Geography Reference
In-Depth Information
the motion is measured by the small difference between the two terms
−
f
k
×
V
and
. Although the field can be determined observationally with quite
good accuracy, observed winds are often 10-20% in error. Such observational
errors inevitably affect the objectively analyzed fields, even though a suitable
analysis procedure may be able to reduce the magnitude of the errors. Never-
theless, using the objectively analyzed winds in initial data can easily lead to an
estimate of the Coriolis force that is 10% in error at the initial time. Because the
acceleration is normally only about 10% of the Coriolis force in magnitude, an
acceleration computed using the observed wind and geopotential fields will gener-
ally be 100% in error. Such spurious accelerations not only lead to poor estimates
of the initial pressure and velocity tendencies, but also tend to produce large-
amplitude gravity wave oscillations as the flow attempts to adjust from the initial
unbalanced state back toward a state of quasi-geostrophic balance. These strong
gravity waves are not present on the synoptic scale in nature, and their presence
in the solution of the model equations quickly spoils any chance of a reasonable
forecast.
One possible approach to avoid this problem might be to neglect the observed
wind data and derive a wind field from the observed field as part of the objective
analysis process. The simplest scheme of this type would be to assume that the
initial wind field was in geostrophic balance. However, the error in the computed
initial local acceleration would still be
−
∇
100%. This can be seen by considering
the example of zonally symmetric balanced flow about a circularly symmetric
pressure system in a model with constant f . In that case ∂
V
/∂t
∼
0 so that if we
neglect the effects of vertical advection the flow is in gradient wind balance (see
Section 3.2.4). In vectorial form this balance is simply
=
(
V
·∇
)
V
+
f
k
×
V
=−
∇
(13.55)
However, if
V
were replaced by
V
g
in (13.55), the Coriolis and pressure gradient
forces would identically balance. Thus, the inertial force would be unbalanced and
(∂
V
/∂t)
t
=
0
≈−
V
g
·∇
V
g
(13.56)
Therefore, by assuming that initially the wind is in geostrophic balance, rather than
gradient balance, we compute a local acceleration that is completely erroneous!
It should now be clear that in order to avoid large errors in the initial accel-
eration, the initial wind field in the above example should be determined by the
gradient wind balance, not by the geostrophic approximation or direct observa-
tions. The gradient wind formula (3.15) is not in itself a suitable balance condition
to use because the radius of curvature must be computed for parcel trajectories.
An appropriate balance condition (which is equivalent to the gradient wind in the
special case of stationary circularly symmetric flow) can be obtained by taking
