214 J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228
crop physiology, but by secondary effects such as the presence and effects of weeds, pests, diseases, lodging
and anaerobic soil conditions Jamieson et al., 1999. These effects are not handled by current crop models,
and some of them interact strongly with both weather and crop management.
The area grown with winter wheat in Denmark increased sevenfold from 1971 to 1997. The increase
in wheat area occurred at the expense of the area with spring barley Hordeum vulgare L.. The in-
crease in winter wheat area can largely be attributed to higher-yielding varieties Silvey, 1994 and the in-
troduction of effective fungicides for disease control Orson, 1995. The relative increase in wheat area
was largest in the counties with sandy soils, indicating that winter wheat has expanded onto lighter soils with
lower soil water-holding capacities. This change in land allocation may have influenced the response of
national yields to weather, because of different yield responses on different soil types Wassenaar et al.,
1999; Olesen et al., 2000.
Only little attention has been given to the problem of scaling simulated crop production across areas
of contrasting soils and climate LeDuc and Holt, 1987; Easterling et al., 1998; Wassenaar et al., 1999.
This upscaling is necessary in order to obtain esti- mates of crop production at aggregated regional or
national levels. The aggregated yield is the weighted sum of yields obtained under different climatic, soils
and management conditions. The interaction between these factors and the correlation of yields over space
affect the aggregated yield variability. Simulated site yields in Denmark have been shown to respond dif-
ferently to climatic variation on different soil types Olesen et al., 2000, which would make the re-
sponse of aggregated yield strongly dependent on the soil × climate interaction. Other factors operating at
higher scales may, however, be linked with soils and climate variation, and influence actual aggregated
yields, e.g., farm types and land use restrictions. The optimal scales of climate and soil data for estimat-
ing county and national yields can thus not be easily deduced.
The purpose of this study was to examine the effects of different scales of climate and soil data on simulated
yield of winter wheat on regional and national scales in Denmark, and to compare these simulated aggregated
yields with observed yields.
2. Materials and methods
The methodology used for upscaling simulated win- ter wheat yield response to climate variability involves
three steps. First the necessary soil, climate and land use data are transformed to the required spatial reso-
lution. Secondly the crop simulation model is used to calculate yield with and without irrigation for all rel-
evant combinations of soils and climate. Finally the output is aggregated to either county or national level
by weighing simulated yields according to the area represented by each simulation run.
Various scales of climate and soil data have been compared. These data have three components: cli-
mate data excluding precipitation, precipitation data and soil data. Each scale is given a three-letter name
denoting each of these components e.g., 1RP, see Table 1. Only 10 of the 18 possible combinations of
scales were evaluated, omitting the combinations of spatially detailed climate data with spatially coarse
soil data. The selected combinations allowed the ef- fect of spatial scale of climate data to be evaluated at
the finest spatial resolution of soil data, whereas the spatial scale of soil data was evaluated at two spatial
scales of climate data. The actual allocation of wheat on different soil types is not known. The comparison
of scales of input data was therefore performed for two different ways of distributing wheat area onto the
soil types within each county. One method assumed a uniform distribution of wheat across all soil types.
The other method gave preference to soils with high water-holding capacity.
2.1. Crop model The CLIMCROP model describes the effects of cli-
mate on crop production and yield of winter wheat Olesen et al., 2000. The model includes a crop model
and a soil model that is updated in daily time steps. The water balance model is based on a reservoir
approach Olesen and Plauborg, 1995 with three reservoirs: interception, root zone and subzone reser-
voirs. Both the maximum root depth and the capacity for plant available water are assumed to vary between
soil types. Soil temperature is simulated using a sim- ple resistance approach where air temperature and
solar radiation drive the changes in soil temperature Olesen et al., 2000.
J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228 215
Table 1 Denomination of the spatial scales of climate and soil data
Index Description
Climate data excluding precipitation 1
One climate station only Ødum 6
Six climate stations with spatial representation according to a maximum correlation scheme Precipitation data
O Precipitation data from each 1 or 6 climate station used directly
R Precipitation data from each 1 or 6 climate station scaled to the precipitation ratio applicable for each 1 × 1 km
2
grid G
Precipitation data from all 650 Danish stations interpolated onto a 10 × 10 km
2
grid Soil data
P Data on top and subsoil types taken from the Danish soil survey at its finest spatial resolution
G The most representative top and subsoil type within each 10 × 10 km
2
grid cell C
The most representative top and subsoil type within each county
The phenology submodel is identical to that of the SIRIUS wheat model Jamieson et al., 1998 with a
few exceptions Olesen et al., 2000. The leaf area growth from emergence to 1 March is described as
a linear function of soil temperature sum. The devel- opment of green leaf area index during the growing
season is described by a logistic equation in soil or air thermal time prior to start of senescence. From
this point green leaf area index declines linearly with thermal time. The rate of leaf area expansion during
the growing season is affected by winter survival through an effect of daily soil minimum temperature
Olesen et al., 2000.
