D-1
Appendix D. Equations and Algorithms
of Water Vapor Density and Water Flux
in KH20 Eddy-Covariance Systems
D.1 Fundamental Equation
A krypton hygrometer (KH20, Campbell Scientific) is a fast-response water
vapor analyzer to measure the high-frequency fluctuations of water vapor
density in the atmosphere. When the three-dimensional wind speeds are
measured nearby using a fast-response sonic anemometer, the fluctuations are
used for the eddy-covariance methodology to estimate the water flux (latent
heat flux) between ecosystems and the atmosphere.
KH20 has a cylindrical path for measurements (FIGURE
). In the lower end
of the path, a krypton lamp emits a major light at 123.58-nm wavelength
(wavelength 1) along with a minor light at 116.49-nm wavelength (wavelength
2). The lights penetrate the air along the path length of
x,
in cm, and are
received by the detector in the upper end of the path that outputs voltage (
V
in
mV). The lights in both wavelengths are absorbed by two air components:
water vapor and oxygen. Without both components along the path, the sensor
outputs voltage
V
01
from wavelength 1 and voltage
V
02
from wavelength 2,
both of which sum up one voltage output as
V
0
(
V
0
=
V
01
+
V
02
) from the sensor
for air free of water vapor and oxygen. Given water vapor density (
ρ
w
in gH
2
O
m
-3
) and oxygen density (
ρ
o
in gO
2
m
-3
), based on the Beer–Lambert Law
(Wallace and Hobbs. 2006), KH20 output
V
can be theoretically expressed as:
V V
xk
xk
V
xk
xk
w
w
o
o
w
w
o
o
=
−
−
+
−
−
01
1
1
02
2
2
exp(
)
exp(
)
ρ
ρ
ρ
ρ
(1)
where, on wavelengths 1 and 2,
k
w
1
and
k
w
2
with subscript
w
indicating water
are the absorption coefficients of water vapor and
k
o1
and
k
o
2
with subscript
o
indicating oxygen
are the absorption coefficients of oxygen. Water vapor has
similar absorption at both wavelengths (Campbell Scientific Inc. 2010), thus
k
k
w
w
1
2
≈
and absorption coefficients of water vapor on both wavelengths
could be represented by the same value denoted by
k
w
in ln(mV) m
3
gH
2
O
-1
cm
-1
.
Similarly, one coefficient also is used by Tanner et al. (1993) and van
Dijk et al. (2003) for the absorption by oxygen at both wavelengths. Thus, the
absorption coefficients for oxygen on both wavelengths (
k
o1
and
k
o2
) can be
represented by the same value denoted by
k
o
in ln(mV) m
3
gO
2
-1
cm
-1
. Further,
equation (1) can be solved for
ρ
w
as:
(
)
ρ
ρ
w
w
w
o o
xk
V
xk
V
xk
= −
+
−
1
1
0
ln
ln
(2)
This is the fundamental equation for KH20 measurements.
