E′ = f (U ) (e - eo ),
(51)
where E is the water vapor transfer expressed as a depth (mm/hr) and f (U ) is a function of the
wind speed [mm/(mb hr)], where E is positive, the direction of vapor transfer is toward the snow
cover (i.e., condensation-forest formation). When E is negative, it indicates a loss from the snow
f (U ) = a + bU ,
(52)
where U is the product of mean wind speed and time expressed in km, b is an empirical constant
expressed in mm/(mb km hr), and a is a constant representing the amount of vapor transfer when
wind velocity is zero [mm/(mb hr)]. a is found to be dependent on the time interval being used.
The values of both a and b varied a) with the heights at which the wind speed and vapor pressure are
measured, b) with the method and the accuracy of snow surface temperature measurement, and c)
with the predominating stability conditions and surface roughness of the sites.
For the evaporation of water, a finite value of a results. This reflects evaporation during calm,
unstable periods caused by radiative heating of the surface. Since stable conditions usually prevail
over a snow cover, the value of a should be zero. Values of a and b can be extrapolated to a constant
height of 1 m above the snow surface, i.e.,
uz ez
=
= z0.17
(53)
u1 e1
where uz , u1 and ez , e1 are mean wind speed and vapor pressure at height z and 1 m above the
surface, respectively.
The latent heat transfer of evaporation or condensation can be expressed as
Ls ρw
Ls ρw
Lsρw E′′ =
E′ =
f (U ) (e - eo ) ,
(54)
10
10
The ratio of sensible heat flux to latent heat flux commonly known as Bowen's ratio, with the
assumption of cw = ch (also Kh = Kw but that does not assume Km ≠ Kh or Kw) can be written as
(
)
pcp T - To
Qh
H
=
=
.
(55)
Qe Ls E 0.622 Ls (e - eo )
Experimental evidence (Dyer 1967, Pruitt et al. 1971) suggests that the assumption of Kh = Kw is
reasonable for all stability conditions. On the other hand, in unstable conditions, Km is not equal to
Kh or Kw (or cm ≠ ch or cw). The sensible heat transfer can be written as
Lsρw
Qh =
γ f (U ) (T - To ) ,
(56)
10
where γ = (pcp)/0.622 Ls is essentially a constant for a given location.
D. Energy balance method
Since the vertical flux of sensible heat cannot be conveniently measured over long time periods,
attempts have been made to measure the other terms in the energy balance equation. The sensible
heat flux is found by integrating the energy balance equation to height h (at which the fluxes are
Lunardini 1981), i.e.,
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