Turbulent sensible heat flux has been measured by numerous investigators since the invention of
the sonic anemometer and the advances in computer technology since 1965. However, to this
author's knowledge, the numerous field experimental results are largely limited to terrains other
than snow-covered ground, which presents unique surface characteristics. Because the snow sur-
face serves as the lower boundary, it is generally reported that the numerous turbulent heat flux
expressions developed from studies on terrains other than snow will not be applicable to snow-
covered ground because the microphysical heat transfer process under extremely stable conditions
is still rather poorly understood.
Another phenomenon due to the presence of a snow surface as the lower boundary surface is the
validity of the widely accepted concept of the constant flux layer. Although this concept is
convenient (because the heat flux is invariant with height), variations of turbulent flux with height
have been reported. The discrepancy is attributed to the fact that a term responsible for temperature
changes due to the divergence of radiant heat transfer in the thermodynamic energy equation is not
included, even though this is considered to be a common micrometeorological practice, especially
in the first few meters above the surface. This phenomenon may become more pronounced over
snow and melting snow because of their high albedo and the upper-boundary snow temperature of
snow surface. With the upper-limit snow surface temperature at 0C, the air over snow is heated to
above 0C, resulting in a stable profile directing heat toward the surface. However, if the air mass is
cool, a temperature maximum has been observed in the air layer ~2050 cm above the surface (De
La Casiniere 1974, Halberstam and Schieldge 1981) and about 5 cm above the snow surface by Yen
(1993). Above this maximum, the temperature profile is mostly unstable in the case of Halberstam
and Schieldge (1981), mostly stable in the work of De La Casiniere (1974), and nearly isothermal
for a plot T vs. ln Z (Yen 1993) as well as results from Granger (1977) in a linear plot. Under these
conditions, not only is the heat flux not a constant with height, but it undergoes a reversal in
direction at the level of the raised maximum.
Since an analytical treatment of turbulence research is out of our reach at the present time, the
following largely deals with how the field measurement system should be designed and set up to
obtain reliable and representative results of universal usage.
A. General problem associated with snow-covered ground
The most prevailing phenomenon of the atmospheric surface layer over snow-covered terrain is
the frequent occurrence of very stable conditions. Because of the low thermal conductivity of snow
and its high albedo and emissivity, the snow surface can get very cold, especially on clear nights.
The snow extracts heat from the air and thus stabilizes the surface layer. Sometimes the surface
layer becomes so stable that turbulence ceases completely and any vertical heat transfer is accom-
plished by much slower molecular transport processes. However, such extremely stable periods do
not persist very long because gravity waves or other disturbances distort the stable temperature
profile and provide the needed energy for renewed turbulent mixing. These processes are apparent-
ly repeated in cyclic fashion and are the key mechanism of the nocturnal boundary layer; they are
believed to be an even more intensive occurrence over snow-covered terrain. Consequently, the
widely practiced MoninObukhov similarity cannot handle such intermittent turbulence.
B. Coverage of frequency intervals
The study of atmospheric turbulence is not a deterministic discipline. Since the air is in random
or chaotic motion, we cannot make a single measurement and say "this is the heat flux." In other
words, we must deal with the statistics of the turbulence. The key statistic in the study of turbulent
heat transfer over snow is the w′T′ covariance w′ T ′ , w′ is the turbulent fluctuation in vertical
velocity, T′ is the turbulent fluctuating temperature, and the overbar indicates a time average. The
sensible heat carried to or from the snow surface is ρcp w′ T ′ , where ρ and cp are the density and the
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