On calculating the Earth's C21 and S21 gravity coefficients in the IERS terrestrial reference frame

Modern models of the Earth's gravity field are developed in the IERS (International Earth Rotation Service) terrestrial reference frame. In this frame the mean values for gravity coefficients of the second degree and first order, C ₂₁(IERS) and S ₂₁(IERS), by the current IERS Conventions are recommended to be calculated by using the observed polar motion parameters. Here, it is proved that the formulae presently employed by the IERS Conventions to obtain these coefficients are insufficient to ensure their values as given by the same source. The relevant error of the normalized mean values for C ₂₁(IERS) and S ₂₁(IERS) is 3×10⁻¹², far above the adopted cutoff (10⁻¹³) for variations of these coefficients. Such an error in C ₂₁ and S ₂₁ can produce non-modeled perturbations in motion prediction of certain artificial Earth satellites of a magnitude comparable to the accuracy of current tracking measurements. Received: 14 September 1998 / Accepted: 20 May 1999     

On a global integrated fundamental network

Editor's comment: This letter has been received fromDr. E.H. Knickmeyer, University of Calgary, Dep. of Surveying Engineering, 2500 University Dr. N. Calgary, Alberta, Canada T2N 1N4, in April 1988. A response to this letter has been written byDr. C. Boucher, who represents the Central Bureau ofIERS andIAG SSG 5.123. Similar letters, dealing with matters of interest for geodesy and for IAG will in the future be published in Bulletin Géodésique with an answer by the person or committee in IAG which is most closely related to or responsible for the matter being dealt with in the letter.     

Further considerations on combining earth rotation observations from different space geodetic systems

Additional results are presented concerning a study that consider improvements over present Earth Rotation Parameter (ERP) determination methods by directly combining observations from various space geodetic systems in one adjustment. Earlier results are extended, showing that in addition to slight improvements in accuracy substantial (a factor of three or more) improvements in precision and significant reductions in correlations between various parameters can be obtained (by combining Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) to Lageos, and Very Long Baseline Interferometry (VLBI) data in one adjustment) as compared to results from individual systems. Smaller improvements are also seen over the weighted means of the individual system results. Although data transmission would not be significantly reduced, negligible additional computer time would be required if (standardized) normal equations were available from individual solutions. Suggestions for future work and implications for the new International Earth Rotation Service (IERS) are also presented.     

The International Association of Geodesy 1862 to 1922: from a regional project to an international organization

Geodesy, by definition, requires international collaboration on a global scale. An organized cooperation started in 1862, and has become todays International Association of Geodesy (IAG). The roots of modern geodesy in the 18th century, with arc measurements in several parts of the world, and national geodetic surveys in France and Great Britain, are explained. The manifold local enterprises in central Europe, which happened in the first half of the 19th century, are described in some detail as they prepare the foundation for the following regional project. Simultaneously, Gauss, Bessel and others developed a more sophisticated definition of the Earths figure, which includes the effect of the gravity field. In 1861, the retired Prussian general J.J. Baeyer took up earlier ideas from Schumacher, Gauss, Struve and others, to propose a Central European Arc Measurement in order to study the figure of the Earth in that region. This led to a scientific organization, which soon extended from Central Europe to the whole continent and later to the globe, and changed its name in 1886 to Internationale Erdmessung (International Geodetic Association). The scientific programme also widened remarkably from more local studies based on geometric data to regional and global investigations, with gravity measurements as an important source of information. The Central Bureau of the Internationale Erdmessung was hosted at the Prussian Geodetic Institute in Potsdam, and with Baeyer as Director, developed as an efficient tool of the Association. The scientific research extended and deepened after 1886, when F.R. Helmert became Director of the Central Bureau. A stronger international participation then took place, while the influence of the German states reduced. Of great practical importance were questions of standardization and reference systems, but first attempts to interpret gravity field variations and to monitor geodynamic phenomena by geodetic methods indicated future tendencies. With the First World War and the expiry of the last international convention in 1916, the international cooperation within the frame of the Association practically came to an end, which ended the first epoch of the Association. Nevertheless, due to the strong commitment of two scientists from neutral countries, the International Latitude Service continued to observe polar motion and to deliver the data to the Berlin Central Bureau for evaluation. After the First World War, geodesy became one of the founding members of the International Union for Geodesy and Geophysics (IUGG), and formed one of its Sections (respectively Associations). It has been officially named the International Association of Geodesy (IAG) since 1932.     

