Retrieval of Sea Surface Wind Speed by One-Dimensional Synthetic Aperture Microwave Radiometer

Sea surface wind speed (SSWS) is an important geophysical parameter that affects ocean dynamic cycles and sea-air interactions (Meissner and Wentz^[1]; Yao et al.^[2]; Fang et al. ^[3]). At present, satellite-borne microwave remote sensing has become the main method of SSWS detection (Wang et al.^[4]).

The SSWS will affect the sea surface emissivity (Wu and Fung^[5]; Wentz^{[6, 7]}; Meissner and Wentz^[8]), resulting in changes to the radiation brightness temperature and thus allowing for a microwave radiometer to retrieve the SSWS (Hong and Shin^[9]). Compared with real aperture microwave radiometers, one-dimensional synthetic aperture microwave radiometers use a small-aperture antenna array instead of a large real-aperture antenna, and the spatial resolution is determined by spectrum sampling, not by the size of antennas (Vine et al.^[10]; Vine^[11]; Li et al.^[12]). Thus, one-dimensional synthetic aperture microwave radiometer can provide remote-sensing images at a higher spatial resolution than those from traditional real aperture microwave radiometers (Schanda^[13]; Ruf et al.^[14]; Chen et al.^[15]). The concept of one-dimensional synthetic aperture microwave radiometer is shown in Fig. 1. Spaceborne one-dimensional synthetic aperture microwave radiometer can generate a two-dimensional image from a space platform movement (Feng et al.^[16]). It scans through a certain angular range with respect to the forward direction of the satellite, with each observation point corresponding to a different incidence angle (Li et al.^[17]).

Figure 1.  Schematic diagram of the scan process of a one-dimensional synthetic aperture microwave radiometer.

Due to one-dimensional synthetic aperture microwave radiometer has higher resolution, it will be widely used on satellite platform to monitor extreme weather such as tropical cyclones in the future. However, one-dimensional synthetic aperture microwave radiometer has multiple continuous incidence angles which considerably influence the brightness temperature, so the SSWS cannot be retrieved at multiple incidence angles using the retrieval algorithms developed for real-aperture microwave radiometers. Therefore, it is necessary to retrieve SSWS at each incidence angle (i.e., 0°, 1°, 2°, 3°, etc.).

At present, the sea surface wind speed retrieval algorithms for microwave radiometer mainly include physical algorithms (Ai et al.^[18]; Bettenhausen et al.^[19]; Brown et al.^[20]; Koner et al.^[21]; Meissner and Wentz^[22]) and empirical algorithms (Wentz and Meissner^[23]; Goodberlet et al. ^[24]; Obligis et al.^[25]; Krasnopolsky et al.^[26]; An et al.^[27]; Jena et al.^[28]; Alsweiss et al.^[29]; Wang et al. ^[30]; Smith et al.^[31]). The physical algorithms are based on the radiative transfer model, which retrieves sea surface SSWS by establishing a cost function of observations and model simulations. However, the physical retrieval algorithms require a large amount of computing resources, so we propose a multiple linear regression algorithm for one-dimensional synthetic aperture microwave radiometer to retrieve the SSWS from space. The algorithm involves a small amount of computing resources and is easy to implement, so it can be used as an on-board processing method in the future. In addition, we study the retrieval results and the sensitivity to the SSWS based on simulation in the range of 0°~65°.

The rest of this paper is organized as follows. The proposed retrieval algorithm and the forward model are presented in section 2. The results and discussion are introduced in section 3. The conclusions are presented in section 4.

In this paper, we use the frequency of WindSat as a reference to assume a one-dimensional synthetic aperture microwave radiometer which operate at frequencies of 6.9, 10.65, 18.7, 23.8, and 36.5 GHz. All frequencies work in a dual polarization manner (vertical and horizontal polarization). We used vertical polarization channels (VR), horizontal polarization channels (HR) and all channels (AR) to retrieve the SSWS via a multiple linear regression algorithm, respectively. Fig. 2 shows the process of retrieving the SSWS.

Figure 2.  Diagram of the process of retrieving the SSWS.

The multiple linear regression equation is as follows (Wilheit and Change^[32]; Lojou et al.^[33]; Milman and Wilheit^[34]):

where W is the SSWS, R and X are linearizing functions, A_i is the regression coefficients, n is the number of channels, and T_{B, meas, i}^θ is the brightness temperature measured by a spaceborne onedimensional synthetic aperture microwave radiometer.

In this paper, we use the following linearization functions:

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. In this paper, the newest version of the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data, ERA5(Li et al.^[35]), is used to establish environmental scenes. The data contain the 10-m wind speed components u and v, the total column cloud liquid water content L, the total column water vapour content V, the average rainfall rate R and the sea surface temperature T_S. The acquisition times are 0:00 and 12:00 on January 15, April 15, July 15, and October 15, 2018. The spatial resolution of the data is 0.25°. The wind speed W and wind direction φ are calculated by using the 10-m wind speed components u and v. Data with R > 0, T_S < 271.15 and L < 0 are eliminated, resulting in approximately 710, 000 sets of data after processing. The seawater salinity S is set to 35 psu because S has little effect on the frequencies of the one-dimensional synthetic aperture microwave radiometer.

