In general, models cannot represent spatial variability on scales smaller than those defined by the spacing between the discrete points, the grid scale.  Model values represent values at the discrete grid points.  However, each grid point is associated with an area that either surrounds that grid point or in an area that lies between the grid points.  This area is referred to as the "grid box".

Grid point values cannot properly represent variability on spatial scales smaller than the grid box and in fact the effective resolution of models is somewhat larger than the grid scale.  

Horizontal resolution

A dual representation of spectral components and grid points is used.  All fields are described in grid point space.  The grid is not completely uniform due to the convergence of the meridians towards the poles, and a Reduced Gaussian Octahedral Grid (Fig2111.A) is used.  This means the separation between grid points is kept almost constant by gradually decreasing the number of grid points towards the poles at all extra-tropical latitudes.  In effect, within each quadrant, two grid boxes (triangles) are removed as one steps away from the equator to the next latitude row.  This equates to a reduction of one grid point per quadrant per latitude row.  This grid point configuration results in a saving in computational time.

Many prognostic variables are evaluated and calculated on the grid.  However, a subset of prognostic variables (surface pressure, temperature, winds and moisture) are calculated using a spectral representation.  This is for the convenience of computing horizontal derivatives and to assist effectiveness in the time-stepping scheme.  Cloud variables are not transformed into spectral space.

The IFS medium range ensemble and HRES use a Gaussian grid (O1280) which has 1280 latitude lines between pole and equator with the number of grid points on each latitude line rising from 20 near the poles to 5136 near the equator giving a resolution of about 9km.  Both the 10 day and 15 day ensembles use this grid. 

The IFS extended range ensemble uses a Gaussian grid (O320) which has 320 latitude lines between pole and equator with the number of grid points on each latitude line rising from 20 near the poles to 1296 near the equator giving a resolution of about 36km.

The IFS seasonal ensemble (SEAS5) uses a Gaussian grid (O320) which has 320 latitude lines between pole and equator with the number of grid points on each latitude line rising from 20 near the poles to 1296 near the equator giving a resolution of about 36km.

(In addition to using grid points, the ECMWF Integrated Forecasting System (IFS) also uses an additional mathematical concept, spectral space, to represent horizontal space. This concept uses a set of wavy basis functions, spherical harmonics, to describe variations in the horizontal. The IFS switches between spectral space and grid point space, in order to perform specific computations.)

Vertical resolution

The vertical resolution varies with geometric height.  The vertical resolution is greatest (most fine) in the planetary boundary layer while more coarse near the model top.  The “σ-levels” follow the earth’s surface in the lower layers of the troposphere, where the Earth’s orography has large variations, but in the upper stratosphere and lower mesosphere they are surfaces of constant pressure.  There is a smooth transition from “σ-levels” to pressure levels between lower and upper levels.

  • The IFS HRES, ENS and Extended Range ENS models have 137 levels in the vertical; the four lowest levels are at 10m, 31m, 54m, 79m above the model surface.
  • The IFS Seasonal model has 91 levels in the vertical; the four lowest levels are at 10m, 34m ,68m, 112m above the model surface.

The heights approximate to geopotential heights, but are referenced to the surface pressure (not mean sea level).  For correct geopotential height with respect to mean sea level the height of the orography must be added.


 

Fig2.1.1.1-1: The Reduced Gaussian Octahedral Grid used by IFS.  Broadly, it is derived from a projection from an enclosing octahedron onto the earth.  A reasonably consistent grid spacing (dx) is maintained, even towards the poles. The apex of the octahedron is truncated.  Colours on the globe show the resolution of the grid. 


Fig2.1.1.1-2: The 137 level configuration used in HRES, ENS and Extended Range configurations.   Sigma levels are terrain-following at lower levels and become constant pressure levels for the upper troposphere and above.


Fig2.1.1.1-3: The 91 level configuration used in the Seasonal configuration.   Sigma levels are terrain-following at lower levels and become constant pressure levels for the upper troposphere and above.

Additional Sources of Information

(Note: In older material there may be references to issues that have subsequently been addressed)