Reviewed papers

The stratospheric aerosol content above Spitsbergen during winter 1991/92
G. Beyerle and R. Neuber
Geophys. Res. Lett., 21 (13), 1291-1294, 1994.
Lidar investigations of polar stratospheric aerosols were performed at Ny-Ålesund, Spitsbergen (79°N, 12°E) between December 1991 and March 1992. Backscatter ratios at wavelengths of 353 and 532 nm and volume depolarization at 532 nm in altitudes ranging from the tropopause up to 30 km are presented. Throughout the whole measurement period a layer of aerosols of volcanic origin was observed. During the period of stable vortex conditions we found averaged peak backscatter ratios of 2.3 at 532 nm at altitudes around 14 km. Before the break-up of the polar vortex in mid-March no aerosols were detected at altitudes above 20 km. Observed volume depolarization profiles suggest that the main aerosol layer consisted of spherical particles throughout the whole period of observation. Enhanced values of volume depolarization in the lower part of the aerosol cloud directly above the tropopause are possibly caused by scattering on volcanic ash particles of sub-micron size.

Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93
G. Beyerle, R. Neuber, O. Schrems, F. Wittrock and B. Knudsen
Geophys. Res. Lett., 21 (1), 57-60, 1994.
Within the period of December 1992 to March 1993 lidar investigations of stratospheric aerosols were performed at Ny-Ålesund, Spitsbergen (79°N, 12°E). Backscatter signals at wavelengths of 353, 532 and 1064 nm and depolarization signals at 532 nm in altitudes ranging from the tropopause up to 30 km were analyzed. Throughout the whole measurement period we observed an aerosol layer of volcanic origin in the lower stratosphere. Depolarization profiles suggest that the volcanic aerosol layer consisted mainly of liquid droplets. Comparison with model calculations indicate median particle radii between 0.1 and 0.2 µm. Surface densities exceeded approximately 40 µm2/cm3 in the lower part of the layer around 12 km. In January 1993 polar stratospheric clouds (PSCs) were frequently observed at altitudes up to 22 km. We analyzed the backscatter and depolarization data with respect to the temperature history of backward trajectories reaching Ny-Ålesund. Signatures for micron sized crystalline PSC particles appear for cooling rates of −1 to −3 K day-1. Larger cooling rates of −4 to −10 K day-1 produced submicron sized aerosols, presumably supercooled droplets, characterized by enhanced backscatter ratios and reduced depolarization.

Untersuchungen stratosphärischer Aerosole vulkanischen Ursprungs und polarer stratosphärischer Wolken mit einem Mehrwellenlängen-Lidar auf Spitzbergen
G. Beyerle
Dissertation, Berichte zur Polarforschung, 138/'94, AWI Bremerhaven, 1994.

Temporal development of Mt. Pinatubo aerosols as observed by lidar and sun photometer at Ny-Aalesund, Spitsbergen
G. Beyerle, A. Herber, R. Neuber and H. Gernandt
Geophys. Res. Lett., 22 (18) 2497-2500, 1995.
Since summer 1991 multiwavelength lidar and sun photometer observations of the Pinatubo aerosol layer are performed at the Arctic NDSC station (Koldewey-Station) in Ny-Ålesund, Spitsbergen. The height integrated backscatter coefficient and the optical density decrease exponentially in time with time constants of 0.89±0.39 and 0.94±0.37 years, respectively. Their wavelength dependence indicates a decrease in median particle radii between 1992 and 1993. It is shown that the observations are consistent with results of parameter-free model calculations. The calculations are based on the assumption that gravitational sedimentation is the dominant process for volcanic aerosol removal in the Arctic stratosphere.

