Fractal Analysis of Temporal and Spatial Distributions of Rainfall by Radar Observation

Susumu Ogawa¹, Muneo Hirano², Toshiyuki Moriyama² and Tatsuya Ando²

¹Waterworks Bureau, Tokyo Metropolitan Government, 2-8-1 Nishishinjuku, Shinjuku-ku, Tokyo 163-01, Japan
²Department of Civil Engineering, Hydraulics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka-shi, Fukuoka 812, Japan

(Received May 24, 1993; Accepted December 10, 1993)

Keywords: Fractal, Fractional Brownian Motion, Radar Rain

Abstract. The temporal and spatial distributions of rainfall by radar observation can be analysed by fractal theory. The fractal dimensions of a storm were calculated by the box counting method with an average 1.38 for the perimeters of raining regions, and the values ranging between 1.5 and 1.9 for the contours of precipitation rates. Moreover, based on the scaling of rain field, the fractal dimensions for the spatial and temporal distributions were found in the range between 2.7 to 2.8, and were between 1.6 to 2.0, respectively. The latter coincided with the values of the contours of precipitation rates. By using the above results, a simulation for a random process of rainfall with the midpoint displacement technique was conducted.