Empirical Algorithm for Signiﬁcant Wave Height Retrieval from Wave Mode Data Provided by the Chinese Satellite Gaofen-3

: Gaofen-3 (GF-3), the first Chinese civil C-band synthetic aperture radar (SAR), was successfully launched by the China Academy of Space Technology on 10 August 2016. Among its 12 imaging modes, wave mode is designed to monitor the ocean surface waves over the open ocean. An empirical retrieval algorithm of signiﬁcant wave height (SWH), termed Quad-Polarized C-band WAVE algorithm for GF-3 wave mode (QPCWAVE_GF3), is developed for quad-polarized SAR measurements from GF-3 in wave mode. QPCWAVE_GF3 model is built using six SAR image and spectrum related parameters. Based on a total of 2576 WaveWatch III (WW3) and GF-3 wave mode match-ups, 12 empirical coefﬁcients of the model are determined for 6 incidence angle modes. The validation of the QPCWAVE_GF3 model is performed through comparisons against independent WW3 modelling hindcasts, and observations from altimeters and buoys from January to October in 2017. The assessment shows a good agreement with root mean square error from 0.5 m to 0.6 m, and scatter index around 20%. In particular, applications of the QPCWAVE_GF3 model in SWH estimation for two storm cases from GF-3 data in wave mode and Quad-Polarization Strip I mode are presented respectively. Results indicate that the proposed algorithm is suitable for SWH estimation from GF-3 wave mode and is promising for other similar data.


Introduction
Ocean surface wave measurements are valuable for various areas. Significant wave height (SWH) is one of the most important parameters for ocean wave observations. For decades, the space-borne synthetic aperture radars (SARs) have demonstrated the capability to provide ocean wave spectra and/or SWH at high spatial resolution under all weather conditions [1][2][3]. Especially, the so-called Wave Mode (WM), adopted by European SARs aboard ERS-1/2, Envisat, and recently launched Sentinel-1A/B, can provide information on ocean swells in open ocean and ice-covered regions at a global scale since 1991 [4][5][6][7]. The SAR WM products have been widely used in the various applications, such as ocean wave operational assimilation at weather centers [8], monitoring of swell propagation [5,6], and detection of crossing swells [9,10].

