For water clouds, the size distribution, N(D), exhibits relatively little dispersion around the mean diameter in comparison with ice clouds. For this reason, the single particle approximation for Babs based on Deff compares well with Babs predicted from Mie theory, providing a new and efficient means of treating radiation transfer at terrestrial wavelengths. The Deff expression for Bext agrees well with Mie theory only under specific conditions: (1) absorption is substantial or (2) occurs in the Rayleigh regime, or (3) size parameter x > 50, where x is based on Deff.
For ice cloud N(D), the dispersion about the mean is much greater than for water clouds, and N(D) is generally bimodal, peaking around 10 - 25 microns. For this is reason, Deff expressions for Babs and Bext are probably inadequate for most applications, at least at terrestrial wavelengths. Even for exponential N(D), errors due to the Deff approximation may be unacceptable. The high concentrations of small crystals (D < 100 microns) have relatively low absorption efficiencies, and their presence makes the parameterization of Babs more challenging. The greater N(D) dispersion for ice clouds makes it desirable to use expressions for the absorption and extinction coefficients that are explicit functions of the N(D) and ice crystal properties. Such analytical expressions for Babs and Bext were developed (for all clouds) that may not be too computationally expensive for many applications. Most schemes for predicting ice cloud radiative properties are founded on the assumption that the dependence of Babs and Bext on the N(D) can be described solely in terms of Deff and IWC. This assumption was tested by comparing the N(D) weighted efficiencies for absorption and extinction, Qabs and Qext, for three N(D) which have the same IWC and Deff, but for which N(D) shape (i.e. dispersion or bimodality) differs, based on analytical solutions for Babs and Bext, which explicitly treat N(D) shape. Uncertainties (percent differences) resulting only from N(D) shape differences can reach 58% for Qabs (or Babs), 98% for Qext (or Bext) and 48% for single scattering albedo in the thermal infrared. This illustrates how satellite retrievals of ice cloud properties depend on implicit assumptions regarding N(D) shape.