Comparative study of stratospheric aerosols and ozone at mid and high latitudes during the Pinatubo episode, 1991-1994
G. Beyerle, I. S. McDermid, R. Neuber and P. von der Gathen
Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference (ILRC), Berlin, 22-26 July 1996, A. Ansmann et al. (eds.), Springer, 1996.
Stratospheric aerosol surface densities and altitude integrated ozone number densities are derived from ground-based lidar measurements at Table Mountain, California (34°N) and Ny-Alesund, Spitsbergen (79°N) during three years following the Mt. Pinatubo eruption in June 1991. At mid latitude aerosol surface densities peak in December 1991. Variations of high latitude surface density data on time scales of days are controlled by dynamical processes. At Table Mountain ozone number densities integrated over the volcanic layer are reduced during late 1991 and throughout 1992 by 5−10%.

Temperature dependence of ternary solution particle volumes as observed by lidar in the Arctic stratosphere during winter 1992/1993
G. Beyerle, B. Luo, R. Neuber, Th. Peter and I. S. McDermid
J. Geophys. Res., 102 (D3), 3603-3609, 1997.
Multiwavelength lidar measurements of stratospheric aerosols performed at the Arctic Network for the Detection of Stratospheric Change station on Spitsbergen during winter 1992/1993 are analyzed. Altitude profiles of particle median radius and volume density are derived for measurements with aerosol depolarization smaller than 0.01. Below an altitude corresponding to 450 K potential temperature the Pinatubo aerosol layer dominated the stratospheric aerosol content with volume densities of more than 5 µm3 cm-3, whereas above 450 K, volume densities were close to background values of 0.1 µm3 cm-3. However, at all altitude levels between 350 and 550 K, volume densities consistently increased by a factor of 2-30 when temperatures approached the frost point. The observations are compared to results from thermodynamic model calculations at altitude levels of 400, 440, and 480 K. Good agreement between the observed and theoretically derived temperature dependencies of volume density suggests that nondepolarizing polar stratospheric cloud particles, as well as volcanic aerosols, at low temperatures are composed of a ternary liquid solution of sulfuric and nitric acid. At all altitude levels, model results indicated more than 90% HNO3 gas phase depletion as temperatures approached the frost point. A mean profile of total H2SO4 volume mixing ratio is derived, decreasing from about 4 parts per billion by volume (ppbv) at 350 K to about 0.5 ppbv above 450 K.

Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign
G. Beyerle, H.-J. Schäfer, O. Schrems and I. S. McDermid
Geophys. Res. Lett., 25 (6), 919-922, 1998.
Dual wavelength aerosol lidar observations of tropical high-altitude cirrus clouds were performed during the ALBATROSS 1996 campaign aboard the research vessel "POLARSTERN" on the Atlantic ocean in October-November 1996. On the basis of 57 hours of night-time observations between 23.5°N and 23.5°S we find in 72% of the altitude profiles indications of the presence of cirrus cloud layers. This percentage drops to 32% at subtropical latitudes (23.5°-30°) based on 15 hours of data. About one-half of the subtropical and tropical cirrus layers are subvisual with an optical depth of less than 0.03 at a wavelength of 532 nm. In general the clouds exhibit high spatial and temporal variability on scales of a few tens of meters vertically and a few hundred meters horizontally. No clouds are observed above the tropopause. An abrupt change in the relation between the color ratios of the parallel and perpendicular backscatter coefficients at about 240 K is interpreted in terms of changes of particle shape and/or size distribution. At temperatures between 195 and 255 K only a small fraction of the observations are consistent with the presence of small particles with dimensions of less than 0.1 µm.

Ray tracing formulas for refraction and internal reflection in uniaxial crystals
G. Beyerle and I. S. McDermid
Appl. Opt., 37 (34), 7947-7953, 1998.
Formulas for the calculation of the direction cosines of refracted and internally reflected rays in anisotropic uniaxial crystals are presented. The method is based on a transformation to a nonorthonormal coordinate system in which the normal surface associated with the extraordinary ray is of spherical shape. A numerical example for the case of refraction and internal reflection in calcite is given.

