176 D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183
H
E
. Calculations of the mean H
S
were also done us- ing four time lags r=0.25, 0.50, 0.75, and 1.00 s and
compared with H
E
. Estimates of latent heat flux density as a residual
term of the energy budget were calculated using H
S
λE
S
and H
E
λE
E
along with the same R
n
and G values. Both λE
E
and λE
S
values were compared with λE values from an eddy-covariance system λE
K
. The WPL correction Webb et al., 1980 was applied to the
eddy-covariance data for λE. As it is a measure of both bias and variance from
the 1:1 line, the root mean squared error M
e
statistic was used to compare H
S
with H
E
, and λE
S
and λE
E
with λE
K
. The M
e
values were calculated as M
e
= v
u u
t 1
n
n
X
i=1
H
S
− H
E 2
9a
M
e
= v
u u
t 1
n
n
X
i=1
λE
S
− λE
K 2
9b
M
e
= v
u u
t 1
n
n
X
i=1
λE
E
− λE
K 2
9c High-frequency temperature data collected at the
canopy top were used to calculate the Tillman 1972 variance method for estimating H under unstable, free
convection conditions using
H
T
= ρC
p
σ
T
C
1 3
kgz ¯
T
12
10 where C
1
= 0.95 is a universal constant Tillman,
1972, k the von Karman constant k=0.41, g the acceleration due to gravity 0.98 m s
− 2
, σ
T
the stan- dard deviation of the temperature, and ¯
T the mean temperature during the sampling interval. Informa-
tion on stability type was evaluated from measured H
E
values. Comparisons between H
E
and H
T
were done only when H
E
was positive and the wind speed was 2.0 m s
− 1
, so that the assumed free convection conditions leading to Eq. 10 were likely to be met.
Table 1 Weighting factor α, coefficient of determination R
2
, root mean square error M
e
, and number of half-hour samples for H
E
vs. H
S
measurements taken over 2.0-m tall grapevines at the Oakville Field Station in Napa Valley, CA on 14–15 August 1995
a
Height m α
R
2
M
e
W m
− 2
n 2.0
0.88 0.80
44 33
2.3 0.81
0.74 62
34 2.6
0.76 0.76
76 34
2.9 0.66
0.81 111
34
a
Regressions were forced through the origin and the M
e
is between H
S
and H
E
. H
S
was calculated using the mean of the 0.25 and 0.50-s time lags. The range of H
E
was −45 to –326 W m
− 2
.
4. Results and discussion
4.1. Comparison according to measurement height The mean H
S
of the r=0.25 and 0.50 s time-lag calculations compared with H
E
values are shown in Table 1 for the Napa Valley experiment. Table 1 also
gives the correction for unequal heating α, coefficient of determination R
2
, root mean square error M
e
, and number of half-hour period n. The largest value for
α and the lowest M
e
were observed at the canopy top 2 m. The α values decreased and the M
e
in- creased with measurement height above the canopy.
The canopy top α values of 0.88 were considerably higher than the α=0.5 value reported for forest, wal-
nut, and maize canopies Paw U et al., 1995, but α was 1.0 for grass Snyder et al., 1996 and for wheat and
sorghum Spano et al., 1997b. Similar results were obtained using the mean of the r=0.25, 0.50, 0.75,
1.00 s time lags.
The results from the experiment at Villasor are shown in Table 2 for the mean H
S
from the r=0.25 and 0.50 s time lags. Again, the smallest M
e
was found for data taken at the canopy height 2.1 m. The α value
0.89 for the canopy top 2.1 m was nearly the same as found in the Napa Valley experiment. Both within
and above canopy α values decreased with height. Assuming a linear change in α with height between
1.8 and 2.1 m, α=1.0 is expected at 1.85 m 88 of the canopy height for the data from Table 2. As found
in the Napa Valley data, using the mean of r=0.25, 0.50, 0.75 and 1.00 s time lags gave similar results.
The experiment at Satiety vineyard in California further confirmed our earlier findings. The results are
D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183 177
Table 2 Weighting factor α, coefficient of determination R
2
, root mean square error M
e
, and number of half-hour samples for H
E
vs. H
S
measurements taken over 2.1 m tall grapevines at Villasor, Italy on 23–26 July 1996
a
Height m α
R
2
M
e
W m
− 2
n 1.5
1.31 0.84
58 88
1.8 1.02
0.88 33
96 2.1
0.89 0.93
34 97
2.4 0.75
0.77 71
61 2.7
0.77 0.91
60 94
a
Regressions were forced through the origin and the M
e
is between H
S
and H
E
. H
S
was calculated using the mean of the 0.25 and 0.50-s time lags. The range of H
E
was −25 to –329 W m
− 2
.
shown in Table 3 for the mean H
S
from the r=0.25 and 0.50 s time lags. Again, the smallest M
e
was found for the measurements taken at the canopy height. The
α=0.74 value for the canopy top was slightly smaller than the values found in Napa Valley and Villasor.
