Spatial correlation of hydrometeor occurrence, reflectivity, and rain rate from CloudSat

This paper examines the along-track vertical and horizontal structure of hydrometeor occurrence, reflectivity, and column rain rate derived from CloudSat. The analysis assumes hydrometeors statistics in a given region are horizontally invariant, with the probability of hydrometeor co-occurrence obtained simply by determining the relative frequency at which hydrometeors can be found at two points (which may be at different altitudes and offset by a horizontal distance, Delta x). A correlation function is introduced (gamma correlation) that normalizes hydrometeor co-occurrence values to the range of 1 to -1, with a value of 0 meaning uncorrelated in the usual sense. This correlation function is a generalization of the alpha overlap parameter that has been used in recent studies to describe the overlap between cloud (or hydrometeor) layers. Examples of joint histograms of reflectivity at two points are also examined. The analysis shows that the traditional linear (or Pearson) correlation coefficient provides a useful one-to-one measure of the strength of the relationship between hydrometeor reflectivity at two points in the horizontal (that is, two points at the same altitude). While also potentially useful in the vertical direction, the relationship between reflectivity values at different altitudes is not as well described by the linear correlation coefficient. The decrease in correlation of hydrometeor occurrence and reflectivity with horizontal distance, as well as precipitation occurrence and column rain rate, can be reasonably well fit with a simple two-parameter exponential model. In this paper, the North Pacific and tropical western Pacific are examined in detail, as is the zonal dependence.