Testing and comparing the modified anomalous diffraction approximation

The modified anomalous diffraction approximation (MADA) is used to predict absorption and extinction in water and ice clouds, but it does not predict the scattering phase function or asymmetry parameter g. In conjunction with g parameterizations, it has been used in satellite remote sensing and to treat the radiative properties of ice clouds in global climate models. However, it has undergone only limited testing. This study 1) compares extinction efficiencies (Qext) predicted by MADA for a laboratory grown ice cloud against corresponding Qext measurements over the wavelength range 2-14 μm; 2) tests absorption efficiencies (Qabs) and Qext predicted by MADA against those predicted by T-matrix theory and the finite difference time domain (FDTD) method; and 3) compares MADA with three popular schemes used for predicting the radiative properties of cirrus clouds. In addition, the photon tunneling process may contribute up to 45% of the absorption in water clouds at some terrestrial wavelengths, but its role in ice clouds is uncertain since it depends on particle shape. For the first time, the efficiency of photon tunneling was parameterized in terms of ice particle shape. Finally, an alternate formulation of MADA that offers some physical insights is presented. MADA errors relative to the Qext measurements were 3.0% on average, while mean MADA errors relative to Qabs from T-matrix, over the wavelength range 2-18 μm (size parameter range 2-22), were 5.9%. The mean error for the single scattering albedo relative to T-matrix calculations was 2.5%. MADA absorption errors relative to FDTD over the wavelength range 3-100 μm were no greater than 15% for six ice particle shapes. Finally, the absorption coefficients predicted by MADA and two other popular parameterizations generally agreed within 5%.