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A. A. White - One of the best experts on this subject based on the ideXlab platform.

  • Dynamical equivalence and the Departure‐Point equation in semi‐Lagrangian numerical models
    Quarterly Journal of the Royal Meteorological Society, 2020
    Co-Authors: A. A. White
    Abstract:

    The kinematics and Newtonian dynamics of a continuous fluid may be presented in a number of ways. Given the kinematic relation between velocity and position, the dynamics may be formulated in terms of momentum or in terms of angular momentum and the scalar product of velocity and position. It is also possible to carry out the formulation in terms of momentum, angular momentum and the scalar product of velocity and position, in which case the kinematic relation becomes a deducible property. The three formulations are dynamically equivalent in the sense that the flow evolution is demonstrably the same in each. It seems desirable to build this elementary symmetry into discrete models. Two-time-level, semi-Lagrangian models are considered here, with emphasis on the Departure-Point equation (from which trajectory origins at the earlier time-level are determined). Once a rule has been chosen for the approximation of trajectory time-averages of vector and scalar products, dynamical equivalence implies a particular form of the Departure-Point equation. One such rule delivers a doubly-implicit equation that is a simple time-centred discretization of the kinematic relation. A second rule leads to a form that differs only slightly from the singly-implicit equation of Gospodinov and co-workers. It is noted that dynamical equivalence relates to the consistency and non-ambiguity of results rather than to their accuracy. © Crown copyright, 2003. Royal Meteorological Society

  • a geometrical view of the shallow atmosphere approximation with application to the semi lagrangian Departure Point calculation
    Quarterly Journal of the Royal Meteorological Society, 2013
    Co-Authors: John Thuburn, A. A. White
    Abstract:

    The widely used shallow-atmosphere approximation is a geometrical approximation in which the metric departs from the usual Euclidean metric. This leads to a number of important consequences: shallow-atmosphere space is intrinsically curved (i.e. non-Euclidean), geodesics are not unique, the status of the centre of the Earth is uncertain, and position vectors are not well-defined. Vector semi-Lagrangian numerical models that use the shallow-atmosphere approximation must allow explicitly for the non-Euclidean geometry. During early testing of a new semi-implicit, semi-Lagrangian dynamical core, a semi-implicit (Crank–Nicolson) discretization of the vector Departure Point equation was found to lead to an instability in deep-atmosphere (i.e. Euclidean) geometry, but not in shallow-atmosphere geometry. The instability can be avoided by an alternative treatment in which the Departure Point equation is projected onto its horizontal and vertical components before discretization. Interestingly, this stable treatment of the deep-atmosphere case makes use of much of the mathematical machinery of the shallow-atmosphere Departure Point calculation. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

  • A geometrical view of the shallow‐atmosphere approximation, with application to the semi‐Lagrangian Departure Point calculation
    Quarterly Journal of the Royal Meteorological Society, 2012
    Co-Authors: John Thuburn, A. A. White
    Abstract:

    The widely used shallow-atmosphere approximation is a geometrical approximation in which the metric departs from the usual Euclidean metric. This leads to a number of important consequences: shallow-atmosphere space is intrinsically curved (i.e. non-Euclidean), geodesics are not unique, the status of the centre of the Earth is uncertain, and position vectors are not well-defined. Vector semi-Lagrangian numerical models that use the shallow-atmosphere approximation must allow explicitly for the non-Euclidean geometry. During early testing of a new semi-implicit, semi-Lagrangian dynamical core, a semi-implicit (Crank–Nicolson) discretization of the vector Departure Point equation was found to lead to an instability in deep-atmosphere (i.e. Euclidean) geometry, but not in shallow-atmosphere geometry. The instability can be avoided by an alternative treatment in which the Departure Point equation is projected onto its horizontal and vertical components before discretization. Interestingly, this stable treatment of the deep-atmosphere case makes use of much of the mathematical machinery of the shallow-atmosphere Departure Point calculation. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

