Recent advances in space geodetic techniques such as Very Long Baseline Interferometry, Global Navigation Satellite Services, Satellite Laser Ranging and advanced numerical weather prediction model simulations, provide huge tropospheric data sets with improved spatial temporal resolution. These data sets exhibit unique fluctuations that have a spatial-temporal structure which are thought to mimic the complex behaviour of the atmosphere. As a result, the analysis of non-stationary structure in the tropospheric parameters derived from geodetic and numerical model simulations could be used to probe the extent of universality in the dynamics of the atmosphere, with applications in space geodesy. In order to identify the physical causes of variability of tropospheric parameters, parametric and nonparametric data analyses strategies which are investigated and reported in this thesis, are used to inform on the geophysical signals embedded in the data structure. In the first task of this research work, it is shown that the fluctuations of atmospheric water vapour over southern Africa are non-linear and non-stationary. Secondly, the tropospheric data sets are transformed to stationarity and the stochastic behaviour of water vapour fluctuations are assessed by use of an automatic algorithm that estimates the model parameters. By using a data adaptive modelling algorithm, an autoregressive-movingaverage model was found to sufficiently characterise the derived stationary water vapour fluctuations. Furthermore, the non-linear and non-stationary properties of tropospheric delay due to water vapour were investigated by use of robust and tractable non-linear approaches such as detrended fluctuation analysis, independent component analysis, wavelet transform and empirical mode decomposition. The use of non-linear approaches to data analysis is objective and tractable because they allow data to speak for themselves during analysis and also because of the non-linear components embedded in the atmosphere system. In the thesis, we establish that the non-linear and non-stationary properties in the tropospheric data sets (i.e., tropospheric delay due to water vapour and delay gradients) could be triggered from strongly non-linear stochastic processes that have a local signature (e.g. local immediate topography, weather and associated systems) and/or exogenous. In addition, we explore and report on the presence of scaling properties (and therefore memory) in tropospheric parameters. This self-similar behaviour exhibit spatial-temporal dependence and could be associated with geophysical processes that drive atmosphere dynamics. Satellite Laser Ranging data are very sensitive to atmospheric conditions, which causes a delay of the laser pulse, hence an apparent range increase. A test for non-linearity is applied within specialised software for these data; it is found that the range residuals (i.e., the observed minus computed residuals) are improved when possible non-linearity of the locally measured meteorological parameters as applied to a range delay model are considered.