290 R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301
crop and a soil coefficient Wright, 1982. The coeffi- cients can then be used more safely in locations other
than those in which they were originally determined Ritchie and Johnson, 1990. The actual values of K
c
obviously depend on the method used to compute reference evapotranspiration and the lack of agree-
ment between the various models Choisnel et al., 1992 prevents the creation of a unique set of K
c
values Howell et al., 1995. The FAO 24 methodology has recently been re-
vised Allen et al., 1998. This methodology will be referred to, in the present paper, as FAO 56. The ref-
erence crop evapotranspiration E , now defined for
a ‘hypothetical crop’ resembling grass Allen et al., 1994, is to be computed using the Penman–Monteith
equation Monteith, 1965. In addition, an extended procedure for adjusting E
to actual crops has been developed Allen et al., 1996. This procedure takes
into account evaporation from the soil surface, and sub-optimal growth conditions such as water stress
and salinity, which result in a reduced leaf area index or an increased surface resistance. A water balance
model of the surface soil layer based on the two-stage drying model described by Ritchie 1972 is used to
estimate soil evaporation and a water balance model of the root zone is added when soil water availability
is sub-optimal.
Independent tests of the FAO 56 procedure are now needed in order to test its validity for a wide range of
crop species and environments. Lysimeters have of- ten been used to provide the ‘true’ evapotranspiration
Wright, 1982; Pruitt, 1991. However, some authors have claimed that measurement errors are more com-
mon than usually thought Allen et al., 1994. Increas- ingly, the Bowen ratio method is employed to estimate
crop evapotranspiration and calculate crop coefficients Hsiao et al., 1985; Grattan et al., 1998 because of its
portability and relative cheapness compared with the other micrometeorological techniques. Errors in the
Bowen ratio estimate of evapotranspiration are com- monly considered to be of the order of 10 Sinclair
et al., 1975; Angus and Watts, 1984. However, recent improvements in the instrumentation and careful data
analysis should enable this error to be reduced Malek and Bingham, 1993; Allen et al., 1994. The removal
of erroneous data Tattari et al., 1995 can result in substantial gaps in the record which can be filled us-
ing procedures that have been proposed for estimation of evapotranspiration by remote sensing Sugita and
Brutsaert, 1991; Zhang and Lemeur, 1995. In the present paper, evapotranspiration of lin-
seed Linum usitatissimum L. was estimated using the Bowen ratio technique during a growing season
in central Italy. Linseed, grown for the production of industrial oil, and its close relative, flax has a
world-wide cultivation area from Canada to India representing a wide range of environmental and man-
agement conditions. The K
c
values reported in FAO 56 and FAO 24 procedures come from a limited num-
ber of experiments carried out in Arizona and eastern Europe and require to be validated for Mediterranean
conditions. Data on the effect of soil water status on the actual water use of linseed in field conditions are
also lacking and this hinders the development and ap- plication of decision support systems for conditions
where shortage of water is important Casa et al., 1997. Most of the relevant informations come from
experiments carried out in India Gupta and Agrawal, 1977; Tiwari et al., 1988; Dutta et al., 1995 where
conditions are different from that in Italy.
The objectives of the present study were thus the following.
1. To evaluate the accuracy of daily evapotranspi- ration estimates from partially incomplete but
quality-checked Bowen ratio data. 2. To estimate linseed water use using the Bowen ratio
method. 3. To test the FAO 56 methodology for estimating K
c
. 4. To investigate the effect of water shortage on evap-
otranspiration by calculating the surface resistance of the crop.
2. Methods
2.1. Site description and sampling procedures Seeds of linseed Linum usitatissimum L., cv.
Mikael were sown in a 1.1 ha field 117 m × 95 m of the Viterbo University experimental farm latitude
42
◦
25
′
N, longitude 12
◦
08
′
E, altitude 310 m on 15 March 1996 at a rate of 60 kg ha
− 1
. The soil, an Ando Eutric Cambisol lithic phase, consisted of 26.6
clay, 13.7 silt and 59.7 sand ISSS method, 17.8 coarse material and 0.9 organic matter. Bedrock was
present at about 1 m, restricting root growth. Vetter
R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301 291
and Scharafat 1964 observed linseed roots reaching a depth of 1.20 m in Germany and Gupta and Agrawal
1977 showed that linseed can take up soil water from a depth of 1.0 m so the complete soil profile was ac-
cessible to the roots. There was no water table within the reach of the roots. Phosphorus and potassium fer-
tilizers were applied during seedbed preparation using 69 kg P
2
O
5
ha
− 1
and 75 kg K
2
O ha
− 1
. Nitrogen, to- talling 92 kg ha
− 1
, was applied as urea, half at sowing and half at the ‘buds visible’ stage of development.
