Nu = Hz/k∆T and eq 83 and 84, it is clearly shown that we do not need to know the value of ∆T to
calculate the value of sensible heat flux H.
Table 4 clearly shows the variations of w′ T ′ with u2m over a period of one year. The slope
varies from 0.0298 for the measurements made from May to August to 0.014 for the period from
December to the next April. In the MayAugust period, the sensible heat flux is about three times
greater than the value calculated for the DecemberApril period for a given Reynolds number Re.
covered ground than over grass-covered ground. This is evidenced in the variation of w′ T ′ with
the ratio of u2m / u* (Fig. 8). This trend can also be seen from Table 4 in which the slopes of the
relation between u* vs. u2m , σw′ vs. u2m , and σ u′ vs. u2m are slightly lowered as the test period
expanded from May to August, December and then to April. The slopes of the relation between σu
vs. u* (Table 4) increases slightly as the test period progressed as was expected, i.e., to have the
same value of u* during the winter period (in this case December to April). It needs a higher value
of mean wind speed u2m and thereby creates a higher value of standard deviation of fluctuating
velocity in the horizontal direction.
Though the study reported here is preliminary in nature, it has clearly established the fact that
the sensible heat flux determined during the winter months or during snow- or ice-covered ground
is about only one third of the value obtained during spring and summer months, i.e., over grass-
covered ground. Therefore it is speculated that the use of expressions involving temperature and
mean velocity gradients evaluated at measurement height z to estimate sensible heat flux from
equations such as eqs 21 or 31 will definitely introduce a significant error because these equations
are derived without the consideration of snow surface as a lower-surface boundary.
For sensible heat flux determined under stable conditions (which exists mostly at night under
calm wind conditions), the data are much more scarce and showed a much greater dispersion,
discussed in section VII, Comparison of Sensible Heat Fluxes. For the case of stable atmospheric
conditions, Hicks and Martin (1972) reported an average value of 9 W/m2 (for a mean wind speed
of 2.7 m/s and ∆T of 3C), which is about one third of the value obtained from this study under
approximately the same test conditions (i.e., 27 W/m2) (but for a period of one year, the heat flux
reduces to 13 W/m2, which is close to the value of 14 W/m2 reported by Dyer (1961) as well as of
16 W/m2 reported by Bernier and Edwards (1989).
For unstable atmospheric conditions, Dyer (1961) conducted sensible heat flux measurements
over level pasture land with a mean wind speed of 4.2 m/s and r eported a heat flux value of 155
W/m2, which is nearly identical to the value of 180 W/m2 calculated from eq 84 based on the
present study. This close agreement may be accidental, because in another study Dyer (1967)
order of 3C, the value of H will be on the order of ~1100 W/m2, which is about seven times greater
than the value reported by Dyer (1961) as well as the value calculated based on eq 84.
In summary, based on several past studies as well as the present one, it can be concluded that not
only does sensible heat flux depend on a number of factors, but it is difficult to obtain consistent
results because of the constant changing of the atmosphere. The fact is that even during an
averaging period of 10 minutes the wind speed and its direction vary greatly. Therefore, the
fundamental assumption of constant, steady, and homogeneous upwind flow never can be realized
in the field measurement to satisfy the condition of a so-called constant flux surface layer. It is
expected that the results obtained with the eddy-correlation technique will provide a much more
reasonable estimation for the sensible heat flux than the other methods discussed in section III,
Computation of Turbulent Fluxes. Due to the constantly changing atmospheric dynamics, the
steady, homogeneous surface layer flow will never be realized in field measurements to ensure the
existence of the constant flux layer. Localized or regional measurements, which are used in this
study, may still provide a much more reliable method to find the sensible heat flux needed for
surface energy balance calculations.
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