A bilinear approximation of the surface relief in terrain correction computations

A new method is presented for the computation of the gravitational attraction of topographic masses when their height information is given on a regular grid. It is shown that the representation of the terrain relief by means of a bilinear surface not only offers a serious alternative to the polyhedra modeling, but also approaches even more smoothly the continuous reality. Inserting a bilinear approximation into the known scheme of deriving closed analytical expressions for the potential and its first-order derivatives for an arbitrarily shaped polyhedron leads to a one-dimensional integration with – apparently – no analytical solution. However, due to the high degree of smoothness of the integrand function, the numerical computation of this integral is very efficient. Numerical tests using synthetic data and a densely sampled digital terrain model in the Bavarian Alps prove that the new method is comparable to or even faster than a terrain modeling using polyhedra.     

The impact of accelerometry on CHAMP orbit determination

 The contribution of the STAR accelerometer to the CHAMP orbit precision is evaluated and quantified by means of the following results: orbital fit to the satellite laser ranging (SLR) observations, GPS reduced-dynamic vs SLR dynamic orbit comparisons, and comparison of the measured to the modeled non-gravitational accelerations (atmospheric drag in particular). In each of the four test periods in 2001, five CHAMP arcs of 2 days' length were analyzed. The mean RMS-of-fit of the SLR observations of the orbits computed with STAR data or the non-gravitational force model were 11 and 24 cm, respectively. If the accelerometer calibration parameters are not known at least at the few percent level, the SLR orbit fit deteriorates. This was tested by applying a 10% error to the along-track scale factor of the accelerometer, which increased the SLR RMS-of-fit on average to 17 cm. Reference orbits were computed employing the reduced-dynamic technique with GPS tracking data. This technique yields the most accurate orbit positions thanks to the estimation of a large number of empirical accelerations, which compensate for dynamic modeling errors. Comparison of the SLR orbits, computed with STAR data or the non-gravitational force model, to the GPS-based orbits showed that the SLR orbits employing accelerometer observations are twice as accurate. Finally, comparison of measured to modeled accelerations showed that the level of geomagnetic activity is highly correlated with the atmospheric drag model error, and that the largest errors occur around the geomagnetic poles. Received: 7 May 2002 / Accepted: 18 November 2002 Correspondence to: S. Bruinsma Acknowledgments. The TIGCM results were obtained from the CEDAR database. This study was supported by the Centre National d'Etudes Spatiales (CNES). The referees are thanked for their helpful remarks and suggestions.     

Geoid determination using adapted reference field, seismic Moho depths and variable density contrast

 The traditional remove-restore technique for geoid computation suffers from two main drawbacks. The first is the assumption of an isostatic hypothesis to compute the compensation masses. The second is the double consideration of the effect of the topographic–isostatic masses within the data window through removing the reference field and the terrain reduction process. To overcome the first disadvantage, the seismic Moho depths, representing, more or less, the actual compensating masses, have been used with variable density anomalies computed by employing the topographic–isostatic mass balance principle. In order to avoid the double consideration of the effect of the topographic–isostatic masses within the data window, the effect of these masses for the used fixed data window, in terms of potential coefficients, has been subtracted from the reference field, yielding an adapted reference field. This adapted reference field has been used for the remove–restore technique. The necessary harmonic analysis of the topographic–isostatic potential using seismic Moho depths with variable density anomalies is given. A wide comparison among geoids computed by the adapted reference field with both the Airy–Heiskanen isostatic model and seismic Moho depths with variable density anomaly and a geoid computed by the traditional remove–restore technique is made. The results show that using seismic Moho depths with variable density anomaly along with the adapted reference field gives the best relative geoid accuracy compared to the GPS/levelling geoid. Received: 3 October 2001 / Accepted: 20 September 2002 Correspondence to: H.A. Abd-Elmotaal     

A study on the combination of satellite, airborne, and terrestrial gravity data

Satellite gravity missions, such as CHAMP, GRACE and GOCE, and airborne gravity campaigns in areas without ground gravity will enhance the present knowledge of the Earths gravity field. Combining the new gravity information with the existing marine and ground gravity anomalies is a major task for which the mathematical tools have to be developed. In one way or another they will be based on the spectral information available for gravity data and noise. The integration of the additional gravity information from satellite and airborne campaigns with existing data has not been studied in sufficient detail and a number of open questions remain. A strategy for the combination of satellite, airborne and ground measurements is presented. It is based on ideas independently introduced by Sjöberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions. In addition, the original approach of Sjöberg and Wenzel is extended to more than two measurement types, combining the Meissl scheme with the least-squares spectral combination. Satellite (or geopotential) harmonics, ground gravity anomalies and airborne gravity disturbances are used as measurement types, but other combinations are possible. Different error characteristics and measurement-type combinations and their impact on the final solution are studied. Using simulated data, the results show a geoid accuracy in the centimeter range for a local test area.     

