Ocean Wind and Current Retrievals Based on Satellite SAR Measurements in Conjunction with Buoy and HF Radar Data

Home , Ocean current, Physical oceanography

remote sensing

Article Ocean Wind and Current Retrievals Based on Satellite SAR Measurements in Conjunction with Buoy and HF Radar Data

He Fang 1, Tao Xie 1,* ID , William Perrie 2, Li Zhao 1, Jingsong Yang 3 and Yijun He 1 ID

1 School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China; [email protected] (H.F.); [email protected] (L.Z.); [email protected] (Y.H.) 2 Fisheries & Oceans Canada, Bedford Institute of Oceanography, Dartmouth, NS B2Y 4A2, Canada; [email protected] 3 State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, Zhejiang, China; [email protected] * Correspondence: [email protected]; Tel.: +86-255-869-5697

Received: 22 September 2017; Accepted: 13 December 2017; Published: 15 December 2017

Abstract: A total of 168 fully polarimetric synthetic-aperture radar (SAR) images are selected together with the buoy measurements of ocean surface wind fields and high-frequency radar measurements of ocean surface currents. Our objective is to investigate the effect of the ocean currents on the retrieved SAR ocean surface wind fields. The results show that, compared to SAR wind fields that are retrieved without taking into account the ocean currents, the accuracy of the winds obtained when ocean currents are taken into account is increased by 0.2–0.3 m/s; the accuracy of the wind direction is improved by 3–4◦. Based on these results, a semi-empirical formula for the errors in the winds and the ocean currents is derived. Verification is achieved by analysis of 52 SAR images, buoy measurements of the corresponding ocean surface winds, and high-frequency radar measurements of ocean currents. Results of the comparisons between data obtained by the semi-empirical formula and data measured by the high-frequency radar show that the root-mean-square error in the ocean current speed is 12.32 cm/s and the error in the current direction is 6.32◦.

Keywords: ocean currents; polarization; ocean surface wind; synthetic-aperture radar

1. Introduction Ocean surface currents are a defining feature of the interactions between the ocean and the atmosphere. Almost all ocean processes can be related to the ocean currents, making them an important physical parameter for marine meteorology and physical oceanography [1]. Observations of the ocean currents can enhance our understanding of the physical mechanisms of atmospheric–oceanic interactions and our ability to improve numerical weather predictions (NWP) model forecasts. Therefore, near-real time sea surface current information is needed for ocean operations [2]. Thus far, methods for measuring ocean surface currents can be classified into two categories: direct measurements and remotely sensing measurements. Direct measurements are mainly achieved by buoys and electromagnetic current meters, which have the disadvantage that they can only report data at a relatively few sampling locations, often with limited coverage in time, difficulty and expense in deploying instruments, and vulnerability to severe environmental conditions. With improved remote sensing techniques in recent years, the monitoring of surface currents has greatly improved, making it possible to even perform real-time observations over extended areas of the sea surface [3]. Among these techniques, SAR has become a new technical means to observe ocean surface features because of its high resolution and capacity to operate in almost all weather conditions, day or night [4,5].

Remote Sens. 2017, 9, 1321; doi:10.3390/rs9121321 www.mdpi.com/journal/remotesensing Remote Sens. 2017, 9, 1321 2 of 13

SAR can observe a variety of ocean surface phenomena by measuring the backscatter resulting from the radar’s electromagnetic waves from the ocean surface. Among these, are ocean surface currents which can be derived from fully polarimetric SAR images [6–8]. Moreover, some studies suggest that ocean surface currents also have significant effects on the electromagnetic backscattering signals per se, and therefore on the retrievals of associated ocean surface parameters [9,10]. Estimates of the wind stress, as determined from wind speed measurements retrieved from conventional radar scatterometers mounted on satellites, are usually derived neglecting ocean currents. Moreover, the scatterometer measures relative motion, not wind alone. Therefore, the scatterometer-derived wind stress is a more accurate representation of the boundary conditions needed for both atmospheric and oceanic models than stress fields derived neglecting ocean currents [11]. In terms of global averages, ocean winds are about 6 m/s and the downwind (or upwind) currents in the same ocean area are on the order of 0.3 m/s. It is known that modulations of wind stress by downwind and upwind ocean currents can result in differences that are typically 10%, and can reach 20% in strong currents [12]. There are two processes by which ocean currents can affect wind stress. One process is that the ocean surface current per se changes the surface relative wind speed of the wind, which changes the effective wind stress. A second process is that the sea surface temperature (SST) gradients change the stability of air-sea boundary layer and the associated wind field near the ocean surface. When the wind passes over an SST frontal area, the associated acceleration and deceleration that is experienced causes convergence and divergence of the wind stress, which are linearly correlated with along-wind and cross-wind SST gradients, respectively [13,14]. The accuracy of wind data retrieved from SAR images is closely related to the normalized radar cross section (NRCS). Previously, we have shown that ocean surface currents have a significant influence on the backscatter of electromagnetic (EM) signals and may be relevant to SAR measurements. According to this approach [15], the one-dimensional linear wave-current fractal ocean surface is

N−1 n 0 0 (s−2)n k0b n 0 y = f (x , t) = ∑ σCb 1 − C0 × sin k0b x − ωnt + ϕn (1) n=0 ωn p where ωn = gkn is the dispersion relationship; k0 = 2π/λ0 is the dominant ocean wave number, λ0 is the dominant wavelength; b (b > 1) is the scale factor for amplitude and frequency; σ is the standard r 2[1−b2(s−2)] deviation of f (x, t) which is related to the significant wave height hs by σ = hs/4; C = , 1−b2N(s−2) n and s (1 < s < 2) is the roughness coefficient of the fractal sea surface. Here, kn = k0b , ωn, ϕn are wave number, the radian frequency and the phase of the n-th wave components, respectively. The dispersion 2 relation for the coupled wave–current dynamics in deep water can be written as (ω − kC0) = kg, where g = 9.8 m/s is the acceleration due to gravity. After some mathematical manipulation, the EM backscatter coefficient for the coupled wave-current fractal sea surface is as [15]

∞ N−1 h n i 1 (s−2)n k0b γ(t) = 2 ∑ ∏ Jpn −2σkemCb × 1 − ω C0 cos θ L cos θ =− n p ∞ n=0 (2) N−1 1 n jpTξ(t) ×sinc kem sin θ + 2 ∑ pnk0b L e n=0 where L denotes the fractal sea surface over which the surface integration is carried out where T x ∈ [−L/2, L/2], Bessel functions are Jp(u), and p (p0, p1, p2,... pN−1) , pn = −∞, ... , −2, −1, 0, 1, 2, ... + ∞; T ξ(t) = [ζ0(t), ζ1(t), ζ2(t) ... ζN−1(t)] . For remote sensing with RADARSAT-2 SAR, this latter equation suggests that we can calculate the NRCS of the fractal sea surface with the following expression:

σ0 = 2 log10 γ (3) where the frequencies of the transmitter and receiver are both f = 5.4 GHz; the electromagnetic wavenumber is k = 2π f /v, where v = 3 × 108 m/s. Letting N = 25, s = 1.3, b = 2e/3, and dominant Remote Sens. 2017, 9, 1321 3 of 13

wavelength λ0 = 200 m, then the dominant wavenumber is given by k0 = 2π/λ0. Assuming sea state conditions where significant wave heights of 2 m, σ is taken as 0.5, and the illumination area is L = 10λ0. To find the effect of ocean currents on the EM backscatter of the fractal sea surface, the above parameters are applied to our EM backscatter model for an assumed 1D drifting fractal sea surface. As an example, the ocean current velocities are assumed to range from −1.5 m/s to 1.5 m/s in steps of 0.5 m/s in our simulations. The NRCSs of these wave–current effects in the coupled ocean surface model, with incidence angles ranging from 0◦ to 70◦, have been computed in our previous work [16]. Obviously, the NRCS is different when the incidence angle has a fixed value. Based in the approach given above, we analyzed full polarimetric SAR images, the buoy measurements of surface wind vectors and high-frequency radar measurements of ocean surface currents to investigate the effect of the currents on the retrieved SAR winds. We will show that sea surface currents are a factor that causes error in the accuracy of the SAR retrieval wind field. Thus, a semi-empirical formula for associated modifications, or differentials, in the wind fields and surface currents are derived for the retrieval of the sea surface current field.

