Comparison of Lorenz and Charney–Phillips vertical discretisations for dynamics–boundary layer coupling. Part I: Steady states


  • D. Holdaway,

    Corresponding author
    1. College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK
    2. Goddard Earth Sciences Technology and Research, Universities Space Research Association, MD, USA
    3. Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, MD, USA
    • Code 610.1, Goddard Space Flight Center, Greenbelt, MD 20771, USA.
    Search for more papers by this author
  • J. Thuburn,

    1. College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK
    Search for more papers by this author
  • N. Wood

    1. Met Office, Exeter, UK
    Search for more papers by this author
    • The contribution of this author was written in the course of his employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.


Accurate coupling between the resolved-scale dynamics and the parametrised physics is essential for accurate modelling of the atmosphere. Previous emphasis has been on the temporal aspects of this so-called physics–dynamics coupling problem, with little attention on the spatial aspects. When designing a model for numerical weather prediction there is a choice for how to vertically arrange the predicted variables, namely the Lorenz and Charney–Phillips grids, and there is ongoing debate as to which is the optimal. The Charney–Phillips grid is considered good for capturing the potential vorticity dynamics and wave propagation, whereas the Lorenz grid is more suitable for conservation. However the Lorenz grid supports a computational mode. It is argued here that the Lorenz grid is preferred for modelling the stably stratified boundary layer. This presents the question: which grid will produce more accurate results when coupling the large-scale dynamics to the stably stratified planetary boundary layer? The question is addressed by examining the ability of both the Lorenz and Charney–Phillips grids to capture the steady state of a set of equations that simultaneously represents both large-scale dynamics and the planetary boundary layer. The results show that the Charney–Phillips grid is able to capture accurately the steady boundary-layer solution provided the Richardson number is calculated without vertically averaging the shear. Averaging the shear suppresses the negative feedback of the shear on the diffusion coefficient; the positive feedback, via the vertical gradient of potential temperature, then leads to the formation of unrealistic step-like features. Copyright © 2012 Royal Meteorological Society