P.A. Harrison et al. Agricultural and Forest Meteorology 101 2000 167–186 169
2. What climatic criterion can be used to determine realistic, spatially variable sowing dates across
Europe? 3. How can different wheat varieties cultivated in
Europe be represented in the broad-scale model? 4. How can the scaled-up broad-scale model be vali-
dated?
2. Methods
2.1. Estimating daily temperature data A spatial climatic database for Europe extend-
ing from 11
◦
W to 42
◦
E and from 35 to 71.5
◦
N at a resolution of 0.5
◦
latitudelongitude was utilised. This contained observed time series data for monthly
minimum, mean and maximum temperatures from 1961 to 1990 Hulme et al., 1995 and period-mean
standard deviations of daily mean temperatures about each monthly mean Carter et al., 1991. Observed
time series of daily minimum and maximum temper- atures covering varying lengths from 10 to 106 years
were obtained for 219 sites. The sites are distributed throughout Europe, but there was a paucity of sites in
eastern Europe and northern Fenno-Scandinavia.
The effect of using three methods for estimating daily temperatures from monthly values were investi-
gated with the AFRCWHEAT2 model: 1. A sine curve interpolation is a simple and com-
monly adopted technique, which involves fitting a sine curve with an annual period to mean monthly
observations of temperature. The sine curve inter- polation of Brooks 1943 was used.
2. A stochastic weather generator, a more complex method, involves simulating daily weather as a
stochastic process, in which the observed statis- tical properties of individual weather variables
and the correlation structure between variables are reproduced. Two stochastic weather generators
WGEN: Richardson and Wright, 1984; Richard- son and Nicks, 1990; LARS-WG: Racsko et al.,
1991; Semenov and Barrow, 1997 were used.
3. An intermediate approach, based on an adaptation of the sine curve interpolation routine of Brooks
1943, calculates daily deviations from monthly mean temperatures which are randomly generated
assuming a normal distribution with known mean and standard deviation. Barrow and Hulme 1996
found that daily maximum and minimum temper- atures in monthly subsets generally conformed to
normal or transformed normal distributions at nine sites in the UK.
The three methods for estimating daily temperature data were compared at eight sites located in differ-
ent regions of Europe. As the purpose of this exercise was to compare the different methods, a typical sow-
ing date and a single cultivar Avalon were used for each site. The mean and maximum difference in the
prediction of dates of each development stage between using observed and estimated daily data were anal-
ysed. Mean differences in the dates of double ridges, anthesis and maturity are shown in Table 1.
For all methods the estimated mean date falls well within the range of dates predicted using observed
daily data. The sine curve method predicts the small- est difference for the southern European sites Mont-
pellier, Brindisi, Seville where deviations are within 1 day on average. Predictions using this method are
slightly worse at the other sites, but are still within 8 days for double ridges, 4 days for anthesis and 3 days
for maturity. In general, daily temperatures are more variable at the northern and eastern European sites.
Thus, the simple sine curve interpolation is the most accurate at the sites where temperatures are the least
variable. The sine curve method with random daily temperature variability shows more consistent devia-
tions for all sites of between 1 and 4 days at double ridges and between 0 and 2 days at anthesis and matu-
rity. The two weather generators give marginally bet- ter results at some sites, but gains in accuracy are only
small. No consistent improvement in the prediction of all development stages throughout the range of sites
is observed.
Maximum differences for the date of maturity range from 2 to 8 days for the sine curve interpolation and
from 2 to 7 days for the sine curve interpolation with random daily variability. Maximum differences were
not computed for the two weather generators as an individual generated year of climatic data cannot be
directly related to a specific observed climatic year. Maximum differences for all other modelled pheno-
logical stages were similar to those described for the date of maturity, with the exception of double ridges.
