Tuesday, 11 February 2003
Exploring the stochastic micro-structure of rain: scale dependence of spatial correlations
We begin by arguing the central role of the Poisson process in characterizing rain micro-structure. In particular, importance of statistical stationarity and the essential distinction between Poisson distribution and Poisson process are emphasized. Two new tools are introduced and it is argued that these (the pair correlation function and the Ornstein-Zernike fuctuation-correlation equation) are ideally suited for scale dependent exploration of rain micro-structure. The importance and likely ubiquity of negative spatial correlations at small separation distances are discussed because all instruments are likely to yield negative pair correlation functions when pushed to their resolution limits. It is pointed out that Poisson statistics on a given scale are probably a result of cancellation on sub-scales.