f
2
R
s
= R
s
1000 + K
R
1000R
s
+ K
R
5 f
3
T = T – T
L
T
H
– T
a
K
T
– T
L
T
H
– K
T a
6 where a = T
H
− K
T
K
T
− T
L
. In order to mini- mize the number of unknown parameters G
cm
, K
D
, D
c
, K
R
, K
T
, T
L
, T
H
we assumed that the lower and upper limiting temperatures were T
H
= 40°C and T
L
= 0°C, which are the values sug-
gested by Stewart 1988 for pine trees. The model was combined with Ritchie 1972
model as modified by Bonachela et al. 1999 to calculate E
s
. The combined model was tested against the data of Section 2.2 spring 1996. The
model was then used to calculate the daily crop coefficient K
c
, ratio of evaporation to grass ET of the orchard, case A, typical of intensive plan-
tations using weather data of Cordoba from 1964 to 1986, as K
c
is a commonly used parameter for calculating irrigation requirements. The model
was also applied to a traditional orchard case B with the same LAI and ground cover of 30,
assuming that maximum G
c
was 80 of that of the intensive orchard, due to the lower radiation
interception. The value of 80 corresponds to the ratio of intercepted radiation between the two
orchards. Although future work should be di- rected to the scaling-up of olive canopy conduc-
tance our assumption is supported by the general link between canopy conductance, and assimila-
tion e.g. Wang and Leuning, 1998 and the rela- tion
between assimilation
and radiation
interception of olive trees shown by Mariscal et al. 2000.
3. Results and discussion
3
.
1
. Radiation balance Net radiation above the tree was not statisti-
cally different from net radiation above the alley, thus data from the two net radiometers above
were averaged. Hourly net radiation was regressed on solar radiation:
R
n
= 0.81R
s
− 69 W m
− 2
, r
2
= 0.99
7 Regression of R
n
against R
s
for 24-h periods had an intercept not different from 0 and a slope
of 0.6. Soil heat flux was related to R
n
below the canopy R
nb
: G = 0.17R
nb
− 16 W m
− 2
, r
2
= 0.74
8
3
.
2
. Aerodynamic conductance The relation between friction velocity u and
wind speed above the olive orchard is shown in Fig. 1. There was an apparent reduction in slope
for U
o
greater than 1 m s
− 1
, which could be due to swaying of the trees. The linear regression was:
u = − 0.026 + 0.302U
o
r
2
= 0.92
9 with the intercept different from 0 at the 95
probability level. The regression forced through the origin yielded a slope of 0.282. From the
logarithmic wind profile we may calculate:
z − d z
o
= exp
k uu
n
10 where k is Von Karman’s constant 0.4, d zero
plane displacement m, z
o
roughness length m, and z is the measurement height m. Assuming
that d is in the interval 0.5 – 0.75 h, where h is the mean tree height 4 m then z
o
would lie between 0.48 and 0.61 m.
Fig. 1. Relation between friction velocity u and wind speed above the olive orchard, Cordoba, Spain, April 1997. Data
shown are hourly averages.
Fig. 2. Daily course of latent heat flux measured above total and below soil an olive orchard. Data are the averages of
hourly fluxes for DOY’s 171, 172 and 173, Cordoba, Spain, June 1997.
roughness elements which are concentrated in the tree canopies. Measured aerodynamic conduc-
tance yielded values around four times higher than those of a nearby grass Festuca arundinacea,
L. plot.
3
.
3
. Soil and plant e6aporation Fig. 2 presents the daily course of total LE
and soil LE
s
latent heat flux measured in Section 2.1. Data correspond to averages of hourly data
for DOY’s 171, 172 and 173, which are the only days when complete 24 h data are available. Both
LE and LE
s
were close to 0 during the night, and reached maximum values of 222 and 54 W m
− 2
, respectively, 2 h after solar noon. The latent heat
flux corresponding to transpiration LE − LE
s
reached a maximum of 167 W m
− 2
, but it was fairly constant during most of the daylight period
09:00 – 18:00 h ranging from 131 to 167 W m
− 2
. Total values of evapotranspiration, soil evapo-
ration and transpiration were 3.12, 0.74 and 2.38 mm per day, respectively. At the time these mea-
surements were made, the soil surface was dry. Nevertheless, soil evaporation contributed 24 to
the orchard ET. The ratio soil evaporationET would probably increase substantially when the
soil is partially wetted by drip irrigation.
