# A Modified Model for Electromagnetic Scattering of Sea Surface Covered with Crest Foam and Static Foam

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Two Whitecap Stages: Crest Foam and Static Foam

#### 2.1. Foam Coverage and Foam Thickness

_{p}is the phase speed of the dominant wave, g = 9.81. c

_{min}= (gλ

_{min}/2π)

^{1/2}(λ

_{min}= 20 cm). c = (2g/k

_{p})

^{1/2}(k

_{p}is the spectral peak wavenumber). U

_{10}is the wind speed at 10 m above the sea surface, in m/s. ∆T is the sea–air temperature difference (∆T = T

_{sea}− T

_{air}), in °C. 𝑎 = 0.8 is for crest foam and 𝑎 = 5 is for static foam. This expression of whitecap coverage fits well with the measured model in [18]. The coverages of individual crest foam and static foam in [18] are obtained by

#### 2.2. The Ratio of Crest Foam and Static Foam in the Same Sea State

_{a}and W

_{b}(the expressions of W

_{a}and W

_{b}are in Equations (1) and (2)), respectively. Therefore, we obtain the formula

_{a}), the new coverage ratio of static foam ((1−m) × W

_{b}), the new model and the global whitecap coverage model, respectively. It can be seen that the new crest foam coverage reaches 2% at U

_{10}= 20 m/s, while the individual crest foam coverage in Figure 1a is 3% at U

_{10}= 20 m/s. The new static foam coverage is close to 4% at U

_{10}= 20 m/s, while the individual static foam coverage in Figure 1a is about 10%. The global whitecap coverage model fitting well with the measured data of foam coverage in the northern and southern halfspheres, while the crest foam and static foam are not distinguished in the model, it only represents the whole whitecap coverage in the world ocean. The new model is the sum of the new crest foam coverage and the new static foam coverage. Obviously, the agreement of the new model is consistent with the global whitecap coverage model. The difference between the new model and the model in [26] is that the new model divides the crest foam and static foam, and points out the different contributions of crest foam and static foam in a given sea state. Because of the crest foam and static foam have different contributions on EM scattering, thus compared with the model in [26], this new model can better describe the EM scattering of the foam-covered sea surface.

## 3. The Modeling of Sea Surface Covered with Foam

#### 3.1. Sea Spectrum

_{H}and B

_{L}are the capillary waves and gravity waves of the sea surface. The formulas of B

_{H}and B

_{L}and the other parameters are illustrated in Appendix A. Figure 3 shows the sea spectrum when the wind speed (U

_{10}) is 5 m/s, 10 m/s and 15 m/s, separately.

#### 3.2. The Foam-Covered Sea Surface

_{10}= 10 m/s, the size of the sea surface is 300 m × 300 m. M and N are the sampling numbers of facets along x- and y-axes, respectively. ΔT = 10 °C. Figure 4a shows the sea surface with no foams. Figure 4b shows the sea surface covered with individual crest foam marked with red asterisk, N

_{c}= W

_{a}× M × N facets with higher slope in the sea surface are selected for crest foam. Figure 4c shows the sea surface covered with individual static foam marked with a green triangle, N

_{s}= W

_{b}× M × N facets with higher slope are chosen for static foam. Furthermore, Figure 4d shows the crest foam and static foam coexisting in the sea surface, N

_{c}= m × W

_{a}× M × N facets with a higher slope for crest foam, the next N

_{s}= (1−m) × W

_{b}× M × N facets with a higher slope are chosen for the static foam. Figure 4e shows the uniform distribution of foam fragments, while the wind speed increases to U

_{10}= 15 m/s, Figure 4e shows the distribution of foam starting to pile up, consistent with the measured sea surface image [17]. Meanwhile, the roughness of the sea surface increases.

#### 3.3. The Dielectric Constant of Sea Surface Covered with Foam

_{s}= 32.54‰, ε

_{∞}= 4.9. ε

_{0}= 8.854 × 10

^{−12}F/m. The detailed formulas of other parameters are shown in Appendix B.

