## Abstract

One-dimensional synthetic aperture microwave radiometer (1D-SAMR) can provide remote sensing images at a higher spatial resolution than those from traditional real aperture microwave radiometers. As 1D-SAMR operates at multiple incidence angles, we proposed a multiple linear regression method to retrieve sea surface temperature at an incidence angle between 0° and 65°. Assuming that a 1D-SAMR operates at various frequencies (i.e., 6.9, 10.65, 18.7, 23.8 and 36.5 GHz), a radiation transmission forward model was developed to simulate the brightness temperature measured by the 1D-SAMR. The sensitivity of the five frequencies to sea surface temperature was examined, and we evaluated the reliability of the regression method proposed in this study. Furthermore, 11 schemes with various frequency combinations were applied to retrieve sea surface temperature. The results showed that the five-frequency combination scheme performed better than the other schemes. This study also found that the accuracy of retrieved sea surface temperature is dependent on incidence angles. Finally, we suggested that the incidence angle range of the 1D-SAMR is necessary to be 30°–60° based on the relationship between the accuracy of retrieved sea surface temperature and the incidence angles.

## 1. Introduction

Sea surface temperature (SST) is an important geophysical indicator to detect global climate change, the cycles of water and energy as it plays an important role in the interactions between air and ocean (Curry et al. 2004; Reynolds et al. 2002). On-site measurement methods of SST, e.g., ship and marine buoys measurements, can provide near-true values that are essential for validating synthetic data obtained from satellite approaches. However, conventional on-site methods cover only a limited measured region and have a long time sampling period. In other words, on-site measurement methods have a limitation to provide measurements for a large-scale region during a long-term period. As an alternative, therefore, the demands of remote sensing images such as satellite data have been rapidly growing to derive SST at a global scale.

Among infrared and microwave remote sensing methods that are currently employed to measure SST (Guan and Kawamura 2003), the microwave remote sensing method has an advantage that the wavelength is much longer than that of aerosol particles, water vapor molecules and cloud droplets, compared with infrared remote sensing. Therefore, in addition to strong precipitation conditions, passive microwave remote sensing is capable of continuously detecting SST (Chelton and Wentz 2005; Ulaby et al. 1983).

A real aperture microwave radiometer, one of the instruments of passive microwave remote sensing, provides a spatial resolution of Δ*x*, which is limited by the size of the antenna (*D*) and wavelength (*λ*) due to the relationship of Δ*x* ∝ *λ*/*D*. For example, the WindSat microwave radiometer with antenna diameter of 1.8 m, the first fully polarized microwave radiometer in space, has a ground field of view at a spatial resolution of 39 km × 71 km on a 6.8 GHz channel (Gaiser et al. 2004). The Copernicus Imaging Microwave Radiometer (CIMR) has a longer antenna diameter of 7 m to provide a higher spatial resolution (Kilic et al. 2018).

Therefore, the concept of synthetic aperture microwave radiometry was proposed to improve the spatial resolution (Ryle 1962). Synthesis aperture radiometer can synthesize a large aperture by sparsely arranging a number of small aperture antennas to achieve high spatial resolution (Ruf et al. 1988; Schanda 1979). With the objective of designing an optimized satellite instrument dedicated to an “all-weather” estimation of the SST at high spatial resolution (15 km), the instrument concepts using synthetic interferometric antennas have been studied in Prigent et al. (2013). The analysis showed that two-dimensional interferometric systems would be very complex and would not meet the user requirements in terms of SST retrieval accuracy. A one-dimensional interferometric system could be proposed, but its development requires additional investigation.

One-dimensional synthetic aperture microwave radiometer (1D-SAMR) can generate a two-dimensional image from a space platform movement. The concept of 1D-SAMR is shown in Fig. 1. The major characteristic of 1D-SAMR is multiple continuous incidence angles. Today, many studies have used 1D-SAMR in the world. For example, HUST-ASR developed by Huazhong University of Science and Technology, Wuhan, China (Chen et al. 2010; Dong et al. 2011; Li et al. 2008a,b), generated good images of natural scenes such the sun and buildings when operating at an 8 mm frequency band and observation angles between −30° and +30°. If a 1D-SAMR is used to observe SST in the future, the multiple incidence angles characteristic needs special attention. In this paper, based on the radiation transmission model, we proposed an algorithm that retrieves SST at a range of incidence angles between 0° and 65°. In addition, we investigated the relationship between SST retrieval results and incidence angles by using various frequency combinations. It is noteworthy that the SST retrieval algorithm is validated with simulation.

