CODE’s new solar radiation pressure model for GNSS orbit determination

The Empirical CODE Orbit Model (ECOM) of the Center for Orbit Determination in Europe (CODE), which was developed in the early 1990s, is widely used in the International GNSS Service (IGS) community. For a rather long time, spurious spectral lines are known to exist in geophysical parameters, in particular in the Earth Rotation Parameters (ERPs) and in the estimated geocenter coordinates, which could recently be attributed to the ECOM. These effects grew creepingly with the increasing influence of the GLONASS system in recent years in the CODE analysis, which is based on a rigorous combination of GPS and GLONASS since May 2003. In a first step we show that the problems associated with the ECOM are to the largest extent caused by the GLONASS, which was reaching full deployment by the end of 2011. GPS-only, GLONASS-only, and combined GPS/GLONASS solutions using the observations in the years 2009–2011 of a global network of 92 combined GPS/GLONASS receivers were analyzed for this purpose. In a second step we review direct solar radiation pressure (SRP) models for GNSS satellites. We demonstrate that only even-order short-period harmonic perturbations acting along the direction Sun-satellite occur for GPS and GLONASS satellites, and only odd-order perturbations acting along the direction perpendicular to both, the vector Sun-satellite and the spacecraft’s solar panel axis. Based on this insight we assess in the third step the performance of four candidate orbit models for the future ECOM. The geocenter coordinates, the ERP differences w. r. t. the IERS 08 C04 series of ERPs, the misclosures for the midnight epochs of the daily orbital arcs, and scale parameters of Helmert transformations for station coordinates serve as quality criteria. The old and updated ECOM are validated in addition with satellite laser ranging (SLR) observations and by comparing the orbits to those of the IGS and other analysis centers. Based on all tests, we present a new extended ECOM which substantially reduces the spurious signals in the geocenter coordinate z (by about a factor of 2–6), reduces the orbit misclosures at the day boundaries by about 10 %, slightly improves the consistency of the estimated ERPs with those of the IERS 08 C04 Earth rotation series, and substantially reduces the systematics in the SLR validation of the GNSS orbits.

Satellite laser ranging to GPS and GLONASS

Satellite laser ranging (SLR) to the satellites of the global navigation satellite systems (GNSS) provides substantial and valuable information about the accuracy and quality of GNSS orbits and allows for the SLR-GNSS co-location in space. In the framework of the NAVSTAR-SLR experiment two GPS satellites of Block-IIA were equipped with laser retroreflector arrays (LRAs), whereas all satellites of the GLONASS system are equipped with LRAs in an operational mode. We summarize the outcome of the NAVSTAR-SLR experiment by processing 20 years of SLR observations to GPS and 12 years of SLR observations to GLONASS satellites using the reprocessed microwave orbits provided by the center for orbit determination in Europe (CODE). The dependency of the SLR residuals on the size, shape, and number of corner cubes in LRAs is studied. We show that the mean SLR residuals and the RMS of residuals depend on the coating of the LRAs and the block or type of GNSS satellites. The SLR mean residuals are also a function of the equipment used at SLR stations including the single-photon and multi-photon detection modes. We also show that the SLR observations to GNSS satellites are important to validate GNSS orbits and to assess deficiencies in the solar radiation pressure models. We found that the satellite signature effect, which is defined as a spread of optical pulse signals due to reflection from multiple reflectors, causes the variations of mean SLR residuals of up to 15 mm between the observations at nadir angles of 0∘ and 14∘. in case of multi-photon SLR stations. For single-photon SLR stations this effect does not exceed 1 mm. When using the new empirical CODE orbit model (ECOM), the SLR mean residual falls into the range 0.1–1.8 mm for high-performing single-photon SLR stations observing GLONASS-M satellites with uncoated corner cubes. For best-performing multi-photon stations the mean SLR residuals are between −12.2 and −25.6 mm due to the satellite signature effect.