## 4. Electromagnetic Calculation Method

#### 4.1. The Modified Facet-Based Two-Scale Model

_{1}·r+φ) field-based scattering model is proposed. The curvature modified factor (c

_{pp}) and the shadowing function (S(v)) are introduced, the scattering field of the facet-based two-scale model is obtained by

_{1}is the projection of the k(

**k**s −

**k**i) on the tilted element.

**k**

_{i}is the incident wave vector,

**k**

_{s}is the scattering wave vector. Δx and Δy are the size of each facet along x and y-axes, respectively. r is the position vector of each facet relative to the origin of coordinates. k

_{1}·r is the phase delay caused by the relative position of each facet. k

_{1}·r+φ is the phase modified. Hypothesis the large-scale roughness waves are geometrically illustrated by a discrete set of ζ (ρ, t), then γ

_{x}= ∂ζ/∂x and γ

_{y}= ∂ζ/∂y are the corresponding slopes.φ = ξ·k

_{1}·(Δx,Δy,(γ

_{x}·Δx + γ

_{y}·Δy)), −1/2≤ξ≤1/2, the specific theory is in [42]. In each facet, KA is adopted to calculate the specular scattering, and IEM computes the diffusion scattering. The Radar Cross Section (RCS) formulas are obtained by Equations (18) and (19).

_{x}, Z

_{y}) is the slope probability density distribution of Cox–Munk. In Equation (19), σ is the Root-Mean-Square (RMS) height of the small-scale sea surface. In each facet, the coordinate system is called the local coordinate. (

**x**,

**y**,

**z**) is the global coordinate. θ

_{i}is the global incident angle of each facet. θ

_{i}’ is the local incident angle of each facet. The normal vector of the local coordinate is

**n**= (−γ

_{x}

**x**−γ

_{y}

**y**+

**z**)/(1+ γ

_{x}

^{2}+ γ

_{y}

^{2})

^{1/2}. ω

^{(n)}is the spectral function of the sea spectrum. This paper adopts the n = 1 of Equation (19) proposed by Fung et al. [43]. In the cartesian coordinates, ω(k

_{x}, k

_{y}) is the two-dimensional sea spectrum, from Equation (14), ω(k

_{x}, k

_{y}) = s(kcosφ, ksinφ). ω(2ksinθ

_{i}

^{’}, 0) is the small-scale waves, and refers to the two-dimensional sea spectral density corresponding to the Bragg wave vector propagating along the radar line of sight. The formulas of the math symbols in Equations (17)–(19) from [44,45,46] are given in Appendix C.

_{cut}) to divide the large- and small-scale waves, the k

_{cut}has a great impact on the results of EM scattering. In this paper, the adaptive cutoff wavenumber [47] is chosen to generate the capillary wave for each facet of the sea surface. The expression is obtained by

_{cut}can be calculated from Equation (20).

#### 4.2. The Foam Layer Scattering Model

_{upper}= σ

^{IEM}= Equation (19).

_{s}are the power density of incident wave and scattered wave, respectively. μ = cosθ, μ

_{s}= cosθ

_{s}, μ

_{o}= cosθ

_{o}, μ

_{t}= cosθ

_{t}. σ

_{b}is the standard deviation height of the bottom sea surface and k

_{l}is the spatial wave number of the foam layer. κ

_{s}, κ

_{a}and κ

_{e}are volume scattering, absorption and extinction rate. κ

_{e}= κ

_{s}+κ

_{a}. τ = κ

_{e}d is the optical thickness and a = κ

_{s}/κ

_{e}is the polarization absorption. The expressions of them are as follows

_{bi}and k

_{br}are the imaginary and real parts of the host medium wave number.

_{i}= 10° and θ

_{i}= 60°. In the simulation, f = 10 GHz, U

_{10}= 10 m/s, for HH polarization. It can be seen that foam layer thickness and the incident angle have a great influence on the RCS. As the incident angle increases, the RCS gets smaller than it was before. This is why foam layer thickness is considered in this paper.

