10 P. Lagacherie et al. Agriculture, Ecosystems and Environment 81 2000 5–16
old means that the smallest value of the support of the possibility distribution representing the hydro-
logic property at point x is above the threshold. The modality possibly above the threshold means that the
smallest value of the core of the possibility distribu- tion is above the threshold. The next two modalities
were defined similarly. Undecided was used when the threshold falls within the core of the distribution the
true value can be above or below the threshold.
A Graphic User Interface for Windows written in Delphi 3 Borland
TM
using MapObjects
TM
ESRI
TM
was build for exploring interactively different values of the threshold Z
.
3. Application to the mapping of wheat yields over the Hérault-Libron-Orb valleys
3.1. The IMPEL project and the objective The spatial procedure presented above was applied
to the Hérault-Libron-Orb valleys south of France within the framework of the EC funded research
project IMPEL Integrated Model to Predict European Land use Rounsevell et al., 1998. This project aims
at integrating physical and socio-economic models to evaluate the impact of climate change on Euro-
pean land use systems at the regional scale. IMPEL is spatially distributed, based on a multidisciplinary,
modular approach, and comprises •
a climate module to downscale baseline climate data gridded to 0.5
◦
latitudinallongitudinal and Global Climate Model Experiment datasets IPCC, 1995,
using a stochastic weather generator,
Fig. 5. Location of the study area in the Languedoc-Roussillon region, Wassenaar et al., 1999.
• a soil and crop module to evaluate the soil water
balance and crop yields for a wide range of Euro- pean crops,
• a land degradation module to evaluate the impact
of soil erosion and changes in soil quality on crop productivity at the scale of soil map units and
• a socio-economic module to evaluate optimal land
use allocation and management requirements at the scale of individual farms.
Application of the spatial procedure dealt only with the second module of the IMPEL model, i.e. the soil and
crop model Euro-Access 2 AgroClimatic Change and European Soil Suitability developed earlier Love-
land et al., 1994. Spatial procedure was applied to the mapping of actual and expected crop yields over the
demonstration region by coupling Euro-Access 2 with a set of soil and climate data, which were considered
as easily available in almost all EC regions •
a 1:250,000 soil-landscape map of the region with a geo-referenced soil database in which STUs were
described qualitatively as presented in Fig. 1, •
a limited set 100 of profiles with soil descrip- tions and measurements of soil properties texture,
calcium content, organic matter content, bulk den- sity, water retention curve,
• pedotransfer functions providing hydraulic soil
properties, •
maps of soil forming factors as relief DEM, geo- logy or land-use over the studied region.
3.2. The region The study region Fig. 5 is located 60 km west
of Montpellier and covers an area of approximately
P. Lagacherie et al. Agriculture, Ecosystems and Environment 81 2000 5–16 11
1200 km
2
. The region exhibits typical northern Mediterranean climate characteristics, i.e. a substan-
tial average annual rainfall on average 700 mm per year, a high within-year rainfall variability with rain-
fall peaks in autumn and spring and strong droughts in summer, high between-year rainfall variability,
frequent and violent rainstorms and a large potential evapotranspiration PET on average 1000 mm per
year due to the high average temperature and radia- tion and frequent and strong winds. The temperature
exhibits only small variations across the studied re- gion annual minimal temperature ranging from 8.7
to 10.1
◦
C, annual maximal temperature from 19.1 to 19.6
◦
C. Conversely, the weather stations within the region reveal a strong within-region-variability
regarding rainfall 570–810 mm, which demonstrates a clear south–north gradient. PET measurements are
only available from two weather stations, Narbonne and Montpellier-Fréjorgues which are situated at ei-
ther side of the region Fig. 5. The difference in an- nual average PET registered at both weather stations
does not exceed 6.
The regional soil pattern is extremely complex mainly due to the large geological variations. The ba-
sic substratum is an heterogeneous Miocene marine sediment on which either Lithic Leptosols, Calcaric
Regosols or Calcaric Cambisols FAO-UNESCO, 1981 have formed. This substratum is partially
overlain by Pleistocene alluvial deposits. These de- posits have produced stony soils ranging from Cal-
caric to Chromic Luvisols. The most recent alluvial Holocene deposits contain Calcaric Fluvisols. Lo-
cal volcanic activity and recent colluvial phenom- ena have contributed to the soil heterogeneity. The
soil-landscape map of the studied region at 1:250,000 Bornand et al., 1994 defines 36 soil-landscape units
including 96 STUs in total.
3.3. Mapping hard wheat yields over the region 3.3.1. Deriving agrotransfer functions from a set of
typical soil–climate situations A limited number of simulation sites were selected
in order to take into account the soil and climate vari- ability of the region Wassenaar et al., 1999. Sixty-
three soil profiles located within or at the vicin- ity of the study region were extracted from the
Languedoc-Roussillon soil database Bornand et al., 1994 providing each of them the required input data
for the Euro-Access model. The total set of profiles represented the range of soil types that occur in the
region in terms of their hydraulic behaviour Bornand et al., 1992; Bonfils, 1993.
Climate variability of the region was considered through a set of theoretical weather stations defined
by assembling daily input data from available stations located within and near the study region. As stated in
the previous section, temperature and PET exhibit only slight variations throughout the region, which allows
the use of a unique data set of daily parameters, i.e. the one of the Montpellier-Fréjorgues weather station.
Three weather stations, Béziers, Pézenas and Aniane, were selected to represent the south–north gradient as-
sociated with change in elevation as this is the only noticeable climatic trend affecting the region.
The 63 soil profiles were combined with the three selected weather stations to obtain 189 theoretical
soil–climate situations representing the range of soil– climate spatial variations observed within the region.
The simulations were made using the crop model Euro-Access 2. A detailed description of the model
and of the calibration protocol is provided in Wasse- naar et al. 1999.
Fig. 6 presents an example of agrotransfer func- tions obtained from the set of simulations. The three
presented agrotransfer functions estimate the average hard wheat yield for a wheat–wheat rotation for the
period 1984–1991 as a function of awc for the three typical climate conditions of the studied region.
3.3.2. Estimating possibility distributions of available water capacity over the region
Available water capacity was estimated over the region according to the procedure presented above.
First, the qualitative descriptions of the 96 STUs of the soil-landscape map of the Languedoc-Roussillon
were converted into possibility distributions of the soil variables involved in the awc formula and in pedo-
transfer functions Eq. 1. A user-friendly computer interface Fabre, 1998 enabled a fast interpretation
of the qualitative description and the creation of the CSP to solve. The soil survey manual soil survey;
Staff, 1993 provides the coding systems for the dif- ferent variables, except for interpretation of textural
classes which uses the French GEPPA triangle Baize and