Geography Reference
In-Depth Information
The direction and magnitude of the
Q
vector at a given point on a weather map
can be estimated by referring the motion to a Cartesian coordinate system in which
the x axis is parallel to the local isotherm with cold air on the left. Then (6.51) can
be simplified to give
∂T
∂y
∂v
g
∂x
i
∂x
j
R
p
∂u
g
Q
=−
−
where we have again used the fact that ∂u
g
/∂x
∂v
g
/∂y. From the rules for
cross multiplication of unit vectors, the above expression for
Q
can be rewritten
as
=−
k
R
p
∂T
∂y
∂
V
g
∂x
Q
=−
×
(6.55)
Thus, the
Q
vector can be obtained by evaluating the vectorial change of
V
g
along the isotherm (with cold air on the left), rotating this change vector by 90˚
clockwise, and multiplying the resulting vector by
.
The
Q
vector, and hence the forcing of vertical motion, can be estimated with
the aid of (6.55) from observations of and T on a single isobaric surface. Exam-
ples for two simple cases, both of which have temperature decreasing toward the
north, are shown in Figs. 6.13 and 6.14. Figure 6.13 shows an idealized pattern of
cyclones and anticyclones in a slightly perturbed westerly thermal wind. Near the
center of the low, the geostrophic wind change moving eastward along the isotherm
(i.e., with cold air to the left) is from northerly to southerly. Thus the geostrophic
wind change vector points northward, and a 90
◦
clockwise rotation produces
a
Q
vector parallel to the thermal wind. In the highs, by the same reasoning,
the
Q
vectors are antiparallel to the thermal wind. The pattern of
|
∂T /∂y
|
∇·
Q
thus yields
descent in the region of cold air advection west of the trough, and ascent in the
warm air advection region east of the trough.
In the situation shown in Fig. 6.14, the geostrophic flow is confluent so that the
geostrophic wind increases eastward along the isotherms. In this case the vectorial
Fig. 6.13
Q
vectors (bold arrows) for an idealized pattern of isobars (solid) and isotherms (dashed)
for a family of cyclones and anticyclones. (After Sanders and Hoskins, 1990.)