However, the height where α=1.0, based on the as- sumption of a linear trend from 1.9 to 2.2 m, was about
Fig. 2. Eddy-covariance H
E
vs. mean surface renewal H
S
sensible heat flux density using the time lags r=0.25 and 0.50 s from data collected at Villasor during 23–26 July 1996. H
S
was determined as the sum of two layers where the layers were from z=0 to 1.5 m and from z=1.5 to 2.1 m. The solid line represents a linear regression forced through the origin and the dashed line the 1:1 line.
Table 3 Weighting factor α, coefficient of determination R
2
, root mean square error M
e
, and number of half-hour samples for H
E
vs. H
S
measurements taken over 2.2-m tall grapevines at Satiety Vineyard, Woodland, CA on 11–20 September 1998
a
Height m α
R
2
M
e
W m
− 2
n 1.0
2.93 0.59
61 305
1.3 1.68
0.50 57
318 1.6
1.37 0.58
51 344
1.9 1.09
0.81 42
397 2.2
0.74 0.86
54 434
a
Regressions were forced through the origin and the M
e
is between H
S
and H
E
. H
S
was calculated using the mean of the 0.25 and 0.50-s time lags. The range of H
E
was −162 to –265 W m
− 2
.
1.98 m 90 of the canopy height for the Table 3 data. The results were relatively independent of time
lag, similar to the previous experiments. Eq. 7 is a fundamental formula for energy conser-
vation where α accounts for uneven heating or cooling within the air volume below the measurement height z
and other factors discussed earlier. If the volume of air
178 D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183
is heated or cooled evenly and other factors are neg- ligible, α=1.0 is expected. In all experiments, the H
S
values overestimated H at and above the canopy top measurements α 1 and underestimated H at heights
below the canopy top α1. In both cases, a decrease in α with height was obtained. This was consistent
with the theory discussed by Paw U et al. 1995 and the results reported in previous experiments Spano
et al., 1997a, b. The α values depend on the temper- ature measurement level in relation to the postulated
height to which the renewal volume was heated or cooled during the ramp event.
When the measurement level is higher than the mean height of the air volume being heated or cooled,
entrainment with air aloft could affect the estimation, and H
S
values result in an overestimate α1. When the measurement level is lower than the mean height
of the air volume being heated or cooled, air above the measurement level within the renewal parcel air is
actually heated or cooled, but not accounted for in the energy balance in the parcel being considered. Thus,
Fig. 3. Eddy-covariance H
E
vs. mean surface renewal H
S
sensible heat flux density using the time lags r=0.25 and 0.50 s from data collected at Satiety during 11–20 September 1998. H
S
was determined as the sum of two layers where the layers were from z=0 to 1.3 m and from z=1.3 to 2.2 m. The solid line represents a linear regression forced through the origin and the dashed line the 1:1 line.
H
S
values result in an underestimate of H and α will be 1.
Based on the results of all the experiments, H
S
val- ues from temperature data collected at about 90 of
the canopy height would likely provide good estimates of H with α=1.0 i.e. no calibration would be needed.
It is expected that most of the results would be within about 45 W m
− 2
of H
E
. There was little difference ob- served between H
S
values coming from the mean of two time lags or four time lags, so using 76-mm di-
ameter thermocouples, the 8-Hz data, and time lags r=0.25 and 0.50 s yield acceptable performance.
4.2. Layer-wise comparisons Although good estimates of H from H
S
were pos- sible without accounting for uneven heating of the air
volume below the canopy top, a method to determine H
S
without calibrating against H
E
is desirable. One possible method is to separately calculate H layer-wise
within the canopy volume assuming α=1.0. Since the
D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183 179
heating and cooling of the canopy air is related to the distribution of plant elements, temperature fluctua-
tions could be uneven with height. Vertical variation in the heating can be sampled by sensors at two or
more heights. Therefore, the SR heat flux can be cal- culated separately for each layer using fluctuation data
from each height, which defines the top of each layer assuming uniform heating and α=1.0. The total heat
flux from a canopy would equal the sum of the layer calculations. Thus, calculating the heat flux separately
by layer and summing over layers should provide an estimate of H without the need for calibration to de-
termine α for the canopy. For practical purposes, the fewer the number of thermocouples needed the better.
Therefore, the canopy was separated into two layers. The lower layer was from the ground to one height
within the canopy, and the upper layer was from that level to the canopy top. Using the Villasor data, the
layers were from z=0–1.5 m and from z=1.5–2.1 m. Most of the canopy foliage fell within the upper
layer.
Fig. 4. Eddy-covariance H
E
vs. mean surface renewal H
S
sensible heat flux density using the time lags r=0.25 and 0.50 s from data collected at Satiety during 11–20 September 1998. H
S
was determined as the sum of two layers where the layers were from z=0 to 1.0 m and from z=1.0 to 2.2 m. The solid line represents a linear regression forced through the origin and the dashed line the 1:1 line.
