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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.