Nitrogen supply is the main factor controlling crop growth and yield of winter cereals under the humid
temperate conditions of northern Europe Asseng et al., 2000. The optimal nitrogen fertilisation to win-
ter wheat crops varies from 124 kg N ha
− 1
on sandy soils to 180 kg N ha
− 1
on loamy soils Knudsen et al., 1997. The maximum leaf area index has in many
studies been found to be proportional to nitrogen up- take e.g., van Keulen and Stol, 1991; Grindlay, 1997;
Sylvester-Bradley et al., 1997. The model uses a maximum leaf area index of 5 on loamy soils Olesen
et al., 2000. The observed variation in optimal nitro- gen fertilisation would thus imply a maximum leaf
area index of 3.4 on the sandy soils, given that nitro- gen use efficiencies were identical across soil types.
The leaf area parameters in the model were there- fore adjusted depending on soil type and irrigation
management in accordance with Danish nitrogen fertiliser recommendations for different soil types
Plantedirektoratet, 1997. Both leaf area expansion rate and maximum leaf area index were reduced by
40 under unirrigated conditions on soil types 1 and 2, and on soil type 3 with a sandy subsoil. For soil
type 7 and soil type 3 with a clayey subsoil the reduc- tion was set to 20. The reduction was set to 20
on soil types 1–3 Table 3.
Dry matter production is calculated using a radia- tion use efficiency which is restricted by low tempe-
ratures and reduced transpiration Aslyng and Hansen, 1982.
The sowing date was set to 15 September in all si- mulation runs, because a sensitivity analysis had
shown that the simulated effects of a realistic varia- tion in sowing date on yield was small under current
climatic conditions in Denmark Olesen et al., 2000. The crop is harvested at physiological maturity, and
yield is based on 15 grain moisture.
Irrigation scheduling is assumed to follow the prin- ciples of the MARKVAND scheduling programme,
which calculates an allowable relative soil water deficit that depends on crop growth stage Plauborg et al.,
1996. A maximum of 25 mm is applied in each irri- gation event. There must be at least 7 days between
each application.
2.2. Climate data Two scales of climate data excluding precipitation
were compared in the study Table 1. In the first case data were used from one climate station Ødum
only. In the second case data from six climate sta- tions were used within their respective geographical
regions Fig. 1a. Rainfall has much higher spatial and
216 J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228
Fig. 1. Regions allocated to six climate stations a and administrative counties b in Denmark.
temporal variability than the other climatic variables Table 2. A separate analysis of three different scales
of precipitation data was therefore performed. Six Danish meteorological stations were selected
for the upscaling study Fig. 1a. Climatological nor- mals for the stations are shown in Table 2. Data from
the period 1970 to 1997 were used. Missing data for some of the stations were replaced by data from
nearby stations Olesen, 1991. The six meteorologi- cal stations have data on temperature, global radiation,
precipitation, wind speed and air humidity. Global ra- diation was either measured directly or estimated from
sunshine hours using a modification of Ångstrøm’s formula as given by Rietveld 1978. Potential evap-
otranspiration was estimated using a modification of the Penman equation Mikkelsen and Olesen, 1991.
J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228 217
Table 2 Climatological normals for the six climate stations for the period 1961–1990 Olesen, 1991
Station Mean temperature
◦
C Precipitation mm
Potential evapotranspiration mm Year
April–July Year
April–July Year
April–July Tylstrup
7.4 11.4
668 204
553 344
Ødum 7.3
11.5 631
199 552
339 Borris
7.7 11.5
843 224
555 340
Jyndevad 7.9
11.8 859
248 554
337 Årslev
7.8 11.8
624 197
561 343
Roskilde 7.6
11.8 586
197 573
351
Each of the six stations was assumed to represent the climate of a region, which was delineated based
on a maximum correlation scheme using summer pre- cipitation as the determinant Fig. 1a. The pairwise
correlation of inter-annual variations in total summer precipitation April–July between each of the six sta-
tions and each of the 650 Danish precipitation stations was calculated. Only pairs of stations with more than
30 years of data in common for the period 1900–1995 were used. The correlation decreased with increasing
distance between the station pairs. For each of the six reference stations a geographical response surface of
correlation in summer precipitation was generated us- ing inverse distance interpolation. A composite map
was generated by allocating each point 1 km reso- lution to the reference station with which it has the
highest correlation.