GF-3 SAR WM Data
The Level-1A GF-3 WM data, single look complex (SLC) images, used here were taken from January to October 2017, covering a period of 10 months. In WM, which is dedicated to observing ocean surface waves over open ocean, GF-3 collects small SAR images (called imagettes, see examples in Figure 1) with an approximate size of 5 km × 5 km every 50 km along the orbit with resolution of about 4 m. Compared to traditional WM aboard European SAR satellites, GF-3 WM operates in a different configuration, as follows.
(1) Polarization. Different from the single-polarized WM on ERS-1/2 SAR, Envisat ASAR, and Sentinel-1A/B, GF-3 WM can acquire imagettes in quad-polarization (VV+HH+VH+HV). (2) Incidence angle. WM imagettes from European SAR satellites are acquired at one or two specific incidence angles. In contrast, although a certain fixed incidence angle was adopted for a specific orbit, the incidence angle could be switched from 20 to 50 • for WM on GF-3 for the period of ten months on which we focused. Hence, we categorized the GF-3 WM data into six groups with respect to incidence angle. Here, they are called incidence angle modes of WV01 for 21 •  at a global scale e.g., [4]. However, currently, the GF-3 SAR payload can only work in WM for up to 50 min in one acquisition, owing to power limitations [31]. Thus, as shown in Figure 2, GF-3 WM measurements are not globally distributed for any of the 6 incidence angle modes in the period from January to October 2017.
Remote Sens. 2018, 10, 363 4 of 23 50°, and details are listed in Table 1. (3) Geographic distribution. Traditional European SAR WM could monitor swells in the open ocean at a global scale e.g., [4]. However, currently, the GF-3 SAR payload can only work in WM for up to 50 min in one acquisition, owing to power limitations [31]. Thus, as shown in Figure 2, GF-3 WM measurements are not globally distributed for any of the 6 incidence angle modes in the period from January to October 2017. In this study, only the GF-3 WM data exhibiting a pure ocean wave pattern (for a typical example, see Figure 1a) are used in the tuning and validation of the new empirical model. The following quality control procedures are applied here.
(1) Homogeneity check. Here, the homogeneity quality control is performed using the parameter of normalized variance ( _ ) computed from VV-polarized imagettes, defined as the imagette variance normalized with mean intensity: where 〈 〉 is the mean intensity of GF-3 WM data in VV polarization. Theoretically, if the SAR image is contaminated with islands, slicks, current shears, atmospheric effects (i.e., Figure 1b) etc., the normalized variance takes values larger than expected from pure wave modulation only. Otherwise, for cases in which ocean wave modulation is weak and the majority of a detected signature is speckle noise, the normalized variance should be small and close to 1.0, as in the example shown in Figure 1c (although some kind of signature like atmospheric waves is visible in Figure 1c, there is no apparent ocean surface wave patterns). The normalized variance _ , has thus been used as a parameter to reject non-wave SAR data in various studies e.g., [23,[37][38][39][40][41]. Figure 3 shows the possibility distribution of normalized variance from GF-3 WM imagettes during the period from January to October 2017. For the histogram, the GF-3 WM normalized variance values are mostly distributed in the range of 1.1 to 1.6 (92% approximately). Hence, only GF-3 WM data with 1.1 < _ < 1.6 remain here for the development and validation of the SWH retrieval empirical algorithm.
(2) Ice rejection. For the SAR images acquired in the ice; for instance, Figure 1d presents homogeneous features but should be obviously excluded for our SWH retrieval. Because the _ check mentioned above fails to reject these cases ( _ = 1.37 in Figure 1d), we further discarded the GF-3 WM acquisitions in high latitudes (>60°) to avoid sea ice near the polar regions.
Therefore, a total of 12,772 GF-3 WM data packets were selected out of 14,428 imagettes for the 10 months in 2017, resulting in a rejection rate of around 10%. Detailed numbers for each incidence angle mode (WV01 to WV06) can be found in Table 1. In this study, only the GF-3 WM data exhibiting a pure ocean wave pattern (for a typical example, see Figure 1a) are used in the tuning and validation of the new empirical model. The following quality control procedures are applied here.
(1) Homogeneity check. Here, the homogeneity quality control is performed using the parameter of normalized variance (cvar_vv) computed from VV-polarized imagettes, defined as the imagette variance normalized with mean intensity: where I is the mean intensity of GF-3 WM data in VV polarization. Theoretically, if the SAR image is contaminated with islands, slicks, current shears, atmospheric effects (i.e., Figure 1b) etc., the normalized variance takes values larger than expected from pure wave modulation only. Otherwise, for cases in which ocean wave modulation is weak and the majority of a detected signature is speckle noise, the normalized variance should be small and close to 1.0, as in the example shown in Figure 1c (although some kind of signature like atmospheric waves is visible in Figure 1c, there is no apparent ocean surface wave patterns). The normalized variance cvar_vv, has thus been used as a parameter to reject non-wave SAR data in various studies e.g., [23,[37][38][39][40][41]. Figure 3 shows the possibility distribution of normalized variance from GF-3 WM imagettes during the period from January to October 2017. For the histogram, the GF-3 WM normalized variance values are mostly distributed in the range of 1.1 to 1.6 (92% approximately). Hence, only GF-3 WM data with 1.1 < cvar_vv < 1.6 remain here for the development and validation of the SWH retrieval empirical algorithm.
(2) Ice rejection. For the SAR images acquired in the ice; for instance, Figure 1d presents homogeneous features but should be obviously excluded for our SWH retrieval. Because the cvar_vv check mentioned above fails to reject these cases (cvar_vv = 1.37 in Figure 1d), we further discarded the GF-3 WM acquisitions in high latitudes (>60 • ) to avoid sea ice near the polar regions.
Therefore, a total of 12,772 GF-3 WM data packets were selected out of 14,428 imagettes for the 10 months in 2017, resulting in a rejection rate of around 10%. Detailed numbers for each incidence angle mode (WV01 to WV06) can be found in Table 1.        The SWH hindcasts used here are from the database of IOWAGA (Integrated Ocean Waves for Geophysical and other Applications) project of IFREMER. The wave hindcasts were performed using the ocean wave model of WaveWatch III (WW3), with the parameterization of Rascle et al. [42] forced by the European Centre for Medium-range Weather Forecasts (ECMWF) winds. The outputs employed are a global grid of 0.5 × 0.5 • × 3 h.

