are affected by high rain rates. Future tion models, and buoy observations, but inaccurate wind investigations will focus on correction of the NRCS in VV direction from these sources inevitably yield wind speed and VH polarizations for intense rainfall regions, which retrieval errors from SAR images. can potentially improve dual-polarization SAR wind Dual-polarization (VV, VH) SAR can simultaneously vector retrievals in extreme wind conditions. measure ocean surface backscatter with different scattering characteristics, compared to single polarized SAR images (HH or VV or HV or VH). The NRCS in VV 4. Discussion polarization is dependent on radar incidence angle and Conventional C-band geophysical model functions wind direction as well as wind speed, whereas NRCS in (GMFs) for wind speed retrieval are generally derived VH polarization is only dependent on wind speed. We from VV-polarized scatterometer measurements. Al- can use NRCS in VH polarization to first retrieve wind though wind speeds and directions are unknown and speed. The resulting wind speed and the radar incidence

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FIG. 9. (a) SAR-retrieved wind speeds from the C-2POD model vs QuikSCAT-measured wind speeds, (b) SAR- retrieved wind speeds from the CMOD5.N model vs from the C-2POD model, (c) SAR-retrieved wind directions vs QuikSCAT-measured wind directions, and (d) vector correlation of wind directions from SAR and QuikSCAT (sample size is 4). Hurricane Bill winds from SAR and QuikSCAT are acquired at 2226 and 2254 UTC 22 Aug 2009, respectively. angle and NRCS in VV polarization are utilized to esti- strongly dampen the co- (HH or VV) and cross-polarized mate wind direction. As a result, dual-polarization SAR (HV or VH) NRCS. Intense rainfall in high wind condi- observations provide a good opportunity to obtain wind tions can lead to NRCS attenuation (Powell 1990), and vector measurements from space. thus underestimation of high wind speeds (Tournadre There are several important factors that affect the and Quilfen 2003). Studies using scatterometer data 2 dual-polarization SAR wind vector retrieval accuracy. have shown that for wind speeds above 30 m s 1 and 2 The NRCS calibration error is one of them. For high rain rates exceeding 15 mm h 1, the error in the winds 2 2 winds over 20 m s 1, the 0.5–1.0-dB NRCS calibration can be more than 10 m s 1 (Yang et al. 2004). Thus, the 2 error will cause 3–8 m s 1 errors in wind speed (Yang et al. accurate retrieval of high wind speeds in intense rain 2011a). Moreover, there is potential interchannel cross areas has the potential to be improved only if the talk, which cannot be corrected, for dual-polarization NRCS could be modiﬁed in these regions. data (Touzi et al. 2010). Investigation has demonstrated that the highest wind regions within hurricanes are usu- 5. Conclusions ally accompanied by signiﬁcant rain (Weissman and Bourassa 2011). Heavy rain contamination and addi- We have presented a method to simultaneously de- tional effects associated with severe sea states can termine hurricane wind speed and direction with C-band

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FIG. 10. (a) SAR-retrieved wind speeds from the C-2POD model vs QuikSCAT-measured wind speeds, (b) SAR- retrieved wind speeds from the CMOD5.N model vs from the C-2POD model, (c) SAR-retrieved wind directions vs QuikSCAT-measured wind directions, and (d) vector correlation of wind directions from SAR and QuikSCAT (sample size is 4). Hurricane Bertha winds from SAR and QuikSCAT are acquired at 1014 and 0942 UTC 12 Jul 2008, respectively.

RADARSAT-2 dual-polarization SAR observations. dual-polarization SAR images of Hurricanes Bill and Thus, a new cross-polarized wind speed retrieval model Bertha are used to evaluate the proposed approach. for dual polarization (C-2POD) is ﬁrst developed by us- The retrieved winds are shown to be comparable to the ing SAR-observed NRCS in VH polarization, with col- collocated QuikSCAT data. located wind speeds from in situ buoys, airborne SFMR Compared to the CMOD5.N model (as shown in data, and H*Winds. This model and the VV-polarized Figs. 9a and 10a), the proposed dual-polarization SAR geophysical model function CMOD5.N are used to wind vector retrieval algorithm not only improves the construct a cost function. Optimum wind speeds and wind speed retrieval accuracy but also derives wind di- directions can be estimated when the cost function rection without ambiguity. Although we use reprocessed achieves its minimum. The hurricane inﬂow angles are QuikSCAT data from the Ku-2011 GMF to validate our further used to remove wind direction ambiguities. method, there are still some inherent wind speed errors They are estimated utilizing a parametric model with present in the data, especially when wind speeds are 21 inputs of maximum wind speed (Vmax), storm motion above 35 m s . Moreover, studies have shown that rain speed (Vs), and radius of maximum wind (Rmax). Here, is one of the main sources of error in scatterometer Vmax and Rmax are derived from the retrieved wind winds (Draper and Long 2004; Nie and Long 2008; Allen speeds, and Vs is from the NHC best-track data. Two and Long 2005; Weissman et al. 2013). The proposed

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