Convex optimization under inequality constraints in rank-deficient systems

Many geodetic applications require the minimization of a convex objective function subject to some linear equality and/or inequality constraints. If a system is singular (e.g., a geodetic network without a defined datum) this results in a manifold of solutions. Most state-of-the-art algorithms for inequality constrained optimization (e.g., the Active-Set-Method or primal-dual Interior-Point-Methods) are either not able to deal with a rank-deficient objective function or yield only one of an infinite number of particular solutions. In this contribution, we develop a framework for the rigorous computation of a general solution of a rank-deficient problem with inequality constraints. We aim for the computation of a unique particular solution which fulfills predefined optimality criteria as well as for an adequate representation of the homogeneous solution including the constraints. Our theoretical findings are applied in a case study to determine optimal repetition numbers for a geodetic network to demonstrate the potential of the proposed framework.     

A High-Resolution Solar Telescope Using Dark-Lens Diffractive Optics

A telescope based upon dark-lens diffractive optics would be a uniquely new instrument for solar astronomy. The image formation process in such a telescope gives an intrinsically higher resolving power and a greatly reduced image intensity compared to that of refracting or reflecting optical systems of similar lens dimension. This low image intensity would be an advantage for solar observations made using a very large imaging element. After a brief overview of the history of solar instrument development, a quantitative evaluation of the dark-lens diffracting solar telescope concept is presented, showing the potential of this imaging method to meet or even to exceed the most demanding resolution goals currently being considered for future space-borne solar telescopes.     

Water source characterization through spatiotemporal patterns of major,minor and trace element stream concentrations in a complex,mesoscale German catchment

The link between spatiotemporal patterns of stream water chemistry and catchment characteristics for the mesoscale Dill catchment (692 km²) in Germany is explored to assess the catchment scale controls on water quality and to characterize water sources. In order to record the spatiotemporal pattern, ‘snapshot sampling’ was applied during low, mean and high flow, including 73 nested sites throughout the catchment. Water samples were analysed for the elements Li, B, Na, Mg, Al, K, Ca, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Rb, Sr, Mo, Ba, Pb and U using inductively‐coupled‐plasma mass spectrometry, and for electric conductivity and pH. Principle component analysis and hierarchical cluster analysis were used to find typical element associations and to group water samples according to their hydrochemical fingerprints. This revealed regional hydrochemical patterns of water quality which were subsequently related to catchment attributes to draw conclusions about the controls on stream chemistry. It was found that various lithologic signals and anthropogenic point source inputs controlled the base flow hydrochemistry. During increased flows, stream waters were diluted causing additional hydrochemical variability in response to heterogeneous precipitation inputs and differences in aquifer storage capacities. The hydrochemical patterns further displayed in‐stream mixing of waters. This implied, that stream waters could be apportioned to the identified water sources throughout the catchment. The basin‐wide hydrochemical variability has the potential to outrange the tracer signatures typically inferred in studies at the hillslope scale and is able to strongly influence the complexity of the catchment output. Both have to be considered for further catchment scale tracer and modelling work. Despite the likelihood of non‐conservative behaviour, the minor and trace elements enhanced the rather qualitative discrimination of the various groundwater types, as the major cations were strongly masked by point source inputs. Copyright © 2007 John Wiley & Sons, Ltd.     

Comprehension and appropriateness of complex mobile pictographs for crisis communication

Natural Hazards - In crisis situations, illiterates and people with other linguistic challenges are unable to understand text messages to inform or be informed of a situation. Pictographic...     

Calibration measurements on the DEPFET Detectors for the MIXS instrument on BepiColombo

The Mercury Imaging X-ray Spectrometer (MIXS) will be launched on board of the 5th ESA cornerstone mission BepiColombo. The two channel instrument MIXS is dedicated to the exploration of the elemental composition of the mercurian surface by imaging x-ray spectroscopy of the elemental fluorescence lines. One of the main scientific goals of MIXS is to provide spatially resolved elemental abundance maps of key rock-forming elements. MIXS will be the successor of the XRS instrument, which is currently orbiting Mercury on board of NASAs satellite MESSENGER. MIXS will provide unprecedented spectral and spatial resolution due to its innovative detector and optics concepts. The MIXS target energy band ranges from 0.5 to 7 keV and allows to directly access the Fe-L line at 0.7 keV, which was not accessible to previous missions. In addition, the high spectroscopic resolution of FWHM ≤ 200 eV at the reference energy of 1 keV after one year in Mercury orbit, allows to separate the x-ray fluorescence emission lines of important elements like Mg (1.25 keV) and Al (1.49 keV) without the need for any filter. The detectors for the energy and spatially resolved detection of x-rays for both channels are identical DEPFET (DEpleted P-channel FET) active pixel detectors. We report on the calibration of the MIXS flight and flight spare detector modules at the PTB (Physikalisch-Technische Bundesanstalt) beamlines at the BESSY II synchrotron radiation facility. Each detector was calibrated at least at 10 discrete energies in the energy range from 0.5 to 10 keV. The excellent spectroscopic performance of all three detector modules was verified.     

Impact of Earth radiation pressure on GPS position estimates

GPS satellite orbits available from the International GNSS Service (IGS) show a consistent radial bias of up to several cm and a particular pattern in the Satellite Laser Ranging (SLR) residuals, which are suggested to be related to radiation pressure mismodeling. In addition, orbit-related frequencies were identified in geodetic time series such as apparent geocenter motion and station displacements derived from GPS tracking data. A potential solution to these discrepancies is the inclusion of Earth radiation pressure (visible and infrared) modeling in the orbit determination process. This is currently not yet considered by all analysis centers contributing to the IGS final orbits. The acceleration, accounting for Earth radiation and satellite models, is introduced in this paper in the computation of a global GPS network (around 200 IGS sites) adopting the analysis strategies from the Center for Orbit Determination in Europe (CODE). Two solutions covering 9 years (2000–2008) with and without Earth radiation pressure were computed and form the basis for this study. In previous studies, it has been shown that Earth radiation pressure has a non-negligible effect on the GPS orbits, mainly in the radial component. In this paper, the effect on the along-track and cross-track components is studied in more detail. Also in this paper, it is shown that Earth radiation pressure leads to a change in the estimates of GPS ground station positions, which is systematic over large regions of the Earth. This observed “deformation” of the Earth is towards North–South and with large scale patterns that repeat six times per GPS draconitic year (350 days), reaching a magnitude of up to 1 mm. The impact of Earth radiation pressure on the geocenter and length of day estimates was also investigated, but the effect is found to be less significant as compared to the orbits and position estimates.