Determination of the earth rotation parameters from optical astrometry observations, 1962.0–1982.0

The optical astrometric data of the years 1962–1982 have been reduced once again at the Bureau International de l’Heure (BIH) in order to redetermine the Earth Rotation Parameters (ERP). This new reduction is based on serie largely revised by the stations since their use in the operational work of theBIH, and on some series which were not available previously. A total of 113 stations is considered, totaling nearly 500,000 measurements of time or latitude. TheERP are determined at five-day intervals. A new approach is developed: the catalog and local errors are analysed and corrected as group unknowns, which values are adjusted together with the main unknowns. The results obtained in the new reduction are compared to other series obtained by astrometry and space geodesy.     

Combination procedure for length-of-day time series according to the noise frequency behavior

 Length-of-day (LOD) estimates from seven Global Positioning System (GPS) and three satellite laser ranging (SLR) analysis centers were combined into an even-spaced time series for a 27-month period (1996–1998). This time series was compared to the multi-technique Earth-orientation-parameter (EOP) combined solution (C04) derived at the Central Bureau of the International Earth Rotation Service (IERS/CB). Due to inhomogeneities in the different series derived from the various techniques (time, length, quality, and spatial resolution), the concept of a combined solution is justified. The noise behavior in LOD for different techniques varies with frequency; the data series were divided into frequency windows after removing both biases and trends. Different weight factors were assigned in each window, discriminating by technique, and produced one-technique combined solutions. Finally, these one-technique combined solutions were combined to obtain the final multi-technique solution. The LOD combined time series obtained by the present method based on the frequency windows combined series (FWCS) is very close to the IERS C04 solution. It could be useful to generate a new LOD reference time series to be used in the study of high-frequency variations of Earth rotation. Received: 28 March 2000 / Accepted: 15 February 2001     

The North American datum of 1983: Project methodology and execution

A new adjustment of the geodetic control networks in North America has been completed, resulting in a new continental datum—the North American Datum of 1983 (NAD 83). The establishment ofNAD 83 was the result of an international project involving the National Geodetic Survey of the United States, the Geodetic Survey of Canada, and the Danish Geodetic Institute (responsible for surveying in Greenland). The geodetic data in Mexico and Central America were collected by the Inter American Geodetic Survey and validated by the Defense Mapping Agency Hydrographic/Topographic Center. The fundamental task ofNAD 83 was a simultaneous least squares adjustment involving 266,436 stations in the United States, Canada, Mexico, and Central America. The networks in Greenland, Hawaii, and the Caribbean islands were connected to the datum through Doppler satellite and Very Long Baseline Interferometry (VLBI) observations. The computations were performed with respect to the ellipsoid of the Geodetic Reference System of 1980. The ellipsoid is positioned in such a way as to be geocentric, and its axes are oriented by the Bureau International de l'Heure Terrestrial System of 1984. The mathematical model for theNAD readjustment was the height-controlled three-dimensional system. The least squares adjustment involved 1,785,772 observations and 928,735 unknowns. The formation and solution of the normal equations were carried out according to the Helmert block method. [Authors' note:This article is a condensation of the final report of the NAD 83 project. The full report (Schwarz,1989) contains a more complete discussion of all the topics.]     

The geopotential value <Emphasis Type="Italic">W</Emphasis><Subscript>0</Subscript> for specifying the relativistic atomic time scale and a global vertical reference system

The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W ₀. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W ₀ have been investigated. The rounded value W ₀ = 62636856.0 ± 0.5) m ² s ⁻² has already been adopted by the International Astronomical Union for the definition of the constant L _G = W ₀/c ² = 6.969290134 × 10⁻¹⁰ (where c is the speed of light), which is required for the realization of the relativistic atomic time scale. The constant L _G , based on the above value of W ₀, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W ₀ is used to specify a global vertical reference system (GVRS). W ₀ ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W ₀, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J ₂) as primary constants (parameters), then the ellipsoidal parameters (a,α) can be computed and adopted as derived parameters. The scale of the International Terrestrial Reference Frame 2000 (ITRF2000) has also been specified with the use of W ₀ to be consistent with the geocentric coordinate time. As an example of using W ₀ for a GVRS realization, the geopotential difference between the adopted W ₀ and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.     

