Quantifying the dependence of drop spectrum width on cloud drop number concentration for cloud remote sensing

In-situ measurements of liquid cloud and precipitation drop size distributions from aircraft probes are used to examine the relationship of the width of drop size distributions to cloud drop number. The width of the size distribution is quantified in terms of the parameter k=(rv/re)3, where rv is the volume mean radius and re is the effective radius of the distributions. We find that on small spatial scales (~100 m), k is positively correlated with cloud drop number. This correlation is robust across a variety of campaigns using different probe technology. A new parameterization of k versus cloud drop number is developed. This new parameterization of k is used in an algorithm to derive cloud drop number in liquid phase clouds using satellite measurements of cloud optical depth and effective radius from the MODIS sensor on Aqua. This algorithm is compared to the standard approach to derive drop number concentration that assumes a fixed value for k. The new parameterization generally increases the derived number concentration over ocean, where N is low, and decreases it over land, where N is high. The general tendency of the parameterization is to narrow the distribution of derived number concentration. Regional biases are as large as 20% with the magnitude of the bias closely tracking the regional mean number concentration. Interestingly, biases are smallest in regions of frequent stratocumulus cloud cover, which are a regime of significant interest for study of the aerosol indirect effect on clouds.