Developing and Bounding Ice Particle Mass- and Area-dimension Expressions for Cirrus Clouds

Considerable uncertainty in the modeling of cirrus cloud microphysical processes and in remote sensing retrievals of cirrus cloud properties can be traced to the uncertainties associated with the ice particle mass- and projected area-dimension (m-D & A-D) power laws that supply a priori information. Thus there is a need for more accurate m-D and A-D expressions with quantified uncertainties.

Ice particle m-D and A-D power laws differ between small and relatively large ice particles having the same shape; a power law cannot describe the m-D or A-D relationship across all sizes. Therefore size-resolved measurements of m and A are needed to determine the general form of m-D and A-D expressions.

To develop m-D and A-D expressions for cirrus clouds in terms of temperature T and cloud type, the following strategy was developed: (1) use 2D-S probe size-resolved measurements of ice particle number, projected area and mass concentration, where mass is estimated from the Baker-Lawson m-A power law, to generate m-D and A-D expressions for 10 μm < D < 1280 μm; (2) test the 2D-S m-D expression for -40°C < T < -20°C against size-resolved ice particle mass measurements for this same T regime; (3) if agreement in (2) is good, then assume that the 2D-S mass estimates for T < -40°C are adequate provided PSD area ratios (a proxy for mean ice particle shape for D > 60 μm) for T < -40°C are not much different than for -40°C < T < -20°C; (4) assume that the m-D and A-D uncertainties measured for -40°C < T < -20°C also apply at colder temperatures. This strategy has been implemented and the above strategy was partly successful. The 2D-S data is from the SPARTICUS cirrus cloud field campaign, using hundreds of PSD from synoptic and anvil cirrus clouds. The size-resolved ice particle mass measurements were obtained from a cloud seeding field study (Mitchell et al. 1990, JAM), using 827 ice particles having shapes characteristic of cirrus cloud ice particles formed between -20 and -40°C. The m-D and A-D relationships are best described by 2nd order polynomial fits, and the m-D curve fit for -40°C < T < -20°C (derived from 2D-S measurements) agreed well with the cloud seeding m-D measurements (within 35% based on mean size resolved values). This strategy appears successful for T > -55°C since PSD area ratios changed little between -20 and -55°C. However, PSD area ratios changed significantly for T < -55°C in both synoptic and anvil cirrus, indicating a need for direct ice particle mass measurements at these coldest temperatures. Nonetheless, the 2D-S m-D expressions for T < -55°C compare favorably against recent m-D power laws for small ice particles. Moreover, m-D power laws developed from cirrus measurements of ice water content and PSDs described in two recent studies compare favorably with the m-D expressions in this study.

A methodology for extracting m-D and A-D power laws from the curve fit expressions, appropriate for a given PSD moment, has been developed. This may be a convenient way for cloud and climate models to utilize these curve-fit expressions while still preserving their model architecture that is based on m-D and A-D power laws.

This methodology was also used to estimate the uncertainty in the m-D power law exponent while the cloud seeding m-D data was used to estimate the overall uncertainty in particle mass for a given D. It was found that the majority of uncertainty is associated with the power law prefactor. This information should be useful in bounding uncertainties in cloud property retrievals.