Data sparsity and the tropical‐cyclone analysis and prediction problem: Some simulation experiments with a barotropic numerical model

Abstract

AbstractSome simulation experiments relevant to the problem of determining the minimum data requirements for the accurate reconstruction of tropical‐cyclone‐scale vortices from given sparse data distributions are described. Also, the accuracy with which the vortex track can be predicted using these data is investigated. The experiments are based on a 96‐hour numerical integration of the barotropic vorticity equation on a beta‐plane, starting with a symmetric tropical‐cyclone‐scale vortex embedded in zonal shear flow. After 48 hours, when asymmetries in the vortex circulation have developed, the model fields in this ‘control’ calculation are used as a ‘perfect’ data set to assess the analysis strategy described. The 20 km horizontal resolution of these new initial data is progressively degraded to test the ability of the analysis procedure to reconstruct the perfect analysis. The analyses of the degraded data sets are used as an initial condition for a further 48‐hour integration of the model, and the resulting vortex tracks are compared with that in the second half of the control run. The influence of the analysed vortex asymmetry on the subsequent vortex track is also studied.As the resolution of the simulated initial data is degraded, so is the information that these data provide on the symmetric circulation and the vortex‐induced asymmetries, and ultimately it becomes necessary to introduce ‘synthetic’ data in the analysis. The calculations indicate some of the problems that need to be overcome to introduce such data properly.The analysis method provides a general way to partition the flow into four components: the large‐scale environment, the symmetric vortex, the vortex asymmetry, and the small‐scale environment. The large‐scale environment is characterized by the lowest few wave numbers in a two‐dimensional Fourier analysis. The residual field is subjected to an azimuthal Fourier analysis about the cyclone centre, and the last three components of the partition are defined by the symmetric component, the wave‐number‐one component and the sum of all higher wave‐number components of this analysis, respectively. An attractive feature of such a partition is that the total flow across the centre of the symmetric vortex, which governs the vortex motion in a barotropic model, is contained in only two components: the large‐scale environment and the vortex asymmetry.