Can We Retrieve Sea Surface Salinity With Polarimetric Radar Measurements?

Sea surface salinity (SSS) is measured operationally with radiometers [e.g., soil moisture and ocean salinity (SMOS)] with a resolution from 25 to 40 km. In this contribution, we theoretically evaluate radar sensitivity to SSS, especially we focus on synthetic aperture radar (SAR) due to its intrinsic high-resolution imaging capabilities. This work focuses first on the variations in the dielectric properties of seawater with salinity at different SAR frequency bands (P-, L-, and C-bands) and then evaluate the consequences of both on the normalized radar cross section (NRCS) and copolar phase difference (CPD). The main challenge is to disentangle the sensitivity to dielectric properties from the surface roughness contribution in the SAR backscattered signals. In line with the literature, the results show that the NRCS sensitivity with salinity increases with decreasing operating frequency. In addition, we present new theoretical results on salinity sensitivity to CPD that have not been explored in the existing literature.


I. INTRODUCTION
S EA surface salinity is an important parameter driving ocean circulation and is currently measured at a 25-40-km resolution with soil moisture and ocean salinity (SMOS) [1], [2]; other sensors have shown this capability such as soil moisture active passive (SMAP) [3], [4] and Aquarius [3], [5]. Nevertheless, it might be interesting to derive sea surface salinity (SSS) with higher resolution (subkilometric) for coastal areas' monitoring. Independent of resolution restrictions, the problem of sidelobe illumination for hot land surfaces restricts passive systems to remain hundreds of kilometers from the shore line. An example where high resolution may be beneficial is the study of the sedimentation process in estuaries, where the salinity is subject to strong gradients [6]. SAR sensors enable to achieve resolution from meter to a couple of tens of meters. In practice, a spatial averaging is performed to derive geophysical parameters (e.g., wind speed and direction), leading to resolutions from hundreds of meters to kilometers. A classical variable used for geophysical parameter retrieval in oceanography is the normalized radar cross section (NRCS) in the VV polarization at the C-band because of its sensitivity to the sea surface roughness [7]. Indeed, geophysical models have been developed in the past mainly at the C-band for wind retrieval (CMOD5N, CMOD7N) [7].
The purpose of this work is to investigate possible schemes for salinity retrieval using SAR imaging. A first experiment Manuscript  at the P-band has been carried out in [8] with promising results. In this study, we perform a more general theoretical sensitivity evaluation considering the main ocean physical parameters such as SSS, sea surface temperature (SST), wind speed and direction, and measurement configuration such as radar operating frequency and incidence angles. We propose to evaluate the impact of salinity variations on two radar measurables: NRCS and copolar phase difference (CPD). The first part of this letter recalls the dielectric properties of seawater at different SAR frequencies (P-, L-, and C-bands) and presents the models used for NRCS and CPD calculation. The second part highlights the main results of this theoretical study. The main challenge in this exercise is to disentangle in the SAR backscattered signal the sensitivity with the roughness and the sensitivity with the dielectric properties. Solutions to maximize the dielectric properties impact and minimize the roughness impact based on physical consideration will be finally discussed at the end of this letter.

A. Dielectric Properties of Seawater at SAR Frequencies: Debye Model
The complex dielectric permittivity of seawater has been derived as follows and is commonly used in the literature [2], [5], [9], and [10] S salinity in practical salinity unit (psu or g/kg) or SSS; conductivity (S/m); ω = 2π f radar angular frequency, τ : relaxation time.
In this letter, we adopt the following convention: The real part ε ′ is denominated the relative permittivty and the imaginary part ε ′′ the loss factor. Fig. 1 presents the real and imaginary parts of the seawater dielectric permittivity for usual radar frequencies from very high frequency (VHF) to the C-band at T = 25 • C. In Fig. 1(a) is plotted the relative permittivity and in Fig. 1 We can observe in Fig. 1(a) that ε ′ varies only a little with the salinity within the considered range of SAR frequencies (ranging roughly from 70 to 80 at the P-and L-bands and from 67 to 75 at the C-band with decreasing salinity). On the contrary, ε ′′ associated with the imaginary part of the dielectric permittivity is subject to strong variation at low frequencies depending on the salinity (at biomass frequency from 0 to 300 with increasing salinity). The impact of the salinity can therefore be exploited at different frequencies of interest. We focus on the behaviors at the BIOMASS [11], [12] operating frequency (435 MHz), ROSE-L [13] operating frequency (assumed 1.4 GHz), and Sentinel-1 [14] operating frequency (5.405 GHz).