Altimeter SWH Data
Space-borne radar altimeters are another remotely sensed SWH data source, which are generally regarded to be more accurate than SAR derived SWH. To date, the existing altimeters are carried on the satellites of HY-2A, Jason-2/3, Cryosat-2, SARAL/Altika, and Sentinel-3. Using the temporal and spatial co-location criteria of 1 h and 100 km, only Ku-band HY-2A, Jason-2/3, and the Ka-band SARAL/Altika could be co-located with GF-3 WM images during our study period, with the location depicted in Figure 4. Following the calibrations proposed by Liu et al. [43]: where SW H * alt and SW H alt are the calibrated and raw altimeter wave heights, SWH derived from different altimeters were corrected to be of consistent quality. The SWH hindcasts used here are from the database of IOWAGA (Integrated Ocean Waves for Geophysical and other Applications) project of IFREMER. The wave hindcasts were performed using the ocean wave model of WaveWatch III (WW3), with the parameterization of Rascle et al. [42] forced by the European Centre for Medium-range Weather Forecasts (ECMWF) winds. The outputs employed are a global grid of 0.5 × 0.5° × 3 h.

Altimeter SWH Data
Space-borne radar altimeters are another remotely sensed SWH data source, which are generally regarded to be more accurate than SAR derived SWH. To date, the existing altimeters are carried on the satellites of HY-2A, Jason-2/3, Cryosat-2, SARAL/Altika, and Sentinel-3. Using the temporal and spatial co-location criteria of 1 h and 100 km, only Ku-band HY-2A, Jason-2/3, and the Ka-band SARAL/Altika could be co-located with GF-3 WM images during our study period, with the location depicted in Figure 4. Following the calibrations proposed by Liu et al. [43]: SARAL: HY-2A: where * and are the calibrated and raw altimeter wave heights, SWH derived from different altimeters were corrected to be of consistent quality.

Buoy SWH Data
In situ SWH observations were collected from 27 National Data Buoy Center (NDBC) buoys whose locations are depicted in Figure 4 as red crosses. The hourly NDBC buoy records of SWH were co-located with GF-3 WM SAR data. In this study, the spatio-temporal criteria of 100 km and 0.5 h, yields 111 match-ups for the first 10 months of 2017.

Radar Incidence Angle
Existing empirical SWH retrieval models for ERS-2 and Envisat/ASAR, i.e., CWAVE_ERS and CWAVE_ENV, are independent of incidence angle, due to their fixed angle of radar incidence in SAR WM configuration. In fact, the incidence angle is an important parameter that should be taken into

Buoy SWH Data
In situ SWH observations were collected from 27 National Data Buoy Center (NDBC) buoys whose locations are depicted in Figure 4 as red crosses. The hourly NDBC buoy records of SWH were co-located with GF-3 WM SAR data. In this study, the spatio-temporal criteria of 100 km and 0.5 h, yields 111 match-ups for the first 10 months of 2017.

Radar Incidence Angle
Existing empirical SWH retrieval models for ERS-2 and Envisat/ASAR, i.e., CWAVE_ERS and CWAVE_ENV, are independent of incidence angle, due to their fixed angle of radar incidence in SAR Remote Sens. 2018, 10, 363 9 of 23 WM configuration. In fact, the incidence angle is an important parameter that should be taken into consideration to build such empirical models [25,26,28]. With respect to Sentinel-1 A, whose WM configuration has two fixed incidence angles, CWAVE_S1A and CWAVE_Fnn [23] were developed for each of the two incidence beams respectively. Inspired by this, in order to deal with the radar incident dependency for GF-3 WM, as mentioned above, we subdivided the GF-3 WM images into six incidence modes (see Table 1 for details) and tuned our QPCWAVE_GF3 model for each incidence mode respectively.

Normalized Radar cross Section (NRCS)
SAR-observed NRCS σ 0 is directly related to the sea surface roughness of short surface waves, and is widely used for ocean wind retrievals i.e., [32,44,45]. Thus, NRCS can represent information on wind sea (short wave roughness) and co-polarized (VV) NRCS has been introduced into SAR empirical SWH algorithms [19,20,23]. Besides, C-band cross-polarization (VH or HV) has demonstrated good performance to extract high winds even in hurricanes when saturation was observed in co-polarization i.e., [46,47]. Thus, the SAR SWH empirical model could be expected to provide better performance on estimation of wind wave energy in high sea state by taking VH NRCS into consideration (see Section 5.1 for detailed discussion). Therefore, both co-and cross-polarized (VV/VH) NRCS measurements (denoted as σ 0 vv and σ 0 vh respectively) are included in our QPCWAVE_GF3 empirical model. In fact, SAR NRCS does not provide ocean wind speed directly, since NRCS observations depend also on incidence angle and relative wind direction. However, the NRCS, instead of SAR-derived wind speed, is chosen here as the input for our proposed empirical model. The reason is that the wind speed retrieval from co-polarized NRCS usually needs prior information of wind direction i.e., [32,48], and the wind speed estimation accuracy depends on the selection of different GMFs [16][17][18]. Thus, by including NRCS, we propose our SWH empirical model which could be implemented without using SAR-derived wind speeds.

