Sea Surface Temperature Retrieval From the FY-3D MWRI Measurements

Sea surface temperature (SST) is a key climate variable, which affects the behavior of the Earth’s atmosphere. In this article, a method coupled with microwave sea surface emissivities (SSEs) is developed to retrieve SST from the intercalibrated measurements acquired by the microwave radiation imager (MWRI) on Fengyun 3D (FY-3D) satellite. First, the spatiotemporal matching samples over sea surfaces in 0.25 $^{\circ }\,\,\times0.25^{\circ }$ between FY-3D MWRI measurements and the fifth generation of European center for medium-range weather forecast (ECMWF) atmospheric reanalysis (ERA5) data in January, April, July, and October 2020 are collected and used to determine the unknown coefficients of the SST retrieval algorithm. To improve the accuracy, besides grouping the samples by sea surface wind speed and SST, pseudo-SSEs are introduced into the SST retrieval algorithm. The root-mean-square errors (RMSEs) of the SST retrieval algorithm in the three steps are 1.18, 0.73, and 0.68 K, respectively. Then, the SSTs in 2020 between 60°S and 60°N are retrieved from the FY-3D MWRI measurements without precipitation and heavy clouds. Finally, the SSTs retrieved in this work are validated with the GMI SST and the iQuam in situ data. The errors of the retrieved SSTs in the three steps are 0.19 ± 1.23, 0.17 ± 1.15, and 0.01 ± 1.15 K against the GMI SST, respectively, while they are 0.48 ± 1.24, 0.37 ± 1.13, and 0.12 ± 1.10 K against the iQuam in situ data, respectively. The errors of both the retrieval algorithm and the derived SSTs in this work are obviously reduced after introducing the pseudo-SSEs into the algorithm, which proves that the SST retrieval algorithm developed in this work is valid and accurate.

are deployed in the oceans, they measure SST at discrete and sparse sites.Satellite remote sensing is the only way to provide a global, homogeneous, and continuous coverage of SST, which is the most important alternative to the in situ data.Since the 1970s, multiple-window channel algorithms were developed to retrieve SST from infrared satellite data, and the results well agree with in situ data [3], [4], [5], [6], [7].However, the satellite infrared remote sensing is vulnerable to clouds, and thus it is usually not used to estimate SST under clouds.Fortunately, microwaves can penetrate clouds with little attenuation, providing an uninterrupted view of the ocean surfaces.Satellite microwave radiometry has the capability to measure SST in all weather conditions except rain and heavy clouds, and a root-mean-square error (RMSE) of about 0.6 • against oceans buoys was obtained [8].Like early infrared remote sensing, the SST is expressed as a function of microwave brightness temperatures (TBs) at top of atmosphere, and the coefficients are determined by regression on the samples of SST and TBs.To improve the algorithm accuracy, the samples are divided into several groups by SST and sea surface wind speed [9], [10], [11].Much research indicates that sea surfaces are non-Lambertian, and sea surface emissivity (SSE) plays important role in SST retrieval [7], [12].In contrast to infrared SSE [13], [14], the microwave SSE is more complicated: it is not only a function of wind speed but also a function of SST, sea surface salinity, etc., [15].Due to the above reason, the microwave SSEs are not involved in the statistical algorithms to retrieve SST from passive microwave measurements [7], [10], [11], [16].
The fourth satellite of Chinese second-generation polarorbiting meteorological satellite, Fengyun 3D (FY-3D), was successfully launched into space on November 15, 2017.Because FY-3D crosses the equator in the ascending node around 14:00 local time, it is referred to as an afternoon satellite.Its altitude, inclination angle, and orbital period are 836 km, 98.75 • , and 101.49min, respectively.On FY-3D satellite, the microwave radiation imager (MWRI) is one of 11 payloads.It weighs 175 kg, and consists of an offset parabolic main reflector with sizes of 97.74 × 89.7 cm.It scans the Earth surfaces with an Earth incidence angle (EIA) of about 53.2 • in ten channels at frequency of 10.65, 18.7, 23.8, 36.5, and 89.0 GHz with both vertical polarization (v-pol, V) and horizontal polarization (h-pol, H).In the following, the ten MWRI channels are named 10V, 10H, 18V, 18H, 23V, 23H, 36V, 36H, 89V, and 89H, respectively.In the MWRI, a cold reflector and a hot reflector provide an end-to-end calibration system for the ten channels [17].Table I lists the instrument parameters of FY-3D MWRI, including central frequency, bandwidth, polarization, instantaneous field of view (IFOV), 1558-0644 © 2023 IEEE.Personal use is permitted, but republication/redistribution requires IEEE permission.
