[1] We present a method to derive velocity uncertainties from GPS position time series that are affected by time-correlated noise. This method is based on the Allan variance, which is widely used in the estimation of oscillator stability and requires neither spectral analysis nor maximum likelihood estimation (MLE). The Allan variance of the rate (AVR) is calculated in the time domain and hence is not too sensitive to gaps in the time series. We derived analytical expressions of the AVR for different kinds of noises like power law noise, white noise, flicker noise, and random walk and found an expression for the variance produced by an annual signal. These functional relations form the basis of error models that have to be fitted to the AVR in order to estimate the velocity uncertainty. Finally, we applied the method to the South Africa GPS network TrigNet. Most time series show noise characteristics that can be modeled by a power law noise plus an annual signal. The method is computationally very cheap, and the results are in good agreement with the ones obtained by methods based on MLE.Citation: Hackl, M., R. Malservisi, U. Hugentobler, and R. Wonnacott (2011), Estimation of velocity uncertainties from GPS time series: Examples from the analysis of the South African TrigNet network,
[1] Accurate ionospheric specification is necessary for improving human activities such as radar detection, navigation, and Earth observation. This is of particular importance in Africa, where strong plasma density gradients exist due to the equatorial ionization anomaly. In this paper the accuracy of three-dimensional ionospheric images is assessed over a 2 week test period (2-16 December 2012). These images are produced using differential Global Positioning System (GPS) slant total electron content observations and a time-dependent tomography algorithm. The test period is selected to coincide with a period of increased GPS data availability from the African Geodetic Reference Frame (AFREF) project. A simulation approach that includes the addition of realistic errors is employed in order to provide a ground truth. Results show that the inclusion of observations from the AFREF archive significantly reduces ionospheric specification errors across the African sector, especially in regions that are poorly served by the permanent network of GPS receivers. The permanent network could be improved by adding extra sites and by reducing the number of service outages that affect the existing sites.
BackgroundSouth Africa is mostly a semi-arid, water-stressed country, with an average precipitation of about 450 mm/yr, well below the world average of about 860 mm/yr. Traditionally river water and surface water run-off has been stored in strategically placed large storage dams built in catchment areas. The supply of surface water either from rivers or runoff has been vulnerable to short and long term climate fluctuations with reduced water supplies being affected by drought (Hartnady et al., 2014). The desalination of sea water could be seen as an alternative source of water to supplement Municipal water supply but the process is expensive primarily because of the high cost of energy required to pump sea water or other saline water through membranes in a process known as reverse osmosis. Desalination plants using reverse osmosis have been installed in coastal towns such as Mossel Bay, Knysna and Plettenberg Bay (Mallory et al., 2012) A high percentage of the Earth's fresh water is stored underground which can be extracted either through pumping or using artesian pressure through wells. In semi-arid areas such as the Klein Karoo in the Western Cape, aquifers may not recharge at a sufficiently sustainable rate relative to the rate of withdrawal, especially during periods of drought. In situations such as these, the extraction of water is therefore considered as "mining" of a non-renewable resource which has to be carefully managed (Hartnady et al., 2014). The Blossoms Well FieldConsidering the above and contemporary concern about global warming and its effects on water and food security, the Oudtshoorn Municipality in the Klein Karoo has embarked upon the exploration of a deep artesian aquifer situated approximately 30 km south of the town in the Northern foothills of the Outeniqua mountain range. In addition, the Municipality is developing what is known as the Blossoms Well Field of boreholes of between 500 m and 600 m deep within the area of the aquifer to supplement the current water supply for both the town and the surrounding rural areas. The aquifer is fed by water infiltrating primarily from the southern slopes of the Outeniqua range (see Figure 2). The area of the well field is shown in Figure 1 together with boreholes used in this project. A simplified profile AB of the geology extending from the Outeniqua range to the Blossoms wellfield in the vicinity of C1B3 and C1G1 is shown in Figure 2.
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