Geoscience Reference
In-Depth Information
(c)
Equation (4.7) can be adapted to determine the turbulent sensible heat flux at the surface,
if the temperatures at the surface and in the air are known.
(d)
In principle (not in practice), the wind function should incorporate the effect of the surface
roughness,
z
0
.
(e)
But, on an hourly basis,
f
e
(
u
1
) cannot be improved by including the effect of the stability
of the atmosphere.
4.7
Multiple choice. Indicate which of the following statements are correct. In the case of a uniform,
horizontal surface, evaporation can be expressed by the following equations. The subscripts 1 and
2 refer to the reference levels,
z
1
and
z
2
, respectively, within an atmospheric-surface layer under
neutral conditions. Assume
d
0
=
0.
u
2
∗
ρ
(
q
1
−
q
2
)
(
u
2
−
u
1
)
(a)
E
=
dq
dz
(b)
E
=−
(
ku
∗
z
)
ρ
(
dq
dz
)
(
du
/
dz
)
/
E
=−
u
2
(c)
∗
ρ
ρ
k
2
(
u
2
−
u
1
)(
q
1
−
q
2
)
[ln(
z
2
/
z
1
)]
2
(d)
E
=
ρ
k
2
u
2
(
q
s
−
q
2
)
[ln(
z
2
/
z
0
)][ln(
z
2
/
z
0v
)]
(e)
E
=
4.8
Consider the empirical mass transfer equation (4.24) as developed by Penman (1948). Calculate
the value of the scalar roughness,
z
0v
,which is implied by that equation for a neutral atmosphere
above a surface with a mom
e
ntum roughness of
z
0
=
0.05 m, for an air temperature of 20
◦
C, and
for a typical wind speed of
u
2
=
5ms
−
1
.
How many millimetres per month (mm month
−
1
)ofliquid water can be evaporated at 25
◦
Cby
an energy supply of1Wm
−
2
? Prove your answer.
4.9
4.10
The following measurements were recorded at a micrometeorological site: net radiation,
R
n
=
200
Wm
−
2
; heat flux into the ground,
G
=
40Wm
−
2
; and evaporation rate,
E
=
5
×
10
−
8
ms
−
1
.
(a) Calculate the turbulent sensible heat flux,
H
, inWm
−
2
. (b) How large was Bowen's ratio?
(c) Was the atmosphere stable or unstable? Why? (d) Was the soil warming up or cooling? Why?
4.11
The following measurements were recorded at a micrometeorological site: net radiatio
n,
R
n
=
250
Wm
−
2
; heat flux into the ground,
G
=
30Wm
−
2
; and sensible, heat flux,
H
=
ρ
c
p
w
T
=
55
Wm
−
2
. (a) Calculate the evaporation rate,
E
, inkgm
−
2
s
−
1
and inmmd
−
1
. (b) How large was
Bowen's ratio? (c) Was the atmosphere stable or unstable? Why? (d) Was the soil warming up or
cooling? Why?
4.12
Calculate, inmmd
−
1
, for a typical summer day, the different measures of evaporation listed below.
The data for that day and, thus also,
R
n
, are given and calculated in Problem 2.17, and the wind
speed at 10 m above the ground was measured as 10.4kmh
−
1
. Assume that the average daily ground
heat flux,
G
, isnegligible. (a) Potential evaporation by means of Penman's method; use Penman's
wind function. (b) Potential evaporation under conditions of minimal advection according to
