Microwave Emissivity and Accumulation Rate of Polar Firn

Abstract Radiative transfer theory is formulated to permit a meaningful definition of emissivity for bulk emitting media such as snow. The emissivity in the Rayleigh-Jeans approximation is then the microwave brightness temperature T B divided by an effective physical temperature 〈 T 〉 . The 〈 T 〉 is an average of the physical temperature, T(z), weighted by a radiative transfer function ƒ(z). Similarly, where e ( z ) is the local emittance. An approximate ƒ(z) is used to determine analytically the effects of various absorption coefficients, of scattering coefficients that vary with depth, and of the seasonal variation of T ( z ). It is shown that a mean emissivity, which is equal to the mean annual T B divided by the mean annual surface temperature T m , is a useful quantity for comparing theory and observations. Snow-crystal size measurements, r ( z ), at seven locations in Greenland and Antarctica are used to determine the Mie/Rayleigh scattering coefficient γ s ( z ) and to calculate the mean emissivities. The observed mean emissivities are determined by a which is the average of 12 monthly Nimbus-5 (1.55 cm) microwave observations, and the T m measured at the same locations. The calculated emissivities are about one-half of the observed values. The assumption that each snow crystal is an independent and equally effective scatterer, and the use of an approximation to ƒ(z) , tend to over-estimate the effect of scattering. Therefore, a parameter multiplying γ s ( z ) is used. The emissivities calculated with a single value of this empirical parameter for all seven locations agree well with the observed emissivities, showing that the microwave emissivity variations of dry polar urn can be characterised as a function of the crystal sizes. One optical depth corresponds to a typical fini depth of 5 m, but significant radiation emanates from up to 30 m. Since r(z) depends on the snow accumulation rate A and T m . the sensitivity of the emissivity to changes in T m or A are estimated using this semi-empirical theory. The results show that a one degree change or uncertainty in T m is approximately equivalent to a 10% change in A, and that such a change will affect the emissivity by 0.003 to 0.014 or the T B by about 0.6 K to 3 K, depending on the location.