Volume 6, Issue 1

The NKG 2008 GPS campaign was carried out in September 28 – October 4, 2008. The purpose was to establish a common reference frame in the Nordic- Baltic-Arctic region, and to improve and update the transformations from the latest global ITRF reference frame to the national ETRS89 realizations of the Nordic/Baltic countries. Postglacial rebound in the Fennoscandian area causes intraplate deformations up to about 10 mm/yr to the Eurasian tectonic plate which need to be taken into account in order to reach centimetre level accuracies in the transformations. We discuss some possible alternatives and present the most applicable transformation strategy. The selected transformation utilizes the de facto transformation recommended by the EUREF but includes additional intraplate corrections and a new common Nordic-Baltic reference frame to serve the requirements of the Nordic/Baltic countries. To correct for the intraplate deformations in the Nordic-Baltic areawe have used the commonNordic deformation model NKG RF03vel. The new common reference frame, NKG ETRF00, was aligned to ETRF2000 at epoch 2000.0 in order to be close to the national ETRS89 realizations and to coincide with the land uplift epoch of the national height systems. We present here the realization of the NKG ETRF00 and transformation formulae together with the parameters to transform from global ITRF coordinates to Nordic/Baltic realizations of the ETRS89.

The Australian Height Datum (AHD) is the national vertical datum for Australia, and AUSGeoid09 is the latest quasigeoid model used to compute (normalorthometric) AHD heights from Global Navigation Satellite System (GNSS) derived ellipsoidal heights. While previous studies have evaluated the AUSGeoid09 model across Australia, such studies have generally not focused on mountainous terrain. This paper investigates the performance of AUSGeoid09 in a relative sense in the MidHunter and Snowy Mountains regions of New South Wales, from a user’s perspective. Relative (i.e. height difference between two points) comparisons were undertaken between AUSGeoid09-derived heights and officialAHDheights. The performance of AUSGeoid09 was compared to its predecessor AUSGeoid98. In both study areas, an overall improvement was evident when applying AUSGeoid09 to compute AHD height differences. AUSGeoid09 generally provided AHD height differences at the ±0.05mto ±0.09m level (1 sigma) and substantially increased the percentage of GNSS-derived height differences meeting 3rd order differential levelling specifications. This is a very encouraging result, considering the difficulties of spirit levelling in mountainous terrain and the increasing popularity of GNSS-based height transfer in practice.

The traditional way of solving non-linear least squares (LS) problems in Geodesy includes a linearization of the functional model and iterative solution of a nonlinear equation system. Direct solutions for a class of nonlinear adjustment problems have been presented by the mathematical community since the 1980s, based on total least squares (TLS) algorithms and involving the use of singular value decomposition (SVD). However, direct LS solutions for this class of problems have been developed in the past also by geodesists. In this contributionwe attempt to establish a systematic approach for direct solutions of non-linear LS problems from a "geodetic" point of view. Therefore, four non-linear adjustment problems are investigated: the fit of a straight line to given points in 2D and in 3D, the fit of a plane in 3D and the 2D symmetric similarity transformation of coordinates. For all these problems a direct LS solution is derived using the same methodology by transforming the problem to the solution of a quadratic or cubic algebraic equation. Furthermore, by applying TLS all these four problems can be transformed to solving the respective characteristic eigenvalue equations. It is demonstrated that the algebraic equations obtained in this way are identical with those resulting from the LS approach. As a by-product of this research two novel approaches are presented for the TLS solutions of fitting a straight line to 3D and the 2D similarity transformation of coordinates. The derived direct solutions of the four considered problems are illustrated on examples from the literature and also numerically compared to published iterative solutions.

Global surface pressure grids from 14.5 years of 6-hourly analyses out of both the operational ECMWF weather prediction model and ERA-Interim are mapped to a common reference orography by means of ECMWF’s mean sea-level pressure diagnostic. The approach reduces both relative biases and residual variability by about one order of magnitude and thereby achieves a consistency among both data sets at the level of about 1 hPa. Remaining differences rather reflect temperature biases and also resolution limitations of the reanalysis data set, but are not anymore related to the local roughness in orography or to changes in the spatial resolution of the operational model. The presented reduction method therefore allows to obtain surface pressure time series with the long-time consistency of a reanalysis from an operational numerical weather model with much higher resolution and much shorter latency, making the results suitable for geodetic near realtime applications requiring continuously updated time series that are homogeneous over many years.