## 2. Methodology

The sensitivity of the C-band to SST, such as the 6.925 GHz of the Advanced Microwave Scanning Radiometer for EOS (AMSR-E), is an essential frequency for retrieving SST (Wentz and Meissner 2007). WindSat uses similar frequencies to AMSR-E that uses frequencies of 6.925, 10.65, 18.7, 23.8, and 36.5 GHz to retrieve SST. Therefore, this study assumed that the frequencies of the 1D-SAMR are 6.9, 10.65, 18.7, 23.8, and 36.5 GHz and all frequencies work in a dual-polarization manner (vertical and horizontal polarizations).

### a. Retrieval method

The mathematic form of the retrieval method is derived from a multilinear regression algorithm (Wentz and Meissner 2000) as in Eq. (1). Since 1D-SAMR has multiple incidence angles that considerably influence the brightness temperature, this study proposed a new model that derives a set of regression coefficients at 1° intervals. As shown in Fig. 2, radiation transmission forward model and environmental scenes are crucial for deriving regression coefficients and verifying the feasibility of this algorithm:

where *R* and *X* are linear functions, *n* is the number of the frequency selected, *A*_{0} and *A*_{i} are the regression coefficients, and $TB,imeas$ is the brightness temperature measured by a spaceborne 1D-SAMR.The linear function is as follows:

### b. Data

To establish environmental scenes that exist in nature, the newest version of the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data, namely, ERA5, was employed. It provides the 10 m wind speed components (*u* and *υ*), the total column of cloud liquid water content (*L*), total column water vapor content (*V*), average rainfall rate (*R*), and SST (*T*_{S}) at 0.25°. The time of the data are 0000 and 1200 UTC on 15 January, 15 April, 15 July, and 15 October 2018. The wind speed (*W*) and wind direction (*φ*) are obtained from the 10 m wind speed components *u* and *υ*. We obtain approximately 730 000 sets of data from ERA5 excluding for precipitation conditions (*R* > 0, *T*_{S} < 271.15 K, and *L* < 0 mm). Statistical histograms of the wind direction, wind speed, SST, total column of cloud liquid water content, and total column of water vapor content are shown in Fig. 3, where the magnitude of an integer is 10°. Since the seawater salinity (*S*) has little effect on the frequencies, we set the seawater salinity to 35 psu. Dividing the data into training and test sets on average, the training set was used for deriving the multiple linear regression coefficients, and the algorithm was validated using the test set.

### c. Ocean–atmospheric radiation transmission forward model

The brightness temperature from a spaceborne 1D-SAMR incorporating the theory of polarized radiation transmission (Meissner and Wentz 2012) can be expressed as

where *T*_{B,p} is the brightness temperature received by the radiometer; *T*_{BU} and *T*_{BD} are the atmospheric upward and downward radiation brightness temperature, respectively; *T*_{S} is the SST; and *T*_{cold} is the effective cold-space temperature, which is usually assumed to be a fixed value of 2.7 K. Also, *E*_{p} is the total sea surface emissivity, *R*_{p} = 1 − *E*_{p} is the sea surface reflectivity, *τ* is the atmospheric transmittance, *T*_{BΩ} is the downwelling sky radiation that is scattered from the ocean surface, and *τT*_{B,scat,p} is the atmospheric path correction in the downwelling scattered sky radiation. Subscript *p* is the polarization mode, *p* = v, h.

Among the atmospheric radiation and the sea surface emissivity models that are usually categorized in the radiation transmission forward models, the sea surface emissivity model adopted in this paper was developed by Meissner and Wentz (2012). The model can calculate the sea surface emissivity for incidence angles ranging from 0° to 65° and SST within approximately −2° to 40°C. According to Meissner and Wentz (2012), the sea surface emissivity (*E*_{p}) has three components:

where *E*_{0,p} is the specular sea surface emissivity that is a function of frequency (*f*), seawater salinity(*S*), SST (*T*_{S}), and Earth incidence angle (*θ*_{EIA}), which is also related to the complex permittivity of seawater (*ε*) that is evaluated by Meissner and Wentz (2004, 2012). Also, Δ*E*_{W,p} and Δ*E*_{φ,p} are the increments of sea surface emissivity associated with wind speed and wind direction, respectively.