Three different spatial scales of precipitation data were used. In the first case precipitation data were
taken directly from the climate station that gave the main climatic variables one or six stations. In the
second case the precipitation data from the station pro- viding the climate variables were scaled with the map
of relative normal rainfall within 1 × 1 km
2
grid cells. This grid map was obtained by interpolation of nor-
mal summer rainfall from all 650 Danish precipitation stations relative to each of the six climate stations. In
the third case precipitation data were obtained from all 650 precipitation stations with daily data interpolated
inverse distance weighted onto a 10 × 10 km
2
grid. This spatial interpolation may increase the frequency
of wet days. An initial test, however, showed that this had no effect of weather on crop yield.
Monthly mean temperatures and precipitation sums were obtained from each year and each county by
averaging overall available temperature and station data within each region. These data were used for
estimating effect of temperature and precipitation on measured and simulated yield.
2.3. Soil data The soil data were composed of two data sets: sur-
face soil and subsoil. The surface soil map was based on topsoil texture collected from approximately 32 000
sites on agricultural land at a depth of 0–20 cm Land- brugsministeriet, 1976. The survey was transformed
into a 1:50 000 digital soil data map with eight texture classes Table 3.
The map of the subsoil defined two types of sub- soil at 1 m depth on arable land in Denmark. The two
types were clayey subsoil more than 10 clay, gener- ally more than 15 clay and sandy subsoil less than
10 clay, generally less than 5 clay. The subsoil polygons have been digitised from different geological
and soil maps at scales from 1:100 000 to 1:750 000 Larsen and Sørensen, 1996.
The winter wheat crop was assigned different ef- fective root depths depending on topsoil and subsoil
type, resulting in different plant-available water ca- pacities on the different soil types Table 3. These
water capacities were derived from inventories of soil water retention in Danish soils Madsen and Holst,
1987 and experience on root growth on different soil types Madsen, 1983; Andersen, 1986.
Three different scales of soil data were compared in the study. The first scale used the dominant topsoil
and subsoil types at county level Fig. 1b. The second scale used the dominant topsoil and subsoil type within
10 × 10 km
2
grid cells. The third scale was based on the original maps of topsoil and subsoil at their finest
spatial resolution.
218 J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228
Table 3 Classification of soil types on agricultural area in Denmark according to surface texture
a
Soil type Clay
Silt Fine sand
Organic matter Area 1000 ha
W mm Sandy
Clayey Sandy
Clayey 1
0–50 0–200
0–500 100
761 55
61 85
2 0–50
0–200 500–1000
100 325
16 120
156 3
50–100 0–250
100 523
441 105
153 4
100–150 0–300
100 81
763 145
179 5
150–250 0–350
100 26
195 156
210 6
250–1000 0–500
100 20
8 170
227 0–500
200–1000 100
7 100
206 31
105 150
8 Atypical
8 Total classified area
1942 1519
a
The characteristics of the soil types are shown in terms of clay 2 mm, silt 2–20 mm, fine sand 20–200 mm and organic matter contents g kg
− 1
. The area and the capacity for plant available water in winter wheat W are shown for each soil type with either a sandy or a clayey subsoil. The soil type classification does not conform directly with the FAO classification, however, soil types 1 and 2 are
mainly sand, type 3 is mainly loamy sand, types 4 and 5 are mainly sandy loam, and type 6 is dominated by loam or sandy clay loam.
2.4. Wheat area Data on the agricultural area and on the area cropped
with winter wheat were obtained from the Danish Bu- reau of Statistics at the county level for every year in
the period 1971–1997. The fraction of total agricul- tural area grown with wheat, P , in the counties
was found in any given year to be a linear function
Fig. 2. Winter wheat area in percent of agricultural area as a function of weighted capacity for plant available water for the soils in the county for three different years. The lines show regression lines for each year separately.
of the area weighted plant-available water capacity of the soil, W mm:
P = −ab + bW 1
where a is the soil water capacity at which the area becomes zero mm, and b is the slope of the regres-
sion line mm
− 1
. The relationship is illustrated in Fig. 2 for three different years.The area with winter
J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228 219
Fig. 3. Intercept a and slope b of the regression lines relating winter wheat area to capacity for plant available water in the counties in Denmark shown as a function of year. The points represent results from regressions on data from individual years, and the lines show the
fitted segmented linear models.
