Ice cloud inhomogeneity: Quantifying bias in emissivity front radar observations

In numerical models the infra-red emissivity of ice clouds is generally com puted from the optical depth. The convex relationship between these two qua ntities implies that if ice clouds are inhomogeneous, emissivities calculat ed from a grid-box mean optical depth will be biased high. An analogous eff ect in stratocumulus albedo and liquid water path is compensated for by mul tiplying liquid water by 0.7 to calculate albedo. However it is unclear tha t a similar correction is valid for all cloud types. In this paper profiles of radar reflectivity in mid-latitude winter ice clouds are analysed to de rive the variability of optical depth and quantify any biases introduced in to emissivities calculated from grid-box mean optical depths. The bias is s mall for grid-lengths of 10km, but the average optical depth should be mult iplied by a correction factor of 0.44 for calculating emissivities in a 300 km box.