End-to-End Simulation of WCOM IMI Sea Surface Salinity Retrieval

The Water Cycle Observation Mission (WCOM) is an Earth science mission focused on the observation of the water cycle global climate change intensity through three different payloads. WCOM’s main payload is an interferometric microwave imager (IMI). IMI is a tri-frequency, one-dimensional aperture synthesis microwave radiometer operating at the L-, S-, and C-bands to perform measurements of soil moisture and ocean salinity. Focusing on sea surface salinity (SSS), an end-to-end simulator of WCOM/IMI has been realized and tested on climatological data. Results indicate a general agreement between original and retrieved SSS, with a single measurement root mean square error of 0.26 psu and with an orbital measurement of 0.17 psu in open sea. In accordance with previous studies, good results are obtained in open sea, while strong contamination is observed in coastal areas.


Introduction
The Chinese Water Cycle Observation Mission (WCOM), subject to the Strategic Space Science Priority Project of the Chinese Academy of Sciences, is planned to be launched in the near future.The WCOM aims to observe and track the main parameters related to the global water cycle, including soil moisture, ocean salinity, snow water equivalent, soil freeze-thaw, atmospheric water vapor, and precipitation [1].
To achieve the goals above, the WCOM relies on the following three payloads: (1) An interferometric microwave imager (IMI), a tri-frequency one-dimensional (1D) interferometric microwave radiometer operating at the L-, S-, and C-bands to measure soil moisture and sea surface salinity; (2) a polarimetric microwave imager (PMI), a conically scanning polarimetric radiometer operating at multiple frequencies between the C-and the W-band, with full polarimetric capabilities for most of them (it aims to measure land and sea surface temperature, water vapor, and precipitation); and (3) a dual-frequency polarized SCATterometer (DFPSCAT) to measure the snow water equivalent and soil freeze-thaw [2].
L-band microwave radiometry has been widely agreed as the most effective tool to measure soil moisture and ocean salinity from space.In fact, three satellite missions embarking with L-band radiometers have been launched in the past decade, namely ESA's Soil Moisture and Ocean Salinity mission (SMOS) [3], NASA's Aquarius/SAC-D [4], and Soil Moisture Active/Passive mission (SMAP) [5].However, the retrieval of salinity is still considered challenging due to the low sensitivity of brightness temperature (T B ) to salinity (from 0.8 K down to 0.2 K per psu, depending on ocean Like SMOS's MIRAS, IMI adopts aperture synthesis technology to overcome the barrier that the antenna size places at the L-band.Specifically, IMI is a tri-frequency (L-, S-, and C-bands) 1D interferometric radiometer consisting of a deployable 6 m parabolic cylinder mesh reflector and a tri-frequency patch feed array.Additionally, as a 1D interferometric radiometer, IMI has a lower system complexity compared with the two-dimensional MIRAS, indicating that it is much easier to control its in-orbit instrument stability and calibration accuracy.
As mentioned above, besides the L-band, the IMI also operates at the S-and C-bands, which can improve its sensitivity to soil moisture on land and assist in taking measurements of SSS and sea surface temperature (SST) on the ocean.

End-to-End Simulation Model and Method
The end-to-end simulation for ocean salinity in this paper is based on previous work regarding the 1D interferometric radiometer IMI simulation system [7], the sea radiometer transfer model, and a salinity retrieval algorithm.The simulation system is built on the Matlab platform.
The end-to-end simulation flow is shown in Figure 1.It begins with the input salinity data and ends with the retrieved SSS from the simulated "measured" T B .In the simulation, the original SSS, together with auxiliary data, were processed into the target T B scenes in different bands.These then formed the visibility function through the radiometer simulation.Afterwards, the visibility function was again reconstructed into T B .Finally, the retrieved SSS were achieved through the comparison between the reconstructed T B and the modeled T B .The modules used in the end-to-end simulation chain are highlighted as grey cases at the top of Figure 1.
ends with the retrieved SSS from the simulated "measured" TB.In the simulation, the original SSS, together with auxiliary data, were processed into the target TB scenes in different bands.These then formed the visibility function through the radiometer simulation.Afterwards, the visibility function was again reconstructed into TB.Finally, the retrieved SSS were achieved through the comparison between the reconstructed TB and the modeled TB.The modules used in the end-to-end simulation chain are highlighted as grey cases at the top of Figure 1.
Figure 1.The end-to-end simulation system of sea surface salinity (SSS) for the tri-frequency one-dimensional interferometric microwave imager, which consists of three major modules highlighted as grey cases at the top (i.e., the brightness temperature (T B ) generation module, radiometer module, and sea surface salinity (SSS) retrieval module).

