The problem of the disagreement between cirrus crystal sizes determined remotely and by in situ measurements is shown to be due to inappropriate application of Mie theory. We retrieved the absorption optical depth at 8.3 and 11.1 μm from 11 tropical anvil cirrus clouds, using data from the High Resolution Infrared Radiation Sounder (HIRS). We related the absorption optical depth ratio between the two wavelengths to crystal size (the size was defined in terms of the crystal median mass dimension) by assuming Mie theory applied to ice spheres and anomalous diffraction theory (ADT) applied to hexagonal columns, hexagonal plates, bullet rosettes, and aggregates (polycrystals). The application of Mie theory to retrievals yielded crystal sizes approximately one third those obtained with ADT. The retrievals of crystal size by use of HIRS data are compared with measurements of habit and crystal size obtained from in situ measurements of tropical anvil cirrus particles. The results of the comparison show that ADT provides the more realistic retrieval. Moreover, we demonstrate that at infrared wavelengths retrieval of crystal size depends on assumed habit. The reason why Mie theory predicts smaller sizes than ADT is shown to result from particle geometry and enhanced absorption owing to the capture of photons from above the edge of the particle (tunneling). The contribution of particle geometry to absorption is three times greater than from tunneling, but this process enhances absorption by a further 35%. The complex angular momentum and T-matrix methods are used to show that the contribution to absorption by tunneling is diminished as the asphericity of spheroidal particles is increased. At an aspect ratio of 6 the contribution to the absorption that is due to tunneling is substantially reduced for oblate particles, whereas for prolate particles the tunneling contribution is reduced by 50% relative to the sphere.
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