Time-series of precipitable water vapour (PWV), derived from continuous Global Positioning System (GPS) observations, are analysed for the two South African stations HRAO and SUTH. Since water vapour is a major greenhouse gas, observed changes in atmospheric PWV could be indicative of weather and climate change. Our main contribution is a realistic noise model of the PWV observations which enables one to draw correct conclusions about the significance of the derived PWV increase or decrease for given time spans longer than five years. It is demonstrated that the PWV residuals that are obtained after fitting a trend and yearly signal to the data are, due to the simple model’s exclusion of short-term scatter, much larger than the PWV uncertainties provided by the GPS analysis software. Although a better solution for the associated uncertainties is obtained by using the variance of these PWV residuals for the uncertainty rescaling, it is shown that the ARMA(1,1) noise model better represents the associated statistical uncertainties than the simple white noise model. The ARMA(1,1)-derived PWV trend uncertainties are approximately 2 times greater than those for a rescaled white noise model. Finally, it is argued that the variability of the annual signal prevents any trend estimation using time series shorter than about five years. A quantitative measure is presented to determine the minimum period of continuous GPS observational data required to measure PWV trends to a specified accuracy. As result of our study, we conclude that no statistically significant PWV trends are observed at the two GPS stations between 1998 and 2006.

A new Satellite Laser Ranging (SLR) analysis program is being developed at Hartebeesthoek Radio Astronomy Observatory (HartRAO) that can model satellite orbits with high accuracy utilising advanced modelling and SLR data. We introduce the background to SLR analysis to an interdisciplinary audience and present the results of processing one month of LAGEOS-1 and LAGEOS-2 data in combined and separate solutions. The inclusion of Earth-tide modelling is shown to be necessary to reduce range bias and to minimise observed minus computed (O-C) residuals. The combined solution shows a reduction in range bias when allowance is made for the SLR station displacement vector due to solid Earth-tide and the effect of the Earth-tide on the static gravity field. In order to make the comparison it is necessary to set the a-priori estimation error of unmodelled forces to a low value as it tends to absorb range biases and improve O-C residuals if included as an additional solve-for parameter. A comparison between the SLR station position perturbation resulting from solid Earth-tide and range bias indicates a correlation, which probably results from an overestimate of the Earth-tide vector and indicates that SLR will be able to differentiate between and evaluate different Earth-tide models. These are preliminary results and further improvement is envisaged due to the planned inclusion of additional advanced modelling procedures. Applications of this software will include velocity field determinations for crustal dynamics studies.

Parameterised post Newtonian (PPN) parameters γ and β (which should equal unity if general relativity is valid) are estimated through the analyses of four years of LAGEOS 1 and LAGEOS 2 data. To reduce the chance of possible imprinting of general relativistic effects which could be contained in the Earth gravity model used, several low order spherical harmonic coefficients are solved in the orbit estimation and propagation process. After convergence is reached, the solved PPN parametersand γ and β are kept fixed at their solved values and scaling coefficients are introduced to explore the possibility of open parameter space in the accelerations due to the Schwarzschild field, frame dragging and de Sitter (geodesic) precession. It is found that some parameter space is available in the radial acceleration component, which could be taken up by including post-post-Newtonian components of general relativity, or it could be due to some other radial acceleration component that is not adequately modelled. The inclusion of scale coefficients in the least-squares process proves to be a valuable tool in evaluating the solutions for γ and β. A comparison with results obtained for the PPN parameters by other authors utilising different techniques such as VLBI and radar measurements to planets and probes are made.

We investigate the use of distribution functions to characterise the geophysical signals and noise components embedded in the geodetic Very Long Baseline Interferometry (VLBI) data sets across some of the International VLBI Service (IVS) stations. The rationale of using α-stable distributions as a tool to model the noise components in geodetic observables is due to the existence of impulsive signals/noise bursts (which often take the form of excursions with intermittent occurrences) in the data sets suggesting deviations from Gaussian distribution. A deviation from Gaussian distribution type would therefore suggest that statistical techniques such as least squares analysis, often used for analyzing the geodetic data (which are often based on Gaussian assumptions) could not be robust. In this paper, the properties of a long-range α-stable distribution with long tails and infinite moments in geodetic data are investigated by way of statistically testing their distribution using a family of stable distributions. The choice of stable distributions is based on the ease with which the statistical properties of the non-Gaussian processes are defined. Results indicate that the independent geophysical noise components reconstructed from geodetic VLBI baseline data exhibit distributions that have asymptotic power-law decay (albeit variable power indices) whose underlying process can be modelled as a long-range dependent process with an α-stable distribution (i.e., the stable varieties have small characteristic exponents).

A new geodetic observatory at Matjiesfontein will house a 1-metre aperture Lunar Laser Ranging (LLR) optical telescope to acquire millimetre Earth-Moon distance measurements. Large optical telescopes utilised for laser ranging observations of Earth-Moon distance, with sub-centimetre level accuracy can suffer from structural deformations induced by thermal variations, wind loadings and/or gravitational forces. These variables need to be measured to enable correction of the resulting pointing errors. This paper presents the proposed locations of temperature sensors on the composite structure of the Hartebeesthoek Radio Astronomy Observatory (HartRAO) LLR 1-metre optical telescope. Furthermore, we describe a mathematical model for (i) obtaining thermal measurements from a network of temperature sensors, (ii) interpolating the temperatures across the telescope composite structure, and (iii) predicting thermally-induced structural deformations. Currently, the available thermal simulation results of the LLR telescope tube assembly indicate isotherms with gradients of about 1°C followed by thermal deformations that vary between 2.9 µm and 40.7 µm along the optical tube axes. The physical implementation of the above mathematical model is part of the next phase of this research work coupled with experiments to derive thermally-induced pointing errors. The errors will be incorporated into the steering control software to compensate for thermally-induced misalignment of the telescope axes.