## Emissivity and backscatter model of sea ice in the microwave range

Objectives: to establish a set of baseline emissivity values of various sea ice types in order to improve ice concentration retrievals as well as in order to improve atmospheric retrievals over ice.

The task was solved in two parts:

- Empirical emissivities were derived from areas of known ice composition using microwave radiometer data from the AMSR-E and AMSU instruments.

- A sea ice and snow emissivity model was developed and utilized in the evaluation and understanding of the empirically derived emissivities from 1)

The Microwave Emission Model for Layered Snow-packs (MEMLS) is a model suitable for simulations of all kinds of physical effects and it has been tested and validated for snow-cover on land with satisfactory results. Here MEMLS is extended to include emission from sea ice. The sea ice model and modifications are described in the next section.

Extension of MEMLS to sea ice emission:

MEMLS, developed by Wiesmann and Mätzler uses the physical snow quantities and structure as input i.e. sequence of layers (j), density (D), exponential correlation length (pec), thermometric temperature (T) and moisture (W). In order to apply this model to compute the emission of both snow and sea ice it is necessary to include modules that compute the dielectric properties, and scattering of sea ice. Small liquid brine inclusions also called brine pockets dominate scattering in nilas and first-year ice. In multiyear ice, the voids and air bubbles in the upper ice are the primary scatters.

The permittivity of liquid brine is an order of magnitude larger than the permittivity of solid ice and the permittivity of sea ice is therefore primarily a function of brine volume. The permittivity of sea ice is computed using Polder - Van Santen mixing formulas. It is a function of pure ice permittivity, inclusion shape and orientation, volume and the brine pockets permittivity (spheres are used because sea ice is assumed isotropic here). These mixing formulas do not account for scattering and therefore the accuracy of the permittivity estimates decreases as a function of frequency. Radiative processes at high frequency are usually confined to the snow cover and it is therefore not expected to be a significant source of error.

MEMLS is valid for snow cover in the range 5-100 GHz. The primary limitation is the estimation of the scattering coefficient using empirical relations, which fit scattering in natural snow cover. For use of MEMLS outside of this frequency range, and for sea ice, it is necessary to compute the scattering coefficient using theoretical relations. The scattering in sea ice is therefore computed using the improved Born approximation The scattering [using the improved Born approximation] increases by a power law of the microwave frequency times the correlation length with a power of approximately 2.5.

Above a certain frequency or above a certain correlation length, the increase will saturate in a similar way as Mie scattering does for spheres. It is further noted by Mätzler and Wiesmann that the improved Born approximation fits observations for snow grains which are large compared to the wavelength. It is therefore assumed, in this study, that the improved Born approximation is valid also at high frequency (157 and 183 GHz). Scatters are exclusively air bubbles and voids in multiyear ice and brine pockets in first-year ice.

The scattering coefficient is in general a function of the permittivity of pure ice, the permittivity of brine or air, the permittivity of the sea ice mixture, volume of brine or air, microwave frequency and the correlation length of scatterers.

The task was solved in two parts:

- Empirical emissivities were derived from areas of known ice composition using microwave radiometer data from the AMSR-E and AMSU instruments.

- A sea ice and snow emissivity model was developed and utilized in the evaluation and understanding of the empirically derived emissivities from 1)

The Microwave Emission Model for Layered Snow-packs (MEMLS) is a model suitable for simulations of all kinds of physical effects and it has been tested and validated for snow-cover on land with satisfactory results. Here MEMLS is extended to include emission from sea ice. The sea ice model and modifications are described in the next section.

Extension of MEMLS to sea ice emission:

MEMLS, developed by Wiesmann and Mätzler uses the physical snow quantities and structure as input i.e. sequence of layers (j), density (D), exponential correlation length (pec), thermometric temperature (T) and moisture (W). In order to apply this model to compute the emission of both snow and sea ice it is necessary to include modules that compute the dielectric properties, and scattering of sea ice. Small liquid brine inclusions also called brine pockets dominate scattering in nilas and first-year ice. In multiyear ice, the voids and air bubbles in the upper ice are the primary scatters.

The permittivity of liquid brine is an order of magnitude larger than the permittivity of solid ice and the permittivity of sea ice is therefore primarily a function of brine volume. The permittivity of sea ice is computed using Polder - Van Santen mixing formulas. It is a function of pure ice permittivity, inclusion shape and orientation, volume and the brine pockets permittivity (spheres are used because sea ice is assumed isotropic here). These mixing formulas do not account for scattering and therefore the accuracy of the permittivity estimates decreases as a function of frequency. Radiative processes at high frequency are usually confined to the snow cover and it is therefore not expected to be a significant source of error.

MEMLS is valid for snow cover in the range 5-100 GHz. The primary limitation is the estimation of the scattering coefficient using empirical relations, which fit scattering in natural snow cover. For use of MEMLS outside of this frequency range, and for sea ice, it is necessary to compute the scattering coefficient using theoretical relations. The scattering in sea ice is therefore computed using the improved Born approximation The scattering [using the improved Born approximation] increases by a power law of the microwave frequency times the correlation length with a power of approximately 2.5.

Above a certain frequency or above a certain correlation length, the increase will saturate in a similar way as Mie scattering does for spheres. It is further noted by Mätzler and Wiesmann that the improved Born approximation fits observations for snow grains which are large compared to the wavelength. It is therefore assumed, in this study, that the improved Born approximation is valid also at high frequency (157 and 183 GHz). Scatters are exclusively air bubbles and voids in multiyear ice and brine pockets in first-year ice.

The scattering coefficient is in general a function of the permittivity of pure ice, the permittivity of brine or air, the permittivity of the sea ice mixture, volume of brine or air, microwave frequency and the correlation length of scatterers.