z/L where L is invariant with height within the surface boundary layer. Experimental determina-
tions of φh, φw, and φm are made by measuring the profiles of wind speed, temperature, humidity,
and shear stress as well as the fluxes of heat and water vapor.
A great number of determinations of φh, φw, and φm have been reported in the literature
(McVehil 1964, Dyer 1967, Dyer and Hicks 1970, Oke 1970, Webb 1970, Businger et al. 1971,
Pruitt et al. 1971). However, due to logistical problems in choosing an ideal site to ensure the
existence of the constant flux layer and other problems associated with the eddy correlation mea-
surement technique, most of the results are not in agreement with each other. The following
relationships have been adopted by Anderson (1976) to represent the majority of the determina-
tions. For stable conditions, he suggested that
φh = φw = φm = 1 + 5 ,
z
(23)
L
which implies that Kh = Kw = Km. For unstable conditions he recommended using
-1 / 4
1 - 16 z
φm =
(24)
L
and
-1 / 2
φh = φw = 1 - 16
z
.
(25)
L
Equations 24 and 25 are commonly referred to as BusingerDyer formulas. If the value of H and u*
are not available, the value of z/L can be related to a stability criterion that can be computed from
commonly available data, i.e., z / L = (Kh Km ) φm Ri , then for stable conditions we have
z
= (1 - 5Ri) -1
φh = φw = φm = 1 + 5
(26)
L
and for unstable conditions
-1 / 4
φm = (1 - 16 Ri)
(27)
and
-1 / 2
φh = φw = (1 - 16 Ri)
.
(28)
At the geometric mean height of z2 and z1, the Richardson number can be evaluated from the
2g (z2 - z1) (T2 - T1)
Ri =
.
(29)
(T2 + T1) (u2 - u1)
With the values of φh, φw, and φm calculated from the determined value of Ri along with the values
of wind speed, temperature, and specific humidity gradient, the sensible and water vapor flux can
be determined from eq 21 and 22.
D. Critical Richardson number
Equation 26 can be written as
φh = φw = φm = (1 - αRi ) -1 .
(30)
As z/L (see eq 26) approaches infinity, the values of φh, φw, and φm also approach infinity. Therefore
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