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TABLE I INSTRUMENT PARAMETERS OF THE MWRI ON FY-3D SATELLITE
and noise-equivalent temperature differences (NE T).The FY-3D MWRI measurements can be used to retrieve SST, cloud water, atmospheric precipitable water, soil moisture and temperature, snow cover, and so on.
In this article, an algorithm is developed to retrieve SST from the FY-3D MWRI measurements.In the following, Section II presents the development of SST retrieval algorithm.Section III describes the data and data processing.Section IV focuses on the results and analysis.The last section is devoted to the conclusion and discussion.

A. Development of the SST Retrieval Algorithm
SST can be expressed as a simple function of microwave TBs at top of atmosphere, and thus the selection of microwave channels is important to SST retrieval.The importance of a microwave channel to SST retrieval is usually described by its sensitivity to SST variation: higher its sensitivity, more suitable it is for SST retrieval.In order to quantitate the sensitivity of the FY-3D MWRI channels to SST variation, a numerical experiment is conducted using the ocean microwave radiative transfer model [18], [19] and the Tropical, mid-latitude summer (MLS), mid-latitude winter (MLW), sub-arctic summer (SAS) and US 1976 model atmospheres prescribed in the MODerate spectral resolution atmospheric TRANsmittance algorithm and computer model (MODTRAN) [20].In the experiment, the following parameters are set: 1) SST is equal to the boundary atmospheric temperature; 2) the EIA is set to 53.2 • ; 3) the sea surface wind speed is 7 m/s; and 4) the relative azimuth angle is fixed at 90 • .Fig. 1 displays the sensitivity of TB at frequency from 6.8 to 90 GHz to an SST increment of 1.0 K.The vertical dashed lines are the central frequencies of the MWRI channels.Except the strong oxygen absorption spectra between 52 and 68 GHz, the sensitivities at other frequencies are obviously apart from zero.The sensitivities at 6.9 GHz are positive and largest, which indicates that the 6.9-GHz channel is most suitable for SST retrieval [21].From 6.8 to 52 GHz, the sensitivities first decrease and then decrease with frequency increment.After 68 GHz, relatively small sensitivities are observed.At the five central frequencies of FY-3D MWRI channels, the sensitivities vary from −0.4 to 0.6 K for different model atmospheres, and thus the ten MWRI channels are generally suitable for SST retrieval.Because the 23H channel of FY-3D MWRI is not intercalibrated against the global precipitation Fig. 1.Sensitivity of bright temperature at frequency from 6.8 to 90.0 GHz to an SST increment of 1.0 K. measurement (GPM) microwave imager (GMI) (please see Section III), it is excluded from the SST retrieval algorithm, i.e., the FY-3D MWRI channels 10V, 10H, 18V, 18H, 23V, 36V, 36H, 89V, and 89H channels are used in this work.
Previous research indicated that SST is a simple function of the TBs measured by a microwave imager on satellite.As we know, sea surface wind speed is one of the key variables to determine the microwave SSE, and further influences the microwave TBs at top of atmosphere.Therefore, SST is expressed as a linear function of the TBs grouped by wind speed [9], [18] where T 1 is the SST, N ( = 9) is the number of microwave channels, T b,i is the TB in the channel i, a m,i and b m are unknown coefficients, ω is the wind speed, and [ω m , ω m+1 ] is the wind speed interval where the TBs fall into.The wind speed can also be expressed as a linear function of the microwave TBs at top of atmosphere [10], [11], [22] in which c i and d are unknown coefficients.Further, the SST is more accurately expressed by the TBs grouped by wind speed and SST together where e m,n and g m,n are unknown coefficients, and [T n , T n+1 ] is the nth TB interval.