T B Generation Module
As seen from Figure 1, the T B generation module was used not only in the measurement scene generation as an input to the radiometer module, but also in the SSS retrieval module to calculate and update the modeled T B .
According to [8], the T B at the top of the atmosphere in the Earth reference frame can be calculated using Equation (1).
where T B,sea is the T B radiated by the ocean surface and can be further calculated using Equation (2).
where T B,sea is described as the sum of T B in the case of a flat sea (T B, f lat ) and additional T B due to surface roughness (T B,rough ).T B, f lat is the emission of a flat sea surface, which can be described as a function of the SST and the Fresnel reflectivity.Γ f resnel , which in turns depends on the incident angle (θ) and the complex dielectric constant of sea water (ε).In this paper, ε is calculated using the Klein-Swift model [9] for the L-and S-band and the Meissner-Wentz model [10] for the C-band.For a rough sea surface, T B,rough is computed with a two-scale model [11] for the L-and S-band and is computed with the model from AMSR-E [12] for the C-band.
In Equation (1), T DN and T UP refer to the downward and upward atmospheric radiation, respectively, e −τ atm is the atmospheric opacity, and τ atm is the optical thickness.The model used for the atmosphere is from the ESA's SMOS mission for the L-band and from AMSR-E [12] for the C-band.Finally, Γ is the sea surface reflection coefficient, which can be expressed as Γ = 1 − T B,flat + T B,rough /SST , and T GAL is the cosmic and galactic contribution.
After the calculation of T B in the Earth reference frame, the T B in the antenna reference frame is obtained through multiplying the polarization rotation matrix as shown below.
where, T X , T Y , and T XY are the antenna T B , ϕ is the angle of polarization rotation, T B,H and T B,V are the horizontal and vertical components of T B in the Earth's reference frame, respectively.

Radiometer Module
In Figure 1, the radiometer simulation module processes the "measured" T B calculated from the T B generation module into the visibility function using the model of radiometer system.The visibility function calculation is described considering the weighted function of the antenna pattern [13,14], by applying Equation (4).
where F(ξ, η) is the normalized antenna pattern, which is a complex function including amplitude and phase; T B (ξ, η) is the T B from the observation scene; r ij is the fringe-washing function, which accounts for spatial decorrelation effects and depends on the frequency response of the pair of elements collecting the signals being correlated; and ξ and η are the direction cosine coordinates (ξ = cosφsinθ, η = sinφsinθ, with φ and θ being the angle in the instrument plane and the angle from the normal to the instrument plane, respectively.For IMI, a 1D radiometer, η = 0 and ν = 0 in Equation ( 4).Equation ( 4) is the ideal equation for the visibility function of interferometric synthetic aperture radiometers.To include the image errors introduced by coupling effects between the antennas, T B (ξ, η) in Equation ( 4) is replaced by T B (ξ, η) − T r , where T r is the physical temperature of the receivers and assumed to be 300 K in the simulation.This leads to the formulation of the Corbella equation.
The resulting V i,j (u, v) are processed by the T B reconstruction for generating the "measured" T B .Due to the difference between antenna patterns described in Section 2.3, it is not proper to directly apply the Fourier-based image reconstruction method.Specifically, the G matrix method [15,16] is used to reconstruct the T B map as, expressed in Equation ( 5).
where T is the reconstructed T B , G i + is the pseudoinverse matrix of the G matrix, and subscript i indicates the i-th visibility sample.There are only 18 continuous, non-redundant visibility samples for the eight-element linear feed array, forming a small-sized G matrix, simplifying the calculation of the pseudo-inverse through the Moor-Penrose method, and thus the image reconstruction.