The introduction of the Iau 1980 nutation theory in the computation of the Earth Rotation Parameters by the Bureau International de l'Heure

Summary The status of nutation theory in the computation of the Earth Rotation Parameters from the different observational techniques is reviewed. The impact on the combined solution of the Bureau International de l'Heure is evaluated. In view of the improvement brought by the IAU 1980 Nutation Theory, its introduction in the BIH publications, without waiting for the adoption by the astronomical ephemerides (1984 Jan. 1) is decided.     

A European perspective on Digital Earth

Abstract

The purpose of this paper is to contribute to the definition of a European perspective on Digital Earth (DE), identify some actions that can contribute to raise the awareness of DE in the European context and thus strengthen the European contribution to the International Society for Digital Earth (ISDE). The paper identifies opportunities and synergies with the current policy priorities in Europe (Europe 2020, Innovation Union and Digital Agenda) and highlights a number of key areas to advance the development of DE from a European perspective: (1) integrating scientific research into DE; (2) exploiting the Observation Web with human-centred sensing; and (3) governance, including the establishment of stronger linkages across the European landscape of funding streams and initiatives. The paper is offered also as a contribution to the development of this new vision of DE to be presented at the next International DE Conference in Perth, Australia, in August 2011. The global recognition of this new vision will then reinforce the European component and build a positive feedback loop for the further implementation of DE across the globe.     

On the rotation of the Earth and the terrestrial reference system

The Working Group on the Rotation of the Earth was established in 1978 and developed a programme of international collaboration to Monitor Earth-Rotation and Intercompare the Techniques of observation and analysis (MERIT). The MERIT Short Campaign was held in 1980 to test and develop the organisational arrangements required during the MERIT Main Campaign in 1983–4. The Working Group on the Terrestrial Reference System was established in 1980 to prepare a proposal for the establishment and maintenance of a new Conventional Terrestrial Reference System (COTES) that would be based on the new techniques of space geodesy. The Working Groups collaborated closely and organised two intensive campaigns in 1984 and 1985 that were aimed primarily at determining the relationships between the reference systems of the six different techniques that were used to determine earth-rotation parameters. Observational data were obtained from 35 countries; analyses and intercomparisons of the results were carried out in 7 countries. The Working Groups reviewed the results at the Third MERIT Workshop and recommended that a new International Earth Rotation Service be set up in 1988 and that it be based on the use of very-long-baseline radio interferometry and both satellite and lunar laser ranging.     

On-line Resources Supporting the Data, Products, and Information Infrastructure for the International DORIS Service

The International DORIS Service (IDS) was formed under the direction of the International Association of Geodesy (IAG) in 2003 to support geodetic research utilizing DORIS data and products. The IDS is organized into a hierarchy of components: network of Tracking Stations, Satellite Segment, Data Centers, Analysis Centers, Central Bureau, and Governing Board. The DORIS infrastructure consists of a globally distributed network of over 50 ground beacons and a constellation of five satellites equipped with receivers that relay range rate measurements through a central collection facility to the IDS archives. The Data Centers and Central Bureau supporting the IDS are the primary means of distributing DORIS data, products, and general information to the user community. These facilities utilize Web and ftp servers, as well as an email service, to support the users of DORIS data and products. The current status and recent developments of these components are discussed, as well as a review of available information, data, and geodetic product types.     

THE INTERNATIONAL UNION OF GEODESY AND GEOPHYSICS AT LISBON

Abstract

On the 17th September, 1933, the Fifth General Assembly of the International Union of Geodesy and Geophysics was opened by General Carmono, President of the Republic of Portugal, in the hall normally occupied by the Portuguese Parliament at Lisbon. Great Britain sent to this meeting of the Union twenty-two delegates, of whom the majority travelled to Lisbon by the S.S. Arlanza.     

