The Diabatic Contour Advective Semi-Lagrangian Model

David G. Dritschel School of Mathematics and Statistics, University of St Andrews, St Andrews, United Kingdom

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Maarten H. P. Ambaum Department of Meteorology, University of Reading, Reading, United Kingdom

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Abstract

This article describes a novel algorithmic development extending the contour advective semi-Lagrangian model to include nonconservative effects. The Lagrangian contour representation of finescale tracer fields, such as potential vorticity, allows for conservative, nondiffusive treatment of sharp gradients allowing very high numerical Reynolds numbers. It has been widely employed in accurate geostrophic turbulence and tracer advection simulations. In the present, diabatic version of the model the constraint of conservative dynamics is overcome by including a parallel Eulerian field that absorbs the nonconservative (diabatic) tendencies. The diabatic buildup in this Eulerian field is limited through regular, controlled transfers of this field to the contour representation. This transfer is done with a fast newly developed contouring algorithm. This model has been implemented for several idealized geometries. In this paper a single-layer doubly periodic geometry is used to demonstrate the validity of the model. The present model converges faster than the analogous semi-Lagrangian models at increased resolutions. At the same nominal spatial resolution the new model is 40 times faster than the analogous semi-Lagrangian model. Results of an orographically forced idealized storm track show nontrivial dependency of storm-track statistics on resolution and on the numerical model employed. If this result is more generally applicable, this may have important consequences for future high-resolution climate modeling.

Corresponding author address: Prof. David G. Dritschel, Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, United Kingdom. Email: dgd@mcs.st-and.ac.uk

Abstract

This article describes a novel algorithmic development extending the contour advective semi-Lagrangian model to include nonconservative effects. The Lagrangian contour representation of finescale tracer fields, such as potential vorticity, allows for conservative, nondiffusive treatment of sharp gradients allowing very high numerical Reynolds numbers. It has been widely employed in accurate geostrophic turbulence and tracer advection simulations. In the present, diabatic version of the model the constraint of conservative dynamics is overcome by including a parallel Eulerian field that absorbs the nonconservative (diabatic) tendencies. The diabatic buildup in this Eulerian field is limited through regular, controlled transfers of this field to the contour representation. This transfer is done with a fast newly developed contouring algorithm. This model has been implemented for several idealized geometries. In this paper a single-layer doubly periodic geometry is used to demonstrate the validity of the model. The present model converges faster than the analogous semi-Lagrangian models at increased resolutions. At the same nominal spatial resolution the new model is 40 times faster than the analogous semi-Lagrangian model. Results of an orographically forced idealized storm track show nontrivial dependency of storm-track statistics on resolution and on the numerical model employed. If this result is more generally applicable, this may have important consequences for future high-resolution climate modeling.

Corresponding author address: Prof. David G. Dritschel, Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, United Kingdom. Email: dgd@mcs.st-and.ac.uk

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  • Ambaum, M. H. P., 1997: Isentropic formation of the tropopause. J. Atmos. Sci., 54 , 555568.

  • Dritschel, D. G., 1989: Contour dynamics and contour surgery: Numerical algorithms for extended, high-resolution modelling of vortex dynamics in two-dimensional, inviscid, incompressible flows. Comput. Phys. Rep., 10 , 77146.

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  • Dritschel, D. G., 1997: Introduction to “Contour dynamics for the Euler equations in two dimensions.”. J. Comput. Phys., 135 , 217219.

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  • Dritschel, D. G., and M. H. P. Ambaum, 1997: A contour-advective semi-Lagrangian algorithm for the simulation of fine-scale conservative fields. Quart. J. Roy. Meteor. Soc., 123 , 10971130.

    • Search Google Scholar
    • Export Citation
  • Dritschel, D. G., and M. H. P. Ambaum, 1998: The inclusion of non-conservative forcing into a conservative contour advection algorithm. Numerical Methods for Fluid Dynamics IV, M. J. Baines, Ed., ICFD, 99–110.

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    • Export Citation
  • Dritschel, D. G., and A. Viúdez, 2003: A balanced approach to modelling rotating stably-stratified geophysical flows. J. Fluid Mech., 488 , 123150.

    • Search Google Scholar
    • Export Citation
  • Dritschel, D. G., L. M. Polvani, and A. R. Mohebalhojeh, 1999: The contour-advective semi-Lagrangian algorithm for the shallow-water equations. Mon. Wea. Rev., 127 , 11511165.

    • Search Google Scholar
    • Export Citation
  • Enright, D., R. Fedkiw, J. Ferziger, and I. Mitchell, 2002: A hybrid particle level set method for improved interface capturing. J. Comput. Phys., 183 , 83116.

    • Search Google Scholar
    • Export Citation
  • Haynes, P. H., and M. E. McIntyre, 1987: On the evolution of vorticity and potential vorticity in the presence of diabatic heating and friction or other forces. J. Atmos. Sci., 44 , 828841.

    • Search Google Scholar
    • Export Citation
  • Norton, W. A., 1994: Breaking Rossby waves in a model stratosphere diagnosed by a vortex-following coordinate system and a technique for advecting material contours. J. Atmos. Sci., 51 , 654676.

    • Search Google Scholar
    • Export Citation
  • Smolarkiewicz, P. K., and J. A. Pudykiewicz, 1992: A class of semi-Lagrangian approximations for fluids. J. Atmos. Sci., 49 , 20822096.

    • Search Google Scholar
    • Export Citation
  • Waugh, D. W., and R. A. Plumb, 1994: Contour advection with surgery: A technique for investigating finescale structure in tracer transport. J. Atmos. Sci., 51 , 530540.

    • Search Google Scholar
    • Export Citation
  • Yao, H. B., D. G. Dritschel, and N. J. Zabusky, 1995: High-gradient phenomena in two-dimensional vortex interactions. Phys. Fluids, 7 , 539548.

    • Search Google Scholar
    • Export Citation
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