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Mathematics of Climate and Weather Forecasting

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Numerical simulations of the humid atmosphere above a mountain

Arthur Bousquet / Mickaël D. Chekroun
  • Corresponding author
  • Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA, USA
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/ Youngjoon Hong
  • Corresponding author
  • Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, IL, USA
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/ Roger M. Temam
  • Corresponding author
  • Temam: Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, Indiana, USA
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/ Joseph Tribbia
  • Corresponding author
  • Climate Dynamics and Predictability (CDP) section in the Division of Climate and Global Dynamics (CGD) at the National Center for Atmospheric Research (NCAR)
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Published Online: 2015-12-31 | DOI: https://doi.org/10.1515/mcwf-2015-0005


New avenues are explored for the numerical study of the two dimensional inviscid hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions for the system of equations. Flows above a mountain are classically treated by the so-called method of terrain following coordinate system. We avoid this discretization method which induces errors in the discretization of tangential derivatives near the topography. Instead we implement a first order finite volume method for the spatial discretization using the initial coordinates x and p. A compatibility condition similar to that related to the condition of incompressibility for the Navier- Stokes equations, is introduced. In that respect, a version of the projection method is considered to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. For the spatial discretization, a modified Godunov type method that exploits the discrete finite-volume derivatives by using the so-called Taylor Series Expansion Scheme (TSES), is then designed to solve the equations. We report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated.

Keywords: primitive equations; humidity; finite volume; phase change; projection method; stochastic parameterizations


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About the article

Received: 2015-07-23

Accepted: 2015-11-30

Published Online: 2015-12-31

Citation Information: Mathematics of Climate and Weather Forecasting, Volume 1, Issue 1, ISSN (Online) 2353-6438, DOI: https://doi.org/10.1515/mcwf-2015-0005.

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© 2015 Arthur Bousquet et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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