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Within the ice pack, the brightness temperature of a pixel area derives from various sources -- the water and ice within the field of view, and the atmosphere. To a good approximation
where epsilon W, TW, and CW are emissivity, surface physical temperature, and areal percentage of water, and epsilon I, TI and CI are the corresponding values for sea ice. TA is the contribution attributable to the atmosphere and includes the direct upwelling radiation, the downwelling radiation reflected from the surface, and the radiation from space reflected by the surface. Because the reflectance of water is different from that of ice, the atmospheric contribution can be separated into contributions over water, T[AW], and over ice T[AI]. The atmospheric opacity in the polar region has been estimated to be very small and was neglected. Also, C[W] + C[I] = 1 and epsilon [I] was determined empirically to be about 0.92.
The ice concentration, C[I], can thus be determined from equation the above equation:
where T = epsilon [W] T [W] + T[AW] is the measured brightness temperature of the water determined from the data, and T[eff] = T[I] + T [AI/epsilong I] is the effective surface physical temperature. The value of T[AW] was calculated by using radiative transfer modeling of the atmosphere (Nieman and Wilheit, private communication) and was estimated over the ocean to be about 8 K. The value of T[AI] is considerably smaller because the reflectivity of ice is substantially lower than that of water, and the contribution of downwelling radiation reflected from the surface is therefore smaller. In the polar regions, the atmospheric contribution to the brightness temperature is minimal because the humidity and the water-vapor content in the atmosphere is very low. Therefore, T[eff] is taken to be equal to T[I]. The appropriate physical temperature, T[I], is the temperature at the top of the sea ice below the snow cover, because most of the observed radiation emanates from a thin top layer of saline ice. in the absence of real-time physical temperature data, T[I] was estimated from a compilation of climatological surface air temperatures (Jenne et al 1974) as follows. The actual temperature of the top sea ice surface lies between the surface air temperature, T[air], interpolated from the climatological data, and the temperature of the water underneath the ice. It can be expressed by:
where T[m] is the melting temperature of ice, and f is an empirical parameter deduced from the ESMR data.