174 D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183
the temperature is measured at the canopy top, there is uneven heating and α1.0. For example, Paw U
et al. 1995 found α≈0.5 for temperature data col- lected at the canopy top of a forest, walnut orchard,
and maize crop. However, dTdt was determined us- ing low pass filtering, and not structure functions. For
short canopies, when the temperature was collected above the canopy top, the α values were variable, but
closer to 1.0 Snyder et al., 1996; Spano et al., 1997b. Differences in results were attributed to more even
heating above a canopy than within a canopy and a different methodology to estimate dTdt. In all cases,
the α factor was determined by empirical calibration against sonic anemometer measurements.
In early research, smoothing techniques were used to eliminate the independent random turbulent part of
the scalar signal, leaving only the coherent organized part Paw U et al., 1995; Katul et al., 1996, which
is used in SR analysis to determine ramp characteris- tics. However, a simpler method for calculating a and
l+s involved the use of a structure function and sta- tistical moments as suggested by Van Atta 1977. A
simple explanation of the procedure was presented in the Appendix of Snyder et al. 1996. This approach
gave good results over several crops Snyder et al., 1996; Spano et al., 1997b; Anandakumar, 1999. Chen
et al. 1997 presented a modified structure function approach to estimate H, assuming a sloping rather
than a vertical temperature change at the end of a ramp. This eliminates the quiescent period s between
ramps. Using this approach, they found good results for data collected over straw mulch, forest, and bare
soil.
In previous experiments, the plant canopies studied were variable in height, but all had dense foliage. In a
sparse canopy e.g. grape vineyard, the ground is only partially covered, and less differential heating of the
air volume below the measurement height is expected than in a forest, walnut orchard, or maize crop, which
were reported to have α≈0.5 Paw U et al., 1995. When data were collected at heights well above the
top of short canopies with α≈1.0, there was a con- siderable volume of air under the measurement height
when there was no vegetation. In a sparse vineyard, there is less vegetation than the tall, dense canopies
and more vegetation than for the short canopies, so 0.5α1.0 was expected in the vineyards with data
from the canopy top.
3. Materials and methods
Three experiments were conducted to test the use of the SR method in measuring energy balance in
grape Vitis vinifera L. vineyards. The first experi- ment was conducted in 1995 in the Oakville Field Sta-
tion in Napa Valley, CA latitude 38
◦
26
′
N; longitude 122
◦
24
′
W; elevation 58 m above m.s.l.. The Cabernet Sauvignon grapevines were oriented in north–south
rows with 1.2 m between plants and 2.7 m between rows, they were about 2.0 m tall, and there was ≈100 m
of fetch in the upwind direction south during the experiment. The canopy was estimated to have about
65 ground cover. The vines were irrigated with a drip irrigation system and trained in a conventional
curtain system. High-frequency f=8 Hz temperature data were collected at the canopy top 2.0 m and at
2.3, 2.6, and 2.9 m, using single-wire 76-mm diame- ter thermocouples. Net radiation 3.5 m height, soil
heat flux density 0.02 m depth, sensible heat flux density 3.0 m height, and latent heat flux density
3.0 m height were measured using a net radiome- ter model Q-7, REBS, Seattle, WA, three soil heat
flux plates REBS, Seattle, WA, a sonic anemometer model CA27. Campbell Scientific, Logan, UT, and
a krypton hygrometer model KH20, Campbell Scien- tific, Logan, UT.
A second experiment was conducted in 1996 in a grape vineyard near Villasor, Italy latitude 39
◦
24
′
N; longitude 8
◦
54
′
W; elevation 22 m above m.s.l.. The vines were ≈10-year-old Pinot bianco tops on 1103
Paulsen rootstock. There was a curtain training system with 1.2 m between plants and 2.7 m between rows.
The rows were oriented east–west and the vines were irrigated with drip irrigation. The height of the canopy
was 2.1 m and there was an ≈200 m fetch. Again, ground cover was about 65. Temperature data were
collected below and above the canopy at heights of 1.5, 1.8, 2.1, 2.4 and 2.7 m with 76-mm diameter ther-
mocouples. Energy balance sensors were the same as those used in California.
A third experiment was conducted at Satiety vineyard near Davis, CA latitude 38
◦
24
′
N; longi- tude 122
◦
30
′
W; elevation 20 m above m.s.l. during September 1998. The 2.2-m tall Cabernet Sauvi-
gnon vines were oriented in north–south rows, with a 2.7-m spacing between rows and 1.2 m between
plants. The vines were trained in a curtain system.
