Appendix D. Equations and Algorithms of Water Vapor Density
and Water Flux in KH20 Eddy-Covariance Systems
D-2
D.2 Working Equation
In the field, KH20 measurements output
V
values. To acquire
ρ
w
from
fundamental equation (2), other constants (
x
and
V
0
), parameters (
k
w
and
k
o
),
and variable (
ρ
o
) in this equation are needed. In manufacture process,
x
is
measured in precision and others are statistically estimated in the calibration
process under the calibration background oxygen density (
ρ
oc
in gO
2
m
-3
).
Through the process, the working equation is given
ρ
ρ
w
w
w
I
o
oc
O
O
xk
V
xk
C
xk
C M P
R T
= −
+
+
−
1
1
ln
*
(3)
In this equation,
V
,
P
(high-frequency atmospheric pressure in Pa), and
T
(high-frequency air temperature in K) are variables measured/derived in KH20
eddy-covariance water flux systems;
k
w
,
C
I
[termed as “Constant” in ln(mV)],
x,
and
ρ
oc
are parameters and constants from the calibration process, given in
KH20 Calibration;
k
o
is 0.00345 ln(mV) m
3
g
-1
cm
-1
determined by van Dijk et
al (2003) following Tanner et al. (1993) , considered as universal for all KH20
sensors with
x
around 1.3 cm;
C
o
is the mole fraction of oxygen that is
considered as a constant of 0.2095 in ecosystems (Tanner et al. 1993);
M
o
is the
molar mass of oxygen (32 g mole
-1
); and
R
*
is universal gas constant (8.3143 J
K
-1
mol
-1
).
D.3 Eddy-Covariance Water Flux
Water flux is computed from
w
w
ρ
(Webb et al. 1980) where
w
is vertical
wind speed and overbar averages the data over an averaging interval. In
practice, it is computed from
w
w
w
w
w
w
ρ
ρ
ρ
=
+
' '
(4)
where prime indicates the fluctuation of a given variable away from its mean.
In the right side of this equation, the first term is the eddy-covariance term
which is the covariance of vertical wind speed with water vapor density and the
second term is the WPL term (Webb et al. 1980) which reflects the water flux
caused by changes in air density.
Eddy-covariance term is derived from equation (3) as
( )
w
xk
w
V
k
k
C M P
R T
w T
w
w
o
w
o
o
' '
'
'
*
' '
ln
ρ
= −
+
1
2
(5)
The second term on the right side of this equation is the oxygen correction
term.
w T
' '
is temperature flux. It can be directly measured if a fine wiring
thermocouple is available; otherwise, it is derived from
w T
s
' '
through SND
corrections (van Dijk 2002).