  • dynamical equivalence and the Departure Point equation in semi lagrangian numerical models
    Quarterly Journal of the Royal Meteorological Society, 2003
    Co-Authors: A. A. White
    Abstract:

    The kinematics and Newtonian dynamics of a continuous fluid may be presented in a number of ways. Given the kinematic relation between velocity and position, the dynamics may be formulated in terms of momentum or in terms of angular momentum and the scalar product of velocity and position. It is also possible to carry out the formulation in terms of momentum, angular momentum and the scalar product of velocity and position, in which case the kinematic relation becomes a deducible property. The three formulations are dynamically equivalent in the sense that the flow evolution is demonstrably the same in each. It seems desirable to build this elementary symmetry into discrete models. Two-time-level, semi-Lagrangian models are considered here, with emphasis on the Departure-Point equation (from which trajectory origins at the earlier time-level are determined). Once a rule has been chosen for the approximation of trajectory time-averages of vector and scalar products, dynamical equivalence implies a particular form of the Departure-Point equation. One such rule delivers a doubly-implicit equation that is a simple time-centred discretization of the kinematic relation. A second rule leads to a form that differs only slightly from the singly-implicit equation of Gospodinov and co-workers. It is noted that dynamical equivalence relates to the consistency and non-ambiguity of results rather than to their accuracy. © Crown copyright, 2003. Royal Meteorological Society

A Mcdonald - One of the best experts on this subject based on the ideXlab platform.

E. Groten - One of the best experts on this subject based on the ideXlab platform.

  • The Celestial and Terrestrial Departure Points and their various aspects in geodesy and astrometry
    Studia Geophysica Et Geodaetica, 1994
    Co-Authors: E. Groten
    Abstract:

    Based on the 127th Colloquium Report of the subgroup on coordinate frames and origins of the IAU working group on reference systems, in this paper, the possibility of taking the Celestial Departure Point as the origin of right-ascension on the instantaneous true equator is analysed in view of high-precision geodesy and astrometry. The properties and the applications of the celestial and terrestrial Departure Points in various aspects of practice and theory are generally reviewed. We have found that, referred to the ideal barycentric reference system proposed in the 127th IAU Colloquium, the Celestial Departure Point of a Quasi-Inertial Geocentric Equatorial Coordinate System may be a matchable origin on the moving geocentric true equator.

  • Departure Point, Earth's Rate of Rotation and Coordinate Transformation in Quasi-Inertial Geocentric Equatorial Coordinate System (QIGECS)
    Symposium - International Astronomical Union, 1993
    Co-Authors: E. Groten
    Abstract:

    The paper summarizes the discussion on the origin of right-ascension and puts forward new arguments in view of high-precision Geodesy and Astrometry. From the movement of the Celestial Departure Point, the classical right-ascension precession might be amended by an additional term −0s.000257/century originating from the nutation-precession interaction movement. A similar term might also be introduced in the maintenance of a terrestrial reference system, while the concept of a Terrestrial Departure Point is considered. The definition of the Earth's rate of rotation in an inertial or quasi-inertial system is reviewed. A periodic erroneous term of maximum amplitude 2.65mas is Pointed out in the conventional transfer relation between CRS and TRS, that can for its main part be compensated by introducing the periodic terms of Woolard's equation of the equinox.

  • Departure Point, Earth’s Rate of Rotation and Coordinate Transformation in Quasi-Inertial Geocentric Equatorial Coordinate System (QIGECS)
    Developments in Astrometry and Their Impact on Astrophysics and Geodynamics, 1993
    Co-Authors: E. Groten
    Abstract:

    The paper summarizes the discussion on the origin of right-ascension and puts forward new arguments in view of high-precision Geodesy and Astrometry. From the movement of the Celestial Departure Point, the classical right-ascension precession might be amended by an additional term -0.S000257/century originating from the nutation-precession interaction movement. A similar term might also be introduced in the maintenance of a terrestrial reference system, while the concept of a Terrestrial Departure Point is considered. The definition of the Earth’s rate of rotation in an inertial or quasi-inertial system is reviewed. A periodic erroneous term of maximum amplitude 2.65mas is Pointed out in the conventional transfer relation between CRS and TRS, that can for its main part be compensated by introducing the periodic terms of Woolard’s equation of the equinox.

