Message-ID: <1329332887.745999.1552989188374.JavaMail.confluence@confluence-prod-00.ecmwf.int> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_745998_1581494088.1552989188374" ------=_Part_745998_1581494088.1552989188374 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Gaussian grids

# Naming convention

The Gaussian grids are defined by the quadrature points used to facilita= te the accurate numerical computation of the integrals involved in the Four= ier and Legendre transforms. The grids are labelled by N where N is the num= ber of latitude lines between the pole and the equator.  For example, = for the N=3D640 Gaussian grid, there are 640 lines of latitude between the = pole and the equator giving 1280 latitude lines in total.

The grid points in latitude, =CE=B8k , are given by = the zeros of the Legendre polynomial of order 2xN (i.e., the total number o= f latitude lines from pole to pole):  P 2N 0<= /sup> (=CE=BCk=3Dsin=CE=B8k) =3D 0<= em>.  A consequence of this is that a Gaussian grid has:

• latitude lines which are not equally spaced;
• no latitude points at the poles;
• no line of latitude at the equator;
• latitude lines which are symmetric about the equator.

# Regular (or full) Gaus= sian grid

A regular Gaussian grid has the following characteristics:

• there are 4N longitude points along each latitude circle;
• each latitude circle has a grid point at 0o longitude;
• the longitudinal resolution in degrees is 90o/N;
• the points get closer together (i.e. more crowded) as the latitude incr= eases towards the poles;
• the total number of grid points is 8N2.

# Reduced (or q= uasi-regular) Gaussian grid

A reduced Gaussian grid:

• has the same number of latitude lines (2N) as the corresponding regular= Gaussian grid;
• has a grid point at 0o longitude on each latitude circle;
• has a decreasing number of longitude points towards the poles;
• has a quasi-regular grid spacing in distance at each latitude;
• provides a uniform CFL (Courant=E2=80=93Friedrich= s=E2=80=93Lewy) condition.

Up to IFS cycle 41r1, ECMWF has used a original reduced Gaussian= grid.  This has 4N longitude points at the latitude nearest = to the equator, with the number of longitude points reducing in blocks as t= he latitudes approach the poles.

With the planned horizontal resolution increase, ECMWF introduces a slig= htly different form of the reduced Gaussian grid which is referred to as th= e octahedral reduced Gaussian grid or, more simply, the octahedral grid.

## Notation

The following notation is used when referring to the full (regular), ori= ginal reduced and octahedral reduced Gaussian grids:

• FXXX - full (regular) Gaussian grid with XXX latitude = lines between the pole and equator
• NXXX - original ECMWF reduced Gaussian grid with XXX l= atitude lines between the pole and equator
• OXXX - octahedral ECMWF reduced Gaussian grid with XXX= latitude lines between the pole and equator

## N80 original reduce= d Gaussian grid <= /span>

## O80 octahedral re= duced Gaussian grid 