Geoscience Reference
In-Depth Information
β
≡
H
LE
v
,
(7.1)
With this deinition, in combination with the energy balance equation (Eq. (
1.5
)), the
surface sensible heat lux and latent heat lux can be expressed as a function of avail-
able energy
Q*- G
and the Bowen ratio:
QG
*
−
H
=
β
1
+
β
(7.2)
QG
*
−
LE
=
v
1
+
β
But now the problem of determining the luxes has been shifted to the determination
of the Bowen ratio. For this we can make use of the expressions developed in
Chap-
ter 3
that link the turbulent luxes to vertical differences in the concentration of the
transported quantity:
() ()
,
z
−
z
q z
() ()
−
q z
θ
θ
H
=−
ρ
c
t
2
t
1
LE
=−
ρ
L
v
2
v1
p
v
v
r
r
ah
ae
where
z
t
1
,
z
t
2
,
z
v
1
, and
z
v
2
are the heights where temperature and speciic humidity are
measured, respectively, and
r
ah
and
r
ae
are the aerodynamic resistances for heat and
water vapour transport, respectively. Now, provided that
•
the location of the upper observations of temperature and humidity coincide (
z
t
2
=
z
v
2
);
the locations of the lower observations of temperature and humidity coincide (
•
z
t
1
=
z
v
1
);
the aerodynamic resistances for heat and water vapour are identical, which is a conse-
•
quence of (
z
t
2
=
z
v
2
) and (
z
t
2
=
z
v
2
), in combination with the fact that the similarity relation-
ships for heat and water vapour are supposed to be equal
the Bowen ratio can be determined as:
(
)
c
() ()
/
() ()
/
r
c
θ
z
−
θ
z
H
LE
∆
∆
θ
p
ah
t
2
t
1
p
β
==
=
(7.3)
(
)
L
r
L
q
q z
−
q z
v
v
ae
v
v
2
v
1
Hence, observations of temperature and humidity at two heights, in combination with
soil heat lux and net radiation, sufice to determine the sensible and latent heat lux.
No detailed measurements (or assumptions) regarding the nature of turbulence (e.g.,
with respect to
r
a
) are needed. Because the use of the surface energy balance is an
essential part of the method, it is often referred to as Bowen ratio energy balance
method (or BREB method).
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