162 S. Landau et al. Agricultural and Forest Meteorology 101 2000 151–166
Fig. 3. Yields predicted by the parsimonious hybrid-model plot- ted against observed grain yields in the independent test sample
n=246. The 1:1 line is shown representing perfect agreement.
observed annual average yields well. The correlation between annual average predicted and observed yields
was r=0.77 again significant at the 5 level. This
Fig. 4. Annual average observed yields in the independent test sample closed symbols and annual average predictions from the parsimonious hybrid-model open symbols plotted against year.
indicated that purely temporal variation in annual av- erage yields was more easily accounted for by cli-
matic differences according to the new hybrid-model than the combined spatial-temporal variation in UK
well-managed yields.
4. Discussion
We have developed a new model for wheat grain yield response to environment. The model is ap-
plicable to spatially and temporally distributed UK well-managed yields. This new parsimonious
hybrid-model represents an attempt to bring together empirically-based statistical modelling with mecha-
nistic modelling. The hybrid-model consists of simple expressions of climate-yield mechanisms for which
empirical evidence exists, thus ensuring empirical importance and interpretability.
The hybrid-model adheres to the principle of par- simony. The complexity of the phenology sub-model
is much reduced relative to that of the CERES-wheat sub-routine, and it is driven by daily mean tem-
peratures alone. Although daily series of minimum temperatures, daily radiation levels and daily rainfall
S. Landau et al. Agricultural and Forest Meteorology 101 2000 151–166 163
values remain the initial inputs to the yield response sub-model, its structure is very simple. The rela-
tionship between the aggregated and possibly trans- formed climatic explanatory variables is assumed
to be linear, with individual climate effects simply adding to each other.
We have demonstrated the ability of the parsimo- nious hybrid-model to predict temporally and spatially
distributed UK well-managed yields in a large inde- pendent test 246 aggregated yields, correlation be-
tween observed and predicted yields 0.41, Fig. 3. Predictive power of the developed model on the tem-
poral as well as on the spatial scale is evident be- cause the sample of observed yields was constructed to
cover a range of years 1981–1993 and all major UK wheat-growing regions. In fact, the hybrid-model pre-
dicted temporal differences in annual average yields more accurately correlation between observed and
predicted annual average yield 0.77 than differences in the original spatially and temporally distributed
yields. The latter suggests that within-year variation in yields is more affected by factors not included in
the model — for example differences in sub-optimal management and physical site characteristics.
However, the predictive accuracy achieved was consistent with results in the literature for models
for a single site. The most relevant finding was that of Chmielewski and Potts 1995 whose single-site
yield-climate regression model achieved a corre- lation of 0.44 when predicting a long-term series
1854–1967 of farm yard manure treated grain yields from rainfall and temperature data in an independent
test. The success of the hybrid-model is in sharp con- trast to that shown by the crop models in the previous
validation study Landau et al., 1998. However, the lack of success of the crop models may result from
the fact that these cater for optimally managed yields which are not affected indirectly by weather i.e.
through sub-optimal management. Indirect weather effects, for example negative rainfall effects were
found to play a major role even in well-managed UK yields and explain part of the improved predictive
accuracy of the new model.
4.1. Empirical importance of climate effects The yield response sub-model Tables 5 and 7
serves to identify physiologically and agronomically justified climate effects which are of empirical impor-
tance for well-managed UK wheat trials. These can be ranked in order of importance Table 8, backward
selection procedure: •
Negative effects of rainfall during the estimated early-reproductive phase, the estimated anthesis
phase, the estimated grain-filling phase and the FebruaryMarch period are the most dominant ef-
fects in the climate response sub-model explaining 54 of the grain yield variation accounted for by
the model.
• Yield loss due to extreme frosts accounts for a
further 17 of the explained variation in grain yields.
• Yield is affected by the type of trial variety or
non-variety. In absence of climate effects, smaller yields are predicted for variety trials. But variety
trials are found to be less sensitive to rainfall during grain-filling. Trial type differences amount to 7
of the explained yield variation.
• The model predicts that the longer the duration of
the grain-filling phase, the higher the yields. This climate effect accounts for a further 7 of the vari-
ation explained by the model.
• Damage due to adverse harvest conditions high
rainfall in the week preceding harvest or late har- vesting accounts for 6 of the variation.
• Positive radiation effects during the early-repro-
ductive phase and the anthesis phase contribute 5 of the variation explained by the model.
• The model predicts that rainfall and radiation levels
in the early-reproductive phase interact with each other. Once a drought threshold is reached, radia-
tion has a negative effect, with the strength of the effect depending on the drought level. This interac-
tion accounts for 3 of the variance explained by the model.
• Finally, delaying the sowing date has a negative
effect on yield. This contributes the remaining 1 to the explained variation. However, the forward
selection procedure assigned a higher contribution Table 8.