For the atmospheric part, we use the empirical model of atmospheric absorption emission to calculate *T*_{BU}, *T*_{BD}, and *τ* (Wentz and Meissner 2000). This model needs to input frequency (*f*), Earth incidence angle (*θ*_{EIA}), SST (*T*_{S}), total column cloud liquid water content (*L*), and total column water vapor content (*V*). More details on formulas and empirical coefficient are found in Wentz and Meissner (2000) and Wang et al. (2005).

The 1D-SAMR brightness temperature $\u2061(TB,pmeas)$ was simulated by the sum of a modeled brightness temperature $\u2061(TB,pmod)$ calculated by a radiation transmission forward model and a Gaussian noise generated by a random number generator. The Gaussian noise represents an error of the brightness temperature measurement. We assumed that the measurement error of each channel is 0.5 K to better analyze the effect of different frequency combinations on retrieval of SST. It should be noted that the modeling error and the impact of radio frequency interference (RFI) were not considered in this study.

## 3. Results and discussion

### a. Sensitivity of brightness temperature at five frequencies to environment scene parameters

The ocean emissivity is primarily depending on the environment scene parameters (*T*_{S}, *W*, *V*, and *L*) and the sensitivities to the frequency (Kilic et al. 2018; Wilheit and Chang 1980). Assuming a background field, as shown in Table 1, to formulate the relationship between the sensitivity to environment scene parameters and the incidence angles, the radiation transmission forward model is used to calculate the brightness temperature. The sensitivity (SN) of five frequencies to the environment scene parameters at different incidence angles is calculated by Eq. (8). It should be noted that the sensitivity is not derived from wind speed but from the directional surface roughness of the sea surface that is induced by wind-wave and surface current interactions, subsequently leading to changes in frequency-dependent surface emissivity. However, these direct factors were replaced with wind in modeling and expressed these impacts as the sensitivity to the wind (Meissner and Wentz 2012):

where *M* represents the ERA5 climate variables employed in this study, i.e., SST, wind speed, the total column of water vapor content, and the total column of cloud liquid water content, and *n* is the number of *M*. As before, *p* is the polarization mode, *p* = v, h.

Figure 4 shows the relationship between the incidence angle and the sensitivity of the vertical and horizontal polarization brightness temperature of five frequencies to the ERA5 climate variables. In Figs. 4a and 4b, it is found that the sensitivity to SST is higher at vertical polarization and horizontal polarization decreases with frequencies on the order of 6.9 to 36.5 GHz. The sensitivity to SST at vertical polarization increases with the incidence angles except for 36.5 GHz (Fig. 4a). While the sensitivity to SST at horizontal polarization decreases with the incidence angles for 6.9 and 10.65 GHz (Fig. 4b), the horizontal polarization sensitivity to SST is almost constant regardless of the incidence angles for 18.7 and 23.8 GHz (Fig. 4b). For 36.5 GHz, the vertical and horizontal polarization sensitivity to SST is less than zero in the ranges of 0° ≤ *θ*_{EIA} ≤ 26° and 0° ≤ *θ*_{EIA} ≤ 46°, respectively. The vertical and horizontal polarization sensitivity of 36.5 GHz to SST decreases first and then increases with the incidence angles.

Figures 4c and 4d present the sensitivity to wind speed. The sensitivities of vertical polarization decrease with the incidence angles. In addition to 6.9 and 10.65 GHz, the sensitivities of horizontal polarization increase first and then decrease as the incidence angles increase. In Figs. 4e and 4f, it is prominent that the sensitivities of 23.8 GHz to the total column of water vapor content are the highest because the frequency is in the absorption band of water vapor (Liebe 1985); 23.8 GHz can correct the effect of water vapor in retrieval of SST. In addition, Figs. 4g and 4h show that the sensitivity of 36.5 GHz to the total column of cloud liquid water is the highest because the wavelength of 36.5 GHz is about 8 mm, which is scattered greatly by cloud droplets.

### b. SST RMS error at different incidence angles

The higher number of a frequency combination scheme (e.g., five-frequency combination scheme) is incorporated, the higher accuracy can be achieved for all incidence angles. As the number of frequencies of a spaceborne 1D-SAMR in the future increases, it may require more cost, power, volume, and mass. Therefore, we applied a three-frequency and four-frequency combination scheme to retrieve SST. Table 2 lists the 11 retrieval schemes. The relationship between the root-mean-square (RMS) error of the training and test sets and the incidence angles are shown in Figs. 5a and 5b, respectively.