Fig. 2 shows the results when H
S
was calculated as the sum of H from the two layers. The layer H values
were calculated as the mean H using the time lags r=0.25 and 0.50 s. When compared with H
E
, there was an improvement both in terms of α and the M
e
over using only the canopy top data Table 2. A second test for using layers to eliminate the need
for α was completed using the Satiety data. Fig. 3 shows the results when H
S
was calculated using the sum of H estimates from the two layers z=0–1.3 m
and z=1.3–2.2 m, which roughly correspond to the heights used in Villasor. Again, the layer H values
were calculated as the mean H using α=1.0 and time lags r=0.25 and 0.50 s. The α value was considerably
closer to unity and the M
e
was improved by using the layer estimates rather than using only the canopy top
estimate of H
S
Table 3. Although the z=1.3 m height roughly corresponds to that used in the Villasor ex-
periment, data were also collected at z=1.0 m height in the Satiety experiment. Using the layers z=0–1.0 m
and z=1.0–2.2 m, almost all of the foliage fell within
180 D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183
Fig. 5. Sensible heat flux density from eddy-covariance H
E
vs. the Tillman equation H
T
using data from Satiety during 12–15 September 1998.
the upper layer. When H
S
was calculated as the sum of the two-layer H values using the time lags r=0.25
and 0.50 s, the M
e
was further improved Fig. 4. Therefore, the best estimates of H
S
, without calibrat- ing for α, were obtained using one layer below the fo-
liage and the other layer including most of the foliage. Most likely, the air volume below the foliage had uni-
form heating and the upper layer, containing the fo- liage, had uniform heating that was different from the
lower layer. When determined separately and summed, the H
S
estimate was improved upon treatment of the canopy as one layer.
4.3. Comparison with the variance method Using data from Satiety, estimates of sensible heat
flux density H
T
using the Tillman 1972 equation were calculated and compared to H Fig. 5. Be-
cause there was insufficient data to determine the Monin–Obukhov stability function L, only the free
convection equation of Tillman was used. Free con- vection is most likely to occur under unstable, low
wind-speed conditions. Therefore, we only used H
T
values when H
E
was positive and when the wind speed was 2.0 m s
− 1
. The 2.0 m s
− 1
value could be too high for free convection conditions, but there were
few data with lower wind speeds. Based on the results in Fig. 5, the variance method has limited utility for
measuring over irrigated crops with high λE.
4.4. Energy balance calculations When testing the SR method, H
S
is compared with H
E
estimates from a 1-D sonic anemometer. It was assumed that the H
E
values were accurate, but the output was tested using energy balance closure. Fig. 6
is a plot of H
E
+ λE
K
from a 1-D sonic anemometer and a krypton hygrometer versus R
n
− G for data from the
Satiety experiment. The slope was close to unity and the value of R
2
was high, indicating a good closure. Therefore, it is likely that the 1-D sonic was providing
accurate estimates of H
E
. One of the purposes for this research was to find
a robust, low-cost method to estimate evapotranspi-
D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183 181
Fig. 6. Sensible plus latent heat flux densities from eddy-covariance H
E
+ λE
K
vs. net radiation minus soil heat flux density R
n
− G from
Satiety during September 1998.
ration λE from grape vineyards using the energy balance equation λE=R
n
− G−H. Comparison of λE
S
and λE
E
values with λE
K
is shown in Table 4 for the Satiety experiment. λE
S
was calculated as the resid- ual term of the energy budget using H
S
determined as the sum of two layers. The results showed a slope
Table 4 Slope of the regression b, coefficient of determination R
2
, root mean squared error M
e
, and number of half-hour samples for λE
S
and λE
E
vs. λE
K
measurements taken over 2.2-m tall grapevines at Satiety Vineyard, Woodland, CA on 11–20 September 1998
a
R
2
M
e
W m
− 2
n λE
E
0.97 0.82
56 279
λE
S
0.94 0.78
58 297
a
Regressions were forced through the origin and the M
e
is between λE
E
and λE
S
and λE
S
and λE
K
. λE
E
and λE
S
were calculated as the residual terms of the energy budget using H
E
and H
S
, respectively. H
S
was determined as the sum of two layers where the layers were from z=0 to 1.0 m and from z=1.0 to 2.2 m.
The range of λE
K
was −33 to −455 W m
− 2
.
of the regression through the origin close to unity for λE
E
and more scatter for λE
S
. However, the M
e
value for λE, estimated as a residual of the energy budget,
is approximately the same for surface renewal and eddy covariance. Based on the results from Satiety
and assuming an accurate determination of R
n
and G Fig. 6, the use of surface renewal H values, calcu-
lated by layers, in an energy balance equation provides estimates of λE within about 12 of values calculated
using a sonic anemometer and a krypton hygrometer.
5. Conclusions