B. Fresnel Coefficients
To investigate the theoretical sensitivity of seawater dielectric properties at the P-, L-, and C-bands, we first evaluate the impact of salinity on the Fresnel coefficients in the HH and VV polarizations. The variations with HH being less significant, we present the most significant results in the modulus of VV at the C-and P-bands in Fig. 2.
The Fresnel coefficients correspond to the ratio between the reflected and incident waves in the specular direction and are expressed as follows for the HH and VV polarizations with θ the incidence angle [15]: The strong sensitivity to salinity at the P-band is well represented in Fig. 2(b) (especially around the Brewster angle), whereas salinity is slightly affecting the Fresnel coefficients at the C-band in Fig. 2(a). The Fresnel coefficients describe the forward electromagnetic field (EM) scattering and are only related to the backscattered field. To go further in the analysis, we need to describe the received signal with more representative models. We choose therefore to express the NRCS through tilted Bragg models because most of the relevant parameters can be controlled (salinity, temperature, wind speed and direction, operating frequency, incidence angle). The second SAR measurable that we propose to study is the CPD, for which analytical expression has been derived using roughness approximations.

C. Normalized Radar Cross Section
In the range 30 • -60 • of incidence angle, the most significant contribution to the NRCS is the Bragg scattering [16], and therefore, we allow ourselves for this preliminary study to use the tilted or composite Bragg model introduced in [17] to describe the NRCS σ 0 . More accurate models taking into account the specular and breaking wave scattering contribution [18] have been developed, and it can be interesting to implement them in the future to improve NRCS modelization. The composite Bragg NRCS contribution is expressed as follows from [17], [19] θ incidence angle, ϕ wind direction; η i slope projected onto the incidence plane 2 ; σ 0b pure Bragg scattering at a given local θ ′ , ϕ; P probability density function of η i with η i ∼ N (0, s η ); s η is defined as the standard deviation of slopes. 1 Useful tools and python libraries for SAR ocean scattering can be found in https://github.com/pakodekker/oceansar 2 Estimated from the 1-D elevation spectrum.
In short terms, the model takes into consideration Bragg waves (ripple process) and longer waves that modulate local processes. The outcome of 5 is a sum of pure Bragg contributions weighted by the probability density function of the local slopes considered as a normal random process with standard deviation s η . The standard deviation of the slopes is directly derived from the wave spectrum model. For a nontilted sea surface (θ ′ = θ ), the pure Bragg σ 0b in (5) is expressed as follows: k r radar wavenumber, k bragg = 2k r sin(θ ′ ). θ ′ local incidence angle.
Different development and strategies have been proposed for the 2-D elevation spectrum , in the past 30 years (e.g., Elfouhaily et al. [20], Kudryatsev et al. [21], or Hwang and Fois [22]). We used the 2-D spectrum developed by [20] in this study because it is well-established and recognized in oceanography literature.