SSS Retrieval Module
The SSS retrieval is based on a nonlinear iterative convergence algorithm where the prior values of the parameters to be retrieved were adjusted in order to minimize a cost function [16].T B values were calculated by applying the T B generation module described in Section 2.2.1 and were compared to the "measured" T B resulting from the radiometer simulation module.
The L-and S-band-measured T B data were suitable to retrieve SSS, while the C-band measured T B was used as auxiliary data to assist in the retrieval of SSS, and to retrieve SST.Thus, the cost function based on all the data of the three bands is expressed as Tb,L,p Tb,S,p where, Tb L,p,meas , Tb S,p,meas , and Tb C,p,meas indicate the "measured" T B at different bands (L-, S-, and C-band, respectively) and polarizations (horizontal and vertical), and σ 2 Tb,L,p , σ 2 Tb,S,p and σ 2 Tb,C,p , are the corresponding uncertainties.Lastly, SSS prior and SST prior refer to the prior estimated values for SSS and SST associated with the corresponding uncertainties σ 2 SSS and σ 2 SST .Since the current study focuses on salinity retrieval, the retrieval results of SST are not included.

Simulation Input
For IMI instrument concept proofing and performance validation, a ground-based demonstrator designed with an eight-element L-band radiometer is developed in 2011 [2] and applied in several ground-based experiments targeting different objects, such as buildings, the sun, the cold sky, a noise point source, etc.A picture of the aforementioned IMI prototype and a schematic of the arrangement of the antenna units in the 1D feed array are shown in Figure 2a and Figure 2b, respectively.The scatterometer units involved in the 1D feed array make the prototype a combined active/passive instrument.Anyway, since the performance of the radiometer instrument is the focus of this paper, only the radiometer feed array is adopted in the simulation.Both the actual measured antenna pattern and the distribution of the IMI prototype were applied in the simulation.Specifically, as seen in Figure 2b, the whole eight-element radiometer feed was considered a mixed array constituted by three small-size and five large-size antenna units, in which the minimum antenna spacing of the antenna array u Δ was 0.6125 λ.Along-track and cross-track antenna patterns measured from the prototype experiment for each unit are presented in Figures 3a  and 3b, respectively.
(a) (b) Other simulation inputs include geophysical data and orbit parameters.The orbit is configured as a sun-synchronous orbit with an altitude of 657 km and inclination of 98°, and the local time of the ascending node is at 6:00 a.m.Geophysical data, including SST, 10-meter wind speed, columnar atmospheric water vapor, and cloud liquid water were measured from AMSR-E [17], which are monthly averaged maps that all have spatial resolution of 0.25°.The original salinity map comes from World Ocean Atlas (WOA) 2013 [18], which is an in situ monthly averaged map with a spatial resolution of 1°.In order to be consistent in the simulation, the salinity map is interpolated into a Both the actual measured antenna pattern and the distribution of the IMI prototype were applied in the simulation.Specifically, as seen in Figure 2b, the whole eight-element radiometer feed was considered a mixed array constituted by three small-size and five large-size antenna units, in which the minimum antenna spacing of the antenna array ∆u was 0.6125 λ.Along-track and cross-track antenna patterns measured from the prototype experiment for each unit are presented in Figure 3a and Figure 3b, respectively.Both the actual measured antenna pattern and the distribution of the IMI prototype were applied in the simulation.Specifically, as seen in Figure 2b, the whole eight-element radiometer feed was considered a mixed array constituted by three small-size and five large-size antenna units, in which the minimum antenna spacing of the antenna array u  was 0.6125 λ.Along-track and cross-track antenna patterns measured from the prototype experiment for each unit are presented in Figures 3a  and 3b, respectively.The alias-free field of view (AF-FOV) areas were calculated using u  and applying max sin 1 2 u  = , leading to an observation angle included between −55° and 55°, approximately.All the reconstructed TB data within the AF-FOV were considered valid for the SSS retrieval.
Other simulation inputs include geophysical data and orbit parameters.The orbit is configured as a sun-synchronous orbit with an altitude of 657 km and inclination of 98°, and the local time of the ascending node is at 6:00 a.m.Geophysical data, including SST, 10-meter wind speed, columnar atmospheric water vapor, and cloud liquid water were measured from AMSR-E [17], which are monthly averaged maps that all have spatial resolution of 0.25°.The original salinity map comes from World Ocean Atlas (WOA) 2013 [18], which is an in situ monthly averaged map with a spatial resolution of 1°.In order to be consistent in the simulation, the salinity map is interpolated into a 0.25° × 0.25° dimension.The alias-free field of view (AF-FOV) areas were calculated using ∆u and applying sin θ max = 1/2∆u, leading to an observation angle included between −55 • and 55 • , approximately.All the reconstructed T B data within the AF-FOV were considered valid for the SSS retrieval.
Other simulation inputs include geophysical data and orbit parameters.The orbit is configured as a sun-synchronous orbit with an altitude of 657 km and inclination of 98 • , and the local time of the ascending node is at 6:00 a.m.Geophysical data, including SST, 10-m wind speed, columnar atmospheric water vapor, and cloud liquid water were measured from AMSR-E [17], which are monthly averaged maps that all have spatial resolution of 0.25 • .The original salinity map comes from World Ocean Atlas (WOA) 2013 [18], which is an in situ monthly averaged map with a spatial resolution of 1 • .In order to be consistent in the simulation, the salinity map is interpolated into a 0.25 Besides, the configuration of this simulation included both the measured antenna patterns and the image reconstruction error, and there was no additional noise or drift between the parameters used in the forward models and those used for the retrieval.