The unknown coefficients in (1), (2), and (3) are determined by regression with training samples.Once the coefficients in the retrieval equations are determined, the sea surface wind speed (ω) and SSTs (T 1 and T 2 ) are retrieved from the satellite measurements.
According to the radiative transfer theory, microwave SSE strongly influences the TB at top of atmosphere, and it conversely impacts on SST retrieval.In infrared remote sensing, SSE is a key parameter to retrieve SST [7], [12].Starting with the radiative transfer equation and linearizing the Planck function, Sun and Pinker developed a three-channel algorithm to estimate land surface temperature from the Geostationary Operational Environmental Satellite (GOES-8) infrared data [23].According to the microwave radiative transfer theory and following Sun and Picker's idea, a nine-channel algorithm with microwave SSE to retrieve SST from FY-3D MWRI measurements is developed, i.e., where p m,n , q m,n , and r m,n are unknown coefficients.However, microwave SSE is not only a function of wind speed but also a function of SST, relative azimuth angle, and sea surface salinity.To determine the microwave SSEs, SST should be known first, i.e., the microwave SSEs are coupled with SST.In the training samples for algorithm development, the SST, wind speed, relative azimuth angle, and sea surface salinity are known variables, and accurate SSEs can be calculated using the Wentz and Meissner's SSE model [15] with the known variables.However, in actual retrieval, both the SST and wind speed are derived from satellite measurements, and the relative azimuth angle is usually unknown.Due to this reason, all existing statistical algorithms to retrieve SST from passive microwave measurements do not involve the microwave SSE, and divide the training samples into groups to improve algorithm accuracy instead [9], [10], [11], [16].In a grouping interval, the variations of both wind speed and SST are reduced indeed, as well as the microwave SSE.Although the intervals are narrow, which are about 3.0 K width for SST and 4 m/s width for wind speed [9], [18], the variation of microwave SSE in the intervals still leads to non-negligible errors in the derived SST.
The sea surface salinity generally varies between 32 and 38 ppt.Our simulation reveals that the maximum microwave SSE error caused by the use of a fixed sea surface salinity of 35 ppt is less than 0.02%, which can be negligible.When the SST is 290 K and the wind speed is 20 m/s, the microwave SSE errors in FY-3D MWRI channels introduced by the fixed relative azimuth angle of 90 • are less than 0.01.
With the fixed relative azimuth angle and sea surface salinity, the approximate SSEs are calculated using the Wentz and Meissner's model [15] using the wind speed (ω) derived by (2) and the SST (T 2 ) estimated by (3) where f i is the microwave SSE function in FY-3D MWRI channel i.
Because the inputs are retrievals or fixed values, the microwave SSEs calculated by ( 5) are certainly biased from the accurate ones.Hereafter, we call them the pseudo-SSEs.If the accurate SSEs were used to develop the algorithm, whereas the pseudo-SSEs were used to retrieve the SSTs, the errors in the pseudo-SSEs are amplified and worse retrievals are obtained.But, if the pseudo-SSEs are used in both the algorithm development and SST retrieval, the errors in the pseudo-SSEs are finally canceled out in some degree, and consequently the accuracy of both the algorithm and the derived SSTs is improved.This is justified by the results in Table II and the validation accuracy in Section IV.
To determine the unknown coefficients in ( 1)-( 5), a large number of globally representative training samples of SST, FY-3D MWRI measurements, and wind speed are required.In [9] and [18], Wentz and Meissner used the microwave radiative transfer modeling method to construct a data set, and then determined the unknown coefficients using regression.However, our research revealed that, even under clear sky conditions, there are non-negligible differences between satellite observations and simulations due to the physical imperfects of microwave radiative transfer model and the uncertainties in the climate variables [19], [24], [25].If the algorithm is developed with radiative transfer modeling, the simulation errors will be finally transferred to the derived SSTs, leading to inaccurate results.In [19], the simulation errors were removed against the spatiotemporal matching satellite data and climate variables using empirical functions.In order to remove the retrieval errors, the satellite-derived SSTs were calibrated with in situ data [26], [27], [28], [29].In [11], the spatiotemporal matching samples between satellite observations and the iQuam in situ data were used to develop the SST retrieval algorithm.However, the iQuam in situ data are usually sparse in space and time, which is not beneficial to algorithm development.
