J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228 225
Table 7 Regression of simulated correlation on observed correlation bet-
ween detrended yields in different counties for different scales of climate and soil data and two different methods of distributing
wheat area
a
Scale of input data
Uniform distribution
Soil type-dependent distribution
Slope R
2
Slope R
2
1OP 0.11
0.32
∗∗∗
0.07 0.09
∗∗∗
1RP 0.14
0.35
∗∗∗
0.09 0.14
∗∗∗
1GP 0.16
0.33
∗∗∗
0.15 0.27
∗∗∗
6OP 0.21
0.11
∗∗∗
0.20 0.08
∗∗∗
6RP 0.17
0.09
∗∗∗
0.18 0.08
∗∗∗
6GP 0.22
0.23
∗∗∗
0.17 0.11
∗∗∗
1OG 0.17
0.35
∗∗∗
0.15 0.24
∗∗∗
1OC −
0.24 0.08
∗∗
− 0.24
0.07
∗∗
1RG 0.22
0.46
∗∗∗
0.21 0.37
∗∗∗
1RC −
0.16 0.05
∗∗
− 0.15
0.03
∗ a
The notation for scale of input data is explained in Table 1. Both the slope and coefficient of determination R
2
of the regres- sions are shown.
∗
p0.05;
∗∗
p0.01;
∗∗∗
p0.001.
coefficients of determination were obtained for coun- ties with high soil water capacities. This was espe-
cially the case when six climate stations were used for the upscaling.
The simulated spatial autocorrelation was in most cases much higher than the observed autocorrelation
Fig. 7. Increasing the number of climate stations from one to six or using the much larger network of
precipitation stations reduced the simulated autocorre- lations. This was reflected in the slope of the line relat-
ing simulated to observed spatial correlation Table 7, but not necessarily in the coefficient of determination
of that relationship. The use of dominant soil types on the county scale also reduced the simulation correla-
tion, but the slope of the relationship was reversed.
Table 8 shows the slopes of linear regressions of simulated and observed detrended county yields on
Table 8 Slope of regression of simulated or measured detrended yield
on temperature or precipitation for the periods April–July and October–July
Climate variable Measured
yield Simulated
yield Temperature, April–July
◦
C 0.32
∗∗∗
0.25
∗
Temperature, October–July
◦
C 0.32
∗∗∗
0.16
∗
Precipitation, April–July mm −
0.004
∗∗∗
− 0.001
Precipitation, October–July mm −
0.002
∗∗∗
− 0.003
∗∗∗ ∗
p0.05;
∗∗
p0.01;
∗∗∗
p0.001.
temperature and precipitation for either the whole growing season October–July or the main growing
season April–July. The signs of the response of both simulated and observed yield to temperature and
precipitation were identical, but the significance of the response was higher for observed yields.
4. Discussion
The scales of soil and climate data applied here had only a small effect on the ability of the model to repro-
duce the inter-annual variability in county and national yields Table 6. The ability of the model to reproduce
the observed spatial variation in yields was, however, substantially reduced when the resolution of soil data
was reduced to county level, which can be seen from the increase in the random error associated with coun-
ties Table 5. Decreasing the resolution of soil data to both the 10 × 10 km
2
grid net and to county level sub- stantially reduced mean national simulated yields, es-
pecially when the soil type dependent distribution was used Table 4. Decreasing the spatial resolution of soil
data to a county level completely destroyed the abil- ity of the simulated results to represent the observed
spatial autocorrelation structure Fig. 7 and Table 7. All these effects were brought about by changes in the
weight with which different soil types contributed to regional and national yields. This also had large effects
on simulated irrigation demand Table 4. The results thus collectively suggest that the spatial resolution of
soil data should be 10 × 10 km
2
or finer. There were only small effects of spatial resolution of
climate data on the agreement between simulated and observed inter-annual yield variation, but they were
larger for counties with high water-holding capacities Fig. 6. There were also considerable effects of scale
of climate data on the comparison of simulated and observed spatial autocorrelation Fig. 7 and Table 7.
