Determination of the Ice Particle Size Distributions Using Observations as the Integrated Constraints

The possibility is suggested of estimating particle size distributions (PSD) solely based on the bulk quantities of the hydrometeors. The method, inspired by the maximum entropy principle, can be applied to any predefined general PSD form as long as the number of the free parameters is equal to or less than that of the bulk quantities available. As long as an adopted distribution is "physically based,'' these bulk characterizations can recover a fairly accurate PSD estimate. This method is tested for ice particle measurements from the Tropical Composition, Cloud and Climate Coupling Experiment (TC4). The total particle number, total mass, and mean size are taken as bulk quantities. The gamma distribution and two distributions obtained under the maximum entropy principle by taking the size and the particle mass, respectively, as a restriction variable are adopted for fit. The fitting error for the two maximum entropy-based distributions is comparable to that of a standard direct fitting method with the gamma distribution. The same procedure works almost equally well when the mean size is removed from the constraint, especially for an exponential distribution. The results suggest that the total particle number and the total mass of the hydrometeors are sufficient for determining the PSD to a reasonable accuracy when a "physically based'' distribution is assumed. In addition to the in situ cloud measurements, remote sensing measurements such as those from radar as well as satellite can be adopted as physical constraints. Possibilities of exploiting different types of measurements should be further pursued.