The fifth generation of European center for medium-range weather forecast (ECMWF) atmospheric reanalysis (ERA5) combines vast amounts of historical observations into global estimates using advanced modeling and data assimilation systems, and the ERA5 data have both high spatial resolution and temporal resolution.Our research indicates that the ERA5 SSTs are quite consistent with the iQuam in situ data, and the difference is −0.09 ± 0.46 K in 2020, which is also indirectly proved by the results in Section IV.Therefore, the spatiotemporal matching samples between FY-3D MWRI measurements and ERA5 data are used to determine the unknown coefficients in (1)- (5).Four typical months, January, April, July, and October of 2020, are applied.The FY-3D MWRI Level 1 (L1) data are first re-calibrated using the intercalibration equations in Section III, and then they are resampled into the ERA5 grid space with spatial resolutions of 0.25 •  × 0.25 • in longitude and latitude.The training samples between 60 • S and 60 • N are collected using the following Fig. 2. Spatial distribution of the matching samples between the FY-3D MWRI measurements and the ERA5 data in the four typical months (January, April, July, and October of 2020.)criteria: 1) the FY-3D MWRI measurements and ERA5 data are collocated over sea surfaces at least 100 km far away from land; 2) the absolute time difference is less than 2.5 min; 3) the SST is greater than 273.15K and the wind speed is less than 25 m/s; and 4) the MWRI observations contaminated by precipitation or heavy clouds are excluded using the empirical filters expressed by (9) in Section III.With the above criteria, a total of 2112 951 matching samples are gathered in the four typical months.Fig. 2 shows the spatial distribution of the matching samples.In general, the matching samples are uniformly distributed in the Pacific Ocean, the Indian Ocean, and the Atlantic Ocean.The results indicate that the matching samples have global representativeness, and they are suitable for the algorithm development.
Then, to further improve the algorithm accuracy, besides grouping by wind speed, the SSTs are divided into 13 groups according to the following intervals with an overlap of 3.For each group divided by both wind speed and SST, the unknown coefficients in (3) are also determined using linear regression.The regression RMSEs range is between 0.2 and 1.1 K, and most of them are less than 1.0 K.The total RMSE is 0.73 K.In contrast to the RMSE in the first step, the RMSE in the second step is reduced by 0.45 K.Because of the narrow dynamics in the groups, the regression determinant coefficients (R 2 ) decrease overall, but most of them are still greater than 0.5.
Finally, substituting the MWRI measurements of the training samples into (1)-( 3), the wind speed (ω), and the SST in the second step (T 2 ) are, respectively, predicted.The pseudo-SSEs are calculated with the predicted SST (T 2 ) and wind speed using (5).With the wind speed (ω), SST (T 2 ), and the pseudo-SSEs, the unknown coefficients in (4) are determined for each group of wind speed ω and SST T 2 using linear regression.The regression results show that the RMSEs decrease further, and the total RMSE is reduced to 0.69 K.
So far, the SST retrieval algorithm coupled with microwave SSEs has been developed.The RMSE is reduced from 1.19 K in the first step to 0.74 K in the second step, and after introducing the pseudo-SSEs, it is further reduced to 0.68 K.
It should be pointed out that, in actual SST retrieval from FY-3D MWRI measurements, the central points of the overlaps between two neighboring groups are used to re-divide the intervals without overlaps, and the grouping coefficients are used in terms of which intervals the wind speed and SST in the previous step fall in.

B. Comparison With Wentz and Meissner's Algorithm
Meissner and Wentz [9] and Wentz and Meissner [18], proposed a two-step algorithm to retrieve SST from the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) data.