2. Data and Methods

2.1. Satellite, Buoy, and High-Frequency Radar Data Three types of data are used in this paper to analyze the effects of ocean currents on the winds retrieved from SAR images. They are radar backscatter from fully polarimetric SAR observations, winds from the National Data Buoy Center (NDBC) buoys and ocean currents from the Scripps Institution of Oceanography (SIO) High Frequency Radar National Network (HFRnet). Ocean wind speeds and directions are retrieved from RADARSAT-2 fine quad polarization SAR data. Ocean surface currents are measured by HF radar, including speeds and directions, which are overlain on the retrieved wind fields. Collocated co-temporal NDBC buoy data are used to validate the effectiveness of our experiment. In this approach, we used RADARSAT-2 SAR measurements as the source of the remotely sensed wind data. RADARSAT-2 SAR data have multiple polarization modes, including a fully polarimetric mode in which HH, VV, HV, and VH polarized data are acquired [17]. For the purpose of retrieval of ocean wind speed and direction, we selected the fine quad polarization mode. Because of the complex scattering coefficients (SVV and SVH) used in our retrieval method, the single-look complex (SLC) product type are used. Real(ρVVVH) and Imag(ρVVVH) are complex magnitudes which correspond to the real and imaginary parts of the scattering coefficients in the SLC products, respectively. To analyze the effects of ocean currents on retrieved wind vectors, we collected RADARSAT-2 images and collocated buoy and HF radar data from geographic locations located on the East and West Coasts of the USA, Gulf of Alaska, and the Gulf of Mexico. The NDBC (http://www.ndbc.noaa.gov/) buoy data are co-temporal and collocated with the SAR images. Each individual SAR image covers one NDBC buoy. Buoy measurements also include meteorological parameters (SST, wind speed, wind directions, and related variables) and wave information (such as wave period, wave direction, wave height). The wind speed measurements are adjusted to a height of 10 m. In addition, buoy measurements and the RADARSAT-2 observations are required to occur within a time difference of 30 min. Ocean currents play significant roles in the transportation of mass, nutrients, momentum, and heat [18]. Shore-based high-frequency (HF) radars with operating frequencies of 3–50 MHz are routinely used for remote sensing of coastal ocean surface currents [19]. The Integrated Ocean Observing System (IOOS) high frequency radar network (HFRnet, http://hfrnet.ucsd.edu/thredds/ catalog.html) provides continuous, wide-area ocean current observations in real-time over large coastal areas, with ranges up to 200 km off the coastline. In IOOS, there are primarily two types of HF radars, the Coastal Ocean Dynamics Application Radar (CODAR) and the Wellen Radar (WERA). CODAR long-range SeaSonde radars use a compact directional antenna system consisting of three antenna elements in a single housing for receiving backscatter signals and a separate omnidirectional antenna Remote Sens. 2017, 9, 1321 4 of 13 for transmitting frequency-modulated interrupted continuous radar pulses (FMICW). A WERA system is composed of two separate antenna arrays, one for receiving and the other for transmitting frequency-modulated, continuous wave chirps [20,21]. The HFRnet systems measure the speed and direction of ocean surface currents in near real time. Starting with about 30 radars in 2005, the network has grown to over 130 radars with 33 participating organizations and approximately 10 million radial files [22]. Current speeds and directions provided by these observations are averaged over 1 h periods. Accuracies of the radar-derived velocities have been shown to be typically in the range 5–10 cm/s, as reported in numerous studies. This program covers almost all of the coastal oceans of the United States and including the Great Lakes, East and West Coasts, Hawaii, and the gulfs of Alaska, Maine, and Mexico [23].

2.2. Retrieval Method of Winds from Radarsat-2 SAR Images The ocean backscatter in cross and co-polarizations are quite different. Cross-polarization is essentially independent of wind direction and local incidence angle but has a linear relationship with respect to wind speed [24]. A C-band cross-polarized ocean backscatter model (C-2PO) relating NRCS 0 in VH polarization σVH to equivalent neutral wind speed U10 at 10-m height reference height, has been developed using RADARSAT-2 fine quad-polarization mode SAR data and collocated buoy observations [25,26]. RADARSAT-2 fine quad-polarization mode SLC SAR data are characterized by a nominal spatial resolution of 8.0 × 5.4 m in azimuth and range. For each quad-polarization image with a specific beam mode, the pixel spacing in range and azimuth directions is about 5 m. SAR backscatter signals consist of the backscattered radar signal plus the receiver noise. By subtracting the noise component, and related analysis, the C-2PO model is

0 σVH = 0.580 × U10 − 35.652 (4)

0 where U10 is the wind speed at 10 m reference height and σVH is the NRCS of the VH polarization 0 signals. The units of U10 and σVH are in meters per second and decibels, respectively. Equation (4) can be used to estimate the wind speed. Using the retrieved wind speed and in situ radar incidence angles, we can retrieve wind directions with ambiguities; in this approach, the wind speeds and incidence angles are used as input to the geophysical model function (GMF) called CMOD5. N, as described by [27]. The formulation for CMOD5.N is

0 1.6 σVV(θ,U10, φ) = A0(θ,U10)[1 + A1(θ,U10) cos φ + A2(θ,U10) cos 2φ] (5) where θ, U10, and φ are the radar incidence angles, the wind speed, and the relative direction, respectively. Here, A0, A1, and A2 are coefficients which are dependent on the radar incidence angle and the wind speed. Real and imaginary parts of the polarimetric correlation coefficient (PCC) have odd symmetry with respect to wind direction. For satellite SAR, this odd symmetry of the observed polarimetric active backscatter agrees with theoretical considerations from rigorous derivations using the Maxwell’s equations, two-scale models, and other earlier airborne polarimetric scatterometer observations [28–30]. To solve the problem of the wind direction ambiguity, the odd-symmetry property is applied to remove the wind direction ambiguities in the C-2PO model. Thus, the correlation between VV and VH polarization channels is defined by the PCC as

∗ < SVV·SVH > ρVVVH = q (6) 2 2 < |SVV| >< |SVH| > where SVV is the scattering coefﬁcient of vertical transmitting and vertical receiving polarized ∗ backscatter, SVH is the complex conjugate of SVH which is the scattering coefﬁcient of vertical transmitting and horizontal receiving polarized backscatter. It should be pointed out that PCC Remote Sens. 2017, 9, 1321 5 of 13