We obtain approximately 730, 000 sets of data after processing. Statistical histograms of the sea surface temperature, wind direction, wind speed, total column cloud liquid water content and total column water vapour content are shown in Fig. 3. Finally, we randomly divide the data into a training set and a test set on average. The training set is used to train the retrieval algorithm, and the test set is used to test its performance.

Figure 3.  Distribution histograms of environmental parameters: (a) sea surface temperature, (b) SSWS, (c) sea surface wind direction, (d) total column cloud water vapour content, and (e) total column cloud liquid water content.

According to the theory of polarized radiative transfer (Hilburn et al.^[36]; Meissner and Wentz^{[1, 7]}), the brightness temperature T_{B, mod, p}^θ which is theoretically received by the spaceborne one-dimensional synthetic aperture microwave radiometer can be expressed as follows:

where the subscript θ denotes the incidence angle, 0° ≤ θ ≤ 65°; the subscript p denotes the polarization mode, p = v, h; T_{BU, θ} and T_{BD, θ} are the upwelling and downwelling atmospheric brightness temperatures, respectively; τ_θ is the atmospheric transmittance; E_{p, θ} is the total sea surface emissivity; T_S is the sea surface temperature; T_{BΩ, θ} is the downwelling sky radiation that is scattered from the sea surface; R_{p, θ} = 1 - E_{p, θ} is the sea surface reflectivity; T_cold=2.7K is the effective cold space temperature. τ_θ · T_{B, scat, p, θ} represents the atmospheric path length correction for the downwelling scattered sky radiation.

The forward model of microwave radiative transfer is divided into components related to atmospheric radiation and ocean radiation. We use the sea surface emissivity model developed by Meissner and Wentz^[7] in 2012:

where E_{0, p, θ} is the specular sea surface emissivity, which is a function of the frequency f, incidence angle θ, sea surface temperature T_S and salinity S and can be calculated using Fresnel' s law (Meissner and Wentz^{[7, 37]}); ΔE_{W, p, θ} is the emissivity increase caused by the wind speed W; ΔE_{φ, p, θ} represents the four Stokes parameters of the sea surface wind direction signal and captures the dependence on the wind direction φ.

ΔE_{W, p, θ} is used as the basis for the retrieval of the SSWS, and it is a function of the frequency f, SSWS W, incidence angle θ, sea surface temperature T_S and salinity S. ΔE_{W, p, θ} can be expressed as follows (Meissner and Wentz^[7]):

where x_p represents x_v=4.0 and x_H=1.5, the subscript nad denotes the satellite nadir angle, θ_ref = 55.2° is the reference incidence angle, T_ref = 20°C is the reference temperature, and δ_{k, p} is the interpolation coefficient, which is related to the wind speed.

Scattering can be neglected under nonprecipitating atmospheric conditions (Meissner and Wentz^[7]). In the frequency range below 100 GHz, the main absorptive components of the atmosphere are oxygen, water vapour and liquid water, T_{BU, θ}, T_{BD, θ} and τ_θ can be calculated from the atmospheric profile (Wentz and Meissner^[23]; Waters^[38]). Considering the amount of computation required and the size of the data, we use an empirical model to calculate T_{BU, θ}, T_{BD, θ} and τ_θ(Wentz and Meissner^[23]; Waters^[38]). The empirical model requires the frequency f, incidence angle θ, sea surface temperature T_S, total column liquid water content L, and total column water vapour content V as inputs. It should be noted that Equation (8) is adopted in this paper to calculate the absorption coefficient of liquid water A_L (Rui et al.^[39]) because the empirical model requires the average cloud temperature T_L as an input, which is difficult to obtain.

where A_L is the absorption coefficient of liquid water, V is the total column water vapour content, L is the total column liquid water content, b_L0 and b_L1 are the regression coefficients.

We use the radiation transmission model to calculate the modelled brightness temperature T_{B, mod, p}^θ, and the measured brightness temperature T_{B, meas, p}^θ was simulated by the sum of a T_{B, mod, p}^θ and the Gaussian noises generated by a random number generator. The Gaussian noise represents an error of the brightness temperature measurement. The average value of the Gaussian noise is 0 K, and standard deviations of 0.2 K, 0.4 K, and 0.6 K are considered. Many researchers use Gaussian noise to simulate measured brightness temperatures (Wentz and Meissner^[23]; Bobylev et al.^[40]); this is a reasonable approach for preliminary research in the absence of real satellite observation data. It should be noted that the modelling error and the impact of Radio Frequency Interference (RFI) are not considered in this study.

Sensitivity of the brightness temperature to the SSWS affects the SSWS retrieval accuracy. Theoretically, the greater this sensitivity is, the more information on the SSWS is contained in the brightness temperature, and the higher the retrieval accuracy will be. In addition, the interaction between different frequencies during the SSWS retrieval can also affect the SSWS retrieval accuracy, which is difficult to predict. We assume a particular environmental scene to calculate the sensitivity of the brightness temperature at five frequencies to the SSWS, as shown in Table 1.