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In the first step, the initial estimates of SST and wind speed were obtained using the following quadratic expressions: where subscript j = 1 or 2 denotes either SST ( p 11 ) or wind speed ( p 12 ), and the leading subscript 1 denotes that it is a first-step retrieval.a ij and b ij are unknown coefficients.
In the second step, a large set of localized retrieval algorithms were developed in the SST ranges of ± 1.5 K and wind speed ranges of ± 2.0 m/s centered at the reference values.The final retrieval is the bilinear interpolation of the four nearest first-step retrievals in the 2-D space of wind speed and SST.The localized algorithms are expressed as follows [9], [18]: where the subscript k is the SST or wind speed references values.
With the same training samples in Section II-A, the unknown coefficients in ( 6) and ( 7) are determined using multiple regression.Table II lists the total RMSEs of the Wentz and Meissner's (W&M's) algorithm, and the total RMSEs of the algorithm in this work are also listed for comparison.In the first step, the total RMSE of W&M's algorithm is 0.1 K less than the RMSE of the algorithm in this work.This is mainly attributed to the nonlinear expressions in W&M's algorithm.In the second step, the total RMSE of W&M's algorithm is about 0.3 K larger.After introducing the pseudo-SSEs, the total RMSE of the algorithm in this work is further reduced to 0.68 K.
It should be mentioned that, the W&M's algorithm was first developed for the AMSR-E, which has two SST sensitive channels at 6.925 GHz, and a good accuracy of −0.03 ± 0.69 K against the weekly 100-km resolution Reynold-Smith optimum interpolated (OI) SST was obtained [9].Both the algorithm developed in this work and the W&M's algorithm have outstanding performance under their respective applicable circumstances.
Both the FY-3D MWRI L1 data and GMI L1C data provide TBs at top of atmosphere in the microwave channels, as well as the longitude, latitude, viewing angles, observation time, etc.The FY-3D MWRI data are divided into the ascendingorbit (MWRIA) data and the descending-orbit (MWRID) data due to the abnormal of the hot reflector [30], and different calibration coefficients are applied.The GMI L1C data are used as radiometric references for intercalibration of FY-3D MWRI channels.
The ERA5 data provide hourly estimates of large number of atmospheric, land, and oceanic climate variables with a spatial resolution of 0.25 • × 0.25 • , and resolve the atmosphere using 37 levels from the surface up to a height of 80 km.The ERA5 variables used in this work include SST, wind speed at 10 m above sea surface, geopotential profiles, atmospheric temperature profiles, and atmospheric relative humidity profiles.The ERA5 data are used to simulate the satellite TBs at top of atmosphere for the intercalibration of FY-3D MWRI channels, while the ERA5 SST and wind speed are used to develop the SST retrieval algorithm.
The iQuam in situ data and the GMI SST data are used to validate the SST derived from FY-3D MWRI measurements in this work.The iQuam data are quality-controlled in situ data from the original global telecommunication system (GTS) data sets, including SST and other parameters such as wind speed, wind direction, dew point temperature, and so on [31].The iQuam data with best quality (level 5) are used in this work.The GMI SSTs were produced using the version 8.2 algorithm developed by remote sensing systems (RSS).In [32], the GMI SSTs were compared with the iQuam in situ data, and the difference is −0.09 ± 0.75 K.This indicates that the iQuam in situ data and the GMI SSTs are at the same level of accuracy.
