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
3.1. Evaluation of the errors in the evapotranspiration estimates
After rejection of clearly erroneous Bowen ratio data, 44 BREBS 1 and 82 BREBS 2 of the data
remained and on many occasions estimates were avail- able from both the systems. BREBS 1 had more data
failures due to water vapour condensing in the plastic tubing. Although 40 of the pairs of observations dif-
Fig. 2. Comparison of daily actual evapotranspiration E
a
esti- mated from two different Bowen ratio energy balance systems
BREBS. Dashed lines represent ±20 of the 1:1 E
a
values.
fered by no more than 0.5 mm per day Fig. 2, the ratio of BREBS 1 to BREBS 2 estimates was less than one
for low rates of evapotranspiration rates and greater than one at high rates and only 31 of the data fell
within ±20 of the 1:1 line Fig. 2. The discrepancy between the two systems was partly attributed to their
positions in the field which resulted in different fetch conditions Fig. 1. However, the rate of evapotranspi-
ration was not strongly correlated with wind direction and the effect of fetch was not consistent enough
to reject one or other of the observations. When there were two estimates, an average was therefore
taken.
The method used to calculate daytime E
a
was de- veloped for remote sensing applications where there
is typically only one instantaneous measurement per day. In our case, we had on average 22 valid measure-
ments 20 min averages for each day. The evapora- tive fraction was essentially constant on the clear day
78 DAS, 1 June and varied consistently on the other two days in response to short episodes of downward
sensible heat flux Fig. 3b. Deleting increasing per- centages of data did not introduce large errors even
when more than 50 of the data were deleted from the central 4 h of the day Fig. 3c. Errors in daytime
E
a
did not exceed 10 even when 60 of the data were deleted. This falls within the limits of the Bowen
ratio technique.
294 R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301
R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301 295
The assumption that night-time evapotranspiration was negligible, was tested for the same three days. By
considering only daytime evapotranspiration, underes- timates of 24 h E
a
by 1, 2 and 6 were introduced for days 71, 78 and 86, respectively. The result for day 86
can be explained by the higher night-time windspeed reaching a maximum of 2.5 m s
− 1
compared to other two days in which there was virtually no wind max-
ima less than 0.5 m s
− 1
. However, the absolute error was similar less than 0.1 mm per day for the three
days. 3.2. Water use by the linseed crop
Fig. 4 shows the seasonal progression of actual evapotranspiration E
a
of the linseed crop throughout the growing season as well as the trend of the main
meteorological and crop factors that influenced E
a
. As expected, E
a
rates fell below reference evapotranspira-
Fig. 4. Seasonal trends of a reference E , actual evapotranspiration E
a
and rainfall; b solar radiation and net radiation measured over linseed; c fractional ground cover and green area index GAI and d windspeed and vapour pressure deficit.
tion E during the initial and final parts of the grow-
ing season. The two most important factors influenc- ing the ratio of E
a
to E were expected to be GAI and
soil water status. When the green plant canopy sub- stantially covered the soil, roughly from 55 to 85 DAS
9 May–8 June, E
a
often equalled E , and sometimes
even exceeded it following rainfall. The development of the crop canopy can be seen from Fig. 4c where GAI
and the fraction of ground cover are plotted. The initial growth phase, i.e. when the fraction of ground cover
was less than 10 according to the FAO 56 definition, ended 36 DAS 20 April. The mid-season stage as-
sumed to be when fractional ground cover was more than 75 was reached by 56 DAS 10 May, five days
before the beginning of flowering. A maximum GAI of 1.8 was reached by 66 DAS 20 May, correspond-
ing to a maximum ground cover of 88, after which senescence began, starting about 77 DAS 30 May.