Negative rainfall effects account for the major-
ity of the yield variation explained. Consistent with an assessment by Monteith and Scott 1982 UK
well-managed grain yields are shown to be affected more by indirect climate effects than by direct climate
effects.
164 S. Landau et al. Agricultural and Forest Meteorology 101 2000 151–166
4.2. Physiologicalagronomical interpretation The dominant negative effect of rainfall during
grain-filling is consistent with expectation from the viewpoint of ripening diseases. Amount and duration
both have a detrimental effect on yield by providing favourable conditions for diseases, denying access of
machinery to the land, washing off sprays. Possibly lodging and sprouting may contribute to the effect,
but these would be expected to occur during specific parts of grain-filling, and lodging would be associated
with the intensity of rainfall rather than the average amount. Relevant expressions for the latter effects
were considered, but did not perform as well as the expressions consistent with a disease effect. On the
basis of these arguments, negative rainfall effects dur- ing the anthesis phase are also attributed mostly to
increased incidence of disease.
Apart from
incomplete disease
control and
water-logging, the negative rainfall effects during FebruaryMarch may be due to washing away of
sprays, or leaching of fertiliser treatments since a small, 40 kg ha
− 1
nitrogen is recommended at this time UK Ministry of Agriculture Fisheries and Food,
1985. The main nitrogen application is recommended for the early stem extension stage usually April,
corresponding approximately to the start of the early reproductive phase. It therefore seems likely that the
negative effects of rainfall during the early reproduc- tive phase was related to nitrogen leaching, consistent
with the finding that rainfall during the March to May period has a strong negative effect on crude protein
concentration Smith and Gooding, 1996.
The finding of yield differences between variety and non-variety trials is attributed to differences in
management. However, confounding with a technol- ogy trend or with geographical characteristics cannot
be ruled out because the major trial series contributing non-variety trials UK Agricultural Development Ad-
visory Service trials were carried out in England and Wales before 1989. The dependence of sensitivity to
rainfall on trial type may be explained if variety trials have a higher level of disease control than non-variety
trials.
The positive effect of winter minimum temperatures below a threshold, the positive effect of the duration
of grain-filling and the positive effect of radiation lev- els during the early reproductive and anthesis phases
are in line with physiological expectations of win- ter kill, beneficial effects of prolonged grain-filling
and radiation-driven growth, respectively. In fact, the model assigns more importance to the duration of
grain-filling than to radiation levels, supporting the assessment by Monteith and Scott 1982. However,
the threshold of −3.2
◦
C below which winter kill is estimated to occur is higher than the threshold
value of −20
◦
C suggested by Petr 1991 and the range of threshold values for tiller damage used in
CERES-wheat −18
◦
C to −6
◦
C. The model predicts yield loss due to wet conditions
in the week before harvest. It also includes a penalty for late after August harvesting, which may have
a detrimental effect because the risk of shedding in the meantime and of harvesting under wet conditions
is increased Cranstoun, 1996. Finally, the date of sowing itself is modelled to affect yield. Consistent
with the findings of Green and Ivins 1985 the model assumes that later sowing date reduces yield.
Consistent with the finding of Baier and Robert- son 1968 that yield was most closely related with
soil moisture before anthesis, empirical evidence of drought effects was found only during the early repro-
ductive phase. During this phase, yield loss depend- ing on drought and radiation levels is predicted when
a threshold of 15 drought days during the phase is exceeded. No empirical evidence of such effects was
found during anthesis and grain-filling phases, possi- bly due to the overpowering negative effects of rain-
fall. Drought during later phases may be less damag- ing to wheat crops because of their ability to use stem
reserves Fischer, 1983.
Sensitivity estimates of climate variables showed smaller effects than expected Table 7. The model es-
timates a loss of 0.062 t ha
− 1
for each day by which the duration of grain-filling is reduced compared to
0.175 t ha
− 1
per day estimated from the findings of Vos 1981. The sensitivity to the radiation total dur-
ing the anthesis phase 0.002 t ha
− 1
MJ
− 1
m
2
is also much smaller than sensitivities derived from the litera-
ture 0.0094–0.0144 t ha
− 1
MJ
− 1
m
2
. Finally, the lit- erature estimate of a loss of 0.028 t ha
− 1
for each day delay in sowing after mid-September Green and Ivins,
1985 greatly exceeds the model’s sensitivity estimate of 0.0082 t ha
− 1
per day. These findings suggest that experiments where one factor is varied under condi-
tions of optimal management may exaggerate effects
S. Landau et al. Agricultural and Forest Meteorology 101 2000 151–166 165
compared to that effect averaged over many different sites, years, varieties and where there are interacting
stresses.
5. Concluding remarks