T B Reconstruction Results
The specific scene obtained for a sub-satellite point located at 62.68 W, 13.78 N is shown in Figure 4.The results of the T B generation module at the L-, S-, and C-bands are displayed on the left, center, and right panels, respectively, with horizontal (H-pol) and vertical polarizations (V-pol) on the top and bottom rows, respectively.

TB Reconstruction Results
The specific scene obtained for a sub-satellite point located at 62.68 W, 13.78 N is shown in Figure 4.The results of the TB generation module at the L-, S-, and C-bands are displayed on the left, center, and right panels, respectively, with horizontal (H-pol) and vertical polarizations (V-pol) on the top and bottom rows, respectively.Since the antenna array of IMI is 1D, the output from the TB reconstruction of the radiometer module is also 1D.Results of all the measured polarizations are shown in Figure 5, with the reconstructed TB data represented by the blue solid line and the simulated TB represented by the black dashed line.Good agreement is found between modeled and retrieved TB in the AF-FOV areas, with a root mean square error (RMSE) of 0.09 K. Since the antenna array of IMI is 1D, the output from the T B reconstruction of the radiometer module is also 1D.Results of all the measured polarizations are shown in Figure 5, with the reconstructed T B data represented by the blue solid line and the simulated T B represented by the black dashed line.Good agreement is found between modeled and retrieved T B in the AF-FOV areas, with a root mean square error (RMSE) of 0.09 K.
are expected at the other bands.
Since the antenna array of IMI is 1D, the output from the TB reconstruction of the radiometer module is also 1D.Results of all the measured polarizations are shown in Figure 5, with the reconstructed TB data represented by the blue solid line and the simulated TB represented by the black dashed line.Good agreement is found between modeled and retrieved TB in the AF-FOV areas, with a root mean square error (RMSE) of 0.09 K.

SSS Retrieval Results
In Figure 6, the results of SSS retrieval from a single measurement are shown.The retrieved SSS from each measurement are mapped into Earth coordinates in order to compare them with the WOA salinity data.The differences between WOA SSS and retrieved SSS are generally within ±0.5 psu, with an RMSE of 0.26 psu.