Remote Sens. 2017, 9, 1321 5 of 13 (ρVVVH) is a complex number that indicates the degree of correlation and the relative phase angle of VV and VH polarized backscatter signals. Zhang et al. [31] utilized PCC’s odd characteristic to derive the criteria to facilitate the selection Zhang et al. [31] utilized PCC’s odd characteristic to derive the criteria to facilitate the selection of the of the relative wind direction among the possible values: ∅, 180 − ∅, 180 + ∅ and 360 − ∅ . The relative wind direction among the possible values: , 180 − , 180 + and 360 − . The criteria are criteria are ∅ ∅ ∅ ∅ ◦ ◦ RealReal(ρ(ρVVVH))<<0,Imag0, Imag(ρVVVH))>> 0,0, −180°−180 << ϕφ << −90°;−90 ;

Real(ρ) >0,Imag(ρ) >0,90°<ϕ<−0°;◦ ◦ Real(ρVVVH) > 0, Imag(ρVVVH) > 0, 90 < φ < −0 ; Real(ρ) <0,Imag(ρ) > 0, 0°◦ < ϕ < 90°;◦ Real(ρVVVH)< 0, Imag(ρVVVH) >0, 0 < φ < 90 ; Real(ρ) <0,Imag(ρ) > 0, 90°◦ < ϕ < 180°.◦ Real(ρVVVH)< 0, Imag(ρVVVH) >0, 90 < φ < 180 . where Real and Imag denote the real and imaginary parts of , respectively. where Real and Imag denote the real and imaginary parts of ρ , respectively. To summarize what has been mentioned above, the flowchartVVVH for retrieval of the wind field is To summarize what has been mentioned above, the ﬂowchart for retrieval of the wind ﬁeld is given in Figure 1. given in Figure1.

FigureFigure 1. 1. FlowchartFlowchart for for the the wind wind speed speed an andd direction direction retrieval retrieval algorithm. algorithm.

2.3.2.3. Validation Validation Method Method for for the the Effect Effect of of Oc Oceanean Currents Currents on on the the Winds Retrieved from SAR TheThe following following scheme scheme is is an an outline of the validation using our method:

(1)(1) RADARSAT-2RADARSAT-2 fine ﬁne quad-polarization quad-polarization mode mode SLC SLC SAR SAR data data are are characterized characterized by by a a nominal nominal spatial spatial resolutionresolution of of 8.0 8.0 ×× 5.4 m5.4 m inin azimuth azimuth and and range range and and the the pixel pixel spacing spacing in in range range and and azimuth azimuth directionsdirections is aboutabout 5 m.5 m. We We make make a 20 ×a 20 pixel× 20 boxcar pixel averageboxcar onaverage the NRCS, on the in eachNRCS, polarization, in each polarization,so that the resampled so that the pixel resampled spacing pixel is 100 spacing m. is 100 m

(2)(2) ExtractExtract geophysical geophysical parameters parameters and and SAR SAR system system information information from from quad-polarization RADARSAT-2RADARSAT-2 SAR SAR images, images, such such as as longitude, longitude, latitude, latitude, incident incident angles, angles, and and other other information information forfor each each pixel, pixel, track track angle, angle, radar radar look look direction. direction. (3) Use MATLAB to obtain the NRCS for VV, VH polarization images, and complex backscattering (3) Use MATLAB to obtain the NRCS for VV, VH polarization images, and complex backscattering coefficients S_VV, S_VH for each pixel, for each SAR image. coefficients S_VV, S_VH for each pixel, for each SAR image. (4) Firstly, we use the NRCS for VH polarization data to calculate wind speed at 10-m reference (4) Firstly, we use the NRCS for VH polarization data to calculate wind speed at 10-m reference height (U ) from Equation (4). Secondly, we use the NRCS for VV data to calculate wind height (U ) from Equation (4). Secondly, we use the NRCS for VV data to calculate wind direction direction with10 ambiguities from Equation (5). Finally, using the directional ambiguity removal with ambiguities from Equation (5). Finally, using the directional ambiguity removal criteria criteria previously mentioned, the final wind directions are obtained without ambiguities. previously mentioned, the final wind directions are obtained without ambiguities. (5) Collect ocean currents from HF radar and observed wind fields from NDBC buoys in the same (5) Collect ocean currents from HF radar and observed wind fields from NDBC buoys in the same location and time as the SAR images. location and time as the SAR images. (6) Analyze two groups of experiments. In the first group, directly retrieved winds (including wind speed and directions) from SAR are compared to the winds obtained from the corresponding buoy data and the errors are calculated. In the second group, the ocean current information (including the current speeds and directions), are overlaid on wind fields retrieved from SAR

Remote Sens. 2017, 9, 1321 6 of 13

(6) Analyze two groups of experiments. In the ﬁrst group, directly retrieved winds (including wind speed and directions) from SAR are compared to the winds obtained from the corresponding buoy data and the errors are calculated. In the second group, the ocean current information (including the current speeds and directions), are overlaid on wind ﬁelds retrieved from SAR images, again compared with the corresponding winds observed by buoys, and the errors are calculated. By comparing the errors calculated in both groups, the impact of ocean currents on the winds retrieved from SAR images at the sea surface can be estimated. Remote Sens. 2017, 9, 1321 6 of 13

It is importantimages, to again note compared that thethree with the data corresponding sets used for winds the observed matching by analysis,buoys, and namely the errors RADARSAT-2 are SAR image data,calculated. wind By vectors comparing measured the errors by calculated NDBC in buoys, both groups, andocean the impact current of ocean data currents observed on by HF radar must bethe simultaneous winds retrieved and from collocated. SAR images Generally, at the sea surface for spatial can be estimated. collocation, two points on the ocean surface must beIt lessis important than 2 kmto note apart. that If the the three time data interval sets used for obtainingfor the matching sea surface analysis, information namely is less than 30 min,RADARSAT-2 two events SAR in image time candata, be wind deemed vectors asmeas occurringured by NDBC at the buoys, same and time. ocean current data observed by HF radar must be simultaneous and collocated. Generally, for spatial collocation, two 3. Resultspoints and Discussion on the ocean surface must be less than 2 km apart. If the time interval for obtaining sea surface information is less than 30 min, two events in time can be deemed as occurring at the same time.

3.1. Effect of3. OceanResults Currentsand Discussion on the Retrieval of Sea Surface Wind from SAR

We selected3.1. Effect 168 of Ocean RADARSAT-2 Currents on the fully Retrieval polarimetric of Sea Surface SAR Wind images from SAR for this part of the study. Each SAR image is collocated and cotemporal with buoy wind vector measurements and HF radar measurements We selected 168 RADARSAT-2 fully polarimetric SAR images for this part of the study. Each of ocean surfaceSAR image current is collocated data. Theand RMScotemporal difference with buoy between wind vector of the measurements wind speeds and retrieved HF radar from the selected 168measurements SAR images of ocean and thesurface wind current speeds data. from The theRMS buoy difference data between is 1.62 m/sof the (Figure wind speeds2a). The RMS differenceretrieved between from the the wind selected directions 168 SAR derived images and from the SARwind dataspeeds and from those the buoy derived data is from 1.62 m/s buoy data is 15.87◦ (Figure(Figure2c). 2a). When The RMS the oceandifference currents between vectors the wind observed directions byderived the HFfrom radar SAR data are and overlaid those on SAR derived from buoy data is 15.87° (Figure 2c). When the ocean currents vectors observed by the HF retrieved windradar are ﬁelds, overlaid the on RMS SAR differenceretrieved wind between fields, the the RMS SAR-derived difference between wind the speeds SAR-derived and thewind buoy data ◦ is 1.28 m/sspeeds (Figure and2 theb) andbuoy fordata theis 1.28 wind m/s direction,(Figure 2b) and 12.26 for the(Figure wind direction,2d). In 12.26° other (Figure words, 2d). if In the ocean currents areother considered words, if the in ocean the retrievalcurrents are of considered wind ﬁelds in the from retrieval SAR of wind data, fields then from the SAR retrieved data, then accuracy of the retrieved accuracy of the wind speed is improved by about 0.3 m/s and for the wind direction, by the wind speed is improved by about 0.3 m/s and for the wind direction, by about 3◦. about 3°.

