(ρu′ T ′) dz + cp ∫0 ρu
-ρcp w′T ′ = - (qR + qG + qE ) + cp ∫
T
h
h
dz
x
x
0
T
h
h
+cp ∫ ρw
dz + cp ∫
(ρT )dz
(57)
z
z
0
0
with the use of the equation of continuity
ρu
z
ρw = -∫
dz .
x
0
Equation 57 becomes
h
ρu T
T z
-ρcp w′T ′ = - (qR + qG + qE ) + cp ∫ ρu
- ∫
dz
z
dz
z 0
0
x
(
)
h
h
ρu′T ′ dz + cp ∫
(ρT ) dz .
+ cp ∫
(58)
x
z
0
0
However, the integral terms are not measured in energy balance studies because the contribution
from these terms is considered to be rather small in comparison with qR or qE, but there is
uncertainty whether these terms will be small in comparison with ρcp w′T ′ , especially if air flow
near the test site is obstructed, creating considerable horizontal gradients. Even in the case when
there is no obstruction to the air flow, the integral terms are negligible, thus
ρcp w′T ′ = (qR + qE + qG ) .
(59)
The errors in qR, qE, and qG are cumulative and will be lumped together in calculating ρcp w′T ′ .
Since qR is usually very large, a small error in qR can thus distort the value of H (= ρcp w′T ′)
completely. Therefore, the energy balance method cannot provide the credence in evaluating the
value of ρcp w′T ′ .
IV. FUNDAMENTALS IN MEASURING SENSIBLE
HEAT FLUX BY CORRELATION TECHNIQUES
As indicated in eq 7, the sensible heat flux is
H = ρcp w′T ′ .
(60)
To evaluate the heat flux, H, the covariance of w′ and T ′ , i.e., the fluctuating velocity and temperature,
has to be measured simultaneously. This requires the use of sophisticated measuring devices and
techniques, and the measurement is usually limited to short time spans to have a reasonable approxima-
tion of a pseudo-steady-state condition prevailing during the measurement period (this can be accom-
plished easily by conducting the measurement in artificially controlled conditions such as in a wind
tunnel, etc., but not in a constantly changing atmosphere). The correlation technique is the most
fundamental one, and the data results from this measurement can be used to evaluate various theories,
but we have to be aware that there is great difficulty associated with sampling frequencies, elevations,
and site suitability to derive universally applicable expressions. Such types of measurement are not
standard operations of meteorological stations, and it is unlikely that they will be in the future.
As we are aware, the turbulent exchange heat fluxes of sensible and latent heat are the most important
heat fluxes (the other is radiation heat flux) in the development of the surface energy balance. On a clear
day, the radiative flux will obviously predominate. However, during the night or on a cloudy day, the
turbulent exchange fluxes will be an essential element affecting the surface energy balance.
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