D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183 175
The fetch was 200 m with a canopy ground cover of ≈
65. The vineyard was flood-irrigated during the season, but not during the experiment. High-frequency
f=8 Hz temperature data were collected at the canopy top 2.2 m and at 0.3 m intervals below
the canopy height 1.0, 1.3, 1.6, and 1.9 m. A 1-D eddy-covariance system CA27 sonic anemometer
and KH20 krypton hygrometer was mounted at 2.5 m above the ground, and net radiation R
n
was mea- sured at the 3-m height. Six heat flux plates were
installed at the 0.08-m depth and two thermocouples were buried at depths of 0.02 and 0.06 m near each
of the plates to determine the soil heat flux density G. The G data were collected from a transect start-
ing at the middle of one row and at 0.5 m intervals in the direction of an adjacent row that was 3.0 m
west. A 3-D sonic anemometer Campbell Scientific CSAT3 was also used in this experiment, but unfor-
tunately was only working when the surface renewal thermocouples were not operational. However, both
the 1-D and this 3-D sonic anemometers did provide some coincidental data with a root mean square error
M
e
equal to 24 W m
− 2
, providing confidence in the accuracy of the 1-D sonic data.
In all three experimental vineyards, the foliage was evenly distributed within the upper two-thirds of the
canopy height. The foliage was dense within that vol- ume, but the canopy covered only about 65 of the
horizontal surface area, so about 35 of the soil was exposed to the sky.
All temperature data were collected using a Campbell Scientific CR10 data-logger. The sample
lags for calculating the structure functions were j=2, 4, 6, and 8 corresponding to time lags of r=0.25,
0.50, 0.75, and 1.00 s. Following the approach of Van Atta 1977, the second, third, and fifth powers of a
structure function were used to estimate a and l+s. A detailed description of calculations can be found in
the Appendix to Snyder et al. 1996:
S
n
r = 1
m − j
m
X
i=1+j
T
i
− T
i−j n
8 where m is the number of data points in the time in-
terval, j a sample lag between data points correspond- ing to a time lag r=jf, and T
i
the ith temperature sample in the interval. One assumption in using the
structure function of Van Atta 1977 is that the time lag r is much smaller than l+s. Therefore, the result-
ing values of l+s were screened for a minimum value of 5r s, with maximum value of 900 s. When l+s5r,
then H was considered to be missing data. This oc- curred rarely during day time. When l+s900 s, then
H was set equal to zero.
High-frequency temperature data from each mea- surement height were used to determine SR estimate
of H H
S
using the volume of air from the soil surface to the measurement height. Sensible heat flux density
was also calculated layer-wise within the canopy us- ing temperature measurements at the top of each layer
and assuming uniform heating within the layer below the measurement height α=1.0. If heating of the air
volume below a measurement height is uniform, then temperature fluctuations measured at the top provide
ramp characteristics that represent the entire layer, and they can be used to estimate the uniform change in
transient heat content of the underlying layer. If heat- ing is not vertically uniform, then calculating ramp
characteristics at several heights allows for the deter- mination of transient sensible heat content changes ac-
cording to the layer, assuming α=1.0 for each layer. This is true because, as the vertical thickness of an
air volume decreases, heating within an air layer be- comes more uniform and α approaches 1.0. Summing
the change in heat content over all layers gives the change in heat content of the full air volume under
the highest measurement. Because the ejection of air from the canopy involves the transfer of the entire vol-
ume of air under the highest measurement, separating the air volume into layers provides a method to more
accurately estimate total sensible heat flux density H
S
without calibrating for α. In the Villasor experiment, the H values were summed over two layers 0–1.5 and
1.5–2.1 m to determine H
S
. In the Satiety experiment, H
S
was determined for two different combinations of two layers. The first set of two layers was 0–1.3 and
1.3–2.2 m. The second set of two layers was 0–1.0 and 1.0–2.2 m.
In all cases, the SR method H values H
S
were compared with H values from a 1-D sonic anemome-
ter H
E
. Corrections for uneven heating α were cal- culated using a regression of H
E
versus H
S
through the origin. The α values, coefficient of determination
R
2
, and the root mean square error M
e
were de- termined for the r=0.25 and 0.50 s time lags and the
mean H
S
for the two time lags was compared with
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