D. Copolarized Phase Difference
In [23], the copolarized phase difference is investigated for desert surfaces through two different roughness assumptions, "medium rough" and "very rough." Both are derived from the integral equation model (IEM) [24]. The interesting aspect of these two approximated CPD is their dependency only on the complex dielectric constant ε and the incidence angle θ . Let us denote HHVVr and HHVVR as the copolarized phase differences for the medium rough case and very rough case, respectively. In addition, we recall that the backscattered far-field defined from the IEM E s pp with p the polarization reads [23], [24] With the Kirchhoff field E k pp = C E 0 f pp I k and the complementary field E c pp = C E 0 (F pp I c )/(8π 2 ), C and E 0 are, respectively, C = (− jk)/(4πr )e − jk with wavenumber k and range r , and E 0 is the incident electric field. The expression of the Kirchhoff and complementary coefficients ( f pp , F pp ) and integral terms I k and I c are derived in detail in [23] and [24]. The CPD is defined for a general case from the copolarized backscattered far-fields as HHVV = arg(E s hh ) − arg(E s vv ). For the very rough case, the Kirchhoff field E k pp in (7) is assumed dominant, as derived in [23], leading to (8) highlighting that the CPD depends only on the Fresnel coefficients' phases HHVVR = arg(R hh ) − arg(R vv ).
For the medium rough case, the expression is derived considering that E k pp and E c pp , respectively, the Kirchhoff and complementary fields, are comparable. The proposed medium rough copolarized phase has been derived with that assumption in [23] and takes the following form: The CPD can be estimated by computing HHVV = arg(⟨s hh s * vv ⟩), with s hh and s vv the SAR complex backscattering coefficients in the hh and vv polarizations, respectively, and "⟨⟩ >" the average operator.

III. MAIN THEORETICAL RESULTS
In this section, we present the main results obtained from the Bragg NRCS and CPD models on the salinity impact with different roughness (wind) assumptions, operating frequency, and incidence angles. For this analysis, we consider ocean monitoring conditions from 20 to 40 psu (estuaries output and open ocean) with SAR configurations from 30 • to 60 • of incidence angle. The last paragraph presents a short numerical scenario analysis considering current SAR characteristics and performances.

A. Normalized Radar Cross Section
NCRS Bragg processes from oceanography literature are rather well-developed for different wind conditions (speed and direction) as discussed in Section II-C. Even though such model cannot describe with a high fidelity all the configurations (strong wind, extreme incidence angles, surface current, breaking waves, etc. [18]), it is a first approximation to evaluate the relative impact of wind and salinity in an operational retrieval strategy. As can be observed from Fig. 3, the salinity gains in impact on the NRCS Fig. 4. Copolarized phase difference for medium and very rough surfaces at the C-, L-, and P-bands. Subscript "R" corresponds to very rough approximation, whereas "r" stands for medium rough approximation (a) HHVVR C-band, (b) HHVVr C-band, (c) HHVVR L-band, and (d) HHVVr L-band, (e) HHVVR P-band, and (f) HHVVr P-band.
from the C-band [see Fig. 3 Fig. 3(e) and (f)]. However, the variation induced by the salinity is quite low (some dBs on the range 20-40 psu) compared with the roughness variation brought by the wind. It can be noted from the model results, and it is intuitively consistent from the wavelength scale point of view that the wind impact on the NRCS decreases from the C-band to P-band. For instance, between 5 and 15 m/s a difference of 10 dB is observed for a given incidence angle (i.e., 45 • ) at the C-band in Fig. 3(a) and (b), whereas it is around 2 dB at the P-band in Fig. 3(e) and (f). Those results, even highlighting a higher sensitivity with salinity while decreasing the frequency, are encouraging but still challenging considering an operational retrieval framework.

B. CPD
This approach, less conventional in oceanography applications, has been, however, used for oil spill detection and characterization in some studies [25] by evaluating the coherence between HH and VV.
This copolarized coherence can be related to different spread of the CPD distribution in case of seawater and oil-spill pollution. In the present case, we study the CPD through the IEM model described in Section II-D. Through the CPD model results presented in Fig. 4, we can observe a lower sensitivity to salinity at the P-band in Fig. 4(f) and (e) for medium and very rough cases compared with the C-and L-band results, respectively, in Fig. 4(a)-(c). The two roughness considerations, medium and very rough, show a relatively small impact on the CPD (1 • shift upward from medium rough to very rough). This is an interesting result and one possible solution to disentangle the wind impact with the physical properties variations on the CPD. The maximal sensitivity to salinity is achieved at high incidence angles can be observed in Fig. 4.

