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User Guide to ECMWF Forecast Products > The ECMWF forecasting and assimilation system > The ECMWF global atmospheric model > 
The model equations The rationale for high resolution  
   

The numerical formulation

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The model equations
The numerical formulation
The rationale for high resolution
Topographical and climatological fields
The formulation of physical processes
The land surface model
The ocean wave model
 
 

The model equations are discretized in space and time and solved numerically by a semi-Lagrangian advection scheme. It ensures stability and accuracy, while using as large time-steps as possible to progress the computation of the forecast within an acceptable time.

For the horizontal representation a dual representation of spectral components and grid points is used. All fields are described in grid point space. Due to the convergence of the meridians, computational time can be saved by applying a “reduced Gaussian grid”. This keeps the east-west separation between points almost constant by gradually decreasing the number of grid points towards the poles at every latitude in the extra-tropics. For the convenience of computing horizontal derivatives and to facilitate the time-stepping scheme, a spectral representation, based on a series expansion of spherical harmonics, is used for a subset of the prognostic variables.

The vertical resolution is finest in geometrical height in the planetary boundary layer and coarsest near the model top. The “σ-levels” follow the earth’s surface in the lower-most troposphere, where the Earth’s orogra­phy displays large variations. In the upper stratosphere and lower mesosphere they are surfaces of constant pressure with a smooth transition in between.




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The model equations The rationale for high resolution  
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