(Received June 3, 1994; revised August 4, 1995)
Abstract. The threshold method estimates the total rainfall FG in a region G using the area BG of the subregion where rainfall intensity exceeds a certain threshold value c. We model the rainfall in a region by a marked spatial point process and derive a correlation formula between FG and BG. This correlation depends not only on the rainfall distribution but also on the variation of number of raining sites, showing the importance of taking account of the spatial character of rainfall. In the extreme case where the variation of number of raining sites is dominant, the threshold method may work regardless of rainfall distributions and even regardless of threshold values. We use the lattice gas model from statistical physics to model raining sites and show a huge variation in the number of raining sites is theoretically possible if a phase transition occurs, that is, physically different states coexist. Also, we show by radar observation datasets that there are huge variations of raining sites actually.
Key words and phrases: Threshold method, meteorology, rainfall, radar, marked spatial point process, linear regression, lattice gas model, Gibbsian process, potential, phase transition, non-ergodicity.
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