αRi in eq 30 approaches unity or Ri approaches α1. A critical Ri is designated as Ric = α1, beyond
which no turbulent condition can exist.
In his original work, Richardson (1920) reported Ric = 1.0. However, most investigators (Businger
1973) indicate the value of Ric less than 1.0 and most likely in the range of 0.15 to 0.25. Brutsaert
(1972) reported that the value of Ric increases for the case involving evaporation and radiation, but
its increase will depend on atmospheric conditions. He stated that the value of Ric is not invariant
but rather varies between 0.25, below which turbulence is very likely, and somewhat higher than
0.5, above which turbulence is not likely. In the case of a snow cover, the air temperature normally
exceeds the snow surface temperature (during daylight hours) because of the surface's high albedo
and high emissivity and its limiting temperature of 0C, therefore stable conditions should predom-
inate over the snow surface.
III. COMPUTATION OF TURBULENT FLUXES
A. Two-level measurement
Under conditions of neutral stability, and with the assumption of Kh = Km, the sensible heat flux
can be obtained from the expression
(u2 - u1) (T2 - T1)
H = -ρcp k 2
,
(31)
2
ln z2
z1
and similarly for Km = Kw, we have
ρMw 2 (u2 - u1) (e2 - e1) ,
E=-
(32)
k
2
ln z2
pMa
z1
where Mw and Ma are the molecular weight of water and air, respectively. Equations 21 and 22 can
be used to determine H and E fluxes under all conditions in terms of stability-related functions of
φh, φw and φm.
B. One-level measurement
In numerous cases, the measurements of wind, temperature, and humidity at two levels are not
available. The basic equations for evaluating turbulent fluxes based on one-level measurement
(essentially speaking, it is still a two-level measurement except one of the levels is located at the
surface) are generally expressed in terms of bulk transfer coefficients of heat (ch), water vapor (cw),
and momentum (cm), defined as
(
)
H = -ρcp ch u T - To ,
(33)
ρ Mw
cw u (e - eo ) ,
E=-
(34)
p Ma
and
2
τ = u* ρ = ρcmu 2 ,
(35)
where e, eo are the vapor pressure at z and the snow surface (or at z = zo); and T and To are the
mean air temperature at heights z and zo.
8
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