Increasing the spatial resolution of both the basic cli- mate data and the precipitation data increased the slope
of the regression of simulated on observed spatial au- tocorrelation. This shows that the autocorrelation is at
least partly controlled by the climatic differences and the interaction with soils. The slopes in Table 7 are,
however, all considerably lower than one, and other controlling factors that interact with space and climate
may influence this autocorrelation e.g., farm types,
226 J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228
management. The results also show that a relatively high spatial resolution of climate data is necessary to
represent the observed spatial autocorrelation. Easterling et al. 1998 used a simulation model
to estimate wheat and maize yields in the central Great Plains of USA. They found that disaggregating
climate and soil data to approximately 1
◦
× 1
◦
resolu- tion gave the best agreement between simulated and
observed yields. Denmark spans 3
◦
of latitude and 7
◦
of longitude. A resolution of 1
◦
× 1
◦
is compara- ble to the use of six climate stations and soil data
from a 10 × 10 km
2
grid applied here. This rather detailed level of climate data was, however, only of
some advantage for description of the inter-annual yield variation at county level, whereas the ability
to describe variation in national yields was largely unaffected by scale of climate data.
The proportion of the inter-annual variation in ob- served yields captured by the model was substantially
higher in counties with higher water-holding capaci- ties Fig. 6. There are two possible reasons for this.
Firstly, yields are generally lower on sandy soils and crops here tend not only to suffer from lack of wa-
ter, but also from a higher risk of nutrient deficiency and from a higher disease prevalence such as take-all
Bødker et al., 1990. Secondly, the proportion of livestock farms is much higher in counties with sandy
soils. The livestock density of cattle and pigs in 1997 was 0.3–0.5 LU ha
− 1
in counties dominated by loamy soils and 0.9–1.1 LU ha–
1
in counties dominated by sandy soils. Dairy farmers in Denmark often use win-
ter wheat as a break crop in their forage crop rotation, and less emphasis is therefore put on optimal manage-
ment of the crop. Similar effects have been observed for cereals used as break crops in vine rotations in
Southern France Wassenaar et al., 1999 and for soybean Glycine max [L.] Merr. yields in areas of
cattle production in Iowa, USA Haskett et al., 1995.
The result of these effects is that, as the spatial extent of the model is increased, it gradually subsumes
more elements of the landscape and the ecosystem that are not formally included in the model Rastetter et
al., 1992. This results in reduced ability of the model to properly simulate inter-annual variability in crop
yields at the aggregate level.
Even though the model only explained a very small proportion of the observed inter-annual yield variabil-
ity, the response of the simulated yields to seasonal average temperature variability matched that of the
observed yields Table 8. This was to some extent also the case for effects of seasonal rainfall on yield.
There was no significant trend in any of these climate variables. The effects in Table 8 are therefore caused
by the inter-annual variability in climate, and the de- trending of both simulated and observed yields mainly
corrects for technological and land-use effects.
The results in Table 8 are in line with results reported by Easterling et al. 1996, who used a sim-
ulation model run for representative farms in seven counties to calculate crop production in eastern Ne-
braska. The model was found to reliably estimate crop yields under temperature extremes, whereas the model
failed to simulate effects on yield of extremes in rain- fall. The crop models thus capture some of the broad
effects of climate, especially those of temperature.
The use of different distributions of wheat area across the different soil types had no substantial ef-
fects on the ability of the model to mimic inter-annual yield variations Tables 5 and 6. It, however, resulted
in a change in the relationship of observed to simulated mean county yields Fig. 5. The soil type-dependent
distribution resulted in considerably higher simulated yields, especially on the sandier soils. Assuming that
the simulated mean county yields should be propor- tional to the observed yields, then desired simulated
values should be somewhere between those simulated by the two different methods of distributing wheat
area. This indicates that wheat area is not uniformly distributed on all soil types within a county. However,
the relationship between wheat area and soil water ca- pacity estimated from the county data may not strictly
apply within counties.
5. Conclusions
