The knowledge of the sea surface emissivity can be used to design passive and active microwave sensors for ocean remote sensing applications. In this study, the variability of vertical and horizontal polarizations of Fresnel emissivity over the Persian Gulf water at 5 GHz in a nadir-viewing direction are investigated by using Fresnel's equations. Data sets used to compute Fresnel reflection coefficients were provided from our previous studies on hydrodynamic and electromagnetic properties of Persian Gulf water. The calculations indicated that spatial variability of Fresnel emissivity for both vertical and horizontal polarizations were relatively large compared to its temporal variability. The annual domain-averaged mean for vertical emissivity at the C- band was 0.3914, whereas for the horizontal polarization of the emissivity, it was 0.3645 in a nadir-viewing direction.

Surface emissivity is the ratio of radiation, which is defined as power flux density per solid angle, emitted by a surface to the theoretical blackbody radiation predicted by Planck's law. Traditionally, the sea surface emissivity E has been modeled as the sum of a specular emissivity E₀ (based upon the Fresnel power reflection coefficient) plus an additive rough surface emissivity ΔE_rough Δ E r o u g h that has been empirically determined such as in Stogryn (1967) , equation ( 1-1 ) E=E₀+ΔE_rough E = E 0 + Δ E r o u g h

The emissivity of the specular ocean surface E₀ which is usually known as Fresnel emissivity, is by far larger than rough surface emissivity ΔE_rough Δ E rough . The smooth water emissivity E₀ E 0 is determined using the principal of the conservation of energy at the air/sea interface. This emissivity depends on Fresnel power reflection coefficient, which is a function of the polarization of the electromagnetic (EM) wave, the direction of propagation (incidence angle), and the complex permittivity of sea water. Since the ocean surface is a boundary interface, a calm ocean with negligible wind speed results in specular reflection where the Fresnel formulas describe the reflection and emission. As wind blows over the ocean surface, small-scale capillary waves form and the surface roughness increases, which leads to change in the reflection and emission characteristics as a function of the surface wind speed. Historically, these have been modeled as an additive emissivity term ( Hollinger, 1971 , Stogryn, 1967 , Wentz, 1975 and Wilheit, 1979 ), which depend upon the drag force of the surface wind.

Knowledge of emissivity to an accuracy of order 10⁻³−10⁻⁴ 10 − 3 − 10 − 4 is required to retrieve physical parameters from brightness temperature measurements. The importance of this for ocean remote sensing is that surface emissivity affects the magnitude of two brightness temperature components of the radiative transfer model, namely, the calculation of the reflected down-welling atmospheric emission and the emission from the ocean surface ( EL-Nimri, 2010 ).

The Persian Gulf is one of the world's most important waterways, and it is crowded with ship traffic. During peak periods 60% of the world's oil transport comes from this region. The high volume of ship traffic combined with extensive bottom trawl fishing make this region very risky for moored instrumentation and any field measurements from a ship would be extremely difficult to interpret. As a result, numerical calculations is an essential tool for the study of the physical oceanography of this region. The Persian Gulf is a shallow and evaporative sea with a mean depth of about 35 m and is connected to the Oman Gulf through the narrow Strait of Hormuz ( Fig. 1 ). Due to the vast excess of evaporation over the precipitation plus river runoff, one of the most saline water masses in the world ocean is formed in the Persian Gulf. The salinity in the Persian Gulf experiences dramatic spatial and temporal variations ( Hassanzadeh, Hosseinibalam, & Rezaei-Latifi, 2011 ). The study of electrical parameter of the saline water with variable salinity will give useful input for designing the passive and active microwave sensors ( Calla, Ahmadian, & Hasan, 2011 ).

Bathymetry and map of the Persian Gulf.

In this work, the Fresnel emissivity of the surface layer of Persian Gulf water has been calculated by using Fresnel formulas and numerical modeling for both vertical and horizontal polarization at nadir. Since the Fresnel reflection coefficients are function of the complex dielectric constant, I have applied the Ellison et al. model to its estimate at 5 GHz ( Ellison et al., 1998 and Ellison et al., 2003 ). The salinity and temperature data needed for the model were provided by using a 3-D numerical model described in our previous papers ( Hassanzadeh et al., 2011 and Hosseinibalam et al., 2011 ).

The rest of this paper is organized as follows. In Section 2 the materials and calculation method of emissivity is presented. The results of calculating Fresnel emissivity of the Persian Gulf water for vertical and horizontal polarizations are analyzed in Section 3 . The last section provides the conclusion.