Differences were larger for double ridges, because the timing of this stage is effected by a combination of
170 P.A. Harrison et al. Agricultural and Forest Meteorology 101 2000 167–186
Table 1 Mean difference in the prediction of the dates of double ridges, anthesis and maturity for winter wheat calculated using the AFRCWHEAT2
model with observed daily temperature data and three methods for estimating daily temperature data for eight sites in days Site
Mean date range of Mean difference from mean date of stage using estimated daily data
stage using observed daily data DOY
Sine curve Sine curve with ran-
WGEN LARS-WG
interpolation dom daily variability
a
Double ridges: Jokioinen, Finland
143.1 122–153 +
3.6 −
0.9 −
5.2 +
1.2 Edinburgh, Scotland
63.3 24–104 +
4.6 +
3.6 −
7.5 no data
Wageningen, The Netherlands 96.7 66–123
+ 7.4
+ 2.7
− 0.9
+ 8.5
Rothamsted, England 92.9 64–114
+ 4.7
+ 1.7
− 1.1
+ 5.3
Debrecen, Hungary 103.3 84–117
+ 5.8
+ 2.3
− 2.1
+ 3.2
Montpellier, France 64.1 48–90
+ 0.6
+ 1.7
+ 0.2
+ 2.0
Brindisi, Italy 48.8 42–59
+ 0.2
+ 1.9
− 0.6
no data Seville, Spain
45.8 43–49 +
0.3 +
1.7 −
1.4 −
0.5 Anthesis:
Jokioinen, Finland 176.2 168–183
+ 2.5
+ 0.3
− 2.0
+ 1.8
Edinburgh, Scotland 161.2 150–178
+ 1.5
+ 1.5
− 2.5
no data Wageningen, The Netherlands
160.8 148–171 +
3.1 +
1.7 −
1.1 +
4.0 Rothamsted, England
164.7 152–172 +
2.3 +
1.6 −
1.0 +
2.0 Debrecen, Hungary
154.8 144–163 +
2.5 +
1.3 −
1.3 +
1.3 Montpellier, France
138.9 128–148 +
0.7 +
1.4 −
1.1 +
0.5 Brindisi, Italy
130.0 123–136 +
0.2 +
1.2 −
0.9 no data
Seville, Spain 121.3 118–125
+ 0.1
+ 1.5
− 0.6
+ 0.7
Physiological maturity: Jokioinen, Finland
221.9 209–236 +
2.8 +
1.0 −
0.2 +
2.7 Edinburgh, Scotland
212.5 197–227 +
1.4 +
2.0 −
2.2 no data
Wageningen, The Netherlands 204.5 189–217
+ 2.8
+ 1.8
− 0.9
+ 3.9
Rothamsted, England 211.2 197–221
+ 1.9
+ 1.8
− 0.4
+ 1.8
Debrecen, Hungary 191.2 182–200
+ 2.0
+ 1.6
− 0.9
+ 1.1
Montpellier, France 175.5 164–184
+ 0.7
+ 1.7
− 1.8
− 0.8
Brindisi, Italy 166.4 160–174
− 0.03
+ 1.1
− 1.6
no data Seville, Spain
157.5 152–164 +
0.2 +
1.6 −
0.7 +
0.8
a
Average of 100 simulations.
both high and low temperatures, but consistent with the greater range of predicted dates calculated from
observed daily data. For example, the maximum devi- ation at Edinburgh was approximately 20 days using
both sine curve methods, but this should be compared with an inter-annual range of occurrence for this stage
of 80 days.
These results show that no or small improvements in accuracy are gained by using complex methods for
estimating daily temperatures compared with a sim- pler sine curve interpolation. Given that the more com-
plex methods require longer computing times a key consideration in spatial modelling, we concluded that
the sine curve interpolation is the most appropriate method for use in the broad-scale model.