## 5. Numerical Results and Discussion

#### 5.1. Comparison with Measured Data at Level 3 Sea State

_{10}= 7.7 m/s, ε = (68.9, 34.4), ε

_{f}= (2.38, 0.69), the measured data is level 3 sea state from JOSS-I model for the wind speed between 7.2 m/s and 8.23 m/s. The numerical results of five sea surface models are shown in Figure 8 at VV and HH polarization. The five sea surface models are sea without foam, the proposed sea model, sea surface covered with individual crest foam, sea surface covered with individual static foam and sea surface covered with half ratio of crest foam and half static foam, respectively. The green circles in Figure 8 are the measured data from the JOSS-I model.

_{10}= 7.7 m/s, in the sea surface covered with individual static foam, the whitecap coverage is 0.8% and the foam thickness for static foam is d

_{s}= 2 mm. In the sea surface covered with individual crest foam, the whitecap coverage is 0.16% and the foam thickness for crest foam is d

_{c}= 0.8 mm. In the sea surface covered with half ratio of crest foam and half static foam, the crest foam coverage is 0.08%, while the static foam coverage is 0.4%. At present, two kinds of foam thicknesses coexist on the sea surface: d

_{c}= 0.8 mm and d

_{s}= 2 mm. While in the proposed model, the whitecap coverages of crest foam and static foam are 0.15% and 0.05%, respectively.

_{s}= 2 mm). In addition, the maximum difference of the sea surface covered with individual crest foam is about 3 dB less than measured data at a large incident angle. The sea surface at this moment has the fewest whitecap coverage (0.16%) and the thinnest foam layer (d

_{s}= 0.8 mm). While for the sea surface covered with half crest foam and half static foam, the maximum difference is about 2.5 dB larger than measured data at a large incident angle. This suggests that the EM scattering contributions of different coverage ratios of crest foam and static foam have an obvious effect on horizontal polarization. Therefore, for a given sea state, it is important to determine the coverage ratio of the crest foam and static foam, and consider the different foam layer thickness of each foam.

#### 5.2. Comparison with Measured Data at Level 4 Sea State

_{10}= 10.5 m/s, ε = (68.9, 34.4), ε

_{f}= (2.38, 0.69), the measured data is level 4 sea state from JOSS-I model for the wind speed between 9.26 m/s and 11.32 m/s.

_{s}= 4.8 mm. In the sea surface covered with individual crest foam, the whitecap coverage is 0.41%, d

_{c}= 1.7 mm. In the sea surface covered with half ratio of crest foam and half static foam, the whitecap coverages of crest foam and static foam are 0.2% and 0.95%, respectively. There are also two foam thicknesses that coexist: d

_{c}= 1.7 mm, d

_{s}= 4.8 mm. While in the proposed model, the whitecap coverages of crest foam and static foam are 0.29% and 0.56%, respectively.

#### 5.3. Comparison with Measured Data at Level 5 Sea State

_{10}= 12.5 m/s, ε = (58.8, 36.6), ε

_{f}= (2.18, 0.74) and the measured data is level 5 sea state from JOSS-I model for the wind speed between 11.83 m/s and 13.89 m/s.

_{s}= 8.2 mm. In the sea surface covered with individual crest foam, the whitecap coverage is 0.74%, the d

_{c}= 3 mm. In the sea surface covered with half crest foam and half static foam, the whitecap coverage of crest foam and static foam are 0.37% and 1.45%, respectively. While in the proposed model, the crest foam coverage is 0.5%, and the static foam coverage is 0.93%. Compared with the results of Figure 8 and Figure 9, Figure 10 shows that as the sea state comes to level 5, the whitecap coverages of crest foam and static foam increase accompanied by an increase in foam thickness of each foam. For the results of all the models on HH polarization, the proposed model has a better agreement with the measured data than the other sea models.

#### 5.4. Comparison with Measured Data at Level 6 Sea State

_{10}= 16 m/s, ε = (58.8, 36.6), ε

_{f}= (2.18, 0.74), the measured data is level 6 sea state from the 4FRS model for the wind speed between 15.43 m/s and 17 m/s.