Altitude range resolution of differential absorption lidar ozone profiles
G. Beyerle and I. S. McDermid
Appl. Opt., 38 (6), 924-927, 1999.
A method is described for the empirical determination of altitude range resolutions of ozone profiles obtained by differential absorption lidar (DIAL) analysis. The algorithm is independent of the implementation of the DIAL analysis, in particular of the type and order of the vertical smoothing filter applied. An interpretation of three definitions of altitude range resolution is given on the basis of simulations carried out with the Jet Propulsion Laboratory ozone DIAL analysis program, SO3ANL. These definitions yield altitude range resolutions that differ by as much as a factor of 2. It is shown that the altitude resolution calculated by SO3ANL, and reported with all Jet Propulsion Laboratory lidar ozone profiles, corresponds closely to the full width at half-maximum of a retrieved ozone profile if an impulse function is used as the input ozone profile.

Detection of stratospheric sulfuric acid aerosols with polarization lidar: Theory, simulations and observations
G. Beyerle
Appl. Opt., 39 (27), 4994-5000, 2000.
The derivation of backscatter ratio profiles from polarization lidar measurements is discussed. The method is based on differences in depolarization between molecular backscattering and backscattering from spherical aerosol particles. Simulations show that the polarization algorithms yield backscatter ratios with uncertainties comparable with those obtained by Klett's method, provided that the backscattering process is dominated by molecular scattering. The technique could be utilized for monitoring the stratospheric sulfuric acid aerosol layer during periods of background conditions. The polarization analysis method is discussed in light of simulation results and is applied to polarization lidar profiles observed during the ALBATROSS 1996 field measurement campaign.

Occurrence of solid particles in the winter polar stratosphere above the nitric acid trihydrate coexistence temperature inferred from ground-based polarization lidar observations at Ny-Aalesund, Spitsbergen
G. Beyerle, H. Deckelmann, R. Neuber, J. M. Rosen, E. Reimer and M. R. Schoeberl
J. Geophys. Res., 106 (D3), 2979-2992, 2001.
Depolarization data of stratospheric aerosols obtained by ground-based polarization lidar are analyzed. The measurements were performed at Koldewey station, Ny-Ålesund, Spitsbergen (78.9°N, 11.9°E), during the five winters of 1994-1995 to 1998-1999. The study is focused on stratospheric sulfuric acid aerosols; interference by nitric acid trihydrate containing particles is excluded by imposing a temperature threshold condition of 2 K above the nitric acid trihydrate coexistence temperature. Under the assumption that large sulfuric acid particles freeze first, T-matrix scattering calculations show that volume depolarizations start to increase significantly if ~1% of the aerosols are frozen. Observations in January 1999 and February 1998 indicate the presence of nonspherical particles. We interpret these observations as signatures for the occurrence of sulfuric acid tetrahydrate particles. Temperature histories obtained from back trajectory model calculations and the corresponding polarization lidar measurements are consistent with current knowledge of sulfuric acid tetrahydrate formation.

A lidar and backscatter sonde aerosol measurement campaign at Table Mountain during February-March 1997: Observations of cirrus clouds
G. Beyerle, M. R. Gross, D. A. Haner, N. T. Kjome, I. S. McDermid, T. J. McGee, J. M. Rosen, H.-J. Schäfer and O. Schrems
Journal of the Atmospheric Sciences, 58 (10), 1275-1287, 2001.
Results from a measurement campaign performed at Table Mountain Facility/Jet Propulsion Laboratory/California Institute of Technology (34.38°N, 117.68°W, 2280 m ASL) are presented. Between 19 February and 18 March 1997 more than 400 h worth of lidar data were acquired and four backscatter sondes were launched. About 50% of the observations show the presence of cirrus clouds at altitudes close to and below the tropopause. Of these clouds 80% are characterized as subvisual with optical depths below 0.03 at a wavelength of 532 nm. Simple geometrical considerations lead to cloud spatial scales of 0.31 km vertically and 7.5 km horizontally, respectively. Deviations from color ratio values derived on the basis of geometrical optics are interpreted as small particle signatures. Comparing backscatter ratio profiles observed concurrently by three aerosol lidars, mean deviations of about 10% are found.

