Geography Reference
In-Depth Information
The cooling due to vertical advection of the basic state potential temperature
(usually called the adiabatic cooling) has a typical magnitude of
w
T
θ
0
dθ
0
dz
4
◦
Cd
-1
=
w (
d
−
)
∼
1cms
−
1
and
d
−
where w
∼
, the difference between dry adiabatic and actual
4˚C km
−
1
.
Thus, in the absence of strong diabatic heating, the rate of change of the per-
turbation potential temperature is equal to the adiabatic heating or cooling due to
vertical motion in the statically stable basic state, and (2.53) can be approximated as
∂θ
∂t
+
lapse rates, is
∼
u
∂θ
v
∂θ
∂y
w
dθ
0
∂x
+
+
dz
≈
0
(2.54)
Alternatively, if the temperature field is divided into a basic state T
0
(z) and a devi-
ation T (x, y, z, t), then since θ
θ
0
≈
T
T
0
, (2.54) can be expressed to the same
order of approximation in terms of temperature as
∂T
∂t
+
u
∂T
v
∂T
∂y
∂x
+
+
w (
d
−
)
≈
0
(2.55)
PROBLEMS
2.1.
A ship is steaming northward at a rate of 10 km h
−
1
.The surface pressure
increases toward the northwest at the rate of 5 Pa km
−
1
. What is the pressure
tendency recorded at a nearby island station if the pressure aboard the ship
decreases at a rate of 100 Pa/3 h?
2.2.
The temperature at a point 50 km north of a station is 3˚C cooler than at the
station. If the wind is blowing from the northeast at 20 m s
−
1
and the air is
being heated by radiation at the rate of 1˚C h
−
1
, what is the local temperature
change at the station?
2.3.
Derive the relationship
2
R
×
(
×
r
)
=−
which was used in Eq. (2.7).
2.4.
Derive the expression given in Eq. (2.13) for the rate of change of
k
following
the motion.
2.5.
Suppose a 1-kg parcel of dry air is rising at a constant vertical velocity. If
the parcel is being heated by radiation at the rate of 10
−
1
Wkg
−
1
, what must
the speed of rise be to maintain the parcel at a constant temperature?