_{s}= 17 mm. In the sea surface covered with individual crest foam, the whitecap coverage is 1.5%, d

_{c}= 6 mm. In the sea surface covered with half ratio of crest foam and half static foam, the whitecap coverage of crest foam and static foam are 0.75% and 2.75%, respectively. While in the proposed model, the crest foam coverage is 0.96%, and the static foam coverage is 1.97%. There are also two foam thicknesses that coexist: d

_{c}= 6 mm, d

_{s}= 17 mm. It can be seen that the foam thickness of static foam reaches a new order of magnitude. Compared with the results of Figure 8, Figure 9 and Figure 10, the EM scattering contributions of coverage ratios of crest foam and static foam have a greater impact on HH polarization. The numerical results of sea surface covered with individual static foam, sea surface covered with individual crest foam, sea surface covered with half ratio of static foam and half crest foam are getting worse. However, the results of the proposed model from level 3 to level 6 sea state are still consistent with the measured data, which verifies the correctness of the geometric modeling of the foam-covered sea surface and the effectiveness of the EM scattering model.

#### 5.5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{H}and gravity waves B

_{L}of the sea spectrum. They are given as [32],

_{m}= 363 rad/m, K

_{p}= gΩ

^{2}/U

_{10}

^{2}, the wave age is Ω≈U

_{10}/c(k

_{p}). The expressions of phase velocity of the wave and the other parameters are obtained by

## Appendix B

_{s}(T, 0) and τ(T, 0) are the permittivity change of pure water and the relaxation time of pure water, respectively. T = 20 °C, ω