Errors associated with the use of estimated daily data, calculated according to the sine curve method,
were quantified for the 219 sites. The mean duration of six development phases, calculated using observed
and estimated daily data, is plotted in Fig. 1. The first phase emergence to double ridges is slightly
over-predicted using estimated daily data with a mean bias error MBE of +4.6 days. The second and third
phases double ridges to terminal spikelet and termi- nal spikelet to anthesis are slightly under-predicted
with MBEs of −1.7 and −1.2 days, respectively. All successive phases are predicted reasonably accurately
with root mean square errors RMSEs of less than 1 day. These differences can be explained via the
mechanisms within the AFRCWHEAT2 development
P.A. Harrison et al. Agricultural and Forest Meteorology 101 2000 167–186 171
Fig. 1. Comparison of the mean duration in days of six wheat development phases calculated using the AFRCWHEAT2 model with observed daily data and daily data estimated using a sine curve interpolation routine: a emergence to double ridges; b double ridges to
terminal spikelet; c terminal spikelet to anthesis; d anthesis to beginning of grain filling; e beginning to end of grain filling; and f end of grain filling to maturity.
model. The effects of vernalization and photoperiod interact with thermal time during the emergence to
double ridges phase, whilst only photoperiod interacts with thermal time to predict the phases between dou-
ble ridges and anthesis. All other phases are calculated from thermal time alone. Hence, it would appear that
the effect of vernalization is not accurately reproduced using estimated daily data which causes slightly longer
phase durations. However, the interaction of photope- riod reverses this effect to a limited extent.
To investigate whether there is any spatial pattern to the magnitude of errors, the RMSE between time
series of phenological dates calculated using observed and estimated daily data at each site were interpolated
across Europe. RMSE values for the double ridges stage are shown in Fig. 2. Values in eastern Europe
and northern Fenno-Scandinavia should be interpreted with caution as the number of sites in these regions is
sparse. The largest RMSEs occur in Scotland, where errors range from 8.3 to 16.3 days. Examination of the
172 P.A. Harrison et al. Agricultural and Forest Meteorology 101 2000 167–186
Fig. 2. Root mean square error RMSE between the date of double ridges calculated using the AFRCWHEAT2 model with observed daily data and daily data estimated using a sine curve interpolation routine. Data interpolated from 219 sites.
site climatic data indicates that temperature variability is large over winter in this region. This is reflected in
a high inter-annual variability of the timing of double ridges see Table 1. The average RMSE for double
ridges from the 219 sites is 6.4 days. All other mod- elled stages exhibit lower errors than double ridges,
ranging from 0 to 8 days with a mean value of 2.2 days for anthesis and from 0 to 10 days with a mean
value of 2.1 days for maturity.
2.2. Estimating a spatially variable sowing date The date of sowing is an input variable in the AFR-
CWHEAT2 model and, hence, a method is needed to estimate sowing dates across Europe. In south-
ern Europe winter wheat is sown close to the time when vernalization will be most effective M. Bindi
and F. Miglietta, personal communication, 1992. Ac- cording to the AFRCWHEAT2 model, vernalization
occurs from −4 to 17
◦
C with an optimum temper- ature range of 3–10
◦
C. The date of sowing in the broad-scale model was defined as the first day of au-
tumn after 1 September when the mean temperature is 11.75
◦
C or lower. Based on the sine curve interpo- lation from monthly values, this threshold is reached
at three-quarters of the period between the maximum vernalizing temperature 17
◦
C and the beginning of the optimum range 10
◦
C. Using this threshold as- sumes that temperatures will decrease sufficiently to
be within the optimum vernalizing temperature range after the crop has emerged.
2.3. Accounting for multiple varieties The AFRCWHEAT2 model predicts develop-
ment for specified wheat cultivars. To account for the range of cultivars currently grown in Europe,
model parameters from previous studies in which the AFRCWHEAT2 model was calibrated and validated
against experimental data sets were obtained. These covered six winter wheat cultivars; five from north-
west Europe which differ in their duration of develop- ment phases and one from southern Europe Table 2.
For current climatic conditions, model predictions are only interpreted and validated for the appropriate
region and ignored elsewhere. For possible future changes in temperature, the relative performance of
all cultivars is compared across the entire region.