SSS Retrieval Results
In Figure 6, the results of SSS retrieval from a single measurement are shown.The retrieved SSS from each measurement are mapped into Earth coordinates in order to compare them with the WOA salinity data.The differences between WOA SSS and retrieved SSS are generally within ±0.5 psu, with an RMSE of 0.26 psu.As can be seen from Figure 7, although the SSS retrieval results in the center of the orbit and in the open sea (not near land or poles) are proven to be good, there are large errors, especially at the edge of the orbit and when approaching land.Those errors in the results can be attributed to the Figure 7a presents the half-orbital (about 2930 measurements) results of the SSS retrieval and the original WOA SSS, while their difference is shown in Figure 7b.
As can be seen from Figure 7, although the SSS retrieval results in the center of the orbit and in the open sea (not near land or poles) are proven to be good, there are large errors, especially at the edge of the orbit and when approaching land.Those errors in the results can be attributed to the aliasing effect, instrument imperfection, and the T B retrieval algorithm.Although T B measured from observation angles of −55 • -55 • are treated as AF-FOV and are used to retrieve SSS, the results still presented large errors near −55 • and 55 • due to the low sensitivity of T B to SSS.Even small errors in the reconstructed T B introduced large errors to the retrieved SSS.
To focus on the retrieval results in open sea, orbital SSS retrieval results from the South Pacific Ocean, South Atlantic Ocean, and Indian Ocean-namely Open Sea 1, 2, and 3, respectively-are selected in this study.Figure 8 presents the retrieved SSS of the three open sea areas on the top row and the corresponding error maps compared with the WOA SSS data on the bottom row.To avoid the large errors around the edge of the orbital results, a narrower AF-FOV the from an observation angle of −45-45 • are adopted for the retrieval in the three open sea areas.As can be seen from Figure 7, although the SSS retrieval results in the center of the orbit and in the open sea (not near land or poles) are proven to be good, there are large errors, especially at the edge of the orbit and when approaching land.Those errors in the results can be attributed to the aliasing effect, instrument imperfection, and the TB retrieval algorithm.Although TB measured from observation angles of −55°-55° are treated as AF-FOV and are used to retrieve SSS, the results still presented large errors near −55° and 55° due to the low sensitivity of TB to SSS.Even small errors in the reconstructed TB introduced large errors to the retrieved SSS.
To focus on the retrieval results in open sea, orbital SSS retrieval results from the South Pacific Ocean, South Atlantic Ocean, and Indian Ocean-namely Open Sea 1, 2, and 3, respectively-are selected in this study.Figure 8 presents the retrieved SSS of the three open sea areas on the top row and the corresponding error maps compared with the WOA SSS data on the bottom row.To avoid  As seen from Figure 8, the retrieval results in open sea are much better than the whole halforbital result in Figure 7. Table 2 displays quantitative results of the retrieved SSS in the three open sea areas, including their RMSE and standard deviations (std).From the quantitative analysis, the accuracy of SSS retrieval in open sea is about 0.17 psu, which satisfied the objective of an accuracy of 0.2 psu for salinity observation.including their RMSE and standard deviations (std).From the quantitative analysis, the accuracy of SSS retrieval in open sea is about 0.17 psu, which satisfied the objective of an accuracy of 0.2 psu for salinity observation.Compared with 2D instruments, such as SMOS/MIRAS, the imaging results of the 1D radiometer system manifested larger Gibbs errors [19], even for the observation of open seas.Also, the situation became worse when approaching land.This can be attributed to the number of antenna elements of the 1D radiometer system (i.e., eight) used in this paper being much less than that used in the SMOS/MIRAS 2-D system (i.e., 69).The reduction of the antenna elements leads to the reduction of baselines and, eventually, results with a more severe sampling truncation in the spatial frequency domain.This is challenging for systems with small scale antenna elements, like our IMI prototype.An improved system, which may consist of more antenna elements in the feed array, will be developed in the future based on the IMI prototype.Although larger scale antenna arrays will reduce the Gibbs error, land contamination in the observations cannot be eliminated.Many studies devoted to reducing land contamination in SMOS have been carried out [20].Future work will also focus on the correction of land contamination for our designed system.

Figure 2 .
Figure 2. A ground-based prototype of the one-dimensional interferometric microwave imager (IMI).(a) Photo of the ground-based IMI prototype.(b) Arrangement of the small and large antenna units in the feed array of the IMI prototype.

Figure 3 .
Figure 3.The antenna pattern of the eight-element prototype of the 1D IMI, including the along-track and cross-track antenna patterns in (a) and (b), respectively.

Figure 2 .
Figure 2. A ground-based prototype of the one-dimensional interferometric microwave imager (IMI).(a) Photo of the ground-based IMI prototype.(b) Arrangement of the small and large antenna units in the feed array of the IMI prototype.

