Geocenter coordinates estimated from GNSS data as viewed by perturbation theory

Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global’naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008–2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters. A fair agreement for GPS and GLONASS was found in the geocenter x- and y-coordinate series. Our tests, however, clearly reveal artifacts in the z-component determined with the GLONASS data. Large periodic excursions in the GLONASS geocenter z-coordinates of about 40 cm peak-to-peak are related to the maximum elevation angles of the Sun above/below the orbital planes of the satellite system and thus have a period of about 4 months (third of a year). A detailed analysis revealed that the artifacts are almost uniquely governed by the differences of the estimates of direct solar radiation pressure (SRP) in the two solution series (with and without geocenter estimation). A simple formula is derived, describing the relation between the geocenter z-coordinate and the corresponding parameter of the SRP. The effect can be explained by first-order perturbation theory of celestial mechanics. The theory also predicts a heavy impact on the GNSS-derived geocenter if once-per-revolution SRP parameters are estimated in the direction of the satellite’s solar panel axis. Specific experiments using GPS observations revealed that this is indeed the case. Although the main focus of this article is on GNSS, the theory developed is applicable to all satellite observing techniques. We applied the theory to satellite laser ranging (SLR) solutions using LAGEOS. It turns out that the correlation between geocenter and SRP parameters is not a critical issue for the SLR solutions. The reasons are threefold: The direct SRP is about a factor of 30–40 smaller for typical geodetic SLR satellites than for GNSS satellites, allowing it in most cases to not solve for SRP parameters (ruling out the correlation between these parameters and the geocenter coordinates); the orbital arc length of 7 days (which is typically used in SLR analysis) contains more than 50 revolutions of the LAGEOS satellites as compared to about two revolutions of GNSS satellites for the daily arcs used in GNSS analysis; the orbit geometry is not as critical for LAGEOS as for GNSS satellites, because the elevation angle of the Sun w.r.t. the orbital plane is usually significantly changing over 7 days.

Earth gravity field recovery using GPS, GLONASS, and SLR satellites

The time variable Earth’s gravity field provides the information about mass transport within the system Earth, i.e., the relationship of mass transport between atmosphere, oceans, and land hydrology. We recover the low-degree parameters of the time variable gravity field using microwave observations from GPS and GLONASS satellites and from SLR data to five geodetic satellites, namely LAGEOS-1/2, Starlette, Stella, and AJISAI. GPS satellites are particularly sensitive to specific coefficients of the Earth's gravity field, because of the deep 2:1 orbital resonance with Earth rotation (two revolutions of the GPS satellites per sidereal day). The resonant coefficients cause, among other, a “secular” drift (actually periodic variations of very long periods) of the semi-major axes of up to 5.3 m/day of GPS satellites. We processed 10 years of GPS and GLONASS data using the standard orbit models from the Center of Orbit Determination in Europe (CODE) with a simultaneous estimation of the Earth gravity field coefficients and other parameters, e.g., satellite orbit parameters, station coordinates, Earth rotation parameters, troposphere delays, etc. The weekly GNSS gravity solutions up to degree and order 4/4 are compared to the weekly SLR gravity field solutions. The SLR-derived geopotential coefficients are compared to monthly GRACE and CHAMP results.

Homogeneous reprocessing of GPS, GLONASS and SLR observations

The International GNSS Service (IGS) provides operational products for the GPS and GLONASS constellation. Homogeneously processed time series of parameters from the IGS are only available for GPS. Reprocessed GLONASS series are provided only by individual Analysis Centers (i. e. CODE and ESA), making it difficult to fully include the GLONASS system into a rigorous GNSS analysis. In view of the increasing number of active GLONASS satellites and a steadily growing number of GPS+GLONASS-tracking stations available over the past few years, Technische Universität Dresden, Technische Universität München, Universität Bern and Eidgenössische Technische Hochschule Zürich performed a combined reprocessing of GPS and GLONASS observations. Also, SLR observations to GPS and GLONASS are included in this reprocessing effort. Here, we show only SLR results from a GNSS orbit validation. In total, 18 years of data (1994–2011) have been processed from altogether 340 GNSS and 70 SLR stations. The use of GLONASS observations in addition to GPS has no impact on the estimated linear terrestrial reference frame parameters. However, daily station positions show an RMS reduction of 0.3 mm on average for the height component when additional GLONASS observations can be used for the time series determination. Analyzing satellite orbit overlaps, the rigorous combination of GPS and GLONASS neither improves nor degrades the GPS orbit precision. For GLONASS, however, the quality of the microwave-derived GLONASS orbits improves due to the combination. These findings are confirmed using independent SLR observations for a GNSS orbit validation. In comparison to previous studies, mean SLR biases for satellites GPS-35 and GPS-36 could be reduced in magnitude from −35 and −38 mm to −12 and −13 mm, respectively. Our results show that remaining SLR biases depend on the satellite type and the use of coated or uncoated retro-reflectors. For Earth rotation parameters, the increasing number of GLONASS satellites and tracking stations over the past few years leads to differences between GPS-only and GPS+GLONASS combined solutions which are most pronounced in the pole rate estimates with maximum 0.2 mas/day in magnitude. At the same time, the difference between GLONASS-only and combined solutions decreases. Derived GNSS orbits are used to estimate combined GPS+GLONASS satellite clocks, with first results presented in this paper. Phase observation residuals from a precise point positioning are at the level of 2 mm and particularly reveal poorly modeled yaw maneuver periods.