In linseed, dead leaves are gradually lost, but even at
296 R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301
Fig. 5. a Cumulative rainfall and actual evapotranspiration E
a
; b seasonal trend of volumetric soil moisture measured at four
different depths; c measured filled circles or calculated con- tinuous line soil water deficit SWD.
harvest time the remaining shoot biomass was able to intercept about 60 of incident solar radiation. During
senescence, the stems remained green for much longer than the leaves, so the crop was not completely dry till
well after all the leaves had been shed. For instance, at 100 DAS 23 June no green leaves remained, while
the shoot including the dry capsules, had an average water content of 40 on a fresh weight basis.
In Fig. 5a, cumulative rainfall and E
a
are plotted from 15 days after sowing i.e. six days after emer-
gence when the Bowen ratio was first measured. A to- tal of 238 mm of water was lost as evapotranspiration
by the crop during the growth season. In the same pe- riod, cumulative rainfall was 154 mm, so 84 mm was
extracted from the soil. Fig. 5b shows the time trend of soil moisture at different depths.
The water available to a depth of 0.60 m was com- puted as 67 mm and the water available in the pro-
file to a depth of 1.0 m, was calculated to be 115 mm. Fig. 5c shows that up to 40 DAS 24 April, the mea-
sured soil water deficit exceeded the value calculated from the Bowen ratio data and rainfall. During this
period, the maximum measured SWD was 50 mm and the soil returned to field capacity four times. After 60
DAS 14, the measured SWD lagged behind the cal- culated SWD and the final point suggested that the
measured value was approaching a maximum while the calculated value was still increasing. At maturity
the measured SWD was only 60 of the calculated SWD, which reached almost 140 mm.
3.3. Crop coefficients Measured crop coefficients K
c
, obtained from the ratio of E
a
to E , are plotted in Fig. 6a together with
the values estimated using FAO 56. Values for rainy days are marked separately. The baseline crop coeffi-
cient K
cb
follows the overall trend of measured val- ues quite regularly. When the fractional crop cover
was small, the estimated crop coefficient K
ce
showed typical ‘spikes’ corresponding to high rates of evap-
oration from the soil after rain. This crop coefficient forms the upper envelope for a crop growing without
limitations due to water shortage Allen et al., 1998. The FAO 56 values of K
ce
unadjusted for water short- age were mostly close to the measurements except on
rainy days. After canopy closure there appeared to be no effect of rain on the measured K
c
. Half of the avail- able water had been used up by 75 DAS 29 May
and K
c adj
consequently became less than K
ce
. How- ever, measured K
c
values were close to or exceeded the uncorrected value throughout the whole period of
growth suggesting that the crop did not in fact suffer from a serious shortage of water even after 75 DAS.
Average values for the main linseed growth periods of the measured and estimated crop coefficients are sum-
marized in Table 1. The measured crop coefficient was less than the one calculated for the initial and middle
R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301 297
Fig. 6. a Seasonal trend of measured and estimated crop coef- ficients. Symbols: measured K
c
values for rainy days ∗; mea- sured K
c
values for dry days
s
. Lines: K
cb
continuos; K
ce
dotted; K
e adj
dashed; K
cb
, K
ce
and K
c adj
were estimated us- ing the FAO 56 procedure. K
cb
is the baseline crop coefficient, K
ce
is the estimated K
c
and K
c adj
is the crop coefficient adjusted to take into account water stress; b estimated crop coefficient
K
ce
plotted against measured values of K
c
. Symbols correspond to different growth periods: initial stage
s
; development stage ∗; mid-season stage
h
; late season stage
d
.
periods, but agreed with the FAO 56 K
ce
in other growth periods. The FAO 56 K
c adj
appeared to be too small in the final phases of the growth cycle, appar-
ently overestimating the effect of water shortage on E
a
. In the comparison of estimated daily K
ce
against measured K
c
values Fig. 6b the largest discrepan-
Table 1 Average crop coefficients for linseed measured and calculated
using the FAO 56 procedure Growth period
a
Initial Development
Middle Late
End Measured K
c
0.4 0.8
0.9 0.7
0.2 FAO 56 K
ce
0.7 0.8
1.1 0.7
0.2 FAO 56 K
c adj
0.7 0.8
1.1 0.3
0.1
a
The growth periods are defined as in FAO 56. The initial period is from sowing up to 10 fractional ground cover; middle
period is from 75 ground cover to onset of senescence; end period is at complete senescence.