Figures 5a and 5b show that the RMS error for the test set is comparable to that of the training set. The RMS errors of all schemes decrease at first and then increased slightly with the incidence angle. The minimum values of RMS error occurred at *θ*_{EIA} = 35° and *θ*_{EIA} ≈ 50° for scheme 1 and the other schemes, respectively, resulting from the fact that the influence of 6.9 and 10.65 GHz horizontal polarization brightness temperature on SST decrease as the incidence angles increase.

The ranges of RMS error for scheme 1 to scheme 11 are also shown in Table 2. Scheme 1 performed the best at all incidence angles as it contains all channels sensitive to the SST. The RMS errors of schemes 2 and 3 were similar to each other while scheme 3 performed better than scheme 2 in the range from 0° to 12°. In addition, the RMS error of scheme 7 was lower than that of scheme 6 in the range from 0° to 12°. These results are contradictory to the sensitivity shown in Figs. 4a and 4b (the sensitivity to the SST is lower at 23.8 GHz than at 18.7 GHz), which may be caused the interaction between different frequencies during the SST retrieval. Schemes 2 and 3 performed better than scheme 5 at all incidence angles because the accuracy of SST retrieval is greatly affected by 10.65 GHz. In addition, schemes 9 and 10 performed better than scheme 11. Schemes 4, 6, and 7 containing 36.5 GHz showed a larger RMS error at lower incidence angles. In schemes 6 and 7, the RMS error increased slightly within the incidence angles from 0° to 4°, resulting from the less sensitivity (less than zero) of 36.5 GHz to the SST at lower incidence angles. In addition to schemes 9 and 10, other schemes with four-frequency combinations performed worse than the schemes with three-frequency combinations at some incidence angles.

Overall, all schemes performed poorly at low incidence angles, indicating that a 1D-SAMR is used to retrieve the SST at the incidence angle range between 30° and 60° to provide the reliable SST data.

## 4. Conclusions

In this paper, we proposed a SST retrieval method for the multiple incidence angles characteristic of 1D-SAMR. Under the assumption that the 1D-SAMR operates with multiple incidence angles at 6.9, 10.65, 18.7, 23.8, and 36.5 GHz, the 11 schemes of SST retrieval were examined at the range from 0° to 65° to provide a reference for the development of the 1D-SAMR and a methodology of SST retrieval for a spaceborne 1D-SAMR.

In this paper, we evaluated the sensitivity to SST at the range of 0° and 65°. We found that the sensitivity to SST was higher at vertical polarization than at horizontal polarization and the sensitivity to SST decrease with the frequencies from 6.9 to 36.5 GHz. We also used a retrieval scheme with a multiple linear regression method for five-frequency and three-frequency combination retrieval schemes. The multiple linear regression equations were formulated with the training set in the range of 0° and 65° for each scheme and the developed regression coefficients were validated using the test set. The results indicated that the relationship between RMS errors and the incidence angles for the training and test sets was similar to each other. Scheme 1 and others reached the minimum at 35° and approximately 50°, respectively, resulting from the effect of 6.9 and 10.65 GHz horizontal polarization brightness temperature. Scheme 1 showed the highest retrieval accuracy at all incidence angles because it contains more channels and information. Schemes 2 to 11 performed differently at each of incidence angle as the effects of frequency combinations are variant from the incidence angles. Finally, this study suggested that the incidence angle range of the 1D-SAMR is necessary to be 30°–60° based on the relationship between the RMS error and the incidence angles.

## Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grants 41475019 and 41306187). Many thanks to the ECMWF for providing the ERA5 data.

## REFERENCES

*Bull. Amer. Meteor. Soc.*

*J. Infrared Millimeter Terahertz Waves*

*Bull. Amer. Meteor. Soc.*

*IEEE Trans. Antennas Propag.*

*IEEE Trans. Geosci. Remote Sens.*

*J. Oceanogr.*

*J. Geophys. Res. Oceans*

*Int. Geoscience and Remote Sensing Symp.*, Boston, MA, IEEE

*Radio Sci.*

*IEEE Trans. Geosci. Remote Sens.*

*IEEE Trans. Geosci. Remote Sens.*

*J. Geophys. Res. Oceans*

*J. Climate*

*IEEE Trans. Geosci. Remote Sens.*

*Nature*

*Antennas and Propagation Society Int. Symp.*, Seattle, WA, IEEE

*IEEE Trans. Geosci. Remote Sens.*

*Proc. SPIE*

*Radio Sci.*

Int. Conf. on Microwave and Millimeter Wave Technology, Nanjing, China, IEEE