172 D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183
method for measuring crop evapotranspiration in situ.
Several researchers have investigated the determi- nation of evapotranspiration λE of grapevines using
energy balance. Ham et al. 1991 and Ham and Heil- man 1991 used a sap flow heat balance technique to
measure the transpiration of vines and a Bowen ratio system to estimate λE in a grape vineyard to separate
crop evapotranspiration into transpiration and soil evaporation components. Oliver and Sene 1992 used
eddy-covariance to measure λE over grapevines and they concluded that soil and vines are independent
energy systems with little interaction between them. However, Heilman et al. 1994 showed that sensible
heat from the exposed soil surface is a major contrib- utor to the canopy energy balance and transpiration
of the vines. They concluded that the soil and the canopy are not independent and that the soil energy
balance does affect energy balance of the vines. In a later study Heilman et al. 1996 showed that the
canopy architecture has a substantial effect on soil and canopy energy balance, mainly by changing the
partitioning of vineyard net radiation into its soil and canopy components. Trambouze et al. 1998 used
eddy-covariance to measure λE from vineyards. They reported good λE estimates with very small time
scale information, but they recommended against us- ing eddy-covariance for estimating actual evapotran-
spiration of a vineyard because of the maintenance requirements. Because equipment for the Bowen ra-
tio and eddy-covariance methods is expensive and requires a fairly high level of expertise to operate, a
less expensive and more robust method is desirable for determining evapotranspiration of agricultural
crops.
Tillman 1972 first reported the use of high- frequency temperature variance data to estimate H.
He obtained good results during unstable atmospheric conditions when the data were corrected for stabil-
ity. Later, Weaver 1990 used temperature variance data, similarity theory, and calibration coefficients
that vary depending on the surface and energy bal- ance to determine H over semi-arid grass and brush.
When corrected for stability, Lloyd et al. 1991 and De Bruin et al. 1993 also observed good estimates
of H using temperature-variance data collected over sparse, dry land vegetation, stones, pebbles, etc. In
all of these experiments, the method worked only under unstable conditions, and a stability parameter
was needed for the calculations. Paw U et al. 1995 studied the use of the variance method during stable
conditions and reported that it was inaccurate for data taken within a meter or two of the canopy height for a
maize crop, a walnut orchard, and a mixed deciduous forest. Clearly, the temperature variance method has
little utility for measuring H over canopies with high evaporation rates that are likely to have near neutral
atmospheric conditions close to the surface. Also, a temperature-based method that requires complicated
measurements for determining a stability parameter has little practical value. In recent years, the surface
renewal SR method has shown promise to provide estimates of H from high-frequency temperature data
regardless of and without a measure of stability con- ditions.
The objective of this study was to evaluate: 1 the SR method for estimating H in grape vineyards; 2
the possibility of estimating H without the a factor α=1.0 by separating the canopy volume into layers;
and 3 the accuracy of the SR method for determining λE as a residual term of the energy balance.
2. Theory
The SR method is based on the idea that traces of high-frequency temperature data above and within
plant canopies exhibit ramp-like shapes that are re- lated to coherent structures Paw U and Brunet, 1991.
The mean ramp characteristics include the amplitude a, and inverse ramp frequency, l+s, where l is the ramp
duration and s the time between ramps. During a mea- surement interval, the ramp characteristics are used in
SR analysis to estimate H using a fundamental energy conservation equation Paw U et al., 1995; Snyder
et al., 1996; Spano et al., 1997b. The use of H esti- mated from SR analysis in conjunction with measured
net radiation R
n
and soil heat flux density G can pro- vide an easily transportable and relatively inexpensive
method to estimate λE. Under stable conditions, cold air ejects from a
canopy and is replaced by a sweep of warmer air from above. When this occurs, the temperature trace
Fig. 1 will show a sharp rise followed by a slow decrease as heat is transferred from the warmer air
to cooler canopy elements Gao et al., 1989; Paw U
D. Spano et al. Agricultural and Forest Meteorology 104 2000 171–183 173
Fig. 1. Schematic temperature ramps with amplitude a0 for un- stable and α0 for stable atmospheric conditions. The inverse
ramp frequency l+s in seconds is the sum of the quiescent period s and the ramp duration l.
et al., 1992. When the atmospheric conditions are unstable, warm air ejects from the canopy and cold
air sweeps in to replace it. Then the temperature trace shows a sharp decrease followed by a slow increase
until the next sweep and ejection Fig. 1. The dura- tion of a ramp l is the length of time during which
the air parcel is being heated. In addition, there is a quiescent period of time of duration s between ramp
events. The quiescent period occurs during the transi- tion time when the cold air parcel ejects from and the
warm air parcel sweeps into the canopy. The mean temperature amplitude and the length of time l+s for
a mean ramp during a sample interval determines the rate of heat transfer Snyder et al., 1996; Spano et al.,
1997b.
The rate at which air parcels heat or cool is related to the sensible heat flux between the canopy and the
air above. Assuming uniform heating of an air volume V, the change in heat content 1C is expressed as a
function of the change in temperature with time dTdt as
1C = ρC
p
dT dt
V 1
where ρ is the air density and C
p
the specific heat of air at constant pressure. If the change is measured over
a surface with area A, H is calculated as H = α
1
1C A
≡ α
1
ρC
p
dT dt
V A
= α
1
ρC
p
dT dt
z 2
where α
1
is added to account for uneven heating within the air volume and z is the height of the air volume
measurement height. Because temperature data are measured at a fixed point, one must relate this ‘local’
change of temperature with time in one dimension to the total time derivative of temperature:
dT dt
= ∂T
∂t +
x ∂T
∂x 3
Substituting for dTdt in Eq. 2 and rearranging terms, H can be expressed as a linear function
H = β + αρC
p
∂T ∂t
z 4
where β represents a micro-scale advection term, and α includes effects of uneven temporal heat distribution
in the canopy air and advective effects Paw U et al., 1995. Paw U and Brunet 1991 tested this equation
and reported that in the absence of advection, ∂T∂x≈0 and β≈0. Therefore,
H ≈ αρC
p
∂T ∂t
z 5
When high-frequency temperature data are mea- sured and analyzed for average ramp characteristics,
the change in temperature per unit time ∂T∂t — as the temperature increases or decreases during a ramp
— is equal to the amplitude divided by the length al; so, for the sensible heat transfer during the ramps, one
obtains
H
r
= αρC
p
a l
z 6
During the quiescent period, there is no apparent change in temperature with time and no sensible
heat flux, so H
r
is multiplied by the relative time for heating ll+s to account for the total time of ramp
activity and quiescent periods. Therefore, Eq. 7 provides an estimate of the sensible heat flux density
during the sampling period:
H = H
r
l l + s
= αρC
p
a l + s
z 7
Both a and H are positive under unstable conditions when the heat flux is upward. In Eq. 7, α=1.0 if
the volume of air is heated evenly. Frequently, when
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
