Appendix D. Equations and Algorithms of Water Vapor Density
and Water Flux in KH20 Eddy-Covariance Systems
D-3
The WPL term is given by Webb et al. (1980):
(
)
w
w
T
w T
w
w
w
ρ
µσ ρ
µσ ρ
=
+ +
' '
' '
1
(6)
where
µ
(1.60802 ) is the ratio of dry air molecular weight (28.97 kg kmol
-1
) to
water molecular weight [18.016 kg kmol
-1
, page 466 in Wallace and Hobbs
(2006)],
σ
is mean water vapor mass mixing ratio (ratio of mean water vapor to
mean dry air density computed in the data processing).
As usual in eddy-covariance measurements, the covariance variables:
( )
w
V
'
'
ln
and
w T
' '
need coordinate rotation and frequency corrections. The
general algorithm and procedure for coordinate rotation and frequency
corrections are addressed in Campbell Scientific Inc (2020), but the equation
for frequency response of a KH20 to water vapor density (ln
V
) cannot be found
in previous documents from Campbell Scientific.
D.4 Frequency Response of KH20
KH20 measures the water vapor density averaged over a cylindrical light path
that has a diameter of 9.5 mm and length of 11 to 15 mm (see KH20
Calibration). Andreas (1981) derived the power spectra transfer function for
volume averaging [Equation (18) in Andreas (1981)]. His equation includes the
first order Bessel function of the first kind that makes the integration of the
transfer function over the frequency domain in need of more computation time.
Moene (2003) used a simple function to approximate equation (18) of Andreas
(1981). Moene’s (2003) approximation was developed only for a Krypton
Hygrometer with a diameter-ratio of 0.5. Because the cylindrical light path of
KH20 for measurements has a fixed diameter, but changeable length, Moene’s
(2003) approximation only uses the length as a sensor parameter. In his
original equation, the approximation curve matches the curve for a diameter-
length ratio between 0.5 and 1.0 when the ratio of Kolmogorov microscale (1
mm in the atmosphere) to the path length is 0.014 [Fig. 2 in Andreas (1981)].
Based on the diameter fixed and length range of KH20 cylindrical light path,
its diameter-length ratio is about 0.63 to 0.86 within the applicable range of
Moene’s (2003) approximation for 0.5 to 1.0 as a diameter-length ratio (see
page 650). This approximation is given by:
T
f x u
fx
u
w
VA
ρ
2
2
100
2
_
( , , ) exp
/
=
−
(7)
where
f
is natural frequency,
u
is wind speed in the stream-wise direction, and
100 is used to convert
x
in cm to m. Its application is the same as the power
spectral transfer function for line averaging in other Campbell Scientific open-
path eddy-covariance systems for the EC155 or IRGASON infrared gas
analyzer (Campbell Scientific Inc. 2020)
