Clouds interact with solar and terrestrial radiation and thereby influence the energy budget of the earth. The importance of ice clouds for the climate has been recognized for a long time (e.g., Liou 1986). Many questions concerning the microphysical
Clouds interact with solar and terrestrial radiation and thereby influence the energy budget of the earth. The importance of ice clouds for the climate has been recognized for a long time (e.g., Liou 1986). Many questions concerning the microphysical composition of ice clouds have not been solved yet since it is difficult to measure ice crystals in nature. In general, ice clouds are found in the upper part of the troposphere, requiring aircrafts suited for this height. Low water vapor content and a low abundance of ice nuclei contribute to the low concentration of ice crystals that make their observation difficult. An exception might be tropical anvils or cirrus clouds originating thereof, whose composition and ice load is strongly controlled by the vertical transport from the lower troposphere. Another difficulty is the measurement of the ice particle size with scattering probes like the Forward Scattering Spectrometer Probe (FSSP) since nonspherical particles produce a complicated signal in the detector. Nonscattering optical probes like 2D arrays can sample irregularly shaped crystals, but their detection limit used to be high, typically on the order of some 10 μm. New techniques like the video ice particle sampler (VIPS, McFarquhar and Heymsfield 1996) or the counterflow virtual impactor (CVI, Noone et al. 1993) have been developed to sample micron-sized particles, but the available data are not conclusive yet. The size distribution is still very speculative and better data are highly desired, especially for small ice particles.
The objective of this study is to find a parameterization of re for ice clouds in large-scale models. The problem is split into two parts, namely, to define a size distribution of ice particles and to examine the effect of the different definitions for re. Existing parameterizations of the particle size distribution n(L) do not take into account small ice crystals. Therefore, a new parameterization for n(L) is suggested that includes also small particles. The suggested size distribution is a function of the macroscopic variables temperature (T) and ice water content (IWC). The different interpretations of the theoretical definition (1) lead to large differences in the resulting re. It is possible to find norming factors that allow us to compare re from the different definitions. Finally, a parameterization for re in terms of large-scale variables is sought to replace the expensive explicit calculation of re in ice clouds. A fair agreement is found between observed and calculated re.
2. Shape of ice crystals
Ice crystals occur in many different shapes or habits. Early works suggest that the ambient temperature decides the crystal type (Ono 1970), but more recent research indicates that the growth processes leading to the different habits are complicated and no simple relationship between temperature and habit exists (Dowling and Radke 1990). Despite the variety of naturally occuring habits, all crystals are treated as hexagonal columns for the remainder of this work. This simplification is chosen to make re from the present work applicable in the radiation scheme of Ebert and Curry (1992), which has been developed with the same assumption. The restriction to one habit is inconsistent with observations; nevertheless, radiation schemes suitable for large-scale models have yet to be developed for other habits than hexagonal columns.
3. Size spectrum
The difficulties of measuring the size distribution in ice clouds have been mentioned in the introduction. Several mathematical expressions for the size spectrum have been suggested based on observations. The limited number of data a