C. Sensitivity Scenario Analysis
To provide some order of magnitude regarding the potential of SAR systems for SSS retrieval, we perform an analysis considering "best sensitivity cases scenario" among the different theoretical configurations presented in Sections III-A and III-B. We choose to study an intensity only scenario at P (for BIOMASS mission) and the L-band (as documented radiometric accuracy exists at this frequency), and the corresponding numerical sensitivity values can be found in Table I for moderate wind conditions of 10 m/s in the range 20-30 psu (typical values found in Amazon estuary output [6]). 3 Such results need to be compared with current SAR systems' radiometric accuracy and noise equivalent sigma zero (NESZ). Concerning the measured radiometric accuracy, we can take examples of L-band ALOS-2 [26] and C-band Sentinel-1 [27] that have shown, respectively, around 0.5 and 0.32 dB of overall radiometric accuracy from performance and calibration exercises. Classical NESZ values of spaceborne SAR systems are ranging from −25 to −35 dB (mode-and incidence-angle-dependent) [26], [27].
Given the previous result in Sections III-A and III-B, the numerical examples and the rough analysis of SAR system current capabilities, the sensitivities presented in Table I are an order of magnitude lower than the SAR systems' requirements and measured performance (on average 0.025 dB/psu for Bragg scenario at the P-band and 0.019 at the L-band, whereas current spaceborne sensors have 0.2-0.5 dB measured radiometric accuracy). From the NESZ perspective, BIOMASS operating more in the range 25 • -30 • of incidence angle, the Bragg modeling results suggest that the backscatter power even in low to moderate wind (5-15 m/s) conditions is much higher than the expected −27 dB NESZ [28].

IV. DISCUSSION
From Section III, the NRCS and CPD models exhibit behaviors that may be interesting for SSS retrieval schemes, however, with variation close to the SAR sensors' detection limits.
At the C-band, the NRCS for the VV polarization appears to be unaffected by salinity variation but is known to be sensitive to wind conditions: it is indeed an observable used to derive wind speed by inverting geophysical models such as CMOD5N [7]. On the contrary, the CPD at the C-band exhibits clear variations with salinity. At the L-band, we observe stronger variations compared with the C-band on both NRCS and CPD with salinity; it corresponds interestingly to a medium case where both NRCS and CPD are sensitive to salinity. P-band CPD highlights moderate sensitivity to salinity; it is, however, at this frequency that we obtain theoretically the most sensitive NRCS among the three frequency bands. The order of magnitude analysis presented in Section III-C suggests that L-band current sensors and P-band SAR sensors with same accuracy specifications than current spaceborne sensors cannot measure 1-psu variation in a typical estuary output range of salinity (20-30 psu) with moderate wind conditions.
From a general point of view, it can be noted that the consequence of decreasing the operating frequency seems to decrease the sensitivity of the NRCS to roughness and therefore decrease the possible errors associated with wind. The second possibility to minimize the impact of the roughness appears to be possible through the use of CPD. In the same fashion than decreasing the operating frequency, the CPD sensitivity to roughness is in the same order of magnitude than its sensitivity to salinity.
Even though the retrieval capabilities appear to be challenging from this theoretical sensitivity study, one advantage of SAR imaging is its intrinsic high resolution (meters to several tens of meters). Therefore, a consequent averaging can be performed to improve the estimation (decreasing noise variance) of parameters and achieve an acceptable resolution for oceanographic applications (subkilometric).

V. CONCLUSION
The purpose of this work was to evaluate capabilities to retrieve SSS at high resolution from SAR images. We exploited first the interesting dielectric properties of sea water variations with salinity at different SAR frequency bands (P-, L-, and C-bands) and then evaluated the consequences both on the NRCS and CPD. A scenario analysis showed that the sensitivity to salinity using the Bragg models at the P-and L-bands (in dB/psu) is currently an order of magnitude below the current spaceborne SAR specifications. Retrieval strategies have been discussed and have to be further analyzed with in situ data and SAR measurements to evaluate operational retrieval capabilities. Further research into the influence swell, current, and bathymetry on SSS retrievals is also recommended.