Figure 2. (a) SAR-retrieved wind speeds from C-2PO model compared to wind speeds observed by Figure 2. (buoya) SAR-retrieved measurements; ( windb) SAR-retrieved speeds from wind C-2POspeeds with model superimposed compared ocean to wind current speeds speeds observed by buoy measurements;compared to winds (speedsb) SAR-retrieved observed by buoys; wind (c) SAR-retrieved speeds with wind superimposed directions derived ocean from applying current speeds compared tothe winds C-2PO speedsmodel compared observed to wind by buoys; directions (c) observed SAR-retrieved by buoys; wind (d) SAR-retrieved directions derivedwind directions from applying the C-2POwith model superimposed compared ocean to windcurrent directions directions comp observedared to wind by buoys; directions (d observed) SAR-retrieved by buoys. wind directions

with superimposed ocean current directions compared to wind directions observed by buoys.

Remote Sens. 2017, 9, 1321 7 of 13

3.2. Ocean Current Vector Retrieval from Empirical Formulae Remote Sens. 2017, 9, 1321 7 of 13 If ocean surface currents are taken into account when surface winds are retrieved from fully polarimetric SAR images, the accuracy of the wind speed is improved by 0.3 m/s and the accuracy of 3.2. Ocean Current Vector Retrieval from Empirical Formulae the wind direction, by 3°. Therefore, the error in vector winds retrieved from SAR images relative to the Ifactual ocean wind surface vectors, currents namely are the taken difference into account wind whenfields surface(DWF), windsis partially are retrieved caused by from the fullyocean polarimetricsurface currents. SAR images, From theour accuracy analysis of of the 168 wind fully speed polarimetric is improved SAR by 0.3images m/s andand the the accuracy data from of thecorresponding wind direction, observed by 3◦. Therefore, buoy wind the vectors error in and vector HF windsradar retrievedmeasurements from SAR of ocean images surface relative currents, to the actualwe have wind estimated vectors, namelythe DWF. the differenceThus, we windcan linearly fields (DWF), fit the isDWF partially vector caused with bythe the vector ocean of surface the sea currents.surface currents From our measured analysis by of the 168 HF fully radar polarimetric to derive an SAR empirical images formula. and the dataThereafter, from corresponding 52 SAR images observedare reselected buoy windto make vectors the sea and surface HF radar wind measurements field inversion ofocean by using surface the above currents, mentioned we have model. estimated The theempirical DWF. Thus, formula we can is used linearly to obtain fit the the DWF sea vector surface with current the vector vectors. of the sea surface currents measured by the HF radar to derive an empirical formula. Thereafter, 52 SAR images are reselected to make the sea3.2.1. surface Empirical wind fieldFormulae inversion of Ocean by using Currents the above and DWF mentioned Vector model. The empirical formula is used to obtain the sea surface current vectors. The vector wind fields, denoted U, retrieved from SAR are decomposed into an east–west U V 3.2.1.component Empirical Formulae and a north–south of Ocean Currents component and DWF Vector, using a Cartesian coordinate system (positive ∅ X-axis points east and positive Y-axis points→ north), and the wind direction is represented by . Similarly,The vector vector wind winds fields, measured denoted byU SARthe, buoys, retrieved denoted from SARU are, are decomposed decomposed into as an U east–west (east– componentwest) and UVSAR and (north–south), a north–south with component wind directionVSAR, represented using a Cartesian as ∅ coordinate. The currents, system denoted (positive as XU-axis, are points decomposed east and positive into U Y -axisand pointsV , and north), the current and the directions wind direction are represented is represented as ∅ by.∅ SAR. → Similarly,As can vector be inferred winds measured from the bydefinition, the buoys, the denoted differentialUBouy wind, are field decomposed is the partial as U errorBouy (east–west)between the → vector winds retrieved from SAR data and the vector winds measured by buoys, i.e., U =U − and VBouy (north–south), with wind direction represented as ∅Bouy. The currents, denoted as USea, are U. Thus, the east–west component can be represented as U =U −U , and the north–south decomposed into USea and VSea, and the current directions are represented as ∅Sea. componentAs can be can inferred be represented from the definition, as V =V the differential−V. windFor the field 168 is fully the partial polarimetric error between SAR images, the vector we → → → retrieve the wind field information U and V, the corresponding buoy wind vectors U and winds retrieved from SAR data and the vector winds measured by buoys, i.e., UDif = UBouy − USAR. Thus, V, and the HF radar measurements of ocean surface currents, U and V. Thus, the relation the east–west component can be represented as UDif = UBouy − USAR, and the north–south component can between the east–west DWF velocities and the radar-measured current velocities can be obtained, as be represented as VDif = VBouy − VSAR. For the 168 fully polarimetric SAR images, we retrieve the wind shown in Equation (7); the relation between the north–south DWF velocities and the radar measured field information USAR and VSAR, the corresponding buoy wind vectors UBouy and VBouy, and the HF radar current velocities is shown in Equation (8). Figure 3 gives the corresponding scatter diagrams. measurements of ocean surface currents, USea and VSea. Thus, the relation between the east–west DWF velocities and the radar-measured currentDWF velocities(U) = 0.1455 can be × obtained, U − 0.022 as shown in Equation (7); the relation(7) between the north–south DWF velocities and the radar measured current velocities is shown in Equation (8). DWF(V) = 0.1518 × V − 0.019 (8) Figure3 gives the corresponding scatter diagrams.

FigureFigure 3. 3.Scatter Scatter diagrams diagrams between between the DWFthe DWF velocities velocities andHF and radar HF oceanradar currentocean current velocities, velocities, in which, in Uwhich, and V U represent and V represent the east–west the east–west and the and north–south the north–south DWF velocities, DWF velocities, respectively; respectively;DWF( UDWF) and(U) DWFand( VDWF) represent(V) represent the east–west the east–west and the and north–south the north–south ocean surface ocean surface current current velocities velocities measured measured by the HFby radar. the HF radar.

DWF(U) = 0.1455 × U − 0.022 (7)

