Modelling and Simulation of Tropospheric Water Vapour With Gaussian Random Fields-Time dependence beyond the frozen flow hypothesis

Abstract

One of the major sources of error in Very Long Baseline Interferometry (VLBI) is signal delay due to tropospheric water vapour. Turbulent convection makes it inherently unpredictable and it must therefore be measured directly or modelled stochastically. In particular, realizations of delay signals are necessary to simulate the performance of existing and future VLBI networks which, in turn, is needed to optimize them and reduce errors. In previous work, modelling of tropospheric delay has been performed only on the spatial structure of refractivity through phenomenological second order statistics derived from Kolmogorov theory. Time dependence has been introduced exclusively through the frozen-flow hyporthesis. In this thesis, refractivity fields are modelled as Gaussian random fields. Efficient software is implemented to generate realizations of such fields sampled on a 3D grid. To achieve realistic time evolution of such gridded fields, it turns out to be both necessary and natural to introduce intrinsic time dependence beyond the frozen-flow hypothesis. Such time dependence can easily be made compatible with the temporal structure of Kolmogorov turbulence. The novel contributions of this thesis are methods of obtaining two kinds of time dependence for refractivity fields beyond the frozen-flow hypothesis. Firstly: Intrinsic time dependence compatible with Kolmogorov theory. Secondly: Translation by horizontal wind with arbitrary height and time dependence. The latter may provide a more realistic description of the planetary boundary layer which has strong wind shear and contains about 15% of the total water vapour; corresponding to delays of several centimetres.