The number of independent variables for cloud properties [N.sub.var] is determined within IMARS from the ice cloud probability (Pcloud) and the intrinsic uncertainty of the ice cloud retrieval (ecloud) as follows [22, 29]:
Only rainfall observations collocated temporarily and spatially with IMARS ice cloud observations are used for the analysis.
In order to generate a set of coincidences for dust loading and cloud properties, the spatial correlation lengths for IMARS [AOD.sub.dust] are used to generate a continuous AOD field for each observation time step.
After having generated the continuous [AOD.sub.dust] fields, IMARS cloud observations are subdivided into three different subsets of dust loading.
As a starting point, CTT histograms are determined from all IMARS ice cloud observations in the analysis region for the three different dust loading sets "background" ("b", black colour in plots), "moderate" ("m", blue), and "high" ("h", red).
The IMARS retrieval information content (see (1)) is a special case of such a distribution information content where the set X in (4) consists of two elements only.