This study proposes a new paradigm for assessing thermosteric effects of warming oceans at a tide gauge station. For demonstration, the trend due to the global thermosteric sea level at the Key West, FL tide gauge station was estimated using the tide gauge measurements and the global sea surface temperature anomalies that were represented by yearly distributed lags. A comparison of the estimate with the trend estimate from a descriptive model revealed that 0.7±0.1 mm/yr, (p<0.01), of the total trend 2.2±0.1 mm/yr (p<0.01) estimated using the descriptive model can be attributed to the global warming of the oceans during the last century at this station. The remaining 1.5±0.1 mm/yr, 70 percent of the total trend, is the lump sum estimate of the secular changes due to the eustatic, halosteric, and various local isostatic contributions.

GPS draconitic signal (351.6 ± 0.2 days) and its higher harmonics are observed at almost all IGS products such as position time series of IGS permanent stations. Orbital error and multipath are known as two possible sources of these signals. The effect of Earth shadow crossing of GPS satellites is another suspect for this signal. Up to now there is no serious attempt to investigate this dependence. AMATLAB toolbox is developed and used to determine the satellites located at the earth shadow. RINEX observation files and precise ephemeris are imported to the toolbox and a cylindrical model is used to detect the shadow regions. Data of these satellites were removed from the RINEX observation files of three IGS permanent stations (GRAZ,ONSAandWSRT) and new RINEX observation fileswere created. The time span of these data is about 11 years. The new and original fileswere then processed using precise point positioning (PPP) method to determine position time series, for further analysis. Both the original and new time series were analyzed using the least squares harmonic estimation (LS-HE) in the following steps. The 1st step is the validation of the draconitic harmonics signature in the original position time series of the three stations. The 2nd step does the same for the new time series. It confirms that the power spectrum at the draconitic signals decreases to some extent for the new time series. The difference between the original and new time series (difference between all three position quantity (X, Y and Z)) is then analyzed in the 3rd step. Signature of the draconitic harmonics is also observed to the differences. The results represent that all eight harmonics of GPS draconitic period do exist at the residuals and mainly they decrease. All of the three stations were then processed together using the multivariate LS-HE method. At the 4th step, the difference of the spectral values between the original time series and new times serieswere analyzed. Decreasing of the spectral values at most harmonics (e.g. 1st, 2nd, 4th, 6th, 7th and 8th) represents the effect of removing satellite observations at shadow of the earth on draconitic harmonics. At least, five harmonics among seven shows the amelioration of results (draconitic error reduction) after removing the earth shadowed data from RINEX raw data. The results show that the draconitic year’s component of data is in part due to eclipsing satellites.

In June–July 2013,we performed a comparison of five absolute gravimeters of different types. The gravimeters were the FG5X-221 of the FGI, the FG5-110 and GBL-M 002 of the TsNIIGaiK, the GABL-PM of the IAE SB RAS, and the GABL-M of the NIIMorGeofizika (Murmansk, Russia). The three last-mentioned are field-type portable gravimeters made by the Institute of Automation and Electrometry in Novosibirsk, and this is the first international comparison for them. This Russian-Finnish Comparison of Absolute Gravimeters RFCAG2013 was conducted at four sites with different characteristics: at the field sites Pulkovo and Svetloe near St. Petersburg, and at the laboratory sites TsNIIGaIK in Moscow and Zvenigorod near Moscow. At the TsNIIGAiK site and at Zvenigorod two piers were used, such that altogether six stations were occupied. The FG5X- 221 provides the link to the CCM.G-K2 Key Comparison in Luxembourg in November 2013. Recently, the Consultative Committee for Mass and Related Quantities and the International Association of Geodesy drafted a strategy on how to best transmit the results of Key Comparisons of absolute gravimeters to benefit the geodetic and geophysical gravimetric community. Our treatment of the RFCAG2013 presents one of the first practical applications of the ideas of the strategy document, andwe discuss the resulting uncertainty structure. Regarding the comparison results, we find the gravimeters show consistent offsets at the quite different sites. All except one gravimeter are in equivalence.