Image Normalized Variance
The normalized variance which is used for the imagette inhomogeneity rejection (see Section 2.1) is also found to contain the longer wave information caused by the swell modulation [19,20,23]. Here, following the existing empirical SAR SWH models, normalized variance computed from VV polarized GF-3 WM imagettes, denoted as cvar_vv here, is selected as another input for the QPCWAVE_GF3 empirical model. See Equation (1) for the details on computation formula of cvar_vv.

Azimuth Cut-Off, Peak Wavelength and Direction
According to the SAR-ocean imaging mechanism of velocity bunching, the relative motions between satellite and ocean surface scatters induce additional Doppler frequency shift, leading to strong cut-off in the SAR spectra in the azimuth direction [1,49]. This cut-off effect suppresses the spectral information provided by the SAR on short to moderate wavelength waves with components of propagation in the azimuth direction. However, it has been found that SAR azimuth cut-off could provide additional information on sea state [50], and is applied to some empirical SWH retrieval algorithms, e.g., [23,24,26,28].
Theoretically, the azimuth cut-off λ c can be expressed by where β = R V is the range (R) to velocity (V) ratio of the SAR platform, f is the wave frequency, and T v k represents the range velocity transfer function [1]. Based on the derivation and analysis from Wang et al. [24], the azimuth cut-off λ c could be theoretically related to the sea state in terms of swh and mean wave period T 0 (related to wavelength λ p according to the wave dispersion law in deep water) by with the dimensionless coefficient C dependent on incidence angle θ, and wave propagation direction ϕ (relative to radar look direction), expressed as In addition, the directionality dependency of the swh ∼ λ c /β relationship has been proven by simulations [26,28]. Therefore, it is evident that azimuth cut-off λ c is related to SWH with the dependency of peak wave direction ϕ and wavelength, as well as radar incidence angle. Thus, considering this complicated relationship, in contrast to the relative simple linear models e.g., [26,28], we include azimuth cut-off λ c , peak wavelength λ p , and direction ϕ into our QPCWAVE_GF3 model, and take their interactions into account as well.

Tuning of the Empirical Model QPCWAVE_GF3
From the analysis above, the empirical model is designed using six SAR-related parameters (VV and VH polarized NRCS σ 0 vv , σ 0 vh ; normalized variance cvar vv ; azimuth cut-off λ c ; peak wavelength λ p , and direction ϕ) and by considering their interactions. The proposed empirical model, called QPCWAVE_GF3 could be written as: We randomly selected 20% of the GF-3 SAR-WW3 co-located data for tuning the model of QPCWAVE_GF3. The numbers of data pairs for each incidence mode are listed in Table 1. It is worth mentioning that the co-located GF-3 WM data with altimeters or buoys, and the GF-3 WM images discussed in Section 5.2.1 were not used in the tuning data, ensuring that the validation was independent. From the Ordinary Least Squares (OLS) regression, 12 coefficients of the empirical model are determined for each incidence mode from WV01 to WV06, as listed in Table 2.