Figure 2 .
Figure 2. A ground-based prototype of the one-dimensional interferometric microwave imager (IMI).(a) Photo of the ground-based IMI prototype.(b) Arrangement of the small and large antenna units in the feed array of the IMI prototype.

Figure 3 .
Figure 3.The antenna pattern of the eight-element prototype of the 1D IMI, including the alongtrack and cross-track antenna patterns in (a) and (b), respectively.

Figure 3 .
Figure 3.The antenna pattern of the eight-element prototype of the 1D IMI, including the along-track and cross-track antenna patterns in (a) and (b), respectively.

Figure 4 .
Figure 4. TB scenes from the forward TB generation module, used as the input of the radiometer simulation.From left to right, the L-, S-, and C-band TB are presented.The horizontal and vertical TB are presented on the top and bottom row, respectively.

Figure 4 .
Figure 4. T B scenes from the forward T B generation module used as the input of the radiometer simulation.From left to right, the L-, S-, and C-band T B are presented.The horizontal and vertical T B are presented on the top and bottom row, respectively.The T B scenes in Figure 4 are used as inputs for the successive radiometer simulation to achieve T B reconstruction results.Due to the lack of measurement data from the S-and C-band antenna array, only T B reconstruction as a result of the L-band is presented in the following figure, similar results are expected at the other bands.Since the antenna array of IMI is 1D, the output from the T B reconstruction of the radiometer module is also 1D.Results of all the measured polarizations are shown in Figure5, with the reconstructed T B data represented by the blue solid line and the simulated T B represented by the black dashed line.Good agreement is found between modeled and retrieved T B in the AF-FOV areas, with a root mean square error (RMSE) of 0.09 K.

Figure 5 .
Figure 5. L-band reconstructed TB output from the radiometer simulation.The blue solid line and the black dashed line present the reconstructed TB and original simulated TB, respectively.From left to right are the horizontal polarization (H-pol), cross polarization (HV-pol, VH-pol), and vertical polarization (V-pol) results.

Figure 5 .
Figure 5. L-band reconstructed T B output from the radiometer simulation.The blue solid line and the black dashed line present the reconstructed T B and original simulated T B , respectively.From left to right are the horizontal polarization (H-pol), cross polarization (HV-pol, VH-pol), and vertical polarization (V-pol) results.

Figure 6 .
Figure 6.Comparison results of retrieval SSS and World Ocean Atlas (WOA) salinity, which are represented by the red stars and the blue circles, respectively.

FigureFigure 7 .
Figure7apresents the half-orbital (about 2930 measurements) results of the SSS retrieval and the original WOA SSS, while their difference is shown in Figure7b.

Figure 6 .
Figure 6.Comparison results of retrieval SSS and World Ocean Atlas (WOA) salinity, which are represented by the red stars and the blue circles, respectively.

Figure 6 .
Figure 6.Comparison results of retrieval SSS and World Ocean Atlas (WOA) salinity, which are represented by the red stars and the blue circles, respectively.

FigureFigure 7 .
Figure7apresents the half-orbital (about 2930 measurements) results of the SSS retrieval and the original WOA SSS, while their difference is shown in Figure7b.

Figure 7 .
Figure 7. (a) Half-orbital SSS retrieval result and the WOA salinity, and (b) corresponding error map when compared with WOA salinity.

Figure 8 .
Figure 8. Simulation results of the orbital retrieved SSS in the three selected open sea areas.SSS retrieval results and the corresponding SSS error maps compared with WOA salinity are shown in the top and bottom rows, respectively.

Figure 8 .
Figure 8. Simulation results of the orbital retrieved SSS in the three selected open sea areas.SSS retrieval results and the corresponding SSS error maps compared with WOA salinity are shown in the top and bottom rows, respectively.As seen from Figure8, the retrieval results in open sea are much better than the whole half-orbital result in Figure7.Table2displays quantitative results of the retrieved SSS in the three open sea areas,

Table 2 .
Root mean square error (RMSE) and standard deviation (std) of the retrieved SSS for the three selected open sea areas.