Application of effective medium approximation theory to ocean remote sensing under wave breaking

Abstract

Based on the effective medium approximation theory of composites, the empirical model proposed by Pandey and Kakar is remedied to investigate the microwave emissivity of sea surface under wave breaking driven by strong wind. In the improved model, the effects of seawater bubbles, droplets and difference in temperature of air and sea interface (DTAS) on the emissivity of sea surface covered by whitecaps are discussed. The model results indicate that the effective emissivity of sea surface increases with DTAS increasing, and the impacts of bubble structures and thickness of whitecaps layer on the emissivity are included in the model by introducing the effective dielectric constant of whitecaps layer. Moreover, a good agreement is obtained by comparing the model results with the Rose's experimental data.wave breaking, whitecaps, emissivity, effective medium approximation, radiant intensity Because of the importance of wave breaking in theoretic researches and engineering applications, it had attracted much attention, such as Munk [1] observed the whitecaps coverage under wave breaking early. Blanchard [2] gave the empirical relationship of whitecaps coverage and the 10 m high wind speed above the sea level. With the analysis of measurement data of the East China Sea and Pacific Ocean, Toba and Chean [3] also gave the empirical relationship of whitecaps coverage and wind speed. Ross and Cardone [4] obtained the whitecaps coverage of different wind speed from space photography of the sea surface state. Xu [5] improved the measurement method of wind-wave breaking, which included the measurement of broken-wave intensity. These relationships between whitecaps coverage and the 10 m high wind speed were directly obtained from measurement of sea surface. However, it is very difficult to measure other important parameters of sea-air interface under wave breaking. Recently, with the development of ocean remote sensing, the modern remote sensing technology has been used to inverse the physical parameters of the sea-air interface [6][7][8] . In order to estimate the effects of the sea-air interface layer on remote sensing measurement, many remote sensing models have been applied to the sea-air interface [9][10][11][12][13][14][15][16][17][18][19][20][21][22] . For example, the sea surface backscattering models were studied. Wu and Fung [9] proposed the two-scale non-coherent emissivity and backscattering models. Jin et al. [10] discussed the backscattering model of rough sea surface with foams. McDaniel [12] derived the backscattering model of non-Gaussian sea surface. In addition, the sea surface microwave emissivity models were proposed by many authors. For example, with least-square method, Stogryn [14] studied whitecaps emissivity model, which included the effects of incident angles and frequencies. Pandey and Kakar [15] had gotten the semi-empirical emissivity model of rough sea surface. Smith [16] gave the brightness temperature model of foam-covered sea surface. Huang and Jin [17] derived the whitecaps emis-

Emissivity Measurements of Foam-Covered Water Surface at L-Band for Low Water Temperatures

“…Over the sea surface, the sea foam layer is an aggregation of seawater-coated air bubbles and free water between interstitial spaces of air bubbles [13][14][15]. Therefore, several effective media approximations (EMA) have been developed to quantitatively calculate the effective permittivity of a foam layer for microwave wavelengths greater than mean air bubble size [16][17][18][19]. For example, considering the interactions of dense coated spherical particles, Liu et al [20] developed Rayleigh method to predict the effective permittivity of a foam layer at different microwave frequencies.…”

“…Anguelova [3] systematically investigated well-known effective permittivity formulae of composite media according their applicability to the sea foam layer. To investigate the emissivity increment induced by a foam-covered sea surface, theoretical models [8][9][10][11][16][17][18][19][20][21] were developed with electromagnetic wave theory, microwave vector radiative transfer equation (VRTE), and EMA theory. For instance, Guo et al [17] investigated the influence of foam microstructures, microwave frequency and foam-layer thickness on the emissivity of a foam-covered sea surface with quasi-crystalline approximation and VRTE, by treating the foam as densely packed air bubbles coated with seawater.…”

Millimetre Wave Emission by Discrete Method in Sea-foam Layer at WindSat Frequencies

“…This all-important puzzle necessitates the development of theoretical models which unveil the effects of foam layer to sea surface emission. Theoretical models such as the vector radiative transfer (VTR) equation [10], [11] the effective medium approximation (EMA) theory, and the dense media transfer (DMRT) method were used to investigate emissivity and scattering by sea foam covered sea surface [12,13,14,15,16,17,18]. Reasonable results were obtained using these theoretical models but the interactions of air-bubbles coated with thin layer of seawater are not considered precisely in the sea foam complex dielectric constant within millimetre wave by a suitable theory.…”