Toward more accurate retrievals of ice water content from radar measurements of clouds

There has been considerable discussion concerning the accuracy of values of ice water content (IWC) in ice clouds derived from measurements of radar r eflectivity (Z). In this paper, the various published relationships that ar e based on ice particle size spectra recorded from aircraft are analyzed, a nd it is shown that a relationship between ice water content and reflectivi ty can be derived (IWC = 0.137Z(0.64) at 94 GHZ and IWC = 0.097Z(0.59) at 3 5 GHz), which only varies by 20%-30% for different climatological areas, pr oviding the same ice density as a function of particle size is assumed. Unc ertainty as to the true variation of density of ice particles with size may reduce the average IWC for a given Z by up to 30% for an IWC of approximat e to 0.1 g m(-3) and 20% for an IWC of approximate to 0.01 g m(-3). Individ ual values of IWC derived from a single measurement of Z are likely to have an error of about + 100% and -50%, bur if some characteristic size estimat e is available, this is reduced to about +50% and -30%. The remaining error s are due to deviations of the size spectra from exponentiality, so there i s no advantage in measuring the characteristic size more precisely than thi s limit. Remote sensing of ice particle size is not trivial, and it is show n that if instead of size, an estimate of the temperature of the ice cloud to within 6 I; is available, then, rather surprisingly, the reduction in th e error of IWC is almost as good as that achieved using size. Essentially t his result is reflecting the well-known correlation of crystal size with te mperature. When the mean values of IWC for a given Z and T are compared for a tropical and midlatitude dataset using a common ice density variation wi th size, then the difference is usually less than 25%. A spaceborne instrum ent may need to integrate over horizontal distances of 10 km to achieve suf ficient sensitivity; this necessity may introduce a bias into the retrieved IWC because the relationship between IWC and Z is not linear, but analysis shows that any bias should be less than 10%.