_{s}= 32.54‰, ε

_{∞}= 4.9. ε

_{0}= 8.854 × 10

^{−12}F/m. The expressions of other parameters are obtained by

## Appendix C

_{pp}) and the shadowing function (S(v)) are introduced by

^{n}in Equation (19) is expressed by

## References

- Nordberg, W.; Conaway, J.; Ross, D.B. Measurements of Microwave Emission from a Foam-Covered Wind-Driven Sea. J. Atmos. Sci.
**1971**, 28, 429–435. [Google Scholar] [CrossRef] [Green Version] - Goldstein, H. Attenuation by Condensed Water. In Propagation of Short Radio Waves; Kerr, D.E., Ed.; McGraw-Hill: New York, NY, USA, 1951. [Google Scholar]
- Martin, S. An Introduction to Ocean Remote Sensing; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
- Raizer, V. Microwave Scattering Model of Sea Foam. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGRSS), Munich, Germany, 22–27 July 2012; pp. 5836–5839. [Google Scholar]
- Droppleman, J.D. Apparent microwave emissivity of sea foam. J. Geophys. Res.
**1970**, 75, 696–698. [Google Scholar] [CrossRef] - Rosencratz, P.W.; Staelin, D.H. The microwave emissivity of ocean foam and its effect on nadiral radiometric measurements. J. Geophys. Res.
**1972**, 77, 6528–6538. [Google Scholar] - Anguelova, M.D.; Gaiser, P.W. Dielectric and Radiative Properties of Sea Foam at Microwave Frequencies: Conceptual Understanding of Foam Emissivity. Remote Sens.
**2012**, 4, 1162–1189. [Google Scholar] [CrossRef] [Green Version] - Zhou, L.; Tsang, L. Polarimetric passive microwave remote sensing of wind vectors with foam-covered rough ocean surfaces. Radio Sci.
**2003**, 38, 1073–1086. [Google Scholar] [CrossRef] - Guo, J.; Tsang, L. Applications of Dense Media Radiative Transfer Theory for Passive Microwave Remote Sensing of Foam Covered Ocean. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 1019–1027. [Google Scholar] [CrossRef] - Kaimykov, A.I.; Pustovoytenkov, V.V. On polarization features of radio signals scattered from the sea at small grazing angles. J. Geophys. Res.
**1976**, 81, 1960–1964. [Google Scholar] [CrossRef] - Lyzenga, D.R.; Maffett, A.I.; Shuchman, R.A. The contribution of wedge scattering to the radar cross section of the ocean surface. IEEE Trans. Geosci. Remote Sens.
**1983**, 21, 502–505. [Google Scholar] [CrossRef] - Churyumov, A.N.; Kravtsov, Y.A. Microwave backscatter from mesoscale breaking waves on the sea surface. Waves Random Media
**2002**, 10, 1–15. [Google Scholar] [CrossRef] - Kudryavtsev, V.; Hauser, D.; Caudal, G. A semi-empirical model of the normalized radar cross section of the sea surface:1. the background model. J. Geophys. Res.
**2003**, 108, 1–24. [Google Scholar] - Kudryavtsev, V.; Hauser, D.; Caudal, G. A semi-empirical model of the normalized radar cross section of the sea surface: surface: 2. radar modulation transfer function. J. Geophys. Res.
**2003**, 108, 1–16. [Google Scholar] - West, J.C.; Zhao, Z.Q. Electromagnetic modeling of multipath scattering from breaking water waves with rough faces. IEEE Trans. Geosci. Remote Sens.
**2002**, 40, 583–592. [Google Scholar] [CrossRef] - Li, J.X.; Zhang, M.; Fan, W.N.; Nie, D. Facet-Based Investigation on Microwave Backscattering From Sea Surface With Breaking Waves: Sea Spikes and SAR Imaging. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 2313–2325. [Google Scholar] [CrossRef] - Monahan, E. Oceanic whitecaps. J. Phys. Oceanogr.
**1971**, 1, 139–144. [Google Scholar] [CrossRef] - Monahan, E.; Woolf, D.K. Comments on variations of whitecap coverage with wind stress and water temperature. J. Phys. Oceanogr.
**1989**, 19, 706–709. [Google Scholar] [CrossRef] [Green Version] - Sharkov, Y.A. Experimental investigations of the lifetime for breaking wave dispersive zone. Izv. Atmos. Ocean. Phys.
**1995**, 30, 808–811. [Google Scholar] - Reising, S.C.; Asher, W.E.; Rose, L.A. Polarimetric emissivity of whitecaps experiment (POEWEX): Preliminary results. In WindSat Science Workshop, November; Noesis, Inc.: Arlington, VA, USA, 2002. [Google Scholar]
- Reul, N.; Chapron, B. A model of sea–foam thickness distribution for passive microwave remote sensing application. J. Geophys. Res.
**2003**, 108. [Google Scholar] [CrossRef] [Green Version] - Anguelova, D.A.; Gaiser, W.G. Microwave emissivity of sea foam layers with vertically inhomogeneous dielectric properties. Remote Sens. Environ.
**2013**, 139, 81–96. [Google Scholar] - Daley, J.C.; Ransone, J.R.; Burkett, J.A. Radar Sea Return-JOSS I; U.S. Naval Research Laboratory: Washington, DC, USA, 1971. [Google Scholar]
- Daley, J.C.; Davis, W.T.; Mills, N.R. Radar Sea Return-high Sea States; U.S. Naval Research Laboratory: Washington, DC, USA, 1970. [Google Scholar]
