Atmospheric, oceanic and hydrological contributions to seasonal variations in length of day

 The annual and semiannual residuals derived in the axial angular momentum budget of the solid Earth–atmosphere system reflect significant signals. They must be caused by further excitation sources. Since, in particular, the contribution for the wind term from the atmospheric layer between the 10 and 0.3 hPa levels to the seasonal variations in length of day (LOD) is still missing, it is necessary to extend the top level into the upper stratosphere up to 0.3 hPa. Under the conservation of the total angular momentum of the entire Earth, variations in the oceanic angular momentum (OAM) and the hydrological angular momentum (HAM) are further significant excitation sources at seasonal time scales. Focusing on other contributions to the Earth's axial angular momentum budget, the following data are used in this study: axial atmospheric angular momentum (AAM) data derived for the 10–0.3 hPa layer from 1991 to 1997 for computing the missing wind effects; axial OAM functions as generated by oceanic general circulation models (GCMs), namely for the ECHAM3 and the MICOM models, available from 1975 to 1994 and from 1992 to 1994, respectively, for computing the oceanic contributions to LOD changes, and, concerning the HAM variations, the seasonal estimates of the hydrological contribution as derived by Chao and O'Connor [(1988) Geophys J 94: 263–270]. Using vector representation, it is shown that the vectors achieve a close balance in the global axial angular momentum budget within the estimated uncertainties of the momentum quantities on seasonal time scales. Received: 6 April 2000 / Accepted: 13 December 2000     

New analytical and numerical approaches for geopotential modeling

 The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential coefficients _n,m . In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal harmonic series is developed for the geopotential and then its coefficients _n,m ^e are transformed to the unknown _n,m . The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From two sets of _n,m (n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068) by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to apply the LS technique for evaluating geopotential coefficients. Received: 12 December 2000 / Accepted: 21 June 2001     

Developing a bivariate spatial association measure: An integration of Pearson's r and Moran's I

 This research is concerned with developing a bivariate spatial association measure or spatial correlation coefficient, which is intended to capture spatial association among observations in terms of their point-to-point relationships across two spatial patterns. The need for parameterization of the bivariate spatial dependence is precipitated by the realization that aspatial bivariate association measures, such as Pearson's correlation coefficient, do not recognize spatial distributional aspects of data sets. This study devises an L statistic by integrating Pearson's r as an aspatial bivariate association measure and Moran's I as a univariate spatial association measure. The concept of a spatial smoothing scalar (SSS) plays a pivotal role in this task. Received: 07 November 2000 / Accepted: 02 August 2001     

Topographic and atmospheric corrections of gravimetric geoid determination with special emphasis on the effects of harmonics of degrees zero and one

 The topographic and atmospheric effects of gravimetric geoid determination by the modified Stokes formula, which combines terrestrial gravity and a global geopotential model, are presented. Special emphasis is given to the zero- and first-degree effects. The normal potential is defined in the traditional way, such that the disturbing potential in the exterior of the masses contains no zero- and first-degree harmonics. In contrast, it is shown that, as a result of the topographic masses, the gravimetric geoid includes such harmonics of the order of several centimetres. In addition, the atmosphere contributes with a zero-degree harmonic of magnitude within 1 cm. Received: 5 November 1999 / Accepted: 22 January 2001     

The international GLONASS experiment: products, progress and prospects

 In October 1998 the IGEX field campaign, the first coordinated international effort to monitor GLONASS satellites on global basis, was started. Currently about 40 institutions worldwide support this effort either by providing GLONASS tracking data or in operating related data and analysis centers. The increasing quality and consistency of the calculated GLONASS orbits (about 25 cm early in 2000), even after the end of the official IGEX field campaign, are shown. Particular attention is drawn to the combination of precise ephemerides in order to generate a robust, reliable and complete IGEX orbits product. Some problems in modeling the effect of solar radiation pressure on GLONASS satellites are demonstrated. Finally, the expected benefits and prospects of the upcoming International GLOnass Service-Pilot Project (IGLOS-PP) of the International GPS Service (IGS) are discussed in more detail. Received: 17 August 2000 / Accepted: 12 April 2001     