Observation and simulation of direct and reflected GPS signals in radio occultation experiments
G. Beyerle and K. Hocke
Geophys. Res. Lett. 28 (9), 1895-1898, 2001.
GPS/MET radio occultation observations are analyzed with the radio holographic method. Using the Multiple Signal Classification algorithm power spectra of 2038 radio holograms observed between 2 February and 16 February 1997 are calculated. In about 28% of the analyzed L1-band spectra secondary frequency components are found at power levels of about 10−20 dB below the main component. These secondary components are interpreted as signatures of GPS signals reflected at Earth's surface. Results from geometrical ray tracing simulations support our interpretation.

GPS radio occultations with CHAMP: A radio holographic analysis of GPS signal propagation in the troposphere and surface reflections
G. Beyerle, K. Hocke, J. Wickert, T. Schmidt, C. Marquardt and C. Reigber
J. Geophys. Res., 107 (D24), 4802, 2002.
Within the first nine months following the activation of the GPS radio occultation experiment aboard the low Earth orbiting satellite CHAMP, more than 25,000 occultation events have been observed. A radio holographic analysis of 3783 occultation events, recorded between 14 May 2001 and 10 June 2001, reveals that in about 20−30% of these events the received signal contains contributions from components reflected at Earth's surface. On the basis of geometrical ray tracing and multiple phase screen calculations, characteristic frequency shifts in the radio holograms' power spectral densities are analyzed quantitatively. These frequency shifts are found to be dominated by surface elevation at the reflection point location and ground-level refractivity. Using temperature and pressure profiles from European Centre for Medium-Range Weather Forecasting (ECMWF) analyses, ground-level specific humidities are derived in good agreement with ECMWF values. Complex patterns found in radio hologram spectra within a subset of observations at low latitudes are interpreted in terms of multipath propagation caused by layered structures in the refractivity field.

Simulation studies of GPS radio occultation measurements
G. Beyerle, M. E. Gorbunov and C. O. Ao
Radio Sci., 38 (5), 2003.
The atmospheric propagation of GPS signals under multipath conditions and their detection are simulated. Using the multiple phase screen method, C/A-code modulated L1 signals are propagated through a spherically symmetric refractivity field derived from a high-resolution radio sonde observation. The propagated signals are tracked by a GPS receiver implemented in software and converted to refractivity profiles by the canonical transform technique and the Abel inversion. Ignoring noise and assuming an ideal receiver tracking behavior, the true refractivity profile is reproduced to better than 0.1% at altitudes above 2 km. The nonideal case is simulated by adding between 14 and 24 dB of Gaussian white noise to the signal and tracking the signal with a receiver operating at 50 and 200 Hz sampling frequency using two different carrier phase detectors. In the upper troposphere and stratosphere the fractional refractivity retrieval error is below 0.3% for 50 Hz sampling and below 0.15% for 200 Hz sampling. In the midtroposphere down to altitudes of about 2 km, phase-locked loop tracking induces negative fractional refractivity biases on the order of −1 to −2% at 50 Hz sampling frequency. Modifications to the receiver tracking algorithm significantly improve the retrieval results. In particular, replacing the carrier loop's two-quadrant phase extractor with a four-quadrant discriminator reduces the refractivity biases by a factor of 5; increasing the sampling frequency from 50 to 200 Hz gains another factor of 2.

Atmospheric sounding by GNSS radio occultation: An analysis of the negative refractivity bias using CHAMP observations
G. Beyerle, J. Wickert, T. Schmidt and Ch. Reigber
J. Geophys. Res., 109 (D1), D01106, 2004.
Validation studies of current GPS radio occultation experiments using meteorological analyses consistently report on a negative refractivity bias in the lower troposphere. End-to-end simulations including the GPS receiver's signal tracking process suggest that receiver-induced phase deviations contribute to this observed bias. We propose a heuristic retrieval algorithm based on the canonical transform and the sliding spectral technique, which seems less susceptible to tracking phase errors than the canonical transform method. The approach is described using simulated profiles and validated on the basis of 4221 CHAMP occultations recorded between 14 May and 10 June 2001. Compared to the canonical transform results, the heuristic method results in a significantly smaller tropospheric refractivity bias at low latitudes at the expense of a reduced vertical resolution.

