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374 PJ. BRf::MAUD AND Y,B. POINTIN ?n thei: motion as detected in successive radar pictures is only the first step m makmg a precipitation forecast, as the intensity of the extrapolated radar echoes must then be converted into rainfaII at the ground (Einfalt, 1991), This conversion can lead, for the required high spatial and temporal resolution, to larger uncertainties than for hourly averages (Messaoud and POintin, 1990), mamly because of the variability of the raindrop size distribution, This paper is concerned only with this first step of producing the best extrapolation method, The approaches used until now can conveniently be considered as falling into one of three categories: cross-correlation techniques. echo centroid methods and more complex methods (Elvander, 1976; ColJier, ] 978, 1989), Cross-correlation techniques were the first to be studied (Wilson and Kessler, 1963) because they are the simplest way to make an estimate of the motion of the radar echoes, The principle consists of overlaying, with a spatial shift, the radar picture observed at I an the picture observed at t - [JI and searching for the optimum relative position of the two pictures corresponding to the best value of the cross-correlation coefficient (Austin and Bellon, 1974), This optimum shift indicates the displacement of the radar echoes, provided that there afe no significant size, shape and intensity changes during the time interval Ot, The forecast is then made by extrapolating this detected motion and applying it unifonnly over the whole radar picture to the time I + 0/, This technique has been operationally used, with some success for the forecast of widespread precipitation over reasonably flat terrain, by Bellon and Austin (1978), but it does not alIow for ditTerent motions of individual radar echoes which can occur in the case of developing convective activity or orographic rainfall. As these are very important types of precipitation for urban hydrology, cross-correlation techniques are not the most appropriate for this purpose. In the case of echo centroid methods, the motion of each radar echo is deduced from the successive positions of its centroid (Barclay and Wilk, 1970; Wilk and Gray, 1970; Bjerkaas and Forsyth, 1980), Therefore, these methods are more elaborate than cross-correlation methods but they still remain too simple, Echo centroid methods perform well in the case of isolated radar echoes (e.g. isolated thunderstorms), but in other cases, such as convective cens embedded within a large stratiform rain area or within a frontal band, these methods may have problems (Zitt"], 1976), Indeed, the successive positions of the echo centroid are not always representative of the real echo motion when the morphological changes of the echo from one picture to the next are important, especially if splits or mergers of echoes OCCur. Because of these problems, echo centroid methods are also not well suited for short-term hydrological purposes, , The third kind of technique, usually named the 'complex method', may ~ .' " :; ! ~ ~ FORECASTING HEAVY RAINFALL FROM RAIN CELL MOTION 315 solve some of the problems of the cross-correlation and echo centroid methods, Blackmer et al. (1973) have used a local cross-correlation technique to estimate the local motion of the echoes which are defined by a fixed reflectivity threshold (afterwards called a 'T echo'), This estimation of the local echo motion leads to more realistic trajectories than those deduced from the successive positions of the centroid, because it is less sensitive to mOr- phological changes, Going further, Einfalt e,t ,al. (1990) d~fined 'structured echoes' which are the union of two or more SImple echoes (T echoes), The matching of these structured echoes with simple echoes permits the possible split or merger of simple echoes to be taken into account. Thi~ technique, which uses complex mathematical tools such as pattern recogmtlon, offers distinct improvements over earlier techniques for detailed rainfall forecasts at short time and spatial scales. Nevertheless, the main characteristics of most existing methods, especially the definition of the tracked,ntities (T echoes), are not based upon the physics of the cloud processes associated with strong radar echoes in contrast to the PARAPLUIE method which is described , below, PARAPLUIE: A HEAVY RAINFALL FORECASTING METHOD 'The PARAPLUIE method (Bremaud, 1991) belongs to the complex method category, and is divided into four steps: (a) tracked entity definition; (b) tracked entity characterization; (c) tracked entity matching for the detection of the ditTerent motions; (d) forecast by extrapolation, The method is fully automated, so it does not require operator intervention. Tracked entity definition In contrast to a large majority of methods, which use the T echo defined by a connectivity property above a fixed given reflectivity threshold, the PARAPLUIE algorithm defines the tracked entities, called 'CEL echoes', by the contour constructed at 6 dB below each enclosed reflectivity maximum, Thus the reflectivity threshold defining the CEL echo is not fixed but varies with the rain type, This definition of our tracked entities, originally introduced by Crane (1979) for aircraft hazard identification, is illustrated in Figs, I and 2 which show for a frontal rain band observed on 11 October 1988 in the Covennes are; of France (Andrieu ,et aI., 1989), a PPI map and a horizontal, reflectivity profile along an east-west line 10 km north of the radar, respec- tively, In Fig, 2, the small-scale variation of the reflectivity profile between 5 and 20 km is due to ground echoes in this mountainous area. These ground echoes are detected by the PARAPLUIE algorithm both by the small size of