SOME EULERIAN AND LAGRANGIAN STATISTICAL PROPERTIES OF RAINFALL AT SMALL SPACE-TIME SCALES

Management of urban hydrological systems requires a knowledge of short-term and small-scale rainfall properties. Small catchment areas, dense building structures, a high degree of impermeable areas, and resulting rapid runoff, mean that the properties of individual rain cells are important considerations. Accordingly, this paper characterizes mainly spatial rainfall properties on a scale suitable for urban hydrology. Because of the usually dominant advective velocity component of individual rain cells the Eulerian view (observations of the moving rain cell by a fixed rain gage network) gives a distorted picture in the direction of movement of the actual rain cell. The extent of distortion depends on the magnitude of the advective velocity. The Lagrangian approach (moving along with the same speed and direction as the cell) gives different information regarding cell characteristics (e.g. size) compared with the Eulerian approach. It is shown that the Lagrangian cell size as indicated by the spatial correlation structure on average is twice the size of the Eulerian cell size. Thus, it is argued that the Lagrangian approach provides a more realistic picture of the rainfall structures compared with the Eulerian approach. The cell properties exhibit a temporal persistence of the spatial characteristics in the direction of movement. This persistence is, however, not strong and thus a forecasting procedure using advection only does not seem appropriate.