GNSS water vapour tomography – Expected improvements by combining GPS,GLONASS and Galileo observations

The German Research Centre for Geosciences (GFZ) operates a GNSS water vapour tomography system using about 350 German GNSS stations. The GNSS data processing at the GFZ works in near real-time and provides zenith total delays, integrated water vapour and slant delay data operationally. This large data set of more than 50,000 slant delays per hour is used to reconstruct spatially resolved humidity fields by means of tomographic techniques. It can be expected that additional observations from the future Galileo system provide more information with improved quality. A simulation study covering 12 h at 14 July 2009 was therefore started to estimate the impact of GPS, Galileo and GLONASS data on the GNSS tomography. It is shown that the spatial coverage of the atmosphere with slant paths is highly improved by combining observations from two or three satellite systems. Equally important for a reliable tomographic reconstruction is the distribution of slant path intersections as they are required to locate the integrated delay information. The number of intersection points can be increased by a factor of 4 or 8 if two or three systems are combined and their distribution will cover larger regions of the atmosphere. The combined data sets can be used to increase the spatiotemporal resolution of the reconstructed humidity fields up to 30 km horizontally, 300 m vertically and 15 min. The reconstruction quality could not be improved considerably using the currently available techniques.     

The Open-Loop Transfer Matrix of an Estimator-Controller

Open-loop transfer matrices of continuous and sampled-data estimator-controllers (including those in predictor-corrector form) are derived. This paper complements an earlier paper in which open-and closed-loop transfer matrices of estimators and closed-loop transfer matrices of estimator-controllers were derived. Three different open-loop transfer matrices of each type of estimator-controller are derived by breaking the loop at different points. An example is included to illustrate the utility of such an open-loop transfer matrix.     

Satellite-Satellite Laser Links for Future Gravity Missions

A strong candidate for use in future missions to map time variations in the Earth's gravity field is laser heterodyne measurements between separate spacecraft. At the shortest wavelengths that can be measured in space, the main accuracy limitation for variations in the potential with latitude is expected to be the frequency stability of the laser. Thus the development of simple and reliable space-qualified lasers with high frequency stability appears to be an important goal for the near future. In the last few years, quite high stability has been achieved by locking the second harmonic of a Nd:YAG laser to a resonant absorption line of iodine molecules in an absorption cell. Such a laser system can be made quite robust, and temperature related frequency shifts can be controlled at a low value. Recent results from laboratory systems are described. The Allan standard deviation for the beat between two such lasers was 2 × 10⁻¹⁴ at 10 s, and reached 7 × 10⁻¹⁵ at 600 s. This revised version was published online in August 2006 with corrections to the Cover Date.     

Development of a GNSS water vapour tomography system using algebraic reconstruction techniques

A GNSS water vapour tomography system developed to reconstruct spatially resolved humidity fields in the troposphere is described. The tomography system was designed to process the slant path delays of about 270 German GNSS stations in near real-time with a temporal resolution of 30 min, a horizontal resolution of 40 km and a vertical resolution of 500 m or better. After a short introduction to the GPS slant delay processing the framework of the GNSS tomography is described in detail. Different implementations of the iterative algebraic reconstruction techniques (ART) used to invert the linear inverse problem are discussed. It was found that the multiplicative techniques (MART) provide the best results with least processing time, i.e., a tomographic reconstruction of about 26,000 slant delays on a 8280 cell grid can be obtained in less than 10 min. Different iterative reconstruction techniques are compared with respect to their convergence behaviour and some numerical parameters. The inversion can be considerably stabilized by using additional non-GNSS observations and implementing various constraints. Different strategies for initialising the tomography and utilizing extra information are discussed. At last an example of a reconstructed field of the wet refractivity is presented and compared to the corresponding distribution of the integrated water vapour, an analysis of a numerical weather model (COSMO-DE) and some radiosonde profiles.     

Medium-scale traveling ionospheric disturbances (MSTID) modeling using a dense German GPS network

The MSTIDs are wave-like perturbations of the ionospheric plasma, which cause the most common ionospheric disturbances in mid-latitude regions. Generally the MSTIDs have velocities of several hundred meters per second and wavelengths of several hundred kilometers. The wave-like effect of the MSTID is one of the main obstacles for accurate interpolation of ionospheric corrections in a medium-scale reference GPS network. In this paper we show a new method of detecting and modeling MSTIDs using dense German GPS network. The between-epoch single difference ionospheric delays from a medium scale dense GPS network are used to estimate the parameter of the MSTID e.g. amplitude, wavelength and velocity. The efficiency of the approach is tested with data from about 320 GPS stations in and near Germany. A MSTID wave moving from east to west across Germany was observed at September 27 in 2009. Its wavelength is about 302 km, with a period of ∼7 min and velocity of about 700 m/s.     

Possible Future Use of Laser Gravity Gradiometers

With the GRACE mission under way and the GOCE mission well along in the design process, detailed questions concerning the type of future mission that may follow them have arisen. It is generally agreed that determining the time variations in the Earth's gravity field with as high spatial and temporal resolution as is feasible will be the main driver for such a mission. The possible use of laser heterodyne measurements between separate satellites in such a mission has been discussed by a number of people. The first suggestion of emphasizing time variation measurements in a laser mission was the TIDES concept presented in 1992 by Colombo and Chao. Then, in 2000, a GRACE Follow-On mission using laser measurements between two drag-free satellites was discussed by Watkins el al. (2000). More recently, the possibility of utilizing laser measurements between more than two satellites in order to determine two or more components of the gravity gradient tensor simultaneously has been proposed by Balmino. This approach may be desirable in order to reduce the aliasing of time variations between geopotential terms of different degree and order, as well as to improve the resolution in longitude, despite the cost of the additional satellites. In this paper, we discuss specific possible mission geometries for measuring the two diagonal in-plane components of the gravity gradient tensor simultaneously. This could be done, for example, by laser heterodyne measurements between two pairs of satellites in coplanar and nearly polar orbits. This revised version was published online in August 2006 with corrections to the Cover Date.