An analysis of the lower tropospheric refractivity bias by heuristic sliding spectral methods
G. Beyerle, J. Wickert, T. Schmidt, R. König and Ch. Reigber
Earth Observation with CHAMP, Results from Three Years in Orbit, Proc. of the Second CHAMP Science Meeting, Potsdam, Germany, 1-4 September 2003, Ch. Reigber et al. (eds.), Springer, 2005.
The canonical transform (CT) and full spectrum inversion (FSI) method together with their heuristic sliding spectral modifications are validated using end-to-end simulation data and one week of CHAMP observations. In general, we observe a pronounced correlation between small refractivity biases and enhanced penetration altitudes. Processing of simulated occultation data shows that the heuristic methods exhibit smaller retrieval errors vindicating the assertion that the sliding spectral approaches react less sensitive to receiver tracking errors. The corresponding mean retrievals errors found in the CHAMP data analysis, however, are consistent within 0.5%; differences are observed with respect to penetration altitudes and the retrieval errors' standard deviations.

GPS radio occultation with GRACE: Atmospheric profiling utilizing the zero difference technique
G. Beyerle, T. Schmidt, G. Michalak, S. Heise, J. Wickert, and Ch. Reigber
Geophys. Res. Lett., 32, L13806, 2005.
Radio occultation events recorded on 28−29 July 2004 by a GPS receiver aboard the GRACE-B satellite are analyzed. The stability of the receiver clock allows for the derivation of excess phase profiles using a zero difference technique, rendering the calibration procedure with concurrent observations of a reference GPS satellite obsolete. 101 refractivity profiles obtained by zero differencing and 96 profiles calculated with an improved single difference method are compared with co-located ECMWF meteorological analyses. Good agreement is found at altitudes between 5 and 30 km with an average fractional refractivity deviation below 1% and a standard deviation of 2−3%. Results from end-to-end simulations are consistent with these observations.

Refractivity biases in GNSS occultation data
G. Beyerle, S. Heise, J. Kaschenz, G. König-Langlo, Ch. Reigber, T. Schmidt and J. Wickert
Atmosphere and Climate, Proc. of the OPAC-2 workshop, Graz, Austria, 13-17 September 2004, U. Fölsche et al. (eds.), pp. 37-43, 2006.
An analysis of atmospheric refractivity profiles observed by the geo-research satellite CHAMP between May 2001 and October 2004 reveals a negative bias compared to ECMWF meteorological fields at altitudes below 5 km. In order to separate bias contributions caused by critical refraction from contributions induced by the receiver tracking process a comprehensive end-to-end simulation study was performed. The simulations are based on radio sonde profiles obtained aboard research vessel “POLARSTERN”. Within a subset of 3039 profiles recorded on the Atlantic ocean between 60°N and 60°S, 1202 profiles (39.6%) are found with vertical refractivity gradients below the threshold value of −157 km-1. Critical refraction layers occur mainly between 1 to 2.5 km altitude, above 3 km the occurrence of critical refraction can be disregarded. End-to-end simulations using these 3039 refractivity profiles confirm that four quadrant carrier phase extraction outperforms the two quadrant method currently implemented on CHAMP. Within regions of low signal-to-noise ratios 'open-loop' tracking methods yield improvements with respect to the current 'fly-wheeling' method.

Observations and simulations of receiver-induced refractivity biases in GPS radio occultation
G. Beyerle, T. Schmidt, J. Wickert, S. Heise, M. Rothacher, G. König-Langlo, and K. B. Lauritsen
J. Geophys. Res., 111, D12101, 2006.
An analysis of 206,422 atmospheric refractivity profiles observed by the CHAMP georesearch satellite between 14 May 2001 and 30 June 2005 reveals significant biases compared to European Centre for Medium-Range Weather Forecasts meteorological fields at altitudes below 5 km. The mean bias decreases down to −2% at altitudes below 2 km; in the Amazon region, positive biases exceeding +1% are observed. In order to identify bias contributions caused by the receiver signal tracking process an end-to-end simulation study implementing different signal tracking modes was performed. The end-to-end simulations are based on 1992 radiosonde profiles obtained regularly aboard R/V Polarstern since December 1982 and were conducted with four receiver models using closed-loop, fly wheeling, and open-loop signal tracking methods. The simulation results confirm that open-loop tracking yields significantly smaller biases and standard deviations of the fractional refractivity errors compared to fly wheeling enabled receivers. In addition, we analyze closed-loop tracking with a second-order loop and demonstrate that similar reductions in biases and standard deviations can be obtained.

