The success rate and precision of GPS ambiguities

 An application of a theorem on the optimality of integer least-squares (LS) is described. This theorem states that the integer LS estimator maximizes the ambiguity success rate within the class of admissible integer estimators. This theorem is used to show how the probability of correct integer estimation depends on changes in the second moment of the ambiguity `float' solution. The distribution of the `float' solution is considered to be a member of the broad family of elliptically contoured distributions. Eigenvalue-based bounds for the ambiguity success rate are obtained. Received: 11 January 1999 / Accepted: 2 November 1999     

Modelling Watersheds as Spatial Object Hierarchies: Structure and Dynamics

The generation, transport and fate of non-point source pollutants in surface water systems is recognized as a major threat to water supplies, aquatic and coastal ecosystems. The transformation and movement of water, carbon and nutrients through watersheds integrates a set of ecosystem processes along hydrologic flowpaths. Human individual and institutional interactions with these processes involve direct addition or abstraction of these substances, or the alteration of land cover and drainage systems. In natural and developed catchments, these processes often vary at granularities ranging from below the level of a hillslope, up through regional watersheds. This suggests the need for the development of hierarchical analysis tools that can address the integration of a set of biophysical, biogeochemical and socioeconomic processes over a spectrum of scales. We describe and illustrate the use of a watershed model implemented as a spatial object hierarchy, representing successively contained landform classes associated with class specific processes as member functions. The model has been linked in a range of looser and tighter couplings with GRASS and ArcView, supplemented by specific terrain analytical functions. We illustrate the data and model system for an instrumented catchment monitored as part of the Baltimore Ecosystem Study (BES), a Long Term Ecological Research (LTER) site centering on integrated carbon, water and nutrient cycling.     

Small Format Digital Cameras for Aerial Survey: Where Are We Now?

This paper introduces the subject of digital sensors for aerial survey by reviewing the use made of small format digital cameras in such an application. The major advantages and disadvantages of employing such consumer technology for aerial survey are highlighted. Finally, a specification is proposed for a minimum requirement for a digital solution based on a single area array sensor.     

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     

Somigliana–Pizzetti gravity: the international gravity formula accurate to the sub-nanoGal level

 The Somigliana–Pizzetti gravity field (the International gravity formula), namely the gravity field of the level ellipsoid (the International Reference Ellipsoid), is derived to the sub-nanoGal accuracy level in order to fulfil the demands of modern gravimetry (absolute gravimeters, super conducting gravimeters, atomic gravimeters). Equations (53), (54) and (59) summarise Somigliana–Pizzetti gravity Γ(φ,u) as a function of Jacobi spheroidal latitude φ and height u to the order ?(10⁻¹⁰ Gal), and Γ(B,H) as a function of Gauss (surface normal) ellipsoidal latitude B and height H to the order ?(10⁻¹⁰ Gal) as determined by GPS (`global problem solver'). Within the test area of the state of Baden-Württemberg, Somigliana–Pizzetti gravity disturbances of an average of 25.452 mGal were produced. Computer programs for an operational application of the new international gravity formula with (L,B,H) or (λ,φ,u) coordinate inputs to a sub-nanoGal level of accuracy are available on the Internet. Received: 23 June 2000 / Accepted: 2 January 2001     

A model for adjustment of differential gravity measurements with simultaneous gravimeter calibration

 A mathematical model is proposed for adjustment of differential or relative gravity measurements, involving simultaneously instrumental readings, coefficients of the calibration function, and gravity values of selected base stations. Tests were performed with LaCoste and Romberg model G gravimeter measurements for a set of base stations located along a north–south line with 1750 mGal gravity range. This line was linked to nine control stations, where absolute gravity values had been determined by the free-fall method, with an accuracy better than 10 μGal. The model shows good consistence and stability. Results show the possibility of improving the calibration functions of gravimeters, as well as a better estimation of the gravity values, due to the flexibility admitted to the values of the calibration coefficients. Received: 15 November 1999 / Accepted: 31 October 2000     

Primary production and fluxes of organic carbon to the seabed in the Eurasian arctic seas, 2003–2012

The primary production and fluxes of organic matter to the seabed and their variations were estimated in the Greenland, Barents, Kara, Laptev, East Siberian, and Chukchi seas in 2003–2012 on the basis of satellite and in situ data. When counting the open water area with the assumptions made for the assessment of the primary production in the sea areas hidden under clouds, an increase in primary production was recorded in all these seas, the total production (phytoplankton and ice algae) has grown from 250 × 10⁶ to 400 × 10⁶ t of C per year over the last ten years. The calculation of the OM flux to the seabed showed growth for certain seas from 4 to 12% per year.