Ellipsoidal geoid computation

Modern geoid computation uses a global gravity model, such as EGM96, as a third component in a remove–restore process. The classical approach uses only two: the reference ellipsoid and a geometrical model representing the topography. The rationale for all three components is reviewed, drawing attention to the much smaller precision now needed when transforming residual gravity anomalies. It is shown that all ellipsoidal effects needed for geoid computation with millimetric accuracy are automatically included provided that the free air anomaly and geoid are calculated correctly from the global model. Both must be consistent with an ellipsoidal Earth and with the treatment of observed gravity data. Further ellipsoidal corrections are then negligible. Precise formulae are developed for the geoid height and the free air anomaly using a global gravity model, given as spherical harmonic coefficients. Although only linear in the anomalous potential, these formulae are otherwise exact for an ellipsoidal reference Earth—they involve closed analytical functions of the eccentricity (and the Earths spin rate), rather than a truncated power series in e². They are evaluated using EGM96 and give ellipsoidal corrections to the conventional free air anomaly ranging from –0.84 to +1.14 mGal, both extremes occurring in Tibet. The geoid error corresponding to these differences is dominated by longer wavelengths, so extrema occur elsewhere, rising to +766 mm south of India and falling to –594 mm over New Guinea. At short wavelengths, the difference between ellipsoidal corrections based only on EGM96 and those derived from detailed local gravity data for the North Sea geoid GEONZ97 has a standard deviation of only 3.3 mm. However, the long-wavelength components missed by the local computation reach 300 mm and have a significant slope. In Australia, for example, such a slope would amount to a 600-mm rise from Perth to Cairns.     

Wet tropospheric effects on precise relative GPS height determination

Summary Considerable interest has been generated recently in the use of the Global Positioning System (GPS) for precise height determination. A major error source in these measurements is the propagation delay due to atmospheric water vapour. In order to achieve the high precisions required for such applications as absolute sea-level monitoring improvement of wet delay modelling is necessary. Results from a GPS campaign show a significant correlation (0.91) between the variability of the wet delay measured using a water vapour radiometer (WVR) at the Onsala site and the absolute value of the residual error in the height determination of a 134 km baseline from Onsala to Jönköping. This correlation indicates that the atmosphericvariability as inferred from the WVR data includes information on the quality of the GPS height estimate. During periods of high atmospheric activity, e.g., during the passage of a weather front, the use of a six-parameter gradient model reduces the spread for the vertical coordinate from 40 mm to 20 mm (with standard deviations of 17 mm and 9 mm respectively) over the 134 km baseline (less than 1 × 10^–7) using 8 hour data spans on 11 different days over a six month period.     

Assessing the Resolving Power of Photographic Systems Used forTerrestrial Remote Sensing

It is often necessary to measure the resolving power of an imaging system comprising "off the shelf" components by a method that can also describe resolution in the object space. Furthermore, the results should allow useful comparisons to be made with alternative systems, where these have undergone a similar evaluation procedure. An example is given of measuring the resolving power of two imaging systems employing catadioptric objectives by a method that does not necessitate extensive laboratory tests, but utilizes the photographic product provided through field trials, or in the course of operational use. While the method reported does not claim to be a rigorous evaluation of the resolving power, it has been found to provide a convenient and practical guide to the image quality associated with a complete camera system, and its relation to the object space.     

Response of GPS occultation signals to atmospheric gravity waves and retrieval of gravity wave parameters

We show that the amplitude of the Global Positioning System (GPS) signals in the radio occultation (RO) experiments is an indicator of the activity of the gravity waves (GW) in the atmosphere. The amplitude of the GPS RO signals is more sensitive to the atmospheric wave structures than is the phase. Early investigations used only the phase of the GPS occultation signals for statistical investigation of the GW activity in the height interval 10–40 km on a global scale. In this study, we use the polarization equations and Hilbert transform to find the 1-D GW radio image in the atmosphere by analyzing the amplitude of the RO signal. The radio image, also called the GW portrait, consists of the phase and amplitude of the GW as functions of height. We demonstrate the potential of this method using the amplitude data from GPS/Meteorology (GPS/MET) and satellite mission Challenge Mini-satellite Payload (CHAMP) RO events. The GW activity is nonuniformly distributed with the main contribution associated with the tropopause and the secondary maximums related to the GW breaking regions. Using our method we find the vertical profiles of the horizontal wind perturbations and its vertical gradient associated with the GW influence. The estimated values of the horizontal wind perturbations are in fairly good agreement with radiosonde data. The horizontal wind perturbations v(h) are ±1 to ±5 m s with vertical gradients dv/dh ±0.5 to ±15 m s km at height 10–40 km. The height dependence of the GW vertical wavelength was inferred through the differentiation of the GW phase. Analysis of this dependence using the dispersion relationship for the GW gives the estimation of the projection of the horizontal background wind velocity on the direction of the GW propagation. For the event considered, the magnitude of this projection changes between 1.5 and 10 m s at heights of 10–40 km. We conclude that the amplitude of the GPS occultation signals contain important information about the wave processes in the atmosphere on a global scale.     