In order to retrieve accurate SST from FY-3D MWRI data, the in-orbit radiometric calibration biases in FY-3D MWRI channels should be assessed and corrected.Among the microwave imagers on satellites, the GMI and FY-3D MWRI have most similar instrument parameters.The GMI is the first microwave imager to employ both external and internal calibration systems, which provide a way to measure the nonlinear response of the electronics in orbit.Latest research showed that the GMI's absolute calibration accuracy is about 0.25 K 1-bias over ocean, and exhibits remarkable long-term radiometric stability [33], [34].The GMI's excellent calibration enables it to server as both precipitation and radiometric standards for other microwave imagers [35].Therefore, following the method in [19], [22], the FY-3D MWRI channels are intercalibrated against the GMI channels using the double difference method.The FY-3D MWRI L1 data, the GMI L1C data, and the ERA5 data in the four typical months (January, April, July, and October 2020) over ocean surfaces are used for intercalibration in this work.First, the satellite data and the ERA5 data are pixel-aggregated into a grid space with longitude and latitude resolutions of 1 • × 1 • .Then, the matching samples are collected in the 1 • × 1 • grid space between 60 • S and 60 • N using the following criteria: 1) the satellite data and ERA5 data are collocated over sea surfaces at least 100 km far away from land; 2) the maximum ERA5 relative humidity is less than 95% and the satellite observations satisfy the empirical filters to remove precipitation and heavy clouds [22], [36], [37]; 3) the absolute time differences between FY-3D MWRI and GMI observations are less than 60 min; and 4) both FY-3D MWRI and GMI observations are time nearest to the same ERA5 data at 0:00, 3:00, 6:00, 9:00, 12:00, 15:00, 18:00, and 21:00.With the above criteria, in the four months, a total of 4519, 2118, 961, and 2608 samples are collected for the MWRIA data, respectively, while a total 3707, 3107, 1951, and 3308 samples are gathered for the MWRID data, respectively.Because of the matching criteria and the orbit difference between FY-3D and GPM satellites, the number of matching samples varies with month, and especially in the July, only 961 matching samples between FY-3D MWRIA and GMI data are collected.In general, the matching TBs are uniformly distributed in the Pacific Ocean, the Indian Ocean, and the Atlantic Ocean, and have global representativeness.
Taking the results in January 2020 as examples, Fig. 3 displays the scatterplots of the theoretical observations (the actual FY-3D MWRI observation minus the double difference) versus FY-3D MWRI measurements.The following quadratic regression equation is applied [19]: where T MWRI_theoretical,i and T MWRI,i are the theoretical observation and the actual observation in the MWRI channel i, respectively, while A i , B 1,i , and B 2,i are the intercalibration coefficients.
The quadratic regression results are also given in Fig. 3.For both the MWRIA and MWRID, the regression determinant coefficients (R 2 ) are greater than 0.957, while the RMSEs are less than 1.0 K except the channels of 36H and 89H, in which the RMSEs are about 1.5 K. Fig. 3 shows that radiometric calibration biases exist in FY-3D MWRI channels, and they vary with TBs.Totally, the radiometric calibration biases (mean of the double differences) in the MWRI channels of 10V, 10H, 18V, 18H, 23V, 36V, 36H, 89V, and 89H are −6.2,−6.Once the coefficients in ( 8) are determined, the FY-3D MWRI data in the four quarters of 2020 are intercalibrated using the intercalibration equations obtained in January, April, July, and October of 2020, respectively.
Then, the re-calibrated FY-3D MWRI data and GMI SST data are resampled into the ERA5 0.25 • × 0.25 • grid space.To exclude the radiances come from land surfaces, the land surfaces and the offshore area within 100 km are masked out using a dilated land mask.
As we know, precipitation and heavy clouds have a significant attenuation on high-frequency microwaves, which is harmful to SST retrieval.At the presence of precipitation or heavy clouds, the TB difference between vertical and horizontal polarizations at the same frequency is significantly reduced.Therefore, the microwave observations contaminated by precipitation or heavy clouds can be screened out by linear combinations of TBs at vertical and horizontal polarizations, which are called the polarization-corrected temperature (PCT) [38], [39], [40].Based on the previous research results and the characteristics of FY-3D MWRI observations, the following empirical filters are used in this work to remove the FY-3D MWRI measurements contaminated by precipitation or heavy clouds: After the data preprocessing, SSTs are retrieved as follows.First, wind speed (ω) is derived from FY-3D MWRI measurements using (2).Next, according to which interval the wind speed falls in, the initial SST (T 1 ) is estimated using (1).Then, according to which interval the derived wind speed and initial SST (T 1 ) fall in, more accurate SST (T 2 ) is retrieved using (3).After that, the pseudo-SSEs in the MWRI channels are calculated using (5).Finally, the final SST (T 3 ) is retrieved using (4).
