which is different from the expression proposed by Panofsky et al. (1977) for z/L ≥ 1.0, i.e.,
1/ 3
σw′
z
= 1.3 1 -
,
(78)
L
u*
but Kai (1982) claimed that his data can be represented rather well by the above expression.
For stable regions (i.e., 0.01 ≤ z/L ≤ 100), even though there are less data available, a similar
expression with an exponent of 1/4 instead of 1/3 can be derived as
1/ 4
σw′
z
= 1.3 1 + 3
.
(79)
L
u*
Table 3 shows the comparison of the ratio σw′ /u* with other results under neutral conditions. It can
be seen that the ratio of σw′ /u* taken from this study is within the range reported by all the
investigators listed in Table 3. Even though the friction velocity u* varies with the homogeneity of
the upwind fetch and the surface roughness, the ratio of σw′ /u* from this study (under neutral
conditions) falls nevertheless within the limits reported by other investigators. This value, along
with the relations given for u* vs. u2m (eq 65), σw′ vs. u2m (eq 66), and σw′ vs. u* (eq 69), cer-
tainly gives credence to the results obtained from this preliminary investigation. The agreement
provides confidence in carrying out the essential purpose of this investigation, i.e., the use of the
eddy correlation technique to determine the sensible heat flux.
Table 4 shows a summary of the computed sonic results. It can be seen that, with the exception
of plots of σw′ vs. u* and - w′ T ′ vs. u2m , the slope of all other plots decreases slightly as the test
runs extended from 30 May 1991 to 15 April 1992, with the lowest slope for the test runs conducted
from 19 December 1991 to 15 April 1992. It seems that in the presence of snow or ice-covered or
slightly less dependent on u2m . In other words, for the same value of u2m , the values of u*, σw′ ,
σ u′ , and w′ T ′ are reduced somewhat as the tests progressed from spring to winter.
B. Sensible heat flux correlation
To facilitate the practical use of the sensible heat flux data presented in Table 4, a dimensionless
analysis is needed to extend the results for other test conditions. For the test period from 19
December 1991 to 15 April 1992, the variation of w′ T ′ (positive for unstable conditions or for heat
rising from the surface) with u2m was given in eq 76 as
w′ T ′ = 0.014 u2m
Table 4. Summary of linear correlation of computed sonic results from 19911992.
9105301331
9105301331
9105301331
9105301331
Test period
to
to
to
to
9108201600
9112111530
9204151725
9104151725
Type of
Correlation
Correlation
Correlation
Correlation
plot
Slope
coefficient
Slope
coefficient
Slope
coefficient
Slope
coefficient
0.1034
0.9722
0.0994
0.9664
0.0893
0.9337
0.0785
0.8992
u* vs. u2m
0.1614
0.9845
0.1572
0.9721
0.1456
0.9241
0.1330
0.8701
u* vs. u2m
σ u′ vs. u2m
0.3723
0.9816
0.3635
0.9812
0.3564
0.9765
0.3487
0.9716
σ u′ vs. u*
3.4431
0.9638
3.4710
0.9634
3.5940
0.9420
3.7788
0.9182
w′ T ′ vs. u2m
0.0398
0.9052
0.0250
0.8649
0.0241
0.8160
0.0140
0.8313
w′ T ′ vs. u2m
0.00005
0.8049
0.0003
0.1583
0.0023
0.0746
0.0045
0.0751
31
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