A Framework and Software Tool to Support Collaborative Landscape Analysis: Fitting Square Pegs into Square Holes

For landscape models to be applied successfully in management situations, models must address appropriate questions, include relevant processes and interactions, be perceived as credible and involve people affected by decisions. We propose a framework for collaborative model building that can address these issues, and has its roots in adaptive management, computer‐supported collaborative work and landscape ecology. Models built through this framework integrate a variety of information sources, address relevant questions, and are customized for the particular landscape and policy environment under study. Participants are involved in the process from the start, and because their input is incorporated, they feel ownership of the resulting models, increasing the chance of model acceptance and application. There are two requirements for success: a tool that supports rapid model prototyping and modification, that makes a clear link between a conceptual and implemented model, and that has the ability to implement a wide range of model types; and a core team with skills in communication, research and analysis, and knowledge of ecology and forestry in addition to modelling. SELES (Spatially Explicit Landscape Event Simulator) is a tool for building and running models of landscape dynamics. It combines discrete event simulation with a spatial database and a relatively simple modelling language to allow rapid development of landscape simulations, and provides a high‐level means of specifying complex model behaviours ranging from management actions to natural disturbance and succession. We have applied our framework in several forest modelling projects in British Columbia, Canada. We have found that this framework increases the interest by local experts and decision‐makers to participate actively in the model building process. The workshop process and resulting models have efficiently provided insight into the dynamics of large landscapes over long time frames. The use of SELES has facilitated this process by providing a flexible, transparent environment in which models can be rapidly implemented and refined. As a result, model findings may be more readily incorporated into decision‐support systems designed to assist resource managers in making informed decisions.     

Precise Real-Time Positioning in WADGPS Networks

In recent years the importance of real-time positioning and navigation with the Global Positioning System (GPS) has grown rapidly. Starting from the establishment of differential GPS (DGPS) reference stations for marine and land navigation, new users and applications have emerged that resulted in a high demand for the establishment of a high-density network of reference stations around the world. Many countries have established their own DGPS service, which is either governmentally or commercially owned. These services are referred to as Local Area DGPS Systems (LADGPS). However, the costs for the establishment and maintenance of a dense network of reference stations are very high. Therefore Wide Area DGPS Systems (WADGPS) are being developed to overcome the main drawbacks of LADGPS. In this case, only a few reference stations are used to cover a large area, such s a continent like Europe. To achieve high positioning accuracies, real-time modeling of the main error sources for long-range baselines is required as errors in the satellite orbit and ionospheric refraction do not cancel entirely in double differencing. In this article, a real-time correction model based on the Kalman filter for WADGPS and networked LADGPS services is discussed and results of field tests in a WADGPS network in Europe are presented. ? 2000 John Wiley & Sons, Inc.     

From GPS and GLONASS via EGNOS to Galileo – Positioning and Navigation in the Third Millennium

Positioning and navigation – as are presently possible with the American Global Positioning System (GPS) and the Russian GLONASS system – is briefly reviewed. Deficiencies, which have led to augmentations like the European Geostationary Navigation Overlay System (EGNOS), are outlined. Europe's decision to get involved in the definition and possible set-up of a Global Navigation Satellite System (GNSS) of the second generation (GNSS-2), called Galileo, is discussed in detail as well as the GPS modernization program that might take place during the sample phase. Finally, some brief thoughts on the benefit of GNSS-2 for geodesy and surveying are given. ? 2000 John Wiley & Sons, Inc.     

Integer estimation in the presence of biases

 Carrier phase ambiguity resolution is the key to fast and high-precision GNSS (Global Navigation Satellite System) kinematic positioning. Critical in the application of ambiguity resolution is the quality of the computed integer ambiguities. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. Very high success rates are therefore required for ambiguity resolution to be reliable. Biases which are unaccounted for will lower the success rate and thus increase the chance of unsuccessful ambiguity resolution. The performance of integer ambiguity estimation in the presence of such biases is studied. Particular attention is given to integer rounding, integer bootstrapping and integer least squares. Lower and upper bounds, as well as an exact and easy-to-compute formula for the bias-affected success rate, are presented. These results will enable the evaluation of the bias robustness of ambiguity resolution. Received: 28 September 2000 / Accepted: 29 March 2001