Two different methods of geoidal height determinations using a spherical harmonic representation of the geopotential, topographic corrections and the height anomaly–geoidal height difference

 It is suggested that a spherical harmonic representation of the geoidal heights using global Earth gravity models (EGM) might be accurate enough for many applications, although we know that some short-wavelength signals are missing in a potential coefficient model. A `direct' method of geoidal height determination from a global Earth gravity model coefficient alone and an `indirect' approach of geoidal height determination through height anomaly computed from a global gravity model are investigated. In both methods, suitable correction terms are applied. The results of computations in two test areas show that the direct and indirect approaches of geoid height determination yield good agreement with the classical gravimetric geoidal heights which are determined from Stokes' formula. Surprisingly, the results of the indirect method of geoidal height determination yield better agreement with the global positioning system (GPS)-levelling derived geoid heights, which are used to demonstrate such improvements, than the results of gravimetric geoid heights at to the same GPS stations. It has been demonstrated that the application of correction terms in both methods improves the agreement of geoidal heights at GPS-levelling stations. It is also found that the correction terms in the direct method of geoidal height determination are mostly similar to the correction terms used for the indirect determination of geoidal heights from height anomalies. Received: 26 July 2001 / Accepted: 21 February 2002     

GPS network monitors the Western Alps' deformation over a five-year period: 1993–1998

  The Western Alps are among the best studied collisional belts with both detailed structural mapping and also crustal geophysical investigations such as the ECORS and EGT seismic profile. By contrast, the present-day kinematics of the belt is still largely unknown due to small relative motions and the insufficient accuracy of the triangulation data. As a consequence, several tectonic problems still remain to be solved, such as the amount of N–S convergence in the Occidental Alps, the repartition of the deformation between the Alpine tectonic units, and the relation between deformation and rotation across the Alpine arc. In order to address these problems, the GPS ALPES group, made up of French, Swiss and Italian research organizations, has achieved the first large-scale GPS surveys of the Western Alps. More than 60 sites were surveyed in 1993 and 1998 with a minimum observation of 3 days at each site. GPS data processing has been done by three independent teams using different software. The different solutions have horizontal repeatabilities (N–E) of 4–7 mm in 1993 and 2–3 mm in 1998 and compare at the 3–5-mm level in position and 2-mm/yr level in velocity. A comparison of 1993 and 1998 coordinates shows that residual velocities of the GPS marks are generally smaller than 2 mm/yr, precluding a detailed tectonic interpretation of the differential motions. However, these data seem to suggest that the N–S compression of the Western Alps is quite mild (less than 2 mm/yr) compared to the global convergence between the African and Eurasian plate (6 mm/yr). This implies that the shortening must be accomodated elsewhere by the deformation of the Maghrebids and/or by rotations of Mediterranean microplates. Also, E–W velocity components analysis supports the idea that E–W extension exists, as already suggested by recent structural and seismotectonic data interpretation. Received: 27 November 2000 / Accepted: 17 September 2001     

LightSquared effects on estimated C/N 0, pseudoranges and positions

We present experimental results showing the impact of the proposed LightSquared (LS) Long-term Evolution (LTE) signals on both GPS and Galileo civil modulations in the L1/E1 band. The experiments were conducted in radiated mode in a large anechoic chamber. Three Galileo enabled receivers were chosen for the tests, and a state of the art GNSS signal generator was used to simulate both GPS and Galileo signals. The LTE signals were generated by an Agilent Programmable Signal Generator with a license to generate the signals according to the 3GPP LTE FDD standard. The interference impact was measured in terms of a Carrier-to-Noise power spectral density ratio (C/N ₀) degradation, in accordance with the methodology which the LS/GPS Technical Working Group (TWG) established by mandate of the FCC. A model for determining the impact of the LS signal on the considered GNSS signals is provided and is validated against experimental data. It is shown that the Galileo E1 Open Service (OS) signal is marginally more susceptible to this form of interference than the GPS L1 C/A signal due to its greater proximity to the lower edge of the L1 band. The impact of LS interference was further analyzed in terms of pseudorange and position errors. Despite its relevance for most GNSS users, this aspect was not considered by the TWG. Measurement and position domain analysis along with the study of the LS impact on the Galileo OS signals are the major contributions. The analysis confirms the results obtained by the TWG and shows that the receiver front-end plays a major role in protecting GNSS signals against RF interference. While it appears that, for now, the LS network will not be deployed, the approach taken and the results obtained herein can be readily adapted for any future terrestrial mobile network that may take the place of LS.     

