A Fast Inverse Algorithm Based on the Multigrid Technique for Cloud Tomography

Abstract

Abstract A fast inverse algorithm based on the half-V cycle scheme (HV) of the multigrid technique is developed for cloud tomography. Fourier analysis shows that the slow convergence problem caused by the smoothing property of the iterative algorithm can be effectively alleviated in HV by performing iterations from the coarsest to the finest grid. In this way, the resolvable scales of information contained in observations can be retrieved efficiently on the coarser grid level and the unresolvable scales are left as errors on the finer grid level. Numerical simulations indicate that, compared with the previous algorithm without HV (NHV), HV can significantly reduce the runtime by 89%–96.9% while retaining a similar level of retrieval accuracy. For the currently feasible two-level flight scheme for a 20-km-wide target area, convergence can be accelerated from 407 s in NHV to 13 s in HV. This reduction in time would be multiplied several times if the target area were much wider; but then segmental retrieval would be required to avoid exceeding the time limit of cloud tomography. This improvement represents an important saving in terms of computing resources and ensures the real-time application of cloud tomography in a much wider range of fields.