The sensitivity of the brightness temperature to the SSWS at different incidence angles can be calculated using Equation (9):

where Se_p is the average value of the sensitivity of the brightness temperature to the SSWS at an incidence angle of θ, n = 30 is the number of SSWS, T_{B, mod, p, θ} is the mode brightness temperature calculated using the forward model of microwave radiative transfer at an incidence angle of θ, p = v, h is the polarization mode, and W is the SSWS.

Figure 4a and 4b shows the average values of the sensitivity of the vertical and horizontal polarization brightness temperatures, respectively, to the SSWS at different incidence angles. The sensitivity of the horizontal polarization brightness temperature to the SSWS is greater than that of the vertical polarization brightness temperature. The sensitivity of the vertical polarization brightness temperature to the SSWS decreases as the incidence angle increases but remains almost unchanged in the range of 0°~30°, which is because the Se_v is not sensitive to the incidence angle in the range of 0°~30°. The 6.9 and 10.65 GHz horizontal polarization brightness temperatures show an increasing sensitivity to the SSWS as the incidence angle increases. At 18.7, 23.8, and 36.5 GHz, the sensitivity of the horizontal polarization brightness temperature to the SSWS first increases and then decreases as the incidence angle increases.

Figure 4.  Sensitivity of the brightness temperature to the SSWS as a function of the incidence angle.

The root-mean-square (RMS) error and mean bias within the range of 0° ~65° are calculated in accordance with Equations (10) and (11).

where RMSE is the RMS error, MB is the mean bias, N is the number of samples, W_k^true is the true SSWS, and W_k is the retrieved value of the SSWS.

Figure 5 shows the relationships between the RMS error and mean bias and the incidence angle. Fig. 5a and 5b show the retrieval results obtained using only the vertical polarization channels (VR). Fig. 5c and 5d show the retrieval results obtained using only the horizontal polarization channels (HR). Fig. 5e and 5f show the retrieval results obtained using all channels (AR). In each subfigure, the left panel shows the retrieval results for the training set, and the right panel shows the retrieval results for the test set. The results show that the RMS errors on the training and test sets are similar. The mean bias values of VR, HR and AR are very low and fluctuate around 0 m s^-1. The black, red and blue lines represent the retrieval results for Gaussian noise with standard deviations of 0.2 K, 0.4 K, and 0.6 K, respectively.

Figure 5.  Relationships between the RMS error and mean bias and the incidence angle: (a) (b) retrieval results for vertical polarization channels, (c)(d) retrieval results for horizontal polarization channels, and (e)(f) retrieval results for all channels.

The RMS error increases as the Gaussian noise increases. However, In Fig. 5a, the RMS error changes very little in the range of 58°~65°. The RMS error of VR first increases and then decreases with increasing incidence angle, and it reaches its minimum and maximum values at 0° and 56°, respectively. The RMS error of HR decreases with increasing incidence angle and reaches its maximum and minimum values at 0° and 65°, respectively. The RMS error of AR first decreases and then increases with increasing incidence angle and reaches its maximum and minimum values at 0° and 59°, respectively. The trend of retrieval accuracy with incidence angle is caused by the sensitivity of brightness temperature to the sea surface wind speed (section 3.1) and the interaction between different channels.

Table 2 shows the maximum and minimum values of RMS error. In general, the retrieval accuracy for HR is higher than that for VR, and the retrieval accuracy achieved using AR is the highest. AR can be used as an SSWS retrieval method for spaceborne one-dimension synthetic aperture radiometer, and it is necessary to retrieve the SSWS at larger incidence angle.

In this paper, we proposed an SSWS retrieval method for the multiple incidence angles characteristic of one-dimensional synthetic aperture microwave radiometer. Assuming that a one-dimensional synthetic aperture microwave radiometer operates at various frequencies (i.e., 6.9, 10.65, 18.7, 23.8 and 36.5 GHz), a radiation transmission model was developed to simulate the measured brightness temperature. Then, the sensitivity of the brightness temperature to the SSWS was calculated, and we used vertical polarization channels (VR), horizontal polarization channels (HR) and all channels (AR) to investigate the SSWS retrieval results at the range of 0°~65°. The conclusions are as follows:

The sensitivity of the vertical polarization brightness temperature to the SSWS gradually decreases as the incidence angle increases, but it remains nearly unchanged in the range of 0° ~30°. At 6.9 and 10.65 GHz, the horizontal polarization brightness temperatures show a sensitivity to the SSWS that increases as the incidence angle increases. At 18.7, 23.8 and 36.5 GHz, the sensitivity first increases and then decreases with increasing incidence angle. The RMS error of VR, HR and AR change differently with increasing incidence angle. In general, the retrieval accuracy when using AR is the highest and the retrieval accuracy when using only the VR is the lowest.

This algorithm is suitable for sea surface wind speed retrieval under multiple incidence angles, and reveals the variation of sea surface wind speed retrieval accuracy with incidence angle. We suggest that AR can be used to retrieve SSWS by spaceborne one-dimension synthetic aperture radiometer and it necessary to retrieve the SSWS at larger incidence angle. Because it is simple to operate the algorithm, it can be used as a method for on-board processing in the future.