A data archive of GPS navigation messages
G. Beyerle, M. Ramatschi, R. Galas, T. Schmidt, J. Wickert, and M. Rothacher
GPS Solutions, 13 (1), 35-41, 2009.
GPS Solutions, 14 (3), 301, 2010.
Since 18 June 2007 navigation data messages transmitted by the GPS constellation are recorded by five receivers within GeoForschungsZentrum's global groundstation network. We describe the recording, processing, validation, analysis and archiving of the navigation data. During the 197 days between 18 June 2007 and 31 December 2007 a total of 125,723,666 subframes were collected. By taking into consideration that the same data set frequently is observed by two or more receivers concurrently, 65,153,955 unique subframes could be extracted from the observations. With an estimated 88,099,200 subframes transmitted by the constellation during this time period a data yield of about 74% was achieved. Simulation studies suggest that with two additional GPS receivers, which are scheduled for addition to the network in 2008, about 95% of the transmitted subframes will be retrieved. The message data archive is open to the scientific community for non-commercial purposes and may be accessed through GFZ's Information System and Data Center (

Carrier phase wind-up in GPS reflectometry
G. Beyerle
GPS Solutions, 13 (3), 191-198, 2009.
GPS Solutions, 14 (3), 301-301, 2010.
Changes in GPS transmitter and receiver antenna orientations induce variations in observed carrier phase values. An analytic formula for this well-known carrier phase wind-up correction is derived which generalizes a previous result. In addition, it is shown that in GPS reflectometry the wind-up values of direct and coherently reflected rays may differ by up to several centimeters. The results are discussed on the basis of simulated measurements.

First results from the GPS atmosphere sounding experiment TOR aboard the TerraSAR-X satellite
G. Beyerle, L. Grunwaldt, S. Heise, W. Köhler, R. König, G. Michalak, M. Rothacher, T. Schmidt, J. Wickert, B. D. Tapley and B. Giesinger
Atmos. Chem. Phys., 11, 6687-6699, 2011.
GPS radio occultation events observed between 24 July and 17 November 2008 by the IGOR occultation receiver aboard the TerraSAR-X satellite are processed and analyzed. The comparison of 15,327 refractivity profiles with collocated ECMWF data yield a mean bias between zero and −0.30% at altitudes between 5 and 30 km. Standard deviations decrease from about 1.4% at 5 km to about 0.6% at 10 km altitude, however, increase significantly in the upper stratosphere. At low latitudes mean biases and standard deviations are larger, in particular in the lower troposphere. The results are consistent with 15,159 refractivity observations collected during the same time period by the BlackJack receiver aboard GRACE-A and processed by GFZ's operational processing system. The main difference between the two occultation instruments is the implementation of open-loop signal tracking in the IGOR (TerraSAR-X) receiver which improves the tropospheric penetration depth in terms of ray height by about 2 km compared to the conventional closed-loop data acquired by BlackJack (GRACE-A).