Remote Sens. 2017, 9, 1321 8 of 13

3.2.2. Cases of Retrieved Ocean Currents The first example is a quad-polarization SAR image acquired on 9 January 2012, at 03:52:26 Remote Sens. 2017, 9, 1321 8 of 13 Coordinate Universal Time (UTC). This SAR image collocates with a NDBC buoy (#46035, 57°133 N 177°44′16 W) in the Bering Sea. The buoy-measured 10-m equivalent neutral wind speed and wind direction DWFare U(V) = =11.5 m/s0.1518 × Vand− 0.019∅ = 266° at 03:50 UTC. (8) Following our methodology as described above, we first use the quad-polarization SAR image 3.2.2. Casesto calculate of Retrieved the complex Ocean backscatter Currents coefficients, and , for each pixel. Therefore, the NRCS Remote Sens. 2017, 9, 1321 8 of 13 values are = || and = || . The NRCS images in VV polarization and VH Thepolarization, first example corresponding is a quad-polarization to the SAR image SAR are sh imageown in acquired Figure 4. onThe 9parameters January 2012,extracted at 03:52:26for 3.2.2. Cases of Retrieved Ocean Currents Coordinate Universal Time (UTC). This SAR image collocates with a NDBC buoy (#46035, this SAR image for ocean surface wind fields are as follows: the wind speed |U| =9.85 m/s and ◦ 0 00 ◦ 0 00 57 1 33theN Thewind177 first direction44 example16 W∅ )is in a= quad-polarization the 252° Bering. These are Sea. shown SAR The inimage buoy-measured Figure acquired 5a. on 10-m9 January equivalent 2012, at neutral03:52:26 wind → Coordinate Universal Time (UTC). This SAR image collocates◦ with a NDBC buoy speed(#46035, and wind 57°1 direction33 N 177°44′16 are UBouy W) in= the11.5 Bering m/s Sea. and The∅Bouy buoy-measured= 266 at 03:50 10-m UTC. equivalent neutral Following our methodology as described above, we first use the quad-polarization SAR image wind speed and wind direction are U =11.5 m/s and ∅ = 266° at 03:50 UTC. to calculateFollowing the complex our methodology backscatter as coefficients,described above,SVV weand firstSVH use, forthe eachquad-polarization pixel. Therefore, SAR image the NRCS = 2 = 2 valuesto are calculateσVV the|S VVcomplex| and backscatterσVH |SVH coefficients,| . The NRCS and images , in for VV each polarization pixel. Therefore, and VH the polarization,NRCS correspondingvalues are to the = SAR| image| and are shown= | in| .Figure The NRCS4. The images parameters in VV extracted polarization for this and SAR VH image → for oceanpolarization, surface windcorresponding fields are to as the follows: SAR image the windare sh speedown in| UFigure| 4.= The9.85 parametersm/s and theextracted wind for direction SAR this SAR◦ image for ocean surface wind fields are as follows: the wind speed |U| =9.85 m/s and ∅SAR = 252 . These are shown in Figure5a. the wind direction ∅ = 252°. These are shown in Figure 5a.

Figure 4. RADARSAT-2 SAR image of the Bering Sea at 03:52:26 on 9 January 2012 showing VH polarization (left) and VV polarization (right). The location of NDBC buoy 46,035 is indicated.

The vector winds retrieved from the SAR images, U, are decomposed in the Cartesian coordinate system described above. Thus, the east–west component is U = −9.37 m/s and the north–south component is V = −3.04 m/s. For vector winds taken from the buoy measurements,

U, the east–west component is U = −11.47 m/s, and the north–south component is V = −0.82 m/s. In this paper, the DWF vectors are defined as the differences between the buoy wind field vectors and the wind field vectors retrieved from the SAR images. Therefore, the east–west DWF is UFigure=U 4. RADARSAT-2−U = −2.11 m/s SAR image, and of the north–southBering Sea at differential03:52:26 on 9wind January velocity 2012 showingis V =VVH − Figure 4. RADARSAT-2 SAR image of the Bering Sea at 03:52:26 on 9 January 2012 showing VH V polarization=2.2 m/s (. leftTherefore,) and VV thepolarization resulting (right speed). The of locationthe DWF of synthesizedNDBC buoy 46,035 vector is isindicated. given by |U| = polarization (left) and VV polarization (right). The location of NDBC buoy 46,035 is indicated. 3.04 m/s and for direction, ∅ = 316° (Figure 5b). The vector winds retrieved from the SAR images, U, are decomposed in the Cartesian coordinate system described above. Thus, the east–west component is U = −9.37 m/s and the north–south component is V = −3.04 m/s. For vector winds taken from the buoy measurements,

U =U −U = −2.11 m/s, and the north–south differential wind velocity is V =V − V =2.2 m/s. Therefore, the resulting speed of the DWF synthesized vector is given by |U| = 3.04 m/s and for direction, ∅ = 316° (Figure 5b).

Figure 5. (a) SAR-retrieved wind speed using the C-2PO model and retrieved wind directions Figure 5. (a) SAR-retrieved wind speed using the C-2PO model and retrieved wind directions without ambiguities derived from PCC between the VV and VH channels; (b) DWF wind speeds withoutand ambiguities wind directions. derived from PCC between the VV and VH channels; (b) DWF wind speeds and wind directions.

→ The vector winds retrieved from the SAR images, USAR, are decomposed in the Cartesian coordinate system described above. Thus, the east–west component is USAR = −9.37 m/s and the north–south component is VSAR = −3.04 m/s. For vector winds taken from the buoy measurements, → UBouy, theFigure east–west 5. (a) SAR-retrieved component wind is UspeedBouy using= −the11.47 C-2POm/s model, and and retrieved the north–south wind directions component is VBouy = −without0.82 m/s ambiguities. In this derived paper, from the DWFPCC between vectors the are VV definedand VH channels; as the differences (b) DWF wind between speeds the buoy wind fieldand vectors wind anddirections. the wind field vectors retrieved from the SAR images. Therefore, the east–west DWF is UDWF = UBouy − USAR = −2.11 m/s, and the north–south differential wind velocity is

VDWF = VBouy − VSAR = 2.2 m/s. Therefore, the resulting speed of the DWF synthesized vector is → ◦ given by |UDWF| = 3.04 m/s and for direction, ∅DWF = 316 (Figure5b).

Remote Sens. 2017, 9, 1321 9 of 13

Remote Sens. 2017, 9, 1321 9 of 13 According to the empirical Equations (7) and (8), the east–west and the north–south components According to the empirical Equations (7) and (8), the east–west and the north–south components of the ocean surface current vector are Ure = −0.28 m/s and Vre = 0.31 m/s, respectively. Thus the → of the ocean surface current vector are U = −0.28 m/s andq V =0.31 m/s, respectively. Thus the speed of the synthesized ocean current vector is |U | = U2 + V2 = 0.42 m/s, with the direction, re re re speed of the◦ synthesized ocean current vector is |U| = U +V = 0.42 m/s, with the direction, ∅re = 306.2 . These results are given in Figure6. The current speed measured by the HF radar at the ∅ = 306.2°. These results are→ given in Figure 6. The current speed measured by the HF radar at the ◦ same time and location is UHF = 0.478 m/s, and the current direction is ∅HF = 311.8 . The error in same time and location is U = 0.478 m/s, and the current direction is ∅ = 311.8°. The error in thethe retrieved retrieved current current speed speed is is 0.072 0.072 m/s m/s and and the the error error in in the the current current direction direction is is 5.6°. 5.6◦ .These These results results are are shownshown in in Table Table 11..

FigureFigure 6. 6. DistributionDistribution map map for for re retrievedtrieved ocean ocean currents currents ( (leftleft: :units units are are centimeters centimeters per per second) second) and and directionsdirections ( (rightright: :units units are are degrees, degrees, blue blue vectors vectors are are retrie retrieved-oceanved-ocean directions directions and and red red vectors vectors are are measuredmeasured by by HF HF radar, radar, respective respectively).ly). The The ocean ocean current current speed is 42 cm/s and and corresponding corresponding current current directiondirection is is 317.6° 317.6◦ at at buoybuoy #46035.#46035.

