Instruction manual

APPENDIX A. KRYPTON HYGROMETER IN WATER VAPOR MEASUREMENTS
A-2
()
LE L
wInV
xk
OC
v
h
w
=
′
′
−
+
1
(9)
Where
OC
1
is defined by Eq. (10).
()
OC L
k
k
CMP
R
wT
v
o
w
oo
1
1
=
−
′
′
−
(10)
It would be more convenient if the oxygen
correction could be written in terms of the
covariance of the vertical wind speed and
temperature instead of the inverse of
temperature. With that in mind, Eq. (6) can be
rewritten to take on the following form.
()
()
′′
=
′
′
−
+
−
′′
w
wInV
xk
k
k
w
v
h
w
o
w
o
ρρ
(11)
The fluctuations of oxygen (O
2
) density are due
to pressure and temperature changes. These
fluctuations can be approximated using the first
derivative.
Differentiating the ideal gas law, Eq. (7), yields
the following.
′
=






′
−






′
ρ
o
oo oo
CM
RT
P
CMP
RT
T
2
(12)
The fluctuations in pressure are very small over
a typical flux averaging period. Thus, Eq. (12)
can be written as follows:
′
=−






′
ρ
o
oo
CMP
RT
T
2
.
(13)
Directly substituting Eq. (13) into Eq. (11) and
multiplying by the latent heat of vaporization
yields the following.
()
LE L
wInV
xk
OC
v
h
w
LE
=
′
′
−
−
(14)
where
()
OC L
k
k
CMP
RT
wT
LE v
o
w
oo
=
−
′′
2
(15)
and
T
is in Kelvin. Eq. (14) and (15) were used in
the example SPLIT programs.
A.2 VARIANCE OF WATER VAPOR
DENSITY
The variance of the water vapor density can be
written as in Eq. (16).
()
()
()
σ
ρρ
ρ
ρ
ρ
v
v
vv
v
NN
2
2
2
2
=
−
=
′
=
′
Σ
Σ
(16)
where
ρ
v
is the instantaneous water vapor
density,
ρ
v
is the average water vapor density,
and
ρ′
v
is the instantaneous fluctuation from the
mean. The water vapor density fluctuations can
be written as in Eq. (17).
′
=−ρρρ
vv
v
(17)
Substitute Eq. (17) and then (4) into Eq. (16).
Expand and collect terms where appropriate.
The final result is Eq. (18), which describes the
water vapor fluctuations and the coinciding
oxygen correction.
() ()()
′
=−
′











−
ρ
vwh
xk InV
22
2
()
()
+
′
′
−
2
1
xk C M P
R
InV T
ooo
h
()
+






′











−
xk C M P
R
T
ooo
2
1
2
(18)
The last two terms in Eq. (18), which are the
oxygen corrections, are cumbersome to
calculate. They can, however, be rewritten in a
simpler approximate form.
Substitute Eq. (7) into (4) and differentiate. This
leads to Equation (19) below.
()
′
=
′
−
−
−






′
ρ
v
h
w
o
w
oo
InV
xk
k
k
CMP
RT
T
2
(19)