3
.
4
. Canopy conductance Fig. 3 shows the daily course of estimated G
c
on a sunny day of June 1997 DOY 172. A typical
asymmetrical pattern is seen, and it may be ex- plained by the combined effects of irradiance and
VPD on stomatal aperture, similar to the response at the leaf level shown by Fereres 1984. Average
G
c
increased rapidly from sunrise to its maximum value 8.5 mm s
− 1
4 h afterwards, and then decreased throughout the daytime period, with a
rapid decline until 13:00 h and a slower change thereafter, when the air humidity deficit had al-
most reached its maximum. Similar trends of G
c
have been reported for other tree species e.g. Nothofagus, Schulze et al., 1995; Maritime pine,
Gash et al., 1989. The parameters of the Jarvis – Stewart model
fitted to our data are shown in Table 1. Data for Aerodynamic conductance m s
− 1
over the orchard was regressed against U
g
: G
a
= 0.0053 + 0.0496U
g
r
2
= 0.85
11 with the intercept not different from 0 at the 95
probability level. The regression forced through the origin yielded a slope of 0.052, which is simi-
lar to the value calculated for Pinus pinaster Ait. 0.056 of 20 m height by Gash et al. 1989. Thus,
olive trees show a comparatively higher aerody- namic roughness than pines which may be due to
the highly heterogeneous arrangement of the
Fig. 3. Daily course of canopy G
c
and aerodynamic G
a
conductance, Olive, Cordoba, Spain, June 1997.
Table 1 Parameters for calculating canopy conductance of olive trees
obtained by optimization
a
Pine Parameter
Olive G
cmax
mm s
− 1
33.4 15.4
K
R
W m
− 2
261 1194
0.061 0.059
K
D
kg g
− 1
11.8 D
c
g kg
− 1
10.9 20.0
20.2 K
T
°C
a
Data for pine trees Gash et al., 1989 are also shown.
that of pine. According to the G
c
model, the response of evaporation to changes in SHD shows
a maximum at SHD = 0.5K
D
, being 8.5 g kg
− 1
for olives 1.4 kPa. Air temperature for maximum G
c
, which is equal to K
T
, was 20.2°C for olive. No attempts to derive low T
L
and high T
H
temperature thresholds were performed because of the limited
range of temperature during our measurements. It is important to emphasize the limitations of this
type of analysis as radiation, temperature and humidity are not varied independently, and more
important, there is a direct dependence between calculated G
c
and the environmental variables via the Penman – Monteith equation, which means
that this type of model of G
c
is statistically incor- rect. However, most of our current knowledge on
canopy conductance for different types of vegeta- tion is based on the same model which has been
shown adequate for predicting evaporation in many cases e.g. Dolman et al., 1988. Neverthe-
less the overall agreement of our olive data with previous studies on pine indicate that olive G
c
responds to environmental conditions very much like coniferous forests despite differences in both
height and LAI. Further research is needed to determine the effect of LAI and soil water deficit
on olive G
c
. The relative sensitivity of LE
p
to changes in G
c
was large Fig. 4, with values around 0.9 during most of the daytime period, indicating that
changes in G
c
will cause changes of the same magnitude in olive evaporation. On the other
hand, the sensitivity of LE
p
to changes in G
a
, which is associated with wind speed, was ex-
tremely low with absolute values typically below 0.03. These sensitivities indicate that accurate pre-
diction of olive evaporation requires a sound model of G
c
a function of irradiance, air humid- ity and temperature and that wind speed will
play a minor role in determining LE
p
.
3
.