- Hwang, P.A. Foam and roughness effects on passive microwave remote sensing of the ocean. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 2978–2985. [Google Scholar] [CrossRef] - Hwang, P.A.; Reul, N.; Meissner, T.; Yueh, S.H. Whitecap and Wind Stress Observations by Microwave Radiometers: Global Coverage and Extreme Conditions. J. Phys. Oceanogr.
**2019**, 49, 2291–2307. [Google Scholar] [CrossRef] - Callaghan, A.H.; Leeuw, G.D.; Cohen, L.H.; O’Dowd, C.D. The relationship of oceanic whitecap coverage to wind speed and wind history. J. Geophys. Res. Lett.
**2008**, 35. [Google Scholar] [CrossRef] [Green Version] - Meissner, T.; Wentz, F.J. Wind-vector retrievals under rain with passive satellite microwave radiometers. IEEE Trans. Geosci. Remote Sens.
**2009**, 47, 3065–3083. [Google Scholar] [CrossRef] - Anguelova, M.D.; Webster, F. Whitecap coverage from satellite measurements: A first step toward modeling the variability of oceanic whitecaps. J. Geophys. Res.
**2006**, 111. [Google Scholar] [CrossRef] [Green Version] - Sugihara, Y.H.; Tsumori, T.; Yoshioka, O.H.; Serizawa, S. Variation of whitecap coverage with wave-field conditions. J. Mar. Syst.
**2007**, 66, 47–60. [Google Scholar] [CrossRef] - Lafon, C.; Piazzola, J.; Forget, P.; Despiau, S. Whitecap coverage in coastal environment for steady and unsteady wave field conditions. J. Mar. Syst.
**2007**, 66, 38–46. [Google Scholar] [CrossRef] - Elfouhaily, T.; Chapron, B.; Katsaros, K. A unified directional spectrum for long and short wind-driven waves. J. Geophys. Res.
**1997**, 102, 15781–15796. [Google Scholar] [CrossRef] - Creamer, D.B.; Henyey, F.; Schult, R.; Wright, J. Improved linear representation of sea surface waves. J. Fluid Mech.
**1989**, 205, 135–161. [Google Scholar] [CrossRef] - Longuet-Higgins, M.S. Integral properties of periodic gravity waves of finite amplitude. Proc. R. Soc. Lond.
**1975**, 342, 157–174. [Google Scholar] - McLean, J.W.; Ma, Y.C.; Martin, D.U.; Saffman, P.G.; Yuen, H.C. Three-dimensional instability of finite-amplitude water waves. Phys. Rev. Lett.
**1981**, 46, 817–820. [Google Scholar] [CrossRef] [Green Version] - Phillips, O.M.; Banner, M.L. Wave breaking in the presence of wind drift and swell. J. Fluid Mech.
**1974**, 66, 625–640. [Google Scholar] [CrossRef] - Stokes, G.G. On the theory of oscillatory waves. Trans. Camb. Philos. Soc.
**1847**, 8, 441–455. [Google Scholar] - Longuet-Higgins, M.S.; Fox, M.J.H. Theory of the almost-highest wave: The inner solution. J. Fluid Mech.
**1977**, 80, 721–741. [Google Scholar] [CrossRef] - Meissner, T.; Wentz, J. The complex dielectric constant of pure and sea water from microwave satellite observations. IEEE Trans. Geosci. Remote Sens.
**2004**, 42, 1836–1849. [Google Scholar] [CrossRef] [Green Version] - Ruppin, R. Evaluation of extended Maxwell-Garnett Theories. Opt. Commun.
**2000**, 182, 273–279. [Google Scholar] [CrossRef] - Li, D.F.; Zhao, Z.Q.; Zhao, Y.W.; Huang, Y.; Liu, Q.H. An Improved Facet-Based Two-scale model for Electromagnetic Scattering from Sea Surface and Wave breaking. In Proceedings of the IEEE Radar Conference, Boston, MA, USA, 22–26 April 2019; pp. 1–4. [Google Scholar]
- Kozlov, A.; Ligthart, I.; Logvin, L.; Besieris, P.; Pusone, M. Mathematical and Physical Modelling of Microwave Scattering and Polarimetric Remote Sensing; Springer: Dordrecht, The Netherlands, 2002; Volume 3. [Google Scholar]
- Fung, A.K. Microwave Scattering and Emission Models and Their Applications; Artech House: Norwood, MA, USA, 1994. [Google Scholar]
- Bourlier, C.; Berginc, G.; Saillard, J. One- and two- dimentional shadowing functions for any height and slope stationary uncorrelated surface in the monostatic and bistatic configurations. IEEE Trans. Antennas Propag.
**2002**, 50, 312–324. [Google Scholar] [CrossRef] - Cox, C.; Munk, M. Statistics of the sea surface derived from sun glitter. J. Mar. Res.
**1954**, 13, 198–227. [Google Scholar] - Voronovich, A.G. On the theory of electromagnetic waves scattering from the sea surface at low grazing angles. Radio Sci.
**1996**, 31, 1519–1530. [Google Scholar] [CrossRef] - Li, D.F.; Zhao, Z.Q.; Qi, C.H.; Huang, Y.; Zhao, Y.W.; Nie, Z.P. An Improved Two-Scale Model for Electromagnetic Backscattering from Sea Surface. IEEE Geosci. Remote Sens. Lett.
**2019**, 1–5. [Google Scholar] [CrossRef]