SWH Retrieval Scheme for GF-3 WM Data
The flowchart of the scheme for the SAR SWH empirical retrieval algorithm based on the developed QPCWAVE_GF3 model is shown in Figure 5, and the details can be summarized as follows. Here, we take the GF-3 wave mode acquisition over Northeast Pacific (147.33 • W/28.50 • N) at 15:35 Universal Time Coordinated (UTC) on 31 January 2017 as an example ( Figure 6) to illustrate the QPCWAVE_GF3 SWH retrieval scheme. (1) Radiometric calibration The following formula is used for calibration of NRCS at VV and VH channels from Level-A GF-3 data: where σ is the NRCS united in dB, DN is the intensity calculated from GF-3 SAR Level-1A data, and and are the external calibration constants stored in the product annotation file according to the polarizations. For instance, in the case shown in Figure 6, VV-and VH-polarized NRCS are −12.89 dB and −23.07 dB, respectively.
(2) SAR cross spectrum estimation Three sub-looks are extracted from the entire integration time using the VV-polarized SLC WM imagette ( Figure 6a) and are then used to compute the SAR cross-spectrum (e.g., Figure 6c,d for an example of the real and imaginary parts of the spectrum respectively) with reduced noise floor [51]. Furthermore, the SAR peak wavelength and direction corresponding to the maximum energy are computed directly from the 2-D cross spectrum.
(3) Cut-off estimation The parameter of azimuth cut-off is derived from estimated cross-spectrum. As shown in Figure  6e, azimuth cut-off could be estimated by fitting a Gaussian function to the auto-covariance function of the cross-spectrum (real part), following the methodology proposed by Kerbaol et al. [49]. The Gaussian fit function is stated as, − where denotes the spatial distance in the azimuth direction. The cut-off of 368.89 m was estimated for the case as depicted in Figure 6e, representing a strong azimuth cut-off effect consistent with the corresponding spectrum shown in Figure 6c.
(4) SWH empirical retrieval Through the incidence angle, the 12 coefficients for the corresponding incidence mode of QPCWAVE_GF3 could be obtained. Thus, the SWH could be estimated from the computed parameters using Equation (8). (1) Radiometric calibration The following formula is used for calibration of NRCS at VV and VH channels from Level-A GF-3 data: where σ 0 is the NRCS united in dB, DN is the intensity calculated from GF-3 SAR Level-1A data, and qv and K are the external calibration constants stored in the product annotation file according to the polarizations. For instance, in the case shown in Figure 6, VV-and VH-polarized NRCS are −12.89 dB and −23.07 dB, respectively.
(2) SAR cross spectrum estimation Three sub-looks are extracted from the entire integration time using the VV-polarized SLC WM imagette ( Figure 6a) and are then used to compute the SAR cross-spectrum (e.g., Figure 6c,d for an example of the real and imaginary parts of the spectrum respectively) with reduced noise floor [51]. Furthermore, the SAR peak wavelength and direction corresponding to the maximum energy are computed directly from the 2-D cross spectrum.

(3) Cut-off estimation
The parameter of azimuth cut-off is derived from estimated cross-spectrum. As shown in Figure 6e, azimuth cut-off could be estimated by fitting a Gaussian function to the auto-covariance function of the cross-spectrum (real part), following the methodology proposed by Kerbaol et al. [49]. The Gaussian fit function is stated as, where x denotes the spatial distance in the azimuth direction. The cut-off of 368.89 m was estimated for the case as depicted in Figure 6e, representing a strong azimuth cut-off effect consistent with the corresponding spectrum shown in Figure 6c.
(4) SWH empirical retrieval Through the incidence angle, the 12 coefficients for the corresponding incidence mode of QPCWAVE_GF3 could be obtained. Thus, the SWH could be estimated from the computed parameters using Equation (8).

Algorithm Validation
To assess the accuracy of the proposed QPCWAVE_GF3 empirical model, the statistics of bias, Root Mean Square Error (RMSE), the Scatter Index (SI), and correlation coefficient (COR) were computed using the following expressions: where and represent the SWH from reference data and GF-3 retrievals using the QPCWAVE_GF3 model at the th SAR WM acquisition, respectively; is the total number of data points in validation, and 〈. 〉 denotes the average operator. Figure 7 illustrates the validation results of QPCWAVE_GF3 empirical GF-3 SWH retrievals against independent WW3 wave model SWH hindcasts. In general, the validation result shows that the accuracy of the QPCWAVE_GF3 model differs for every incidence mode. The GF-3 SAR WM images at lower incidence angles (i.e., RMSE of 0.47 m and SI of 16.72% for WV01 with around 22.3°) perform better than those at larger incidence angles (i.e., RMSE of 0.66 m and SI of 22.39% for WV06 with around 47.4°). This may reveal the fact that lower incidence angles are more favorable for SAR ocean wave height retrieval. It is worth mentioning that the GF-3 WV01 ( around 22.3°) and WV03 ( around 35.8°), which are similar to the radar incidence configuration WV1 (23°) and WV2 (36°) of Sentinel-1A, could produce similar accuracy (WV01: RMSE of 0.47 m and SI of 16.72%;