Emergence was complete by 24 March, at which time the plant population density was 550 plants m
− 2
. Samples of above-ground plant material for growth
analysis and leaf area determination were harvested weekly throughout the growing period using three
replicate 0.5 m
2
quadrats. Green area index GAI was defined as the area of one side of the green leaf blades
per unit area of land surface Casa et al., 1999. The area of the green stems was ignored as calculations
showed that it could be neglected without introducing significant errors. GAI is a more appropriate mea-
sure of the transpiring area of the crop than leaf area index when the foliage is senescent. The crop was
combine-harvested at maturity on 10 July, when it had lost all green colour.
Soil water content was measured weekly for four layers 0.00–0.10, 0.10–0.20, 0.20–0.40 and
0.40–0.60 m at four locations in the field using the gravimetric method. Soil moisture was converted to
a volumetric basis using bulk densities measured in the field at the end of the growing season for the
same locations and layers as the gravimetric samples, using the excavation method of Blake and Hartge
1986. Pressure plate measurements of field capacity −0.03 MPa and wilting point −1.5 MPa were used
to compute the profile available soil water. The soil water deficit SWD, i.e. the amount of water needed
to restore the profile to field capacity, was estimated by adding daily evapotranspiration calculated using
the Bowen ratio method to, and subtracting rainfall from, the SWD of the previous day, subject to the
usual constraint that the SWD cannot be negative. The calculation was started on the 1 April, 17 days
after sowing DAS, when the SWD could be accu- rately derived from soil moisture measurements. An
independent estimate of SWD in the upper 0.60 m obtained from the measurements of soil moisture was
used to check the validity of the computed values. The fraction of solar radiation intercepted was
measured throughout the growing season using tube solarimeters Delta-T Devices, Cambridge, England.
One solarimeter was positioned above the canopy and six below at randomly chosen locations in the field.
The solarimeters were orientated at right angles to the rows, which were aligned approximately north-south.
The fraction of the ground covered by the vegetation was estimated from the fractional radiation intercep-
tion using the relationship of Steven et al. 1986 for barley, which has a similar leaf angle distribution.
2.2. Bowen ratio measurements and data processing Two Bowen ratio energy balance systems BREBS,
Campbell Scientific were installed in the field 34 m from the NE BREBS2 and SW BREBS1 edges
and 47 m from the other two sides Fig. 1. As the pre- vailing wind during the growing season was from the
south-west, the fetch from the two units was normally either 34 BREBS1 or 83 m BREBS2. The net
radiometers were moved upwards periodically to keep them about 1.0 m above the vegetation surface. Tem-
perature and vapour pressure gradients above the crop were measured using two unshielded, unaspirated
76 mm chromel–constantan thermocouples and one precision-cooled mirror dewpoint hygrometer model
Dew 10, General Eastern Corp., USA for each
Fig. 1. Plan of the experimental site.
292 R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301
system. The lower arm was raised during the growing season to keep it 0.30 m above the vegetation surface
while the distance between arms was kept constant at 0.60 m. For each BREBS, two soil heat flux plates
were buried at a depth of 80 mm in the soil and four spatial-average, 40 gauge, chromel–constantan ther-
mocouples were buried at depths of 20 and 60 mm. The soil heat flux at the surface G was computed by
adding the average heat fluxes sensed by the plates to the energy stored in the soil layer above them. The
storage term was calculated by multiplying the rate of change in soil temperature over the 20 min averaging
period by the soil heat capacity Malek, 1993 esti- mated from the interpolated volumetric soil moisture
content of the 0.00–0.10 m soil layer.
Latent and sensible heat fluxes, which were av- eraged over 60 min periods, were computed by the
equations usually employed in this method see e.g. Malek and Bingham, 1993. The temperature and
vapour pressure gradients for the whole dataset were carefully examined for systematic errors caused by
contamination of the thermocouples. Data from the two BREBS were averaged if both were available,
otherwise data from the functioning system were used.