Prediction of Earth rotation parameters by fuzzy inference systems

The short-term prediction of Earth rotation parameters (ERP) (length-of-day and polar motion) is studied up to 10 days by means of ANFIS (adaptive network based fuzzy inference system). The prediction is then extended to 40 days into the future by using the formerly predicted values as input data. The ERP C04 time series with daily values from the International Earth Rotation Service (IERS) serve as the data base. Well-known effects in the ERP series, such as the impact of the tides of the solid Earth and the oceans or seasonal variations of the atmosphere, were removed a priori from the C04 series. The residual series were used for both training and validation of the network. Different network architectures are discussed and compared in order to optimize the network solution. The results of the prediction are analyzed and compared with those of other methods. Short-term ERP values predicted by ANFIS show root-mean-square errors which are equal to or even lower than those from the other considered methods. The presented method is easy to use.Acknowledgments. The presented study was undertaken during a six-month stay of the first author at the DGFI (Deutsches Geodätisches Forschungsinstitut) in Munich. The authors wish to thank the DAAD (German Academic Exchange Service) for its support of this project. The first author would like to express many thanks to Prof. Dr.-Ing. Hermann Drewes and all other administrative and academic staff at the DGFI for providing a very warm welcome which motivated and encouraged him during his study on this project. The cooperation of Dr.-Ing. Katja Heine (TU Cottbus, Germany) is gratefully acknowledged, in particular her hospitality during the two stays of the first author in Cottbus.     

Towards a collaborative global land cover information service

ABSTRACT

The need and critical importance of global land cover and change information has been well recognized. Although rich collection of such information has been made available, the lack of necessary information services to support its easy access, analysis and validation makes it difficult to find, evaluate, select and reuse them through well-designed workflows. Aiming at promoting the development of the needed global land cover information services, this paper presents a conceptual framework for developing a Collaborative Global Land Cover Information Service (CoGland), followed by discussions on its implementation strategies. The framework supports connected and shared land cover and change web services around the world to address resource sharing, community service and cross-board collaboration needs. CoGland can benefit several recent international initiatives such as Future Earth, and many societal benefit areas. The paper further proposes that CoGland be developed within the framework of the Group on Earth Observations with the support of a number of key organizations such as the United Nations Expert Committee on Global Geospatial Information Management, the International Society for Photogrammetry and Remote Sensing, and International Society of Digital Earth. It is hoped that this paper can serve as a starting point for further discussions on CoGland developments.     

A new ΔLOD series in monthly intervals (1892.0–1997.0) and its comparison with other geophysical results

Using the ΔT (integrated variation of the Earth's rotation measured in terestrial time) series (1891.5–1955.5) derived from lunar occultation observations and the UT1–UTC (universal time–coordinated universal time) series (1955.5–1997.5) of the Bureau International de L'Heure/International Earth Rotation Service, a new ΔLOD (variation of the length of day) series in monthly intervals from 1892.0 to 1997.0 is calculated. Using digital filtering, the interannual and decadal components of the ΔLOD series are separated and then compared with those inferred from other geophysical quantities. It is shown that, on the interannual time scale, atmospheric processes can play an important role in exciting astronomical ΔLOD. However, the main oscillation with a mean period of about 5.8 years and peak-to-peak amplitude of about 0.3 ms in the residuals of ΔLOD(Astr) −ΔLOD(Wind) for 1968.0–1997.0 suggests that about half of the amplitude in astronomical ΔLOD must be excited by other geophysical processes, while on the decadal time scale the atmospheric excitation is too small. Geomagnetic core–mantle coupling may be a plausible source of the excitation of ΔLOD on the decadal time scale, but the geomagnetic data are still insufficient and an improved model of core–mantle coupling is required. Received: 3 April 1998 / Accepted: 31 May 1999     