TableTable 1. 1. WindsWinds retrieved retrieved from from fully fully polarimetric polarimetric SA SARR images images and and NDBC NDBC buoy buoy #46035, #46035, ocean ocean surface surface currentscurrents measured measured by by HF HF radar radar and and retrieved retrieved ocean ocean currents. currents. Parameters Parameters of of four four kinds kinds of of data data are are simultaneoussimultaneous and and collocated. collocated. Data Data are are received received on on 9 9 January January 2012. 2012. SAR Image Buoy Data HF Radar Retrieval Currents Time SAR03:52 Image Buoy03:50 Data HF04:00 Radar Retrieval03:50 Currents Time57.036°N 03:52 57.026°N 03:50 57.020°N 04:00 57.026°N 03:50 Site 177.64°W 177.74°W 177.68°W 177.74°W 57.036◦ N 57.026◦ N 57.020◦ N 57.026◦ N Site Wind speed◦ Wind speed◦ Current speed◦ Current speed◦ Wind/current speed 177.64 W 177.74 W 177.68 W 177.74 W 9.85 m/s 11.5 m/s 0.478 m/s 0.406 m/s Wind speed Wind speed Current speed Current speed Wind/current speed Wind direction Wind direction Current direction Current direction Wind/current direction 9.85 m/s 11.5 m/s 0.478 m/s 0.406 m/s 252° 266° 323.4° 317.6° Wind direction Wind direction Current direction Current direction Wind/current direction 252◦ 266◦ 323.4◦ 317.6◦ The second SAR image was acquired on 19 January 2013, at 02:12 UTC. This SAR image collocates with a NDBC buoy #LKWF1 (26°3646N, 80°2′2W) off the U.S. Southeast Coast, off The second SAR image was acquired on 19 January 2013, at 02:12 UTC. This SAR image collocates with a Florida. The buoy-measured 10 m equivalent neutral wind direction and speed are ∅ = 57° and ◦ 0 00 ◦ 0 00 NDBC buoy #LKWF1 (26 36 46 N, 80 2 2 W) off the U.S. Southeast Coast, off Florida. The buoy-measured U =8.9 m/s at 02:10 UTC. → ◦ 10 mUsing equivalent the same neutral verification wind direction procedures and speed as areapplied∅Bouy in= Case57 and 1, the U BouyVH and= 8.9 VV m/s polarized at 02:10 UTC.radar backscatterUsing thecoefficients same verification were determined, procedures asas applied shown in in Case Figure 1, the 7. VH The and resulting VV polarized incidence radar angle backscatter and windcoefficients speed were at each determined, pixel are as shownsubstituted in Figure into7. TheCMOD5.N resulting to incidence calculate angle the andwind wind direction, speed at with each ambiguities.pixel are substituted Using the into directional CMOD5.N ambiguity to calculate removal the wind criteria direction, previously with ambiguities. mentioned, Using the the final directional wind ambiguity removal criteria previously mentioned, the final wind direction, without ambiguities, is then direction, without ambiguities, is then calculated. The wind speed→ retrieved from the SAR image is |calculated.U| = 10.52 m/s The wind and speed wind retrieved direction, from ∅ the= SAR 41° imageas shown is |U SARin Figure| = 10.52 7c. m/sThe speedand wind of the direction, DWF → ◦ synthesized∅SAR = 41 vectoras shown |U in Figure| is 3.14 m/s7c. The speed and ofthe the direction DWF synthesized ∅ is 169.6° vector | asUDWF shown| is 3.14 in Figurem/s and 7d. the ◦ directionAccording∅DWF isto 169.6 the empiricalas shown informula Figure 7fromd. Section 3.2.1, the east–west and the north–south components of the sea current vector are U = −0.059 m/s and V = 0.037 m/s, respectively. Thus, the speed of the synthesized ocean current vector is |U| = U +V = 0.38 m/s and the direction is ∅ = 171°, as indicated in Figure 8. The current speed measured by the HF radar at the same time and location is U = 0.465 m/s, and the current direction is ∅ = 177.2°. The error in retrieval of the speed is 0.085 m/s and the error in the current direction is 6.2°. All the data are shown in Table 2.

Remote Sens. 2017, 9, 1321 10 of 13

Figure 7. RADARSAT-2 SAR image in the North Atlantic, off Florida, at 02:12:56 on 19 January 2013, Figure 7. RADARSAT-2collocated with SARNDBCimage buoy LKWF1 in the showing: North ( Atlantic,a) VH polarization; off Florida, (b) VV at polarization; 02:12:56 on(c) SAR- 19 January 2013, collocated withderived NDBC wind buoy fields; LKWF1and (d) DWF showing: wind fields. (a) VH polarization; (b) VV polarization; (c) SAR-derived wind ﬁelds; and (d) DWF wind ﬁelds.

According to the empirical formula from Section 3.2.1, the east–west and the north–south components of the sea current vector are Ure = −0.059 m/s and Vre = 0.037 m/s, respectively. Thus, the speed of → q 2 2 ◦ the synthesized ocean current vector is |Ure| = Ure + Vre = 0.38 m/s and the direction is ∅re = 171 , as indicated in Figure8. The current speed measured by the HF radar at the same time and location → ◦ is UHF = 0.465Figurem/s 7., RADARSAT-2 and the current SAR image direction in the North is ∅ Atlantic,HF = 177.2off Florida,. The at 02:12:56 error on in 19 retrieval January 2013, of the speed is

collocated with NDBC buoy LKWF1 showing: ◦(a) VH polarization; (b) VV polarization; (c) SAR- 0.085 m/s and thederivedFigure error 8.wind inRetrieved-ocean thefields; current and (d )current DWF direction wind(left) fields.and is 6.2 directions . All the(right data, blue are vectors shown are retrieved-ocean in Table2. directions and red vectors are measured by HF radar) distribution map. Units are centimeters per second, and degrees, respectively. The ocean current speed is 46.5 cm/s and the corresponding current direction is 177.2° at buoy #LKWF1.

Table 2. Winds retrieved from fully polarimetric SAR images and NDBC buoy ##LKWF1, ocean surface currents measured by HF radar and retrieved ocean currents. Parameters of four kinds of data are simultaneous and collocated. Data are received on 19 January 2013.

Sar Image Buoy Data Hf Radar Retrieval Currents Time 02:12 02:12 04:00 03:50 26.602°N 26.613°N 26.587°N 26.613°N Site 80.145°W 80.034°W 80.098°W 80.034°W Wind speed Wind speed Current speed Current speed Wind/current speed 10.52 m/s 8.9 m/s 0.465 m/s 0.380 m/s Wind direction Wind direction Current direction Current direction FigureWind/current 8. Retrieved-ocean direction current (left) and directions (right, blue vectors are retrieved-ocean 41° 57° 177.2° 171° Figure 8. Retrieved-oceandirections and red current vectors (areleft measured) and directions by HF radar) (right distribution, blue vectors map. Units are retrieved-ocean are centimeters per directions and red vectors are measured by HF radar) distribution map. Units are centimeters per second, and second, and degrees, respectively. The ocean current speed is 46.5 cm/s and the corresponding current degrees, respectively.direction is 177.2° The ocean at buoy current #LKWF1. speed is 46.5 cm/s and the corresponding current direction is 177.2◦ at buoy #LKWF1. Table 2. Winds retrieved from fully polarimetric SAR images and NDBC buoy ##LKWF1, ocean surface currents measured by HF radar and retrieved ocean currents. Parameters of four kinds of data Table 2. Windsare simultaneous retrieved from and collocated. fully polarimetric Data are received SAR imageson 19 January and NDBC2013. buoy ##LKWF1, ocean surface

currents measured by HF radar and Sar retrieved Image ocean Buoy Data currents. Hf Parameters Radar Retrieval of four Currents kinds of data are simultaneous and collocated.Time Data are02:12 received on 1902:12 January 2013.04:00 03:50 26.602°N 26.613°N 26.587°N 26.613°N Site 80.145°W 80.034°W 80.098°W 80.034°W Sar Image Buoy Data Hf Radar Retrieval Currents Wind speed Wind speed Current speed Current speed Wind/current speed Time 02:1210.52 m/s 8.9 02:12 m/s 0.465 04:00 m/s 0.380 03:50 m/s 26.602Wind◦ directionN Wind26.613 direction◦ N Current26.587 direction◦ N Current26.613 direction◦ N Wind/currentSite direction ◦ ◦ ◦ ◦ 80.145 41°W 80.03457° W 80.098177.2° W 80.034171° W Wind speed Wind speed Current speed Current speed Wind/current speed 10.52 m/s 8.9 m/s 0.465 m/s 0.380 m/s Wind direction Wind direction Current direction Current direction Wind/current direction 41◦ 57◦ 177.2◦ 171◦

