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 spatial variability which makes especially difficult their interpolation by classical 2D algorithms. In the Sahel, mesoscale convective systems moving westward are the dominant source of rainfall. Their movement is relatively stable, which implies some predictability of the rainfall ahead of the moving storm. It is proposed here to take this feature into account in the interpolation of small time step rainfields, when only a raingauge network is available, A lagrangian approach, based on the interpolation of the arrival times of rainfall at points of observation, is developed to build 2D lagrangian rainfields. These rainfields are interpolated using classical 2D algorithms, such as kriging or moving averaging, The performance of the lagrangian estimates are compared to those of eulerian estimates for three Sahelian squall lines, The relative root mean squared interpolation error of the lagrangian estimates is 20 to 40% lower than that of the eulerian estimates. The superiority of the lagrangian approach is especially noteworthy for the convective rainfields making up the front of the squall lines, The differences between lagrangian kriging and eulerian kriging is far more important than the differences between lagrangian kriging and lagrangian moving averages, This means that the time axis is the main axis of anisotropy for the 3D space-time rainfields, and that for such rainfall systems estimation algorithms should be refined to account for the time covariance rather than for the space covariance. A simulation performed on an idealised model of squall line (constant speed and time invariant hyetogram) shows that the observed Sahelian squall lines behave like the combination of an ideal squall line, moving undistorted at constant speed, and of a white noise whose level ranges from 40 to 100%. (C) 1997 Elsevier Science B.V.