P.A. Harrison et al. Agricultural and Forest Meteorology 101 2000 167–186 173
Table 2 Details of AFRCWHEAT2 model parameters for six winter wheat cultivars
Developmental phase Avalon
a
Riband
b
Slepner
c
Hustler
d
Caribo
e
Alcala
f
Sowing to emergence: Tt: 1201
g
Tt: 1201 Tt: 1201
Tt: 1481 Tt: 1251
Tt: 1201 Emergence to double ridges:
PVTt: 2701 PVTt: 2851
PVTt: 3801 PVTt: 2841
PVTt: 2701
h
PVTt: 2701 PTt: 6001
PTt: 6001 Double ridges to terminal spikelet:
PTt: 1201 PTt: 1001
PTt: 1401 PTt: 901
Terminal spikelet to anthesis: PTt: 4001
PTt: 4001 PTt: 4001
PTt: 1851 Tt: 3509
Tt: 3509 Anthesis to beginning of grain filling
Tt: 1000 Tt: 1000
Tt: 1000 Tt: 409
Beginning to end of grain filling Tt: 5500
Tt: 5500 Tt: 5500
Tt: 2609 End of grain filling to maturity
Tt: 1000 Tt: 1000
Tt: 1000 Tt: 659
a
Avalon: fast developing UK cultivar. Source: J.R. Porter personal communication, 1991.
b
Riband: medium fast developing UK cultivar. Source: Semenov et al. 1993.
c
Slepner: slow developing UK cultivar. Source: Semenov et al. 1993.
d
Hustler: slow developing UK cultivar. Source: Weir et al. 1984.
e
Caribo: slow developing Dutch cultivar. Source: Reinink et al. 1986.
f
Alcala: fast developing Spanish cultivar. Source: M.A. Semenov personal communication, 1994.
g
Tt=thermal time; PTt=photo-thermal time; PVTt=photo-vernal-thermal time see Weir et al. 1984 for appropriate equations. Numbers refer to TtPTtPVTt thresholds above a base temperature in
◦
C.
h
PVTt is only used to calculate the phase from emergence to floral initiation model parameters are 1451 and then PTt is used to calculate the phase from floral initiation to double ridges model parameters are 1251.
Table 3 Comparison of observed and simulated sowing dates
Country Observed
a
Simulated Fenno-Scandinavia:
Finland 28 August–5 September
1–15 September Norway
5–15 September 1–24 September
Sweden 3–30 September
1–30 September Denmark
20–30 September 22 September–3 October
Central and eastern Europe: Poland
15 September–6 October 18 September–5 October
Czech Republic and Slovakia 30 September–5 October
10 September–8 October Romania
11–25 September 13 September–28 October
Bulgaria 5–31 October
23 September–8 November Hungary
10–21 October 3–17 October
North-west Europe: United Kingdom
13 September–26 October 1 September–29 October
The Netherlands 1–27 October
2–14 October Germany
15–25 October 20 September–12 October
France 1 October–15 November
14 September–29 November Southern Europe:
Portugal 20 October–21 November
14 October–31 December Spain
20 October–5 December 2 October–31 December
Italy 20 October–29 December
23 September–31 December
a
Observed dates of sowing from Broekhuizen 1965, Bunting et al. 1982, Weir et al. 1984, Kirby et al. 1985, Thompson and Stokes 1985, Reinink et al. 1986, Porter et al. 1987, Travis et al. 1988, Crofts 1989, Del´ecolle et al. 1989, Masle et al. 1989,
Mukula and Rantanen 1989, Hough 1990, Miglietta 1991, Narciso et al. 1992, Murphy et al. 1993, Nonhebel 1993, Zs. Harnos personal communication, 1994, Russell and Wilson 1994, J. Wolf personal communication, 1994.
174 P.A. Harrison et al. Agricultural and Forest Meteorology 101 2000 167–186
3. Results