Open-loop GPS signal tracking at low elevation angles from a ground-based observation site
G. Beyerle and F. Zus
Atmos. Meas. Tech., 10, 15-34, 2017.
A 1-year data set of ground-based GPS signal observations aiming at geometric elevation angles below +2° is analysed. Within the “GLESER” measurement campaign about 2600 validated setting events were recorded by the “OpenGPS” open-loop tracking receiver at an observation site located at 52.3808°N, 13.0642°E between January and December 2014. The measurements confirm the feasibility of open-loop signal tracking down to geometric elevation angles of −1 to −1.5° extending the corresponding closed-loop tracking range by up to 1°. The study is based on the premise that observations of low-elevation events by a ground-based receiver may serve as test cases for space-based radio occultation measurements, even if the latter proceed at a significantly faster temporal scale. The results support the conclusion that the open-loop Doppler model has negligible influence on the derived carrier frequency profile for strong signal-to-noise density ratios above about 30 dB Hz. At lower signal levels, however, the OpenGPS receiver's dual-channel design, which tracks the same signal using two Doppler models differing by 10 Hz, uncovers a notable bias. The repeat patterns of the GPS orbit traces in terms of azimuth angle reveal characteristic signatures in both signal amplitude and Doppler frequency with respect to the topography close to the observation site. Mean vertical refractivity gradients, extracted from ECMWF meteorological fields, correlate weakly to moderately with observed signal amplitude fluctuations at geometric elevation angles between +1 and +2°. Results from multiple phase screen simulations support the interpretation that these fluctuations are at least partly produced by atmospheric multipath; at negative elevation angles diffraction at the ground surface seems to contribute.

Visualization of Thomas-Wigner rotations
G. Beyerle
Symmetry, 9(12), 292, 2017.
(arXiv:1706.02755 [physics.class-ph], 2017.)
It is well known that a sequence of two non-collinear Lorentz boosts (pure Lorentz transformations) does not correspond to a Lorentz boost, but involves a spatial rotation, the Wigner or Thomas-Wigner rotation. We visualize the interrelation between this rotation and the relativity of distant simultaneity by moving a Born-rigid object on a closed trajectory in several steps of uniform proper acceleration. Born-rigidity implies that the stern of the boosted object accelerates faster than its bow. It is shown that at least five boost steps are required to return the object's center to its starting position, if in each step the center is assumed to accelerate uniformly and for the same proper time duration. With these assumptions, the Thomas-Wigner rotation angle depends on a single parameter only. Furthermore, it is illustrated that accelerated motion implies the formation of a "frame boundary". The boundaries associated with the five boosts constitute a natural barrier and ensure the object's finite size.

Non-reviewed papers

Simulating GPS radio occultation events
G. Beyerle
Scientific Report 05-09, Danish Meteorological Institute, Copenhagen, 2005.
Validation studies of atmospheric refractivity observed by the GPS radio occultation experiment aboard the CHAMP satellite identify significant biases and enhanced standard deviations in the lower troposphere at low latitudes. In order to separate bias contributions caused by critical refraction from contributions induced by the occultation receiver's signal tracking loops an end-to-end simulation tool was developed and implemented within the MATLAB programming environment. With a data set of 1992 refractivity profiles derived from high-resolution low-latitude radio sonde observations simulation studies including several closed-loop and open-loop signal tracking techniques were performed. The individual steps of the simulation processing chain and their underlying algorithms are described. The results from the simulation study show that a receiver model capable of fly-wheeling qualitatively reproduces the CHAMP observations, which are characterized by negative biases in the planetary boundary layer, enhanced standard deviations and frequent occurrences of loss of signal tracking lock in the lower troposphere. Closed loop tracking with reduced loop order is found to be a viable alternative to fly-wheeling and open-loop techniques.

A note on random samples of Lie algebras
G. Beyerle
arXiv:1407.3642 [math.RT], 2014.
Recently, Paiva and Teixeira (arXiv:1108.4396) showed that the structure constants of a Lie algebra are the solution of a system of linear equations provided a certain subset of the structure constants are given a-priori. Here it is noted that Lie algebras generated in this way are solvable and their derived subalgebras are Abelian if the system of linear equations considered by Paiva and Teixeira is not degenerate. An efficient numerical algorithm for the calculation of their structure constants is described.

Data sets and softwares

Ground-based GPS observations at low elevation angles using open-loop signal tracking
G. Beyerle
GFZ Data Services
doi:10.5880/GFZ.2016.1.1.002, 2016.