Combined processing of the IGS and the IGEX network

 Since the beginning of the International Global Navigation Satellite System (GLONASS) Experiment, IGEX, in October 1998, the Center for Orbit Determination in Europe (CODE) has acted as an analysis center providing precise GLONASS orbits on a regular basis. In CODE's IGEX routine analysis the Global Positioning System (GPS) orbits and Earth rotation parameters are introduced as known quantities into the GLONASS processing. A new approach is studied, where data from the IGEX network are combined with GPS observations from the International GPS Service (IGS) network and all parameters (GPS and GLONASS orbits, Earth rotation parameters, and site coordinates) are estimated in one processing step. The influence of different solar radiation pressure parameterizations on the GLONASS orbits is studied using different parameter subsets of the extended CODE orbit model. Parameterization with three constant terms in the three orthogonal directions, D, Y, and X (D = direction satellite–Sun, Y = direction of the satellite's solar panel axis), and two periodic terms in the X-direction, proves to be adequate for GLONASS satellites. As a result of the processing it is found that the solar radiation pressure effect for the GLONASS satellites is significantly different in the Y-direction from that for the GPS satellites, and an extensive analysis is carried out to investigate the effect in detail. SLR observations from the ILRS network are used as an independent check on the quality of the GLONASS orbital solutions. Both processing aspects, combining the two networks and changing the orbit parameterization, significantly improve the quality of the determined GLONASS orbits compared to the orbits stemming from CODE's IGEX routine processing. Received: 10 May 2000 / Accepted: 9 October 2000     

Investigation of tidal effects in lunar laser ranging

 The analysis of lunar laser ranging (LLR) data enables the determination of many parameters of the Earth–Moon system, such as lunar gravity coefficients, reflector and station coordinates which contribute to the realisation of the International Terrestrial Reference Frame 2000 (ITRF 2000), Earth orientation parameters [EOPs, which contribute to the global EOP solutions at the International Earth Rotation Service (IERS)] or quantities which parameterise relativistic effects in the solar system. The big advantage of LLR is the long time span of lunar observations (1970–2000). The accuracy of the normal points nowadays is about 1 cm.  The capability of LLR to determine tidal parameters is investigated. In principle, it could be assumed that LLR would contribute greatly to the investigation of tidal effects, because the Moon is the most important tide-generating body. In this respect some special topics such as treatment of the permanent tide and the effect of atmospheric loading are addressed and results for the tidal parameters h ₂ and l ₂ as well as values for the eight main tides are given. Received: 14 August 2000 / Accepted: 15 October 2001     

Orientation of the Earth by numerical integration

Recent research in the department has involved determining the value of lunar observations in the determination of geodetic and selenodetic control. A fundamental consideration in the research is the determination of the orientation of the Earth in the celestial coordinate system. Classical reductions for precession and nutation can be expected to be consistent with the present day observations, however, corrections to the classical theory are difficult to model due to the large number of coefficients involved. Consequently, a portion of the research has been devoted to numerically integrating the Eulerian equations of motion for a rigid Earth and considering the six initial conditions of the integration as unknowns. Comparison of the three adjusted Eulerian angles from the numerical integration over 1000 daysindicates agreement with classical theory to within 0.003 seconds ofarc. This work was performed under NASA Contract No. NAS 9-13093. Presented at the International Symposium on Computational Methods in Geometrical Geodesy, Oxford, September 2–8, 1973.     

Fuzzy Modelling of African Ecoregions and Ecotones Using AVHRR NDVI Temporal Imagery

Abstract

Conventional methods of deriving global or continental vegetation maps from the National Oceanic and Atmospheric Administration's (NOAA) Advanced Very High Resolution Radiometer (AVHRR) time series data are based on two‐value Boolean logic, which cannot properly model the so‐called ecotone, the transition zone between adjacent ecosystems. New methods and data models that have been developed on the basis of fuzzy logic to address the “mixed pixel” issue in multi‐spectral imagery can also be used with multi‐temporal imagery to handle the mixture of vegetation types within an ecotone. This study introduces the concept of semantic space and its transformation from spectral feature space, which utilizes a fuzzy logic approach to characterize the continuum of vegetation communities in the African continent from AVHRR multi‐temporal (12 months for three years from 1986 to 1988) NDVI data. The fuzzy procedure was based on the Fuzzy c‐Means (FCM) algorithm with significant modifications to improve processing speed for handling large volumes of data. A second‐order mapping approach was also devised to explicitly represent subdominant vegetative coverage in ecotones and other heterogeneous regions. Comparisons between a Sub‐Saharan African Vegetation Map compiled by the International Union for Conservation of Nature (IUCN) in 1986 and the maps derived from this study demonstrated that fuzzy modeling and classification might provide a better and more realistic representation of the vegetative characteristics of the region.