Modeling the Effects of Multi-layer Surface Roughness on 0.5 -2 GHz Passive Microwave Observations of the Greenland and Antarctic Ice Sheets

Abstract:

The Ultra-Wideband Software-Defined Radiometer (UWBRAD) is being developed to provide measurements of ice sheet thermal emission over the frequency range 0.5-2 GHz. In this frequency range, density variations within the firn create a layered structure that cause reflections. The thicknesses of the layers are of the order of centimeters in the top 100 meters, so that there can be hundreds to thousands of layers.

In the incoherent approach of modelling, the radiative transfer equation is applied to each layer. In the coherent approach, the fluctuation dissipation theorem with a layered medium Green’s function is used to calculate the brightness temperature. However, layer roughness effects have not been accounted for. Rough surface scattering would cause coupling of the intensities in all directions and coupling between vertical and horizontal polarizations.

We use a “partially coherent” approach. The snow firn is divided into “blocks” that include multiple layers separated by rough interfaces. The block size is defined such that a coherent incident wave will be attenuated to approximately 50% of its original amplitude upon transmission through the block. Within the block, we treat the wave scattering by rough surfaces coherently by using use the 2^nd order small perturbation method (SPM2). The SPM2 is an efficient analytic method that obeys energy conservation. The block size can be as small as 10 meters for the top layers because of strong density fluctuations, but can be hundreds of meters deeper within the snow firn because of the smaller density variations at greater depths. We calculate the bistatic scattering and transmission coefficients for each block. Finally the scattering and emission from multiple blocks are combined incoherently by using a cascade approach of the input and output intensities of the block.

Using the partially coherent approach, we can obtain the brightness temperatures of layered snow firn when there are hundreds or thousands of layers with hundreds or thousands of rough interfaces. Model predictions of brightness temperatures and their variations with observation angle, polarization, and frequency will be shown in the presentation. Implications of these results for future remote sensing studies of ice sheet thermal mission and temperature profile retrieval will also be discussed.