To validate the final SST, the iQuam in situ data with best quality (quality level = 5) and the GMI SSTs in 2020 are used as references.The matching criteria between the SSTs derived in this work and the iQuam in situ data are: 1) the iQuam in situ data fall into the SST grid and 2) the absolute observation time difference is less than 30 min.The matching criteria between the SSTs derived in this work and the GMI SSTs are: 1) the GMI SST and the SST in this work are collocated in the 0.25 • × 0.25 • grid space and 2) the absolute observation time difference is less than 10 min.With the spatiotemporally matching SSTs, the statistical errors of the retrieved SST (mean ± standard deviation at the mean) are calculated.

IV. RETRIEVAL RESULTS AND ANALYSIS
The sea surface wind speed in 2020 between 60 • S and 60 • N over the sea surfaces is estimated, and it mainly ranges between 0 and 25 m/s.The statistical errors of the wind speed derived using the algorithm in this work (the W&M's algorithm) are −0.09± 1.14 (−0.04 ± 1.10) m/s and 0.01 ± 1.16 (0.03 ± 1.12) m/s against the iQuam in situ data and the GMI product, respectively.Generally, the retrieval accuracy of the wind speed meets the SST retrieval requirements.
The SSTs between 60 • S and 60 • N are derived from the intercalibrated FY-3D MWRI measurements in 2020 using the SST retrieval algorithm developed in Section II.Fig. 4 displays the maps of SSTs retrieved from the MWRIA and MWRID data on January 1, 2020.The SST mainly ranges between 273 and 304 K, and gradually decreases from equator to higher latitude.Over the same area, the SST in daytime (MWRIA) is slightly higher than those at night (MWRID).
The SSTs retrieved from FY-3D MWRI measurements in this work are validated with the iQuam in situ data and the GMI SSTs.With the matching criteria given in Section III, a total of 12 5483 matching SSTs between the results in this work and the iQuam in situ data are collected, while a total of 38 4076 matching SSTs between the results in this work and the GMI SSTs are gathered.Fig. 5 shows the scatterplots of the matching SSTs between the results in this work and the GMI SSTs and of the matching SSTs between the results in this work and the iQuam in situ data.The matching SSTs are generally distributed around the diagonals, and they have obviously linear relation with correlation coefficients (R) greater than 0.98.Fig. 6 displays the histograms of the SST errors produced by our algorithm and the W&M's algorithm against the GMI SSTs and the iQuam in situ data, respectively.The SST errors mainly range between −4.0 and 4.0 K, and   basically obey normal distribution centered at about zero.For the SST errors less than 0.25 K, the histogram frequencies generated by our algorithm are slightly higher than those produced by the W&M's algorithm.Table III lists the error percentages of final SSTs retrieved by our algorithm and the W&M's algorithm, which are about 39.2%, 68.1%, 84.4%, and 92.4% in the ranges of [−0.5, 0.5], [−1.0, 1.0], [−1.5, 1.5], and [−2.0, 2.0] K, respectively.In the first three ranges, the percentages produced by our algorithms are 0.1%-1.3%larger than those generated by the W&M's algorithm, whereas an opposite of about 0.2% is observed in the fourth range.Table IV gives the SST retrieval errors in the three steps of our algorithm and in the two steps of W&M's algorithm.The SST retrieval errors gradually decrease.In the first step and second step, the retrieval errors of W&M's algorithm are smaller than the ones of our algorithm, which are mainly attributed to the nonlinear expressions used in the W&M's algorithm.After introducing the pseudo-SSEs, the SST errors produced by our algorithm are reduced to 0.01 ± 1.15 and 0.12 ± 1.10 K against the GMI SSTs and the iQuam in situ data, respectively, which are about 0.1 K smaller than those of W&M's algorithm.Basically, our algorithm has equivalent performance as the W&M's algorithm in retrieving SSTs from the FY-3D MWRI measurements.It should be noted that, the retrieval errors in Table IV are larger than the algorithm training errors in Table II, which agrees with common sense.The SSTs retrieved in this work have equivalent accuracy as the results derived from Haiyan 2A (HY-2A) Scanning Microwave Radiometer data [11].In general, the SST retrieval algorithm developed in this work is valid, and the derived SSTs are accurate.Fig. 7 displays the SST errors against the iQuam in situ data vary with SST and wind speed.The SST retrieval errors are mainly distributed between −4.0 and 4.0 K.When SST goes from 272 to 305 K, the SST retrieval error monotonically increases from about −0.9 to 0.7 K, while the standard deviation varies from about 1.4 to 0.7 K. Around 290 K, the SST error is about zero.When the wind speed changes from 0 to 16 m/s, the SST error monotonically decreases from 0.5 to −2.2 K with a standard deviation about 1.2 K, and the SST error is approximately zero at the wind speed of 7 m/s.In general, the retrieval errors are minimum for moderate wind speed and SST.