Digital Data Collection and Processing in Field and Lab: The Approach of Kinneret Regional Project

The paper showcases the field- and lab-documentation system developed for Kinneret Regional Project, an international archaeological expedition to the Northwestern shore of the Sea of Galilee (Israel) under the auspices of the University of Bern, the University of Helsinki, Leiden University and Wofford College. The core of the data management system is a fully relational, server-based database framework, which also includes time-based and static GIS services, stratigraphic analysis tools and fully indexed document/digital image archives. Data collection in the field is based on mobile, hand-held devices equipped with a custom-tailored stand-alone application. Comprehensive three-dimensional documentation of all finds and findings is achieved by means of total stations and/or high-precision GPS devices. All archaeological information retrieved in the field – including tachymetric data – is synched with the core system on the fly and thus immediately available for further processing in the field lab (within the local network) or for post-excavation analysis at remote institutions (via the WWW). Besides a short demonstration of the main functionalities, the paper also presents some of the key technologies used and illustrates usability aspects of the system’s individual components.

Comparison of GOCE-GPS gravity fields derived by different approaches

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only ≈10 % ; in the absence of the polar data gap, SLR residuals agree by ≈96 % . From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

Time Variable Gravity: Contributions of GOCE Satellite Data to Monthly and Bi-monthly GRACE Gravity Estimates

A feasibility study by Pail et al. (Can GOCE help to improve temporal gravity field estimates? In: Ouwehand L (ed) Proceedings of the 4th International GOCE User Workshop, ESA Publication SP-696, 2011b) shows that GOCE (‘Gravity field and steady-state Ocean Circulation Explorer’) satellite gravity gradiometer (SGG) data in combination with GPS derived orbit data (satellite-to-satellite tracking: SST-hl) can be used to stabilize and reduce the striping pattern of a bi-monthly GRACE (‘Gravity Recovery and Climate Experiment’) gravity field estimate. In this study several monthly (and bi-monthly) combinations of GRACE with GOCE SGG and GOCE SST-hl data on the basis of normal equations are investigated. Our aim is to assess the role of the gradients (solely) in the combination and whether already one month of GOCE observations provides sufficient data for having an impact in the combination. The estimation of clean and stable monthly GOCE SGG normal equations at high resolution ( >  d/o 150) is found to be difficult, and the SGG component, solely, does not show significant added value to monthly and bi-monthly GRACE gravity fields. Comparisons of GRACE-only and combined monthly and bi-monthly solutions show that the striping pattern can only be reduced when using both GOCE observation types (SGG, SST-hl), and mainly between d/o 45 and 60.

Extracting more out of relocation data: building movement models as mixtures of random walks

We present a framework for fitting multiple random walks to animal movement paths consisting of ordered sets of step lengths and turning angles. Each step and turn is assigned to one of a number of random walks, each characteristic of a different behavioral state. Behavioral state assignments may be inferred purely from movement data or may include the habitat type in which the animals are located. Switching between different behavioral states may be modeled explicitly using a state transition matrix estimated directly from data, or switching probabilities may take into account the proximity of animals to landscape features. Model fitting is undertaken within a Bayesian framework using the WinBUGS software. These methods allow for identification of different movement states using several properties of observed paths and lead naturally to the formulation of movement models. Analysis of relocation data from elk released in east-central Ontario, Canada, suggests a biphasic movement behavior: elk are either in an "encamped" state in which step lengths are small and turning angles are high, or in an "exploratory" state, in which daily step lengths are several kilometers and turning angles are small. Animals encamp in open habitat (agricultural fields and opened forest), but the exploratory state is not associated with any particular habitat type.