Hedonic price models with omitted variables and measurement errors: a constrained autoregression–structural equation modeling approach with application to urban Indonesia

Omitted variables and measurement errors in explanatory variables frequently occur in hedonic price models. Ignoring these problems leads to biased estimators. In this paper, we develop a constrained autoregression–structural equation model (ASEM) to handle both types of problems. Standard panel data models to handle omitted variables bias are based on the assumption that the omitted variables are time-invariant. ASEM allows handling of both time-varying and time-invariant omitted variables by constrained autoregression. In the case of measurement error, standard approaches require additional external information which is usually difficult to obtain. ASEM exploits the fact that panel data are repeatedly measured which allows decomposing the variance of a variable into the true variance and the variance due to measurement error. We apply ASEM to estimate a hedonic housing model for urban Indonesia. To get insight into the consequences of measurement error and omitted variables, we compare the ASEM estimates with the outcomes of (1) a standard SEM, which does not account for omitted variables, (2) a constrained autoregression model, which does not account for measurement error, and (3) a fixed effects hedonic model, which ignores measurement error and time-varying omitted variables. The differences between the ASEM estimates and the outcomes of the three alternative approaches are substantial.     

Watershed Delineation in Flat Terrain of Thar Desert Region in North West India – A Semi Automated Approach Using DEM

Thar desert spreads in western part of Rajasthan, northern part of Gujarat, and some parts of Punjab and Haryana. The terrain is dominated by slightly sloping plains, broken by some dunes and low barren hills. The area is characterized by low average annual rainfall which is erratic in distribution and intensity. Drought will remain a major hindrance for agricultural production in Thar desert. Due to water stress condition, many watershed based development activities has been adopted by government and non-government organizations for the growth and sustainable development of this region. The need of this hour is preparation of a national level watershed atlas of 1:50,000 scale because majority of thematic maps are being produced presently on same or 1:10,000 scale. The manual delineation of watershed boundary in flat terrain based on topographic map will be time consuming and less accurate in the absence of prominent contour lines. Automated approach for watershed delineation using Digital Elevation Model (DEM) along a suitable algorithm has the advantage because the output is not only less time consuming but also independent from human decisions. Hence, a case study has been carried out in Churu sub-basin part of Indus basin which is located in Thar desert region. Depression less DEM with different spatial resolutions was used as input in hydrology tool of ArcGIS spatial analyst function for characterization of watersheds. The Churu sub-basin has been divided into various numbers of watersheds with an average size of 600 km². These watershed boundaries have been validated with respect to high resolution satellite imageries (IRS P6 LISS IV), Survey of India toposheets, ancillary data and limited field checks.     

Land Cover Mapping for Namdapha National Park (Arunachal Pradesh), India Using Harmonized Land Cover Legends

Since last few decades RS-GIS is playing vital role in studying and mapping spatiotemporal responses of land cover, however, as a matter of fact, the mapping outputs largely depend on the expert's/user's preferences because location specific and people specific land cover classification systems are adopted autonomously for image classification in GIS. This may actually lead to an ambiguous definition of a particular land cover type when such different maps are compared at global level. In 1993, FAO and UNEP started efforts for development of a software tool know as LCCS which is a comprehensive standardized tool capable of providing land cover characterization to all possible land cover types in the world regardless of spatial relevance, mapping scale, data collection method etc. Adding to the global efforts of land cover legend harmonization and mapping, this study presents development of harmonized land cover legends for Namdapha National Park located in north-eastern Indian Himalayan region using LCCS and subsequent mapping. The potential of Remote Sensing (RS) and Geographical Information Systems (GIS) in forest/land cover mapping is very well recognized. Therefore, adopting the developed harmonized legends for the study area, land cover mapping was done using RS-GIS approach.