Retrieval of aerosol properties from moments of the particle size distribution for kernals involving the step function: Cloud droplet activation. Wright Jr., D. L., Yu, S., Kasibhatla, P. S., McGraw, R., Schwartz, S. E., Saxena, V. K., and Yue, G. K. J. Aerosol Sci. 33, 319-337 (2002).

Aerosol properties such as the number of particles that activate to form cloud drops and the mass contained within specified size ranges (as in the PM 2.5 and PM 10 regulatory standards)require integration over only part of the full size range of the particle distribution function (PDF) and may be formally expressed as integrals over kernels involving the Heaviside step function. Determination of these properties requires essentially that the size spectrum be partitioned into two (or more)portions, and poses a special challenge for aerosol modeling with the method of moments. To assess the ability of moment-based methods to treat kernels involving step functions, several algorithms for the estimation of aerosol properties associated with cloud activation have been evaluated. For 240 measured continental distributions employed here as test cases, the full size spectrum of the PDF was partitioned into three distinct portions based upon characteristic critical radii for activation in cumulus and stratiform clouds, and mass-and number-concentration metrics were evaluated for each portion. The first six radial moments yielded results accurate to within about 10% or better, on average, and the numbers of particles activated as cloud drops and the aerosol mass taken into cloud water were estimated to an accuracy of 5% or better. Of the moment-based approaches evaluated, the multiple isomomental distribution aerosol surrogate (MIDAS; Wright, J. Aerosol Sci. 31, 1 (2000)) technique performed best. Accurate results were also obtained with the randomized minimization search technique (RMST; Yue et al., Geophys. Res. Lett. 24, 651 (1997); Heintzenberg et al., Appl. Opt. 20, 1308 (1981)).


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