Erroneous data were rejected using an algo- rithm with the criteria specified by Ohmura 1982
which takes into account the resolution limits of the thermometers and hygrometers ±0.006
◦
C and ±
0.01 kPa, respectively in this case. Following Heilman and Brittin 1989, data were also discarded
for periods when the fetch, as calculated from wind direction, was less than twenty times the height of the
arms. Stannard 1997 confirmed theoretically that the Bowen ratio method requires less fetch than the
eddy covariance method.
Daytime latent heat flux was estimated from the remaining data assuming a constant evaporative frac-
tion Sugita and Brutsaert, 1991. Although Zhang and Lemeur 1995 showed that the evaporative fraction
tended to be higher in the morning or evening and that it was more variable on cloudy days, most of the
evapotranspiration from a crop takes place in the cen- tral part of clear days when the evaporative fraction
tends to be most stable. The evaporative fraction was calculated as
f
e
= P
n 1
E
i
P
n 1
E
i
+ H
i
1 where the subscript i refers to the ith measurement;
n is the total number of available daytime measure- ments; E and H refer to latent and sensible heat fluxes,
respectively.
The daytime latent heat flux was calculated as E
d
= f
e
Q
d
2 where Q
d
is the available energy: Q
d
= Z
t
2
t
1
R
n
− G
dt 3
in which R
n
is the net radiation, G the soil heat flux and the integration period t
2
− t
1
that part of the day when R
n
was positive, i.e. approximately the hours of daylight. The daytime latent heat flux was then con-
verted into daily actual evapotranspiration E
a
in mm per day assuming that night-time evapotranspiration
could be neglected. To assess the validity of this approach when data
were missing, tests were carried out by removing in- creasing amounts of data for three days when all mea-
surements were available, and comparing the estimates of evapotranspiration with those obtained using all the
data. This test was done using fluxes averaged over 20 min to maximise the amount of data used. Day
78 after sowing DAS, i.e. the 1 June, was charac- terised by completely clear skies, day 71 25 May was
predominantly clear and day 86 9 June was largely cloudy. From 5 to 60 of the data in 5 increments
was deleted at random for each of the days. The re- sultant 12 tests were repeated 10 times for each day
using a different set of random numbers. It was ex- pected that the accuracy of the estimates of E
a
would decline as fewer measurements were available, partic-
ularly, when the missing data were from the central part of the day.
2.3. Reference evapotranspiration, crop coefficients and surface resistance
Daily reference crop evapotranspiration E was
calculated using the form of the Penman–Monteith equation recommended by the FAO Smith et al.,
1992, for a hypothetical grass crop with a fixed sur- face resistance 70 s m
− 1
and albedo 0.23. Data were obtained from an agro-meteorological station
500 m from the linseed field, except for actual vapour
R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301 293
pressure which was computed from Bowen ratio dew-point temperature measurements. Although the
actual vapour pressure was not measured in standard conditions, the data were considered to be more reli-
able than those derived from the hair hygrometer at the agro-meteorological station.
The ‘measured’ crop coefficient K
c
was calculated as E
a
E and compared with the estimates obtained
using the FAO 56 methodology Allen et al., 1998 in which the estimated crop coefficient K
ce
is partitioned into a baseline crop coefficient K
cb
defined as the ratio of crop to reference evapotranspiration when the
soil surface is dry and transpiration is occurring at the potential rate and a coefficient accounting for surface
soil evaporation K
e
. To take account of water stress, K
cb
is multiplied by a coefficient K
s
which is equal to 1.00 till half the available water is used up and which
then declines linearly to zero when all the available water in the rooting zone has been used up:
E
a
= K
cb
K
s
+ K
e
E
o
4 The term in brackets in Eq. 4 is called K
c adj
. Fol- lowing the procedures in FAO 56, K
cb
was calculated from the measured crop growth stage and plant height
and corrected to take account of the maximum ground cover. K
e
and K
s
were estimated daily. Following Russell 1980, daily values of linseed
surface canopy resistance were computed by inver- sion of the Penman–Monteith equation using inte-
grated daily net radiation, soil heat flux and mean vapour pressure deficit measured in the linseed field,
windspeed and temperature from the meteorological station and estimated E
a
. Aerodynamic resistance was computed using the equation recommended by FAO
Allen et al., 1998, without a stability correction.
3. Results
