Complex dielectric constant of sea foam for microwave remote sensing applications

Increasing demands for accuracy in satellite-based geophysical retrievals of environmental variables from passive radiometric measurements at frequencies from 1 to 37 GHz necessitates forward geophysical models capable of adequate accounting for the foam effect. In addition, the direct and indirect involvement of whitecaps in numerous air sea interaction and climate processes justifies work on parameterizing the high variability of whitecap coverage. As a result there is a rekindled interest in measuring and modeling the microwave emissivity of sea foam. The complex dielectric constant (permittivity) of foam is a basic input in models for microwave foam emissivity.

For a surface foam layer, a mixing rule for foam permittivity needs to deal with two main characteristics of foam as a mixture: densely packed inclusions (air bubbles in seawater) and a wide range of volume fractions of the mixture constituents, from approximately 0% to almost 100%. The former is responsible for scattering in foam; the latter invokes a vertical profile of foam dielectric properties. At microwave frequencies from 1 to 37 GHz, the scattering in foam is weak or negligible. The possibility to ignore scattering in foam simplifies foam permittivity calculations by allowing use of: (i) classical mixing rules, which do not account for scattering explicitly; (ii) only two macroscopic foam characteristics, void fraction and foam-layer thickness. In such an approach to obtain foam permittivity, the main issue is the performance of the classical mixing rules in a wide range of foam void fractions.

We consider popular mixing rules, namely Maxwell Garnett, Polder van Santen, Coherent potential, and Looyenga models. To examine the suitability of a permittivity model for computing the dielectric constant of sea foam in case of weak scattering, the performance of each mixing rule is evaluated on the basis of three criteria: (1) how well a permittivity model deals with a wide range of void fractions; (2) how well a permittivity model meets the boundary conditions at the foam-air and foam-water interfaces; and (3) how the choice of a permittivity model affects estimates of emissivity and brightness temperature due to foam.

The central conclusions of this investigation will be presented. The overall outcome of the three criteria is that the suitability of the classical mixing rules for computing the complex dielectric constant of foam at microwave frequencies can be ranked as: 1) Looyenga model; 2) Polder-van Santen model; 3) Maxwell-Garnett model.