It should be mentioned that, the wind speed retrieval algorithm (2) in Section II was developed without groups.An experiment was conducted to divide the wind speed into nine groups with an overlap of 2 m/s: [0, 3], [1,5], [3,7], [5,9], [7,11], [9,13], [11,15], [13,17], and [15,25] m/s.The total RMSE with groups is 1.05 m/s, which is less than the total RMSE without groups (1.16 m/s).However, the impact of the wind speed retrieval improvement on the final SST is less than 0.05 K, because the SSTs are derived in the wind speed groups with the overlap of 2 m/s.Therefore, the wind speed retrieval algorithm with groups is unnecessary for SST retrieval in this work.

V. CONCLUSION AND DISCUSSION
In this work, the SST retrieval algorithm coupled with the pseudo-SSEs was first developed.Then the SSTs between 60 • S and 60 • N were retrieved from the intercalibrated FY-3D MWRI measurements in 2020.Finally, the derived SSTs were validated with the iQuam in situ data and the GMI SST product, and the errors in the final SSTs are 0.12 ± 1.10 and 0.01 ± 1.15 K, respectively.
The results showed that the SST retrieval errors of the first step and the second step are, respectively, 0.48 ± 1.24 and 0.37 ± 1.13 K against the iQuam in situ data, while they are, respectively, 0.19 ± 1.23 and 0.17 ± 1.15 K against the GMI SST product.After introducing the pseudo-SSEs, both the mean and standard deviations of the retrieval errors decreased, especially the results against the iQuam in situ data.The results indicated that the SST retrieval algorithm developed in this work is accurate, and has equivalent performance as the W&M's algorithm in retrieving SSTs from the FY-3D MWRI measurements.
Due to the lack of wind speed direction, the fixed relative azimuth angle of 90 • was used to calculate the pseudo-SSEs.This reduced the accuracy of both the algorithm and the derived SSTs.In the future, the wind speed and direction will be simultaneously retrieved from the data acquired by microwave scatterometer on satellite.In addition, more training samples, more retrieval, and more validation are needed to further evaluate the algorithm's performance.

Fig. 5 .Fig. 6 .
Fig. 5. Scatterplots of the matching SSTs (a) between the SST retrieved in this work and the GMI SST, and (b) between the SST retrieved in this work and the iQuam in situ SST (R is the correlation coefficient, and the green lines are the diagonals.)

Fig. 7 .
Fig. 7. Retrieved SST errors against the iQuam in situ data vary with (a) SST and (b) sea surface wind speed.

TABLE II COMPARISON
OF THE TOTAL RMSE BETWEEN OUR ALGORITHM AND THE W&M'S ALGORITHM TO RETRIEVE SST FROM THE FY-3D MWRI MEASUREMENTS

TABLE III ERROR
PERCENTAGE STATISTICS OF THE FINAL SST RETRIEVED BY OUR ALGORITHM AND THE W&M'S ALGORITHM

TABLE IV SST
RETRIEVAL ERRORS IN THE THREE STEPS OF OUR AND IN THE TWO STEPS OF ALGORITHM