**Figure 1.**Foam coverage and foam thickness at different wind speeds. (

**a**) Foam coverage models for crest foam and static foam. (

**b**) Foam thickness distributions for crest foam and static foam.

**Figure 2.**Foam coverage at different wind speeds. (

**a**) The ratio of crest foam and static foam. (

**b**) Comparison of the Hwang model and the new whitecap coverage summed by crest foam and static foam.

**Figure 4.**The whitecap coverage in the sea surface. (

**a**) The sea surface without foam. (

**b**) The sea surface covered with crest foam only. (

**c**) The sea surface covered with static foam only. (

**d**) The sea surface covered with the proposed distribution of crest foam and static foam for U

_{10}= 10 m/s. (

**e**) The sea surface covered with the proposed distribution of crest foam and static foam for U

_{10}= 15 m/s.

**Figure 5.**(

**a**) The dielectric constant of seawater. (

**b**) The dielectric constant of sea surface covered with foam.

**Figure 6.**The scattering model of the sea surface covered with the foam layer. (1), (2), (3) and (4) represent the four scattering contributions for Electromagnetic (EM) scattering model.

**Figure 7.**The scattering of foam layer varying with foam layer thickness for θ

_{i}= 10° and θ

_{i}= 60°.

**Figure 8.**Comparison results of Normalized RCS (NRCS) by the proposed model, the sea surface covered with crest foam only, the sea surface covered with static foam only, the sea surface covered half crest foam and half static foam, and the measured data from JOSS-I model. f = 4.455 GHz, U

_{10}= 7.7 m/s. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 9.**Comparison results of NRCS by the proposed model, the sea surface covered with crest foam only, the sea surface covered with static foam only, the sea surface covered half crest foam and half static foam, and the measured data from JOSS-I model. f = 4.455 GHz, U

_{10}= 10.5 m/s. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 10.**Comparison results of NRCS by the proposed model, the sea surface covered with crest foam only, the sea surface covered with static foam only, the sea surface covered half crest foam and half static foam and the measured data from JOSS-I model. f = 8.91 GHz, U

_{10}= 12.5 m/s. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 11.**Comparison results of NRCS by the proposed model, the sea surface covered with crest foam only, the sea surface covered with static foam only, the sea surface covered half crest foam and half static foam and the measured data from 4FRS model. f = 8.91 GHz, U

_{10}= 16 m/s. (

**a**) VV polarization. (

**b**) HH polarization.

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## Share and Cite

**MDPI and ACS Style**

Li, D.; Zhao, Z.; Zhao, Y.; Huang, Y.; Nie, Z.
A Modified Model for Electromagnetic Scattering of Sea Surface Covered with Crest Foam and Static Foam. *Remote Sens.* **2020**, *12*, 788.
https://doi.org/10.3390/rs12050788

**AMA Style**

Li D, Zhao Z, Zhao Y, Huang Y, Nie Z.
A Modified Model for Electromagnetic Scattering of Sea Surface Covered with Crest Foam and Static Foam. *Remote Sensing*. 2020; 12(5):788.
https://doi.org/10.3390/rs12050788

**Chicago/Turabian Style**

Li, Dongfang, Zhiqin Zhao, Yanwen Zhao, Yuan Huang, and Zaiping Nie.
2020. "A Modified Model for Electromagnetic Scattering of Sea Surface Covered with Crest Foam and Static Foam" *Remote Sensing* 12, no. 5: 788.
https://doi.org/10.3390/rs12050788