Interpolation of the raindrop size distribution over a GPM-pixel-sized region.

The raindrop size distribution (DSD) is crucial information on the structure of rainfall. All bulk rainfall variables of interest can be derived as weighted moments of the DSD. Usually the DSD is measured at point locations using disdrometers. In some contexts, such as the investigation of scale-change effects, it would be useful to be able to interpolate the DSD across space between point measurements. Traditionally such studies are performed by interpolating bulk variables individually. Such an approach fails to take into account any interrelationships between the bulk variables and information is lost. We present a spatial interpolation method for the whole drop size distribution. Instead of using multivariate geostatistics, we use a principle component analysis (PCA) to identify orthogonal components of the DSD. These components are independent, and thus we can apply univariate geostatistics to each one individually. Interpolation is carried out using ordinary kriging. Once components are interpolated, the interpolation of the DSD can be recovered at any requested point by recombining and back-transforming the components. The advantages of the method are that the DSD is interpolated in full, the use of PCA allows us to control and quantify the amount of information loss that occurs, and relationships between any bulk variables are maintained through the process. An important feature of rainfall that is considered in the proposed interpolation method is the intermittency and its influence on the spatial distribution of raindrops. We have applied this technique to DSDs recorded at point locations in a GPM-pixel sized area in Ardèche, France in the framework of the HyMeX project. To test the results we use leave-one-out testing and compare to interpolation of individual bulk variables; the results are favourable. An investigation of the radar reflectivity to rain-rate (Z-R) relationship shows that our DSD interpolation technique maintains the relationships between bulk variables. The technique will be useful for investigation of DSD variability and the effects of scale-change over space, which in turn will be beneficial to DSD model verification.