A consistent combination of GNSS and SLR with minimum constraints

In this article, the realization of a global terrestrial reference system (TRS) based on a consistent combination of Global Navigation Satellite System (GNSS) and Satellite Laser Ranging (SLR) is studied. Our input data consists of normal equation systems from 17 years (1994– 2010) of homogeneously reprocessed GPS, GLONASS and SLR data. This effort used common state of the art reduction models and the same processing software (Bernese GNSS Software) to ensure the highest consistency when combining GNSS and SLR. Residual surface load deformations are modeled with a spherical harmonic approach. The estimated degree-1 surface load coefficients have a strong annual signal for which the GNSS- and SLR-only solutions show very similar results. A combination including these coefficients reduces systematic uncertainties in comparison to the singletechnique solution. In particular, uncertainties due to solar radiation pressure modeling in the coefficient time series can be reduced up to 50 % in the GNSS+SLR solution compared to the GNSS-only solution. In contrast to the ITRF2008 realization, no local ties are used to combine the different geodetic techniques.We combine the pole coordinates as global ties and apply minimum constraints to define the geodetic datum. We show that a common origin, scale and orientation can be reliably realized from our combination strategy in comparison to the ITRF2008.

Impact of the arc length on GNSS analysis results

Homogeneously reprocessed combined GPS/GLONASS 1- and 3-day solutions from 1994 to 2013, generated by the Center for Orbit Determination in Europe (CODE) in the frame of the second reprocessing campaign REPRO-2 of the International GNSS Service, as well as GPS- and GLONASS-only 1- and 3-day solutions for the years 2009 to 2011 are analyzed to assess the impact of the arc length on the estimated Earth Orientation Parameters (EOP, namely polar motion and length of day), on the geocenter, and on the orbits. The conventional CODE 3-day solutions assume continuity of orbits, polar motion components, and of other parameters at the day boundaries. An experimental 3-day solution, which assumes continuity of the orbits, but independence from day to day for all other parameters, as well as a non-overlapping 3-day solution, is included into our analysis. The time series of EOPs, geocenter coordinates, and orbit misclosures, are analyzed. The long-arc solutions were found to be superior to the 1-day solutions: the RMS values of EOP and geocenter series are typically reduced between 10 and 40 %, except for the polar motion rates, where RMS reductions by factors of 2–3 with respect to the 1-day solutions are achieved for the overlapping and the non-overlapping 3-day solutions. In the low-frequency part of the spectrum, the reduction is even more important. The better performance of the orbits of 3-day solutions with respect to 1-day solutions is also confirmed by the validation with satellite laser ranging.

Position Errors Caused by GPS Height of Instrument Blunders

Height of instrument (HI) blunders in GPS measurements cause position errors. These errors can be pure vertical, pure horizontal, or a mixture of both. There are different error regimes depending on whether both the base and the rover both have HI blunders, if just the base has an HI blunder, or just the rover has an HI blunder. The resulting errors are on the order of 30 cm for receiver separations of 1000 km for an HI blunder of 2 m. Given the complicated nature of the errors, we believe it would be difficult, if not impossible, to detect such errors by visual inspection. This serves to underline the necessity to enter GPS HI's correctly.

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.

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.

Ice velocities of Nordenskiöldbreen glacier, Svalbard

Precise measurements of ice-flow velocities are necessary for a proper understanding of the dynamics of glaciers and their response to climate change. We use stand-alone single-frequency GPS receivers for this purpose. They are designed to operate unattended for 1-3 years, allowing uninterrupted measurements for long periods with hourly temporal resolution. We present the system and illustrate its functioning using data from 9 GPS receivers deployed on Nordenskiöldbreen, Svalbard, for the period 2006-2009. The accuracy of the receivers is 1.62 m based on the standard deviation in the average location of a stationary reference station (NBRef). Both the location of NBRef and the observed flow velocities agree within one standard deviation with DGPS measurements. Periodicity (6, 8, 12, 24 h) in the NBRef data is largely explained by the atmospheric, mainly ionospheric, influence on the GPS signal. A (weighed) running-average on the observed locations significantly reduces the standard deviation and removes high frequency periodicities, but also reduces the temporal resolution. Results show annual average velocities varying between 40 and 55 m/yr at stations on the central flow-line. On weekly to monthly time-scales we observe a peak in the flow velocities (from 60 to 90 m/yr) at the beginning of July related to increased melt-rates. No significant lag is observed between the timing of the maximum speed between different stations. This is likely due to the limited temporal resolution after averaging in combination with the relatively small distance (max. ±13 km) between the stations.