This report presents the details of the governing equations, physical parameterizations, and numerical algorithms of SNUGCM (CES AGCM). The material provides an overview of the major model components, and the way in which they interact as the numerical integration proceeds. Details on the coding implementation, along with in-depth information. It is our objective that this model provide research community with a reliable, well documented atmospheric general circulation model.

 For the research of prediction to global climate, the work of establishing SNUGCM began at 1993.  After that time, the atmospheric radiation process of this model was changed, and many experiments havebeen performed using it. The AGCM that is used at present is a model which improves parameterization of physics process - land surface, deep convection, and we make progress in performance of model. We made a study of model developing, characteristics of physical parameterization, and climate researches like Asian monsoon. At present we are developing climate – environmental model by coupling land – ocean – atmosphere models.

  According to results of our experiments, it was proved that our model is superior to others and is suitable for research of global warming prediction and monsoon etc. In this background, we take the initiative in CLIVAR A-A/Monsoon Intercomparison Project. On the other hand, the works are going on establishing AGCM for improving deficiencies which are found by many kinds of simulation.

  Basic equation system of SNUGCM is three-dimension hydrostatic primitive equations on sphere with normalized pressure coordinate. Predictive variables of SNUGCM are horizontal velocity, temperature, surface pressure, specific humidity, cloud liquid water, soil temperature, soil moisture, and snow depth. AGCM is basically a program to solve the primitive equation set about atmospheric variables. The governing equation set are as following.


 Governing equation set consist of continuity equation, hydrostatic equation, momentum equation, thermodynamic equations and moisture equation. The equations are as following, you can click each terms to see how it is calculated.

  • Continuity equation: 

  • Hydrostatic equation:
  • Vorticity equation:
  • Divergence equation:
  • Thermodynamic equation:
  • Moisture equation:

where , is surface pressure, horizontal advection term is defined as following,


 , geopotential height, is dry air constant, is vertual temperature, vorticity is defined as ,



, ,

, divergence is defined as,


   is diffusion term of each variables, ,   is diabatic heating from physical process, is frictional heating, is source of constituents from physical process. Most of terms of those equations are calculated at dynamics routines.

The governing equations for the hydrostatic atmosphere

Letting (, ) denote the (longitude, latitude) coordinate, the momentum equations can be written in the vector-invariant form as follows:

where A is the radius of the earth, is the coefficient for the optional divergence damping, D is the horizontal divergence

and , the vertical component of the absolute vorticity, is defined as follows:

where is the angular velocity of the earth. Note that the last term in equation vanishes if the vertical coordinate is a conservative quantity (e.g., entropy under adiabatic conditions [Hsu and Arakawa, 1990] or an imaginary conservative tracer), and the 3D divergence operator becomes 2D along constant surfaces.

 Physics part of GCM calculate the forcing terms in governing equations. If you want to see the parameterizations of physical process of CES AGCM in detail, you can click each process. Just click figure.

   Parameterizations of each physical process are following.

1. Simplified Arakawa-Schubert cumulus convection scheme based on Relaxed Arakawa-Schubert scheme (Moorthi and Suarez, 1992).

2. Large-scale condensation scheme based on Letreut and Li(1991)

3. Diffusion-type Shallow Convection.

4. 2-stream k-distribution radiation scheme (Nakajima and Tanaka,1986).

5. Bonan's Land Surface Model (Bonan 1996).

6. Non-local PBL/Vertical diffusion (Holtslag and Boville 1993).

7. Orographic gravity-wave drag (McFarlane, 1987).

8. Dry adiabatic adjustment