indicates the conditions of neutral, unstable, or stable conditions, respectively. By a simple mathe-
matical operation, the three parameters of Ri, Rif, and z/L are related to φm by
1 z
Kh
Rif =
Ri =
.
(15)
φm L
Km
Similar expressions for mean temperature and humidity gradients can be written as
φh
T
H
z
=-
(16)
ρcp ku*z L
z
and
φw ,
q
E
z
=-
(17)
L
ρku*z
z
where q is the mean specific humidity, E is the water vapor flux, and φh and φw are stability
functions for heat and water vapor.
From the basic turbulent transfer equation, such as eq 8 for momentum and the following
expressions of
T
H
=-
(18)
ρcp Kh
z
for heat and
q
E
=-
(19)
ρKw
z
for water vapor, we can relate the stability-related functions of φm, φh, and φw to the eddy turbulent
transfer coefficients of Kh, Km, and Kw by
Kw φm
φ
Kh
=
= m.
(20)
and
Km φw
φh
Km
The final expression for H and E in terms of these stability-related functions and mean tempera-
ture, vapor pressure, and wind speed gradients can be written as
u T 1
H = - ρcp k 2 z2
(21)
z z φhφm
and
0.622 ρ 2 2 u e 1
E=-
,
(22)
kz
z z φwφm
p
where e and p are vapor pressure in millibars. The value of 0.622 is the ratio of the molecular
weight of water vapor to that of air. Therefore, by determining the gradients of mean wind speed,
temperature, and specific humidity and the values of φh, φw, and φm, the sensible heat and water
vapor flux can be evaluated.
C. Evaluation of φh, φw, and φm
A number of researchers have used the "similarity theory" developed by MoninObukhov
(1954) as a framework to define the functions of φh, φw, and φm in terms of a dimensionless ratio of
6
Previous Page