Crustal uplift rates of 4 GPS stations near Jakobshavn Isbrae (2006-2009)

We analyze 2006-2009 data from four continuous Global Positioning System (GPS) receivers located between 5 and 150 km from the glacier Jakobshavn Isbrae, West Greenland. The GPS stations were established on bedrock to determine the vertical crustal motion due to the unloading of ice from Jakobshavn Isbrae. All stations experienced uplift, but the uplift rate at Kangia North, only 5 km from the glacier front, was about 10 mm/yr larger than the rate at Ilulissat, located only ~45 km further away. This suggests that most of the uplift is due to the unloading of the Earth's surface as Jakobshavn thins and loses mass. Our estimate of Jakobshavn's contribution to uplift rates at Kangia North and Ilulissat are 14.6 ± 1.7 mm/yr and 4.9 ± 1.1 mm/yr, respectively. The observed rates are consistent with a glacier thinning model based on repeat altimeter surveys from NASA's Airborne Topographic Mapper (ATM), which shows that Jakobshavn lost mass at an average rate of 22 ± 2 km**3/yr between 2006 and 2009. At Kangia North and Ilulissat, the predicted uplift rates computed using thinning estimates from the ATM laser altimetry are 12.1 ± 0.9 mm/yr and 3.2 ± 0.3 mm/yr, respectively. The observed rates are slightly larger than the predicted rates. The fact that the GPS uplift rates are much larger closer to Jakobshavn than further away, and are consistent with rates inferred using the ATM-based glacier thinning model, shows that GPS measurements of crustal motion are a potentially useful method for assessing ice-mass change models.

Static GPS measurements and elevation model in the hinterland of Neumayer

As part of the CryoSat Cal/Val activities and the pre-site survey for an ice core drilling contributing to the International Partnerships in Ice Core Sciences (IPICS), ground based kinematic GPS measurements were conducted in early 2007 in the vicinity of the German overwintering station Neumayer (8.25° W and 70.65° S). The investigated area comprises the regions of the ice tongues Halvfarryggen and Søråsen, which rise from the Ekströmisen to a maximum of about 760 m surface elevation, and have an areal extent of about 100 km x 50 km each. Available digital elevation models (DEMs) from radar altimetry and the Antarctic Digital Database show elevation differences of up to hundreds of meters in this region, which necessitated an accurate survey of the conditions on-site. An improved DEM of the Ekströmisen surroundings is derived by a combination of highly accurate ground based GPS measurements, satellite derived laser altimetry data (ICESat), airborne radar altimetry (ARA), and radio echo sounding (RES). The DEM presented here achieves a vertical accuracy of about 1.3 m and can be used for improved ice dynamic modeling and mass balance studies.

Seagrass and associated benthic community data derived from field surveys at Low Isles, Great Barrier Reef, conducted July-August, 1997

The distribution of seagrass and associated benthic communities on the reef and lagoon of Low Isles, Great Barrier Reef, was mapped between the 29 July and 29 August 1997. For this survey, observers walked or free-dived at survey points positioned approximately 50 m apart along a series of transects. Visual estimates of above-ground seagrass biomass and % cover of each benthos and substrate type were recorded at each survey point. A differential handheld global positioning system (GPS) was used to locate each survey point (accuracy ±3m). A total of 349 benthic survey points were examined. To assist with mapping meadow/habitat type boundaries, an additional 177 field points were assessed and a georeferenced 1:12,000 aerial photograph (26th August 1997) was used as a secondary source of information. Bathymetric data (elevation below Mean Sea Level) measured at each point assessed and from Ellison (1997) supplemented information used to determine boundaries, particularly in the subtidal lagoon. 127.8 ±29.6 hectares was mapped. Seagrass and associated benthic community data was derived by haphazardly placing 3 quadrats (0.25m**2) at each survey point. Seagrass above ground biomass (standing crop, grams dry weight (g DW m**-2)) was determined within each quadrat using a non-destructive visual estimates of biomass technique and the seagrass species present identified. In addition, the cover of all benthos was measured within each of the 3 quadrats using a systematic 5 point method. For each quadrat, frequency of occurrence for each benthic category was converted to a percentage of the total number of points (5 per quadrat). Data are presented as the average of the 3 quadrats at each point. Polygons of discrete seagrass meadow/habitat type boundaries were created using the on-screen digitising functions of ArcGIS (ESRI Inc.), differentiated on the basis of colour, texture, and the geomorphic and geographical context. The resulting seagrass and benthic cover data of each survey point and for each seagrass meadow/habitat type was linked to GPS coordinates, saved as an ArcMap point and polygon shapefile, respectively, and projected to Universal Transverse Mercator WGS84 Zone 55 South.