cies appear in the initial growth period, due to the fact that following rain events the estimated crop co-
efficient usually exceeded the measured one Fig. 6a. The agreement between measured and estimated val-
ues r = 0.74, P 0.001, RMSE = 0.24 was good for the middle and later periods of growth but was less
so r = 0.49, P 0.001, RMSE = 0.35 when the initial growth period was included.
3.4. Surface resistance Crop surface resistance showed a seasonal trend
with generally high values at the beginning and end of the period of growth and lower values in the middle,
although there was considerable variability Fig. 7. Two factors might be responsible for this pattern, green
area index and soil water deficit.
For low values of GAI, r
s
should be inversely pro- portional to GAI since it can be estimated by summing
Fig. 7. Seasonal trend of linseed aerodynamic resistance r
a
: dashed line and surface canopy resistance r
s
: symbols. r
a
was com- puted using the equation recommended in FAO 56, while r
s
was derived from evapotranspiration BREBS measurements and in-
version of the Penman–Monteith equation.
298 R. Casa et al. Agricultural and Forest Meteorology 104 2000 289–301
in parallel the resistances for individual leaves above a representative area of ground. Fig. 8 plots r
s
against GAI for all dates when GAI was measured. The data
points span the periods before and after the achieve- ment of maximum GAI but there was no evidence of
hysteresis in the curve. The points are close to the line representing the relationship:
r
s
= r
s min
G where r
s min
is 90 s m
− 1
and G is GAI. The constant of proportionality, r
s min,
which is the surface resistance of an actively growing linseed crop
completely covering the ground and freely supplied with water, was estimated, using the data in Fig. 7, as
the average value of r
s
for DAS 69-75 23 May–29 May, when the ground cover exceeded 0.80, the soil
water deficit was relatively low and rain was not a complicating factor. The equation given above gives a
value for r
s
of 45 s m
− 1
at the maximum GAI recorded whereas Fig. 8 suggests that r
s
does not decrease once GAI exceeds 1.00. Thus, r
s
can be modelled as the higher of the values calculated from GAI and 90 s m
− 1
. Before investigating the effect of soil water deficit
on r
s
, it was necessary to ascertain whether periods of rain were complicating the interpretation since r
s
should be zero for wet foliage. Four occasions were
Fig. 8. Relationship between linseed surface resistance r
s
and green area index GAI. The r
s
values are shown only for the days on which direct GAI measurements were carried out. r
s
was derived from evapotranspiration BREBS measurements and inversion of the Penman–Monteith equation. The data are fitted by
the line representing the relationship r
s
= 90G, where G is GAI.
Fig. 9. Relationship between excess r
s
, defined as the measured r
s
minus the modelled r
s,
calculated from GAI green area index with a minimum value of 90 s m
− 1
, and the measured soil water deficit SWD over the entire growing season.
found when a day on which more than 5 mm rain fell was both preceded and followed by a day with no
significant rain. There was no consistent or significant difference between the values of r
s
on the three days and thus rainfall was not a factor having a main effect
on surface resistance. The effect of soil water deficit on r
s
was evaluated by computing the difference between the measured
and the modelled r
s
and plotting it against the mea- sured soil water deficit Fig. 9. The values of GAI
required by the model were estimated by linear inter- polation between the field measurements. Contrary to
expectations, there was no effect of SWD on surface resistance. This is particularly obvious for deficits ex-
ceeding 50 mm where any affect should be clear. The apparent decrease of resistance at high deficits is prob-
ably an artefact caused by an underestimate of GAI near crop maturity and the extreme sensitivity of r
s
to GAI at values of GAI near zero.
4. Discussion