5
. Model test Calculated and measured daily ET data of the
orchard in spring 1996 Section 2.2 are shown in Fig. 5. This data set was used to derive the
relationships between net and solar radiation and pine Pinus pinaster Ait. trees determined by
Gash et al. 1989 for Les Landes forest are shown for comparison. Maximum G
c
was 15.4 mm s
− 1
, which would correspond to an average 0-deficit stomatal conductance of ca. 13 mm s
− 1
assuming that g
s
scales-up linearly with LAI, which is close to maximum values of stomatal
conductance observed by Orgaz pers. commun. in this orchard. Maximum values of G
c
are lower for olive trees than for pine Table 1 which may
be partly explained by a lower LAI 1.2 vs. 2.3. The response of G
c
to radiation indicates a slower opening of olive stomata as radiation increases
when compared with pine. For instance, 75 of maximum g
s
will be attained at radiation intensi- ties of 620 and 383 W m
− 2
, for olive and pine, respectively. On the other hand, the response of
olive G
c
to specific humidity deficit was similar to
Fig. 4. Daily course of sensitivity of evaporation to canopy dLELEdG
c
G
c
and to aerodynamic conductance dLE LEdG
a
G
a
, Olive, Cordoba, Spain, June 1997.
Fig. 5. Calculated and measured daily ET of the olive orchard, Cordoba, Spain, 1996.
tween 5 and 10, which is extremely wide when compared with commercial orchards 1 – 5. An-
other possible factor could have been an increase in G
c
when irrigation started, although rainfall amount during this spring was probably enough
to avoid any water stress. These results are en- couraging in terms of model validity for condi-
tions of uniformly wetted soil. The under- prediction shown after the start of drip irrigation
may be associated with evaporation from the wet bulbs; the study of this association deserves fur-
ther research.
3
.
6
. Orchard ET and crop coefficient The annual course of simulated average decadal
ET is presented in Fig. 6. Minimum values are close to 1 mm per day during the winter, while
maximum values around 3.5 mm per day occurred in June and July. The differences between the two
orchards are negligible in winter and increase as ET increases, due to changes in the relative im-
portance of E
s
Fig. 7, which is the main compo- nent of ET during the winter and decreases to less
than 10 of ET during the summer. This is caused by the typical Mediterranean pattern of
rainfall in Cordoba, with a wet season from Octo- ber to April and a dry season during the summer.
Average annual ET’s were 855 and 758 mm, for orchard A and B, respectively, while average an-
soil heat flux and R
n
below the canopy, thus it is not strictly independent, although it is so in terms
of the transpiration – evaporation model. Measured ET ranged from 2 to 5.5 mm per
day, while reference grass ET varied from 2.7 to 8.5 mm per day. The agreement between observed
and measured ET was good up to DOY 145 24 May, when drip irrigation was started. From
then on measured ET exceeded estimated ET by 0.5 – 1 mm per day. This difference might be the
contribution of evaporation from the soil wetted by the emitters, which was neither included in the
model nor measured. The wetted area was be-
Fig. 6. Simulated average decadal ET of olive orchards of LAI = 1.4 and 40 A or 30 ground cover B at Cordoba
Spain, 1964 – 1986. Vertical bars represent the S.D. Fig. 7. Simulated average decadal soil evaporation E
s
of olive orchards of LAI = 1.4 and 40 A or 30 ground cover B at
Cordoba Spain, 1964 – 1986. Vertical bars represent the S.D.
Fig. 8. Simulated average decadal crop coefficient ETgrass ET = ET
o
of olive orchards of LAI = 1.4 and 40 A or 30 ground cover B at Cordoba Spain, 1964 – 1986. Vertical
bars represent the S.D.
cases. Therefore, accurate prediction of E
s
is also required to estimate ET of olive orchards.
Crop coefficients varied substantially through the year with maximum values close to one during
winter Fig. 8 and minimum values around 0.4 in August. The variability in decadal K
c
’s also de- creased from winter to summer. The high K
c
in winter is the result of enhanced soil evaporation
due to rainfall, which also explains the greater variability of the K
c
. As the season progressed, the probability of rainfall decreased and so did E
s
, and consequently, the K
c
and its variability. Apart from the decrease in E
s
from winter to summer, increasing VPD from spring to summer and the
reduction in the fraction of intercepted radiation led to a relative minimum in the ratio E
p
ET
o
in the summer Fig. 9.
For annual values the crop coefficient was 0.62 for case A and 0.55 for case B, well below annual
crop maximum K
c
. The variation of the olive K
c
throughout the year and its dependence on VPD, intercepted radiation and E
s
, and thus, on the rainfall pattern, clearly indicates the difficulty in
proposing a unique K
c
value valid for different locations. Even in a given area, interannual vari-
ability in rainfall dates and amount will lead to changes in both winter and spring K
c
.
4. Conclusion