Laser-based validation of GLONASS orbits by short-arc technique

 The International GLONASS Experiment (IGEX-98) was carried out between 19 October 1998 and 19 April 1999. Among several objectives was the precise orbit determination of GPS and GLONASS satellites and its validation by laser ranging observations. Local laser-based orbit corrections (radial, tangential and normal components in a rotating orbital local reference frame) are computed using a geometrical short-arc technique. The order of magnitude of these corrections is at the level of few decimeters, depending on the considered components. The orbit corrections are analyzed as a function of several parameters (date, orbital plane, geographical area). The mean corrections are at the level of several centimeters. However, when averaging over the entire campaign and for all the satellites, no mean radial, tangential and normal orbit corrections are found. The origin of the observed corrections is considered (errors due to the geocentric gravitational constant, the non-gravitational forces, the thermal equilibrium of on-board equipment, the reference systems, the location and the signature of the retroreflector array, and the precision of the satellite laser ranges). Some features are also due to errors in the radio-tracking GLONASS orbits. Further investigations will be needed to better understand the origin of various biases. Received: 17 February 2000 / Accepted: 31 January 2001     

Geoid, topography, and the Bouguer plate or shell

 Topography plays an important role in solving many geodetic and geophysical problems. In the evaluation of a topographical effect, a planar model, a spherical model or an even more sophisticated model can be used. In most applications, the planar model is considered appropriate: recall the evaluation of gravity reductions of the free-air, Poincaré–Prey or Bouguer kind. For some applications, such as the evaluation of topographical effects in gravimetric geoid computations, it is preferable or even necessary to use at least the spherical model of topography. In modelling the topographical effect, the bulk of the effect comes from the Bouguer plate, in the case of the planar model, or from the Bouguer shell, in the case of the spherical model. The difference between the effects of the Bouguer plate and the Bouguer shell is studied, while the effect of the rest of topography, the terrain, is discussed elsewhere. It is argued that the classical Bouguer plate gravity reduction should be considered as a mathematical construction with unclear physical meaning. It is shown that if the reduction is understood to be reducing observed gravity onto the geoid through the Bouguer plate/shell then both models give practically identical answers, as associated with Poincaré's and Prey's work. It is shown why only the spherical model should be used in the evaluation of topographical effects in the Stokes–Helmert solution of Stokes' boundary-value problem. The reason for this is that the Bouguer plate model does not allow for a physically acceptable condensation scheme for the topography. Received: 24 December 1999 / Accepted: 11 December 2000     

The development of an intervening opportunities model with spatial dominance effects

In this paper an intervening opportunities model with spatial dominance is developed. The usual assumption in spatial theory is that decision makers are influenced not just by the size of a destination or distance but by these two factors in combination, that is, spatial dominance. Decision-makers will have more knowledge about, and clearly perceive destinations that exert the greatest amount of spatial dominance on their origins, just as they would primate cities. Thus destinations are ranked in terms of the spatial dominance calculated for each destination. Empirical verification of the model utilizes state-to-state migration flow data for the US. Calibration results compare favourably with the traditional intervening opportunities model and the production constrained gravity model. Received: 7 October 1999/Accepted: 15 June 2000     

A review of algebraic constraints in terrestrial reference frame datum definition

 Station coordinates are combined with velocities estimated by space geodesy techniques to produce the International Terrestrial Reference System. The input is sets of coordinates and velocities calculated by International Earth Rotation Service analysis centers using space geodesy techniques. The working reference system of individual analysis centers is generally conventionally defined. However, the implications of such processing can have an effect on the resulting combined set. The problem of datum definition as a function of coordinate combinations is reviewed. In particular, the problem of minimum constraints is clearly emphasized and the reference system effect is defined. The goal is to build a process that could be used generally to remove uncertainties in the underlying coordinate system without disturbing the underlying information with additional unnecessary information. Received: 25 January 1999 / Accepted: 20 September 2000