Algorithms for geodesics

Karney, Charles F. F.

doi:10.1007/s00190-012-0578-z

Cited by 309 publications

(232 citation statements)

References 16 publications

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“…If a geolocation with spike (in latitude, longitude or at both) is found at a given t, the scheme computes the velocity at points adjacent to the spike using x(t −1) and x(t + 2) and x(t − 2) and x(t + 1) values for each border respectively. Distances should be computed with a WSG-84 ellipsoidal model of the Earth (i.e., Karney, 2013). However, given the high resolution of the transmitted data, the distance between consecutive points are rather small and therefore negligible differences in the computation of velocities are found using rather a spherical or planar approximation.…”

Section: Computing the Velocities And Cutting Time Seriesmentioning

confidence: 99%

The MEDESS-GIB database: tracking the Atlantic water inflow

Sotillo

Garcı́a-Ladona²,

Orfila

et al. 2016

Earth Syst. Sci. Data

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Abstract. On 9 September 2014, an intensive drifter deployment was carried out in the Strait of Gibraltar. In the frame of the MEDESS-4MS Project (EU MED Program), the MEDESS-GIB experiment consisted of the deployment of 35 satellite tracked drifters, mostly of CODE-type, equipped with temperature sensor sampling at a rate of 30 min. Drifters were distributed along and on both sides of the Strait of Gibraltar. The MEDESS-GIB deployment plan was designed as to ensure quasi-synoptic spatial coverage. To this end, four boats covering an area of about 680 NM 2 in 6 h were coordinated. As far as these authors know, this experiment is the most important exercise in the area in terms of number of drifters released. Collected satellite-tracked data along drifter trajectories have been quality controlled and processed to build the presented MEDESS-GIB database. This paper reports the MEDESS-GIB data set that comprises drifter trajectories, derived surface currents and in situ SST measurements collected along the buoys tracks. This series of data is available through the PANGAEA (Data Publisher for Earth and Environmental Science) repository, with the following

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Section: Computing the Velocities And Cutting Time Seriesmentioning

confidence: 99%

The MEDESS-GIB database: tracking the Atlantic water inflow

Sotillo

Garcı́a-Ladona²,

Orfila

et al. 2016

Earth Syst. Sci. Data

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“…The generalized algorithm can be applied for triaxial ellipsoids, biaxial ellipsoids, and spheres; it is particularly interesting to show how the general expressions are reduced in the biaxial case, as the geodesics are expressed in a parameterization other than geodetic coordinates. Finally, it would be interesting to generalize the biaxial ellipsoid solution from the (different) approaches of Sjöberg and Shirazian (2012a), Sjöberg (2012b) and Karney (2013) to the geodesic problem on a triaxial ellipsoid.…”

Section: Introductionmentioning

confidence: 99%

The geodesic boundary value problem and its solution on a triaxial ellipsoid

Πάνου

2013

Journal of Geodetic Science

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Abstract:The geodesic problem on a triaxial ellipsoid is solved as a boundary value problem, using the calculus of variations. The boundary value problem consists of solving a non-linear second order ordinary differential equation, subject to the Dirichlet conditions. Subsequently, this problem is reduced to an initial value problem with Dirichlet and Neumann conditions. The Neumann condition is determined iteratively by solving a system of four first-order ordinary differential equations with numerical integration. The last iteration yields the solution of the boundary value problem. From the solution, the ellipsoidal coordinates and the angle between the line of constant longitude and the geodesic, at any point along the geodesic, are determined. Also, the constant in Liouville's equation is determined and the geodesic distance between the two points, as an integral, is computed by numerical integration. To demonstrate the validity of the method presented here, numerical examples are given. The geodesic boundary value problem and its solution on a biaxial ellipsoid are obtained as a degenerate case.

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“…It has been brought to the attention of the publishers that certain sections of Tseng (2014) are remarkably similar to parts of Karney (2013) and have not been adequately attributed. In addition, some of the material from Karney (2013) has been incorrectly used.…”

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confidence: 99%

“…In addition, some of the material from Karney (2013) has been incorrectly used. The Editor-in-Chief of The Journal of Navigation and Cambridge University Press take an extremely serious view of any and all instances of plagiarism, no matter what the degree.…”

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confidence: 99%