Remote Sens. 2017, 9, 1321 11 of 13

4. Discussion Remote Sens. 2017, 9, 1321 11 of 13 To make a better verification of the retrieval methodology for sea currents, 52 fully polarized SAR4. imagesDiscussion are reselected for retrieval of the wind fields using the C-2PO model. Thereafter, the correspondingTo make wind a better vector verification is determined of the retrieval from the methodology buoy measurements for sea curr andents, the 52 datafully ofpolarized the DWF fields are calculated.SAR images Theare reselected retrieved for east–west retrieval andof the the wind north–south fields using sea the components C-2PO model. of theThereafter, current the speeds are comparedcorresponding to the currentwind vector velocity is determined measured from by the the buoy HF radarmeasurements data, and and the the current data of fieldthe DWF vectors are constructed,fields are ascalculated. shown inThe Figure retrieved9. The east–west root-mean-square and the north–south error of sea the components sea current of velocity the current calculated by thespeeds empirical are compared formula to the given current in Equations velocity measur (7) anded by (8) the is HF 12.42 radar cm/s data, and and the the errorcurrent in field the current directionvectors is are 6.32 constructed,◦. It is important as shown in to Figure mention 9. The that root-mean-square the satellite retrieved error of the ocean sea current surface velocity currents are calculated by the empirical formula given in Equations (7) and (8) is 12.42 cm/s and the error in the only the wind-driven component of currents, and do not include the bulk currents, or wave induced current direction is 6.32°. It is important to mention that the satellite retrieved ocean surface currents currentsare only such the as wind-driven Langmuir component circulation of andcurrents, Stoke and drift. do not In addition,include the wind bulk currents, driven currentsor wave require aboutinduced one inertial currents period such as to Langmuir come into circulation balance an withd Stoke the drift. winds; In addition, therefore wind these driven comparisons currents using instantaneousrequire about observations one inertial period from satelliteto come into and ba buoyslance havewith the additional winds; therefore variability these (errors) comparisons because they are notusing always instantaneous in equilibrium. observations For from the 168 satellite SAR imagesand buoys selected have additional in this paper, variability the sea (errors) surface wind speedsbecause are aboutthey are 8–12 not m/s,always with in equilibrium. the higher For velocities, the 168 greaterSAR images than selected 15 m/s, in removed.this paper, Thisthe sea is because the effectsurface of wind the oceanspeeds surfaceare about currents 8–12 m/s, on with wind the fields higher retrieved velocities, from greater SAR than images 15 m/s, is moreremoved. observable This is because the effect of the ocean surface currents on wind fields retrieved from SAR images is under moderate or low wind conditions. However, the C-2PO wind retrieval model is more applicable more observable under moderate or low wind conditions. However, the C-2PO wind retrieval model for moderate-to-highis more applicable windfor moderate-to-high speeds, rather thanwind lowspee winds.ds, rather In than this paper,low winds. the retrieval In this paper, methodology the for sea surfaceretrievalcurrents methodology is proposed for sea surface for SAR currents images, is pr alsooposed using for wind SAR vectorimages, data also fromusing buoy wind measurementsvector anddata ocean from surface buoy measurements currents measured and ocean by HFsurface radar. curr Itents is notablemeasured that by HF the radar. retrieval It is methodologynotable that is an empiricalthe retrieval formula methodology given in is Equations an empirical (7) formula and (8). given Since in theEquations magnitude (7) andof (8). the Since ocean the magnitude surface current is relativelyof the small,ocean surface a small current error in is calculation relatively small, can generate a small error a large in differencecalculation incan the generate final result. a large Therefore, its applicabilitydifference in the and final accuracy result. Therefore, need to be its further applicab improved.ility and accuracy In future need studies, to be further a highly improved. accurate In relation future studies, a highly accurate relation between the DWF and the ocean surface currents shall be between the DWF and the ocean surface currents shall be based on more accurate experimental field based on more accurate experimental field data observations, on a more accurate retrieval model for datamarine observations, winds, as on well a moreas on accuratethe dynamical retrieval modelling model of forthe marineinteractions winds, between as well the ascurrents on the and dynamical modellingthe winds. of the interactions between the currents and the winds.

Figure 9. (a) Retrieved ocean surface current speeds in the east–west direction from empirical Figure 9. (a) Retrieved ocean surface current speeds in the east–west direction from empirical formulae formulae given in Equations (7) and (8) versus HF radar measurements; (b) Retrieved sea current given in Equations (7) and (8) versus HF radar measurements; (b) Retrieved sea current speeds of speeds of south–north direction from empirical formulae in Equations (7) and (8) versus HF radar south–north direction from empirical formulae in Equations (7) and (8) versus HF radar measurements; (c) Synthetic current speeds in the east–west and south–north direction versus HF radar measurements; (d) Synthetic current directions versus HF radar measurements. Remote Sens. 2017, 9, 1321 12 of 13

5. Conclusions In this paper, we ﬁrst use 168 full polarimetric SAR images from RADARSAT-2, apply the C-2PO wind retrieval model and CMOD5.N GMF as well as wind direction ambiguity removal methods to retrieve the ocean surface wind vectors. Applying the corresponding ocean currents from HF radar measurements and vector winds from buoy observations, we use vector analysis to explore the effect of ocean currents on the retrieval of wind ﬁelds from SAR images. The results suggest that when current speeds and directions are taken into consideration, the accuracy of wind speeds retrieved from SAR images is improved by about 0.3 m/s and wind directions are improved by about 3◦. Thus, we present empirical Equations (7) and (8) to estimate the ocean surface current speed from data collected by SAR fully polarimetric images, wind vectors measured by buoys, and currents measured by the HF radar system. Experimental results show that the retrieval formula using the DWF data method provide results in a good agreement with the ones given by the HF radar observed data. Furthermore, the main conclusion of this work is that the empirical formulae in Equations (7) and (8) can be considered a reliable tool for estimates of ocean surface currents under moderate and low wind speed conditions (5–15 m/s) as provided by corresponding SAR images.