wheat in Denmark increased from 86 500 ha in 1971 to 671 600 ha in 1997. Fig. 2 illustrates that both the slope
and the intercept of the regression line relating wheat area to soil water content in the counties changed over
this period. This development in the structure of the wheat-growing area is illustrated in Fig. 3 by showing
the development of the a and b parameters of Eq. 1 over time. These parameters were estimated by lin-
ear regression. Two different segmented linear models were estimated describing the development of a and
b over time:
a = a
1
, y ≤ y
al
a
1
+ a
2
y − y
al
, y
al
y 2
b =
b
1
, y ≤ y
bl
b
1
+ b
2
− b
1
y − y
bl
y
bh
− y
bl
, y
bl
y ≤ y
bh
b
2
, y
bh
y 3
The parameters of Eqs. 2 and 3 were estimated using the NLIN procedure of SAS SAS Institute,
1996. The parameters of model 2 were estimated as a
1
= 99 S.E. 2.6, a
2
= − 3.8 S.E. 0.36 and y
al
= 79.6 S.E. 1.2. The parameters of model 3 were
estimated as b
1
= 0.107 S.E. 0.009, b
2
= 0.209
S.E. 0.009, y
bl
= 76.5 S.E. 1.4 and y
bh
= 91.5
S.E. 1.4.
220 J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228
Two different methods of distributing wheat area within each county were tested, as the actual distri-
bution is not known. The first method used a uniform distribution of wheat area across all soil types. The
second method used the distribution across soil types implied by Eq. 1, but in such a way that the total
wheat area in a county within any given year matched the agricultural statistics. The hypothesis here is that
the second method would be superior to the first. Other factors that are correlated with the county structure
e.g., farm types may, however, also determine which crops are grown, thus making the wheat area less de-
pendent on soil type.
2.5. Irrigated area The agricultural statistics in Denmark provided data
at county level on number and size of farms with ir- rigation systems. The proportion of the area of the
farms that can be irrigated was taken from an inven- tory published by the Danish Bureau of Statistics in
1976. The irrigated agricultural area in each year and county was then obtained by multiplying the total area
of farms with irrigation systems by the proportion of the farm area that can be irrigated. The irrigated area
was distributed spatially with preference to soils with low water-holding capacity, W. This was done by let-
ting the relative probability of an area being irrigated decline linearly from 1 for soils with W ≤ 60 mm
to 0 for soils with W ≥ 160 mm. This function is based on simulated yield effects from using irrigation
Gregersen and Olesen, 1983.
Both the wheat area and the irrigated area were dis- tributed randomly for each year onto a 400 × 400 m
2
grid overlaying the soil maps. Each soil type was as- signed a probability of being irrigated or cropped with
wheat based on soil type and method of distribution. This probability depended on the soil water-holding
capacity. Grids of different size were tested down to a resolution of 100 × 100 m
2
. The results of using the 400 ×400 m
2
grid did not deviate from those of a finer spatial resolution. This grid size was therefore cho-
sen, because it reduced the number of computations needed.
2.6. Aggregation The crop model was in each case run for all years
for all combinations of soil types, with and without irrigation, within each of the climatic regions andor
grid boxes. The aggregated county or national yields Mg ha
− 1
were calculated as the area weighted sums of these simulated yields.
2.7. Evaluation The relationship between observed and simulated
county yields were first analysed using the following statistical model, which takes the observed yields
to be a function of systematic effects year and simulated yields and random effects county and
residual:
Y
yc
= α + βy + δX
yc
+ G
c
+ E
yc
4 where Y
yc
is the observed yield in county c in year y, and X
yc
is simulated yield. α, β, and δ are fixed effects. G and E are random effects associated with
county and the countyyear combination, respectively. This model was analysed for each spatial combination
using the MIXED procedure of SAS SAS Institute, 1996.
Subsequently the observed and simulated county and national yields were detrended to a 1990 basis
using separate linear time trends for each county estimated by linear regression. The ability of the
model and the upscaling method to capture the inter-annual variability in yields was evaluated for
county and national levels by linear regression of observed detrended yield on simulated detrended
yield. At county level this measure includes the ef- fect of systematic differences between counties. In
addition a linear regression of observed on simulated county residuals from the linear technology trend was
performed.
The ability of the model and upscaling method to capture the spatial variability in yield was eval-
uated by comparing observed and simulated county means of detrended yields. The ability to capture the
interaction between spatial and temporal variability was evaluated by comparing observed and simulated
spatial autocorrelation in yield both visually and by linear regression. This spatial autocorrelation was cal-
culated for observed and simulated yields separately as the pairwise correlation of inter-annual variations
in detrended yields between all combinations of counties.
J.E. Olesen et al. Agriculture, Ecosystems and Environment 82 2000 213–228 221
Fig. 4. Time trend of observed
d
and simulated
s
grain yield for winter wheat for two counties Ringkøbing and Storstrøm. The simulated yields were calculated using scale 6GP with a uniform distribution of winter wheat area within each county.
3. Results
