Geoscience Reference
In-Depth Information
Equation (26.3), the prognostic equation describing for water vapor
fluctuations in the atmosphere:
S
q
q
q
q
E
q
2
+
u
+
v w
+
=
u
rr
+
+
q
q
t
x
y
z
(26.3)
a
a
(
)
(
)
(
)
uq
''
vq
''
wq
''
+
+
x
y
z
explaining each step in the derivation as you do so.
The prognostic equations describing the conservation of mean potential tem-
perature has a similar form, thus:
∂θ
∂θ ∂θ ∂θ
+++
R
E
n
2
u
v w
− −
υ∇θ
θ
t
x
y
z
r
c
r
c
(26.4)
ap ap
(
)
(
)
(
)
∂θ ∂θ ∂ θ
u
''
v
''
w
''
+
+
x
y
z
Give the terms that become negligible in Equations (26.3) and (26.4) when the
following assumptions are made.
(b) There is no mechanism for creating water vapor chemically in the
atmosphere.
(c) There is no phase change between water vapor and liquid/solid water.
(d) There is no horizontal or vertical change in the net radiation flux in the
ABL.
(e) Molecular diffusion can be neglected.
(f ) There is no ascent or subsidence (i.e. no persistent rising or sinking of the
air).
(g) There is no horizontal divergence of turbulent fluxes.
(h) There is no horizontal advection of humidity or potential temperature.
(i) After making all of the above simplifying assumptions, write down the
(much simpler) versions of Equations (26.3) and (26.4) which then apply.
Figure 26.4 sketches the simplified average height dependence of the sensible heat
flux H(z) and the moisture flux E(z) through the daytime atmospheric boundary
layer over uniform terrain in cloudless conditions when there is no subsidence. It
labels five levels different levels (i), (ii), (iii), (iv), and (v). You are only allowed to
choose between the following three options for changes in air temperature - be
warmer, be cooler , or change little ; and you are only allowed to choose between the
following three options for changes in atmospheric humidity - be wetter, be drier ,
or change little . On the basis of the answer to question (i), say how the temperature
and humidity will change over the next few minutes at the levels given below.
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