LAGRANGIAN KRIGING FOR THE ESTIMATION OF SAHELIAN RAINFALL AT SMALL TIME STEPS

Tropical rainfall is mostly of convective origin. The associated small time step rainfields are consequently characterised by a strong spati al variability which makes especially difficult their interpolation by classical 2D algorithms. In the Sahel, mesoscale convective systems m oving westward are the dominant source of rainfall. Their movement is relatively stable, which implies some predictability of the rainfall a head of the moving storm. It is proposed here to take this feature int o account in the interpolation of small time step rainfields, when onl y a raingauge network is available, A lagrangian approach, based on th e interpolation of the arrival times of rainfall at points of observat ion, is developed to build 2D lagrangian rainfields. These rainfields are interpolated using classical 2D algorithms, such as kriging or mov ing averaging, The performance of the lagrangian estimates are compare d to those of eulerian estimates for three Sahelian squall lines, The relative root mean squared interpolation error of the lagrangian estim ates is 20 to 40% lower than that of the eulerian estimates. The super iority of the lagrangian approach is especially noteworthy for the con vective rainfields making up the front of the squall lines, The differ ences between lagrangian kriging and eulerian kriging is far more impo rtant than the differences between lagrangian kriging and lagrangian m oving averages, This means that the time axis is the main axis of anis otropy for the 3D space-time rainfields, and that for such rainfall sy stems estimation algorithms should be refined to account for the time covariance rather than for the space covariance. A simulation performe d on an idealised model of squall line (constant speed and time invari ant hyetogram) shows that the observed Sahelian squall lines behave li ke the combination of an ideal squall line, moving undistorted at cons tant speed, and of a white noise whose level ranges from 40 to 100%. ( C) 1997 Elsevier Science B.V.