• can finite difference time derivatives
• write numerical form of your equations as a definition for the latest time level, with all earlier time levels on the right hand side of the eqn.
• after all variables are found at one time level, use them to define the next time level, when all the variables at the next level are defined use them for the next later time, etc.

• What eqns shall the model be based upon? PE? QG?
• How to approximate continuous derivatives (and maybe integrals)? What numerical method to use? Highly accurate or fast?
• Shall grid points or some other method (more on this below) be used?
• What spacing and orientation of the grid to use? as well as Will different variables be defined at different locations?
• Shall the domain be limited area or global in extent? How will boundary conditions be included?
• What vertical coordinate to use, and how you shall incorporate (or not) topography? Note the relative advantages and disadvantages:
  • height: easy to understand and visualize. But: eqns are complicated by following density differences, there are holes where mountains occur.
  • pressure: simplest continuity eqn. and obs are taken at constant P levels. But: there are holes around mountains, whose location varies in time.
  • potential temperature: adiabatic motion follows a "theta" surface. But: still have time dependent holes around topography and the surfaces are not very horizontal, but intersect the ground at locations that vary in time. Also, the eqns are more complicated.
  • "sigma" coordinates: these are coordinates that tend to follow the terrain. Eliminates the problem of topographic holes. But: eqns are more complicated: must add a prognostic eqn for surface pressure. There are numerical difficulties in steep terrain with the P gradient terms in the momentum eqns.

• Parameterization refers to empirical or simplified treatments of phenomena, especially to assess the impact of that phenomenon upon a model variable.
• Dynamics includes the adiabatic processes:
  • advection,
  • pressure gradient
  • Coriolis terms.
  • Might also include linear diffusion schemes here (a paramerization).
• Physics includes most diabatic processes. Examples include:
  • diffusion (horizontal & vertical)
  • dry convection (eliminate superadiabatic lapse rates)
  • radiation (shortwave -- solar; longwave -- terrestrial)
  • cloud processes (convective; "forced" or "stable lifing" -- from fronts or orography)
  • precipitation processes (convective, "forced" lifting)
  • surface exchange (momentum, heat, moisture)
  • things that affect the parameterizations, such as ocean surface temperature on surface exchange; sea-ice extent on radiation; etc.

• uses a hybrid vertical coordinate that is a compromise between following a constant P surface and a "sigma" coordinate that is parallel to the ground.
• limited area model centered on North America
• uses grid points
• has many physical parameterizations
• is intended for short range forecasts: 0-3 days

• uses "sigma" terrain following coordinate system
• domain covers whole globe
• uses spectral formulation (spherical harmonics)
• has many physical parameterizations
• is intended for aviation uses, especially flights across the oceans (AVN) and for medium range forecasts of 3-10 days (MRF).

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