Acknowledgments: This work was supported by the National Natural Science Foundation of China (41776181), the National Key Research and Development Program of China (2016YFC1401007), the Global Change Research Program of China (Grant No. 2015CB953901), the Canadian Program on Energy Research and Development, the Canadian Space Agency’s DUAP program, and the USA Office of Naval Research, Code 322, “Arctic and Global Prediction”, directed by Drs. Martin Jeffries and Scott Harper. (Grant number and Principal Investigator: Perrie, N00014-15-1-2611). Author Contributions: Tao Xie conceived and designed the experiments. He Fang and Li Zhao performed the experiments. Jingsong Yang and Yijun He supervised the work. He Fang, Tao Xie, and William Perrie wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Klemas, V. Remote Sensing of Coastal and Ocean Currents: An Overview. J. Coast. Res. 2012, 28, 576–586. [CrossRef] 2. Zuckerman, S.; Anderson, S.P.; Stuart, G.; Cooper, C. Real-time Ocean Surface current measurements in the Gulf of Mexico. IEEE Oceans 2015, 1–6. [CrossRef] 3. Paduan, J.D.; Washburn, L. High-Frequency Radar Observations of Ocean Surface Currents. Annu. Rev. Mar. Sci. 2013, 5, 115–136. [CrossRef][PubMed] 4. Romeiser, R.; Breit, H.; Eineder, M.; Runge, H.; Flament, P. Current measurements by sar along-track interferometry from a space shuttle. IEEE Trans. Geosci. Remote Sens. 2005, 10, 2315–2324. [CrossRef] 5. Hansen, M.W.; Collard, F.; Dagestad, K.-F.; Johannessen, J.; Fabry, P.; Chapron, B. Retrieval of Sea Surface Range Velocities from Envisat ASAR Doppler Centroid Measurements. IEEE Geosci. Remote Sens. 2011, 49, 3582–3592. [CrossRef] 6. Toporkov, J.V.; Hwang, P.A.; Sletten, M.A.; Farquharson, G.; Perkovic, D.; Frasier, S.J. Surface Velocity Proﬁles in a Vessel’s Turbulent Wake Observed by a Dual-Beam Along-Track Interferometric SAR. IEEE Geosci. Remote Sens. Lett. 2011, 8, 602–606. [CrossRef] 7. Qazi, W.A.; Emery, W.J.; Fox-Kemper, B. Computing Ocean Surface Currents over the Coastal California Current System Using 30-Min-Lag Sequential SAR Images. IEEE Geosci. Remote Sens. 2014, 52, 7559–7580. [CrossRef] 8. Perrie, W.; He, Y.; Li, H.; Fang, H.; Zhao, S.; Yu, W. Ocean surface wave measurements from fully polarimetric SAR imagery. Sci. China Earth Sci. 2015, 10, 1849–1861. 9. Perrie, W.; Xie, T. Gulf Stream thermal fronts detected by synthetic aperture radar. In Proceedings of the IEEE International Geoscience & Remote Sensing Symposium, Honolulu, HI, USA, 25–30 July 2010. 10. Kuang, H.; Perrie, W.; Xie, T. Retrievals of sea surface temperature fronts from SAR imagery. J. Geophys. Res. Lett. 2012, 10, 1–7. [CrossRef] Remote Sens. 2017, 9, 1321 13 of 13

11. Kelly, K.A.; Dickinson, S.; Mcphaden, M.J.; Johnson, G.C. Ocean currents evident in satellite wind data. J. Geophys. Res. Lett. 2001, 28, 2469–2472. [CrossRef] 12. Zhang, F.W.; Drennan, W.M.; Haus, B.K. On wind-wave-current interactions during the Shoaling Waves Experiment. J. Geophys. Res. Oceans 2009, 14, 287–295. [CrossRef] 13. Small, R.J.; Richards, K.J.; Xie, S.P. Damping of Tropical Instability Waves caused by the action of surface currents on stress. J. Geophys. Res. 2009, 114, 553–556. [CrossRef] 14. O’Neill, L.W.; Chelton, D.B.; Esbensen, S.K. High-Resolution Satellite Measurements of the Atmospheric Boundary Layer Response to SST Variations along the Agulhas Return Current. J. Clim. 2005, 14, 2706–2723. [CrossRef] 15. Xie, T.; Zhao, D.; Perrie, W.; Fang, H. Electromagnetic backscattering from one-dimensional drifting fractal sea surface I: Wave-current coupled model. Chin. Phys. B 2016, 4, 79–102. [CrossRef] 16. Xie, T.; Perrie, W.; Zhao, D.; Fang, H. Electromagnetic backscattering from one-dimensional drifting fractal sea surface II: Electromagnetic backscattering model. Chin. Phys. B 2016, 6, 64–101. [CrossRef] 17. MacDonald, Dettwiler and Associates (MDA). Radarsat-2 Product Description; MDA: Richmond, BC, Canada, 2015. 18. Kohut, J.T.; Glenn, S.M.; Chant, R.J. Seasonal current variability on the New Jersey inner Shelf. J. Geophys. Res. 2013, 109.[CrossRef] 19. Emery, B.M.; Washburn, L.; Harlan, J.A. Evaluating radial current measurements from CODAR High-frequency radars with moored current meters. J. Atmos. Ocean. Technol. 2004, 21, 1259–1271. [CrossRef] 20. Liu, Y.; Weisberg, R.H.; Merz, C.R. Assessment of CODAR and WERA HF radars in mapping currents on the West Florida Shelf. J. Atmos. Ocean. Technol. 2014, 31, 1363–1382. [CrossRef] 21. Shen, Z.; Wu, X.; Lin, H.; Chen, X.; Xu, X.; Li, L. Spatial Distribution Characteristics of Surface Tidal Currents in the Southwest of Taiwan Strait. J. Ocean Univ. China 2014, 13, 971–978. [CrossRef] 22. Harlan, J.; Terrill, E.; Hazard, L.; Otero, M.; Roarty, H. The Integrated Ocean Observing System HF radar network. In Proceedings of the IEEE Washington OCEANS’15 MTS, Washington, DC, USA, 19–22 October 2015. 23. Temll, E.; Otero, M.; Hazard, L.; Conlee, D.; Harlan, J.; Kohut, J.; Reuter, P.; Cook, T.; Harris, T. Lindquist. Data Management and Real-time Distribution in the HF-Radar National Network. In Proceedings of the IEEE Oceans, Boston, MA, USA, 18–21 September 2006. 24. Hwang, P.A.; Zhang, B.; Toporkov, J.V.; Perrie, W. Comparison of composite Bragg theory and quad-polarization radar backscatter from RADARSAT-2: With application radar backscatter from RADARSAT-2: With applications to wave breaking and high wind retrieval. J. Geophys. Res. 2010, C8, 246–255. 25. Vachon, P.W.; Wolfe, J. C-Band Cross-Polarization Wind Speed Retrieval. IEEE Geosci. Remote Sens. Lett. 2011, 3, 456–459. [CrossRef] 26. Zhang, B.; Perrie, W. Cross-Polarized Synthetic Aperture Radar: A New Potential Measurement Technique for Hurricanes. Bull. Am. Meteorol. Soc. 2012, 93, 531–541. [CrossRef] 27. Hersbach, H. Comparison of C-band scatterometer CMOD5.N equivalent neutral winds with ECMWF. J. Atmos. Ocean. Technol. 2010, 4, 721–736. [CrossRef] 28. Yueh, S.H.; Kwok, R.; Nghiem, S.V. Polarimetric scattering and emission properties of targets with reﬂection symmetry. J. Radio Sci. 2016, 29, 1409–1420. [CrossRef] 29. Yueh, S.H. Modeling of Wind Direction Signals in Polarimetric Sea Surface Brightness Temperatures. J. IEEE Geosci. Remote Sens. 1995, 35, 1400–1418. [CrossRef] 30. Tsai, W.Y.; Nghiem, S.V.; Huddleston, J.N. Polarimetric scatterometry: A promising technique for improving ocean surface wind measurements from space. J. IEEE Geosci. Remote Sens. 2000, 38, 1903–1921. [CrossRef] 31. Zhang, B.; Perrie, W.; Vachon, P.W. Ocean Vector Winds Retrieval from C-Band Fully Polarimetric SAR Measurements. IEEE Geosci. Remote Sens. 2012, 11, 4252–4261. [CrossRef]

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).