Geography Reference
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u
u
p s
T, q
v
v
v
u
u
p s
T, q
v
v
u
u
u
p s
T, q
Fig. 13.5
Horizontal staggered grid arrangement in the ECMWF grid point model.
meridional and vertical directions. The continuity equation, for example, can then
be expressed in the form
a cos φ δ λ U
δ φ (V cos φ) +
∂p s
∂t +
1
+
δ σ (p s ˙
σ )
=
0
(13.51)
p s v and are horizontal mass fluxes (see Section
10.3.1). Due to the arrangement of variables on the staggered grid of Fig. 13.5, the
horizontal mass flux divergence evaluated by taking differences over the increments
δλ, δφ in (13.51) is centered at the point where p s is defined. This provides an
improvement on the accuracy possible with a nonstaggered grid in which these
differences would need to be evaluated over grid distances of 2δλ, 2δφ.
Grid staggering provides a similar gain in accuracy in computation of the pres-
sure gradient terms in the momentum equations. Thus,
p s u and V
where U
=
=
δ λ σ
∂u
∂t =
1
a cos φ
RT λ δ λ (ln p s )
+
+···
(13.52)
δ φ σ
∂v
∂t =−
1
a
RT φ δ φ (ln p s )
+
+···
(13.53)
 
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