The signal-to-noise ratio (SNR) from GNSS receivers allows computing the height of a reflecting surface by analyzing the interference pattern. In classical interference pattern technique the distance between the antenna and the reflector is derived from the multipath pattern using a one-dimensional Lomb-Scargle periodogram (LSP) which permits the estimation of constant or quasi static reflector heights only. Inwaters with tidal influence some authors used one-dimensional LSP to iteratively estimate an approximate time-dependent correction term for the variable reflector height. Other authors applied nonlinear least squares adjustment that requires choosing initial parameters what might become crucial due to the multimodality of the problem. We suggest and apply an alternative approach that allows finding the global optimum of a multi-dimensional cost function of a common least squares adjustment based on interval analysis. This method reduces the computational efforts compared to LSP. The technique is demonstrated using a simulated data set derived fromreal measurements on the Weser river, Germany. Additionally, real data from a gauge in the North Sea is analyzed.

We present in this paper some results obtained in the field of space geodesy based on continuous GPS observations at the Astronomical Observatory of Mongolia. Starting with a brief historical overview of the main space geodetic activities carried out by the Astronomical Observatory in the past, we outline here current achievements in the application of GPS techniques in the geosciences research in Mongolia. We setup a local GNSS Data Center of the Mongolian Academy of Sciences to receive, quality control and process into derivative products the observation data coming from its continuously recording stations. The quality check performed on three non-real-time permanent stations reveals that all three stations show smooth trends of each parameter indicating good quality in data record and operation without any anomalous behavior.

Scaled total least-squares (STLS) unify LS, Data LS, and TLS with a different choice of scaled parameter. The function of the scaled parameter is to balance the effect of random error of coefficient matrix and observation vector for the estimate of unknown parameter. Unfortunately, there are no discussions about how to determine the scaled parameter. Consequently, the STLS solution cannot be obtained because the scaled parameter is unknown. In addition, the STLS method cannot be applied to the structured EIV casewhere the coefficient matrix contains the fixed element and the repeated random elements in different locations or both. To circumvent the shortcomings above, the study generalize it to a scaledweighted TLS (SWTLS) problem based on partial errors-in-variable (EIV) model. And the maximum likelihood method is employed to derive the variance component of observations and coefficient matrix. Then the ratio of variance component is proposed to get the scaled parameter. The existing STLS method and WTLS method is just a special example of the SWTLS method. The numerical results show that the proposed method proves to bemore effective in some aspects.

Thermosteric contribution of warming oceans to the global sea level variations during the last century was evaluated at globally distributed 27 tide gauge stations with records over 80 years. The assessment was made using a recently proposed lagged model inclusive of a sea level trend, long and decadal periodicities, and lagged sea surface temperature measurements. The new model solutions revealed that almost all the long period periodic sea level changes experienced at these stations can be attributed to the lagged thermosteric effects of the warming oceans during the 20th century. Meanwhile, statistically significant (p<0.05) anomalous thermosteric contributions to the secular trends, some of them as large as 1.0±0.2 mm/yr, were detected at six tide gauge stations close to the equator and open seas. The findings of this study revealed a more complex impact of the warming oceans at the globally distributed tide gauge stations other than a secular contribution to the sea level trends of the previous studies.

Gravity and topographic/bathymetric data are used for gravimetric modelling of Moho discontinuity by hydrostatic or flexural theories of the isostasy. Here, two hydrostatic models, based on the Vening Meinesz-Moritz (VMM) principle, and two based on the loading theories and flexural isostasy are compared over Tibet Plateau. It is shown that theMoho models generated based on theVMM theory and flexural isostasy have very good agreements if the mean compensation depth and the mean elastic thickness are selected properly. However, the model computed based on the flexural isostasy is smoother. A more rigorous flexural model, which considers the membrane stress and curvature of the lithosphere, is used to model the Moho surface over the study area. It is shown that the difference between the Moho models, derived by considering and ignoring these parameters, is not significant. By combination of the flexural and VMM hydrostatic models new mathematical formulae for crustal gravity anomalies are provided and it is shown that the crustal gravity anomalies produced by them are also equivalent.