John Thuburn - One of the best experts on this subject based on the ideXlab platform.

  • a geometrical view of the shallow atmosphere approximation with application to the semi lagrangian Departure Point calculation
    Quarterly Journal of the Royal Meteorological Society, 2013
    Co-Authors: John Thuburn, A. A. White
    Abstract:

    The widely used shallow-atmosphere approximation is a geometrical approximation in which the metric departs from the usual Euclidean metric. This leads to a number of important consequences: shallow-atmosphere space is intrinsically curved (i.e. non-Euclidean), geodesics are not unique, the status of the centre of the Earth is uncertain, and position vectors are not well-defined. Vector semi-Lagrangian numerical models that use the shallow-atmosphere approximation must allow explicitly for the non-Euclidean geometry. During early testing of a new semi-implicit, semi-Lagrangian dynamical core, a semi-implicit (Crank–Nicolson) discretization of the vector Departure Point equation was found to lead to an instability in deep-atmosphere (i.e. Euclidean) geometry, but not in shallow-atmosphere geometry. The instability can be avoided by an alternative treatment in which the Departure Point equation is projected onto its horizontal and vertical components before discretization. Interestingly, this stable treatment of the deep-atmosphere case makes use of much of the mathematical machinery of the shallow-atmosphere Departure Point calculation. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

  • A geometrical view of the shallow‐atmosphere approximation, with application to the semi‐Lagrangian Departure Point calculation
    Quarterly Journal of the Royal Meteorological Society, 2012
    Co-Authors: John Thuburn, A. A. White
    Abstract:

    The widely used shallow-atmosphere approximation is a geometrical approximation in which the metric departs from the usual Euclidean metric. This leads to a number of important consequences: shallow-atmosphere space is intrinsically curved (i.e. non-Euclidean), geodesics are not unique, the status of the centre of the Earth is uncertain, and position vectors are not well-defined. Vector semi-Lagrangian numerical models that use the shallow-atmosphere approximation must allow explicitly for the non-Euclidean geometry. During early testing of a new semi-implicit, semi-Lagrangian dynamical core, a semi-implicit (Crank–Nicolson) discretization of the vector Departure Point equation was found to lead to an instability in deep-atmosphere (i.e. Euclidean) geometry, but not in shallow-atmosphere geometry. The instability can be avoided by an alternative treatment in which the Departure Point equation is projected onto its horizontal and vertical components before discretization. Interestingly, this stable treatment of the deep-atmosphere case makes use of much of the mathematical machinery of the shallow-atmosphere Departure Point calculation. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

Markus Waibel - One of the best experts on this subject based on the ideXlab platform.

  • personalized real time location based travel management
    2010
    Co-Authors: Jochen Mundinger, Markus Waibel
    Abstract:

    A personalized real-time location-based travel management method, the method including the steps of (a) defining a Departure Point and a destination for multimodal travel, (b) computing in an IT system (30) a list of candidate routes between said Departure Point and said destination, based on schedule information available to said IT system; (c) making travel information relating to a selected route available to a user's personal travel assistant (40) or a database (31) while traveling; and (d) detecting in said IT system an unexpected event during said travel, and computing an alternative list of candidate routes or routes segments in response to said unexpected event.

  • optimized route planning and personalized real time location based travel management
    2010
    Co-Authors: Jochen Mundinger, Markus Waibel
    Abstract:

    A method for optimized route planning for a user, including: (a) determining a Departure Point and a destination Point for multimodal travel; (b) based on said Departure Point and destination Point, computing and proposing criteria for restricting the number of candidate routes to consider, (c) proposing an updated list of candidate routes between said Departure Point and said destination Point, said updated list being either: i) automatically displayed after a delay, and/or: ii) based on user selection of said criteria.