Algorithm Validation
To assess the accuracy of the proposed QPCWAVE_GF3 empirical model, the statistics of bias, Root Mean Square Error (RMSE), the Scatter Index (SI), and correlation coefficient (COR) were computed using the following expressions: where x i and y i represent the SWH from reference data and GF-3 retrievals using the QPCWAVE_GF3 model at the ith SAR WM acquisition, respectively; N is the total number of data points in validation, and . denotes the average operator. Figure 7 illustrates the validation results of QPCWAVE_GF3 empirical GF-3 SWH retrievals against independent WW3 wave model SWH hindcasts. In general, the validation result shows that the accuracy of the QPCWAVE_GF3 model differs for every incidence mode. The GF-3 SAR WM images at lower incidence angles (i.e., RMSE of 0.47 m and SI of 16.72% for WV01 with θ around 22.3 • ) perform better than those at larger incidence angles (i.e., RMSE of 0.66 m and SI of 22.39% for WV06 with θ around 47.4 • ). This may reveal the fact that lower incidence angles are more favorable for SAR ocean wave height retrieval. It is worth mentioning that the GF-3 WV01 (θ around 22.3 • ) and WV03 (θ around 35.8 • ), which are similar to the radar incidence configuration WV1 (23 • ) and WV2 (36 • ) of Sentinel-1A, could produce similar accuracy (WV01: RMSE of 0.47 m and SI of 16.72%; WV03: RMSE of 0.54 m and SI of 20.13%) using our proposed QPCWAVE_GF3 model, compared to those using CWAVE_S1A and CWAVE_Fnn [23].    Figure 8a,b presents the comparisons of SWH derived from GF-3 SAR WM data using the QPCWAVE_GF3 model against the independent data set from altimeters and NDBC buoys, with 1709 and 111 co-located points, respectively. The validation against SWH derived from altimeters (HY-2A, Jason-2/3, SARAL) shows a good agreement with a RMSE of 0.52 m, SI of 20.11%, and correlation coefficient of 0.89. With respect to NDBC buoy measurements, the proposed QPCWAVE_GF3 empirical retrievals present accuracy of 0.57 m, 22.75%, and 0.72 in terms of RMSE, SI, and correlation coefficient, respectively. Both assessments through observation show similar results to the accuracy from the comparison with the WW3 model hindcast.  Figure 8a,b presents the comparisons of SWH derived from GF-3 SAR WM data using the QPCWAVE_GF3 model against the independent data set from altimeters and NDBC buoys, with 1,709 and 111 co-located points, respectively. The validation against SWH derived from altimeters (HY-2A, Jason-2/3, SARAL) shows a good agreement with a RMSE of 0.52 m, SI of 20.11%, and correlation coefficient of 0.89. With respect to NDBC buoy measurements, the proposed QPCWAVE_GF3 empirical retrievals present accuracy of 0.57 m, 22.75%, and 0.72 in terms of RMSE, SI, and correlation coefficient, respectively. Both assessments through observation show similar results to the accuracy from the comparison with the WW3 model hindcast.

Cross-Polarized NRCS Contribution to SWH Empirical Model
One of the features of the GF-3 WM data we focused on is the quad-polarization information provided by SAR data. Accordingly, the SWH retrieval algorithm QPCWAVE_GF3 proposed here includes the cross-polarized NRCS, which have been not taken into account for the empirical models dedicated to single polarization SAR data i.e., [19,20,23], or even Radarsat-2 SAR images with quadpolarization [28]. Therefore, it is interesting to discuss the contribution of cross-polarized NRCS to our proposed empirical SWH retrieval algorithm.
In contrast to the QPCWAVE_GF3 model represented by Equation (8), another empirical model excluding cross-polarized NRCS could be built as ℎ = + + + + σ + and tuned using the same WW3 modelling dataset as QPCWAVE_GF3, with 11 coefficients for the 6 incidence modes of GF-3 WM (not shown). Figure 9a,b show the comparisons of GF-3 SWH retrievals against independent WW3 modelling SWH for all GF-3 WM incidence angles, by using empirical model of QPCWAVE_GF3 (Equation (8)) and the one excluding cross-polarized NRCS (Equation (15)), respectively. In general, the validation results indicate that the accuracy of the empirical model is degraded by rejecting cross-polarized NRCS in terms of RMSE (from 0.54 m to 0.59 m), SI (from 20.64 to 22.32%), and COR (from 0.86 to 0.83).

Cross-Polarized NRCS Contribution to SWH Empirical Model
One of the features of the GF-3 WM data we focused on is the quad-polarization information provided by SAR data. Accordingly, the SWH retrieval algorithm QPCWAVE_GF3 proposed here includes the cross-polarized NRCS, which have been not taken into account for the empirical models dedicated to single polarization SAR data i.e., [19,20,23], or even Radarsat-2 SAR images with quad-polarization [28]. Therefore, it is interesting to discuss the contribution of cross-polarized NRCS to our proposed empirical SWH retrieval algorithm.
In contrast to the QPCWAVE_GF3 model represented by Equation (8), another empirical model excluding cross-polarized NRCS could be built as (15) and tuned using the same WW3 modelling dataset as QPCWAVE_GF3, with 11 coefficients for the 6 incidence modes of GF-3 WM (not shown). Figure 9a,b show the comparisons of GF-3 SWH retrievals against independent WW3 modelling SWH for all GF-3 WM incidence angles, by using empirical model of QPCWAVE_GF3 (Equation (8)) and the one excluding cross-polarized NRCS (Equation (15)), respectively. In general, the validation results indicate that the accuracy of the empirical model is degraded by rejecting cross-polarized NRCS in terms of RMSE (from 0.54 m to 0.59 m), SI (from 20.64 to 22.32%), and COR (from 0.86 to 0.83).
From Figure 9, one can obviously see the much larger inconsistency between GF-3 SWH retrievals from the empirical model without cross-polarized NRCS in high sea states. In order to investigate this, we analyzed the SWH residual of the GF-3 retrieval using the empirical model with and without cross-polarized NRCS with respect to the WW3 SWH, as shown in Figure 10. There is no apparent discrepancy regarding the SWH residual when including and excluding cross-polarized NRCS. However, in the high sea state (SWH above 6 m), the proposed QPCWAVE_GF3 model could be improved by reducing RMSE from 1.54 m to 1.03 m and bias from −1.30 m to −0.76 m with the help of cross-polarized NRCS.
Remote Sens. 2018, 10, x FOR PEER REVIEW 15 of 22 From Figure 9, one can obviously see the much larger inconsistency between GF-3 SWH retrievals from the empirical model without cross-polarized NRCS in high sea states. In order to investigate this, we analyzed the SWH residual of the GF-3 retrieval using the empirical model with and without cross-polarized NRCS with respect to the WW3 SWH, as shown in Figure 10. There is no apparent discrepancy regarding the SWH residual when including and excluding cross-polarized NRCS. However, in the high sea state (SWH above 6 m), the proposed QPCWAVE_GF3 model could be improved by reducing RMSE from 1.54 m to 1.03 m and bias from −1.30 m to −0.76 m with the help of cross-polarized NRCS.  From Figure 9, one can obviously see the much larger inconsistency between GF-3 SWH retrievals from the empirical model without cross-polarized NRCS in high sea states. In order to investigate this, we analyzed the SWH residual of the GF-3 retrieval using the empirical model with and without cross-polarized NRCS with respect to the WW3 SWH, as shown in Figure 10. There is no apparent discrepancy regarding the SWH residual when including and excluding cross-polarized NRCS. However, in the high sea state (SWH above 6 m), the proposed QPCWAVE_GF3 model could be improved by reducing RMSE from 1.54 m to 1.03 m and bias from −1.30 m to −0.76 m with the help of cross-polarized NRCS.    Figure 11a. Moreover, the GF-3 and SARAL were cross co-located at 15:40 UTC, and the cross-over point (147.33°W/28.50°N) is annotated in Figure 11a. This match-up GF-3 WM observation (see Figure 6) has been presented by demonstrating the retrieval scheme in Section 3.6.
Along the transect of GF-3 WM, the WW3 hindcast and SWH retrievals using the proposed QPCWAVE model are shown in Figure 11b as the red circles and green line, respectively. Agreement can be seen regarding the WW3 modelled SWH ranging 3-4 m, mainly located between 10°N and 25°N. However, the GF-3 SWH retrievals from QPCWAVE are underestimated against the WW3 hindcast for SWH above 4 m, especially between 25°N and 35°N (WW3 SWH > 6 m). Moreover, between 25°N and 30°N, where the SAR and altimeter passed nearby in space, the QPCWAVE estimations are closer to the SARAL/Altika-derived SWH (i.e., 5.94 m vs. 6.30 m from GF-3 and SARAL, respectively, for the cross-over point) than WW3 modelling, although underestimation could be found as well. This discrimination is in line with the statistical comparisons shown in Figures 7-9, implying the limitation of our proposed QPCWAVE empirical model in very high sea states (>6 m).   Figure 11a. Moreover, the GF-3 and SARAL were cross co-located at 15:40 UTC, and the cross-over point (147.33 • W/28.50 • N) is annotated in Figure 11a. This match-up GF-3 WM observation (see Figure 6) has been presented by demonstrating the retrieval scheme in Section 3.6.
Along the transect of GF-3 WM, the WW3 hindcast and SWH retrievals using the proposed QPCWAVE model are shown in Figure 11b as the red circles and green line, respectively. Agreement can be seen regarding the WW3 modelled SWH ranging 3-4 m, mainly located between 10 • N and 25 • N. However, the GF-3 SWH retrievals from QPCWAVE are underestimated against the WW3 hindcast for SWH above 4 m, especially between 25 • N and 35 • N (WW3 SWH > 6 m). Moreover, between 25 • N and 30 • N, where the SAR and altimeter passed nearby in space, the QPCWAVE estimations are closer to the SARAL/Altika-derived SWH (i.e., 5.94 m vs. 6.30 m from GF-3 and SARAL, respectively, for the cross-over point) than WW3 modelling, although underestimation could be found as well. This discrimination is in line with the statistical comparisons shown in Figures 7-9, implying the limitation of our proposed QPCWAVE empirical model in very high sea states (>6 m).  Figure 12a. There were no altimeters flying over this area during this time.
These GF-3 SAR images were acquired in the working mode of QPSI rather than WM. The GF-3 QPSI mode has a similar configuration to WM, but with the larger image coverage of 25 × 25 km (see Figure 12b) and is mainly dedicated to land and coastal areas [31]. Thus, the proposed QPCWAVE_GF3 model was applied to these QPSI images (the radar incidence angle of 38.37° is equivalent to WV04 for this case). Figure 12c shows the comparison of WW3 hindcast and GF-3 QPSI SAR SWH estimated using the QPCWAVE_GF3 empirical model along the pass of GF-3. One can see quite good agreement, with a mean bias of 0.54 m, considering the high waves (average of 5.64 m from WW3 along this transect). Furthermore, although only GF-3 WM data were used for development of our proposed empirical model, the case introduced here could demonstrate the capability of the QPCWAVE_GF3 model to estimate from SAR data rather than GF-3 WM.  Figure 12a. There were no altimeters flying over this area during this time.
These GF-3 SAR images were acquired in the working mode of QPSI rather than WM. The GF-3 QPSI mode has a similar configuration to WM, but with the larger image coverage of 25 × 25 km (see Figure 12b) and is mainly dedicated to land and coastal areas [31]. Thus, the proposed QPCWAVE_GF3 model was applied to these QPSI images (the radar incidence angle of 38.37 • is equivalent to WV04 for this case). Figure 12c shows the comparison of WW3 hindcast and GF-3 QPSI SAR SWH estimated using the QPCWAVE_GF3 empirical model along the pass of GF-3. One can see quite good agreement, with a mean bias of 0.54 m, considering the high waves (average of 5.64 m from WW3 along this transect). Furthermore, although only GF-3 WM data were used for development of our proposed empirical model, the case introduced here could demonstrate the capability of the QPCWAVE_GF3 model to estimate from SAR data rather than GF-3 WM. Remote Sens. 2018, 10, x FOR PEER REVIEW 18 of 22

Conclusions
In this paper, we proposed a new approach of a direct retrieval of ocean wave SWH from GF-3 SAR WM data without transformation into wave spectra. The empirical model, called QPCWAVE_GF3, uses parameters from the quad-polarized SAR image and cross-spectrum to estimate the SWH. These inputs include VV-and VH-polarized NRCS, image normalized variance, azimuth cut-off wavelength, and peak wavelength and direction.
Using a co-located dataset of WW3 and GF-3 WM with a total of 2579 data points, the QPCWAVE_GF3 model is trained for six different radar incidence angle modes of GF-3 WM, and empirical coefficients have been determined.
The accuracy assessment of the SWH from GF-3 was carried out through a comparison with independent WW3 modelling hindcasts, and observations from altimeters and buoys for the period of ten months in 2017. The validations show RMSEs from 0.5 m to 0.6 m, and SI around 20% for six different incidence angle modes. Due to the quad-polarization capability of GF-3 WM data, our empirical model QPCWAVE_GF3 performs better in the high sea state by including cross-polarized NRCS. Besides, two cases of storm-induced high waves seen by GF-3 WM and QPSI mode are presented. The case study results indicate that our proposed model could be employed to estimate SWH from other similar quad-polarized SAR images, although it is tuned based on GF-3 WM data.
Future work will be dedicated to using more data, especially those in high sea states, to tune our empirical model, so that its accuracy can be improved in extreme wave conditions. In addition, the possibility of estimating SWH from C-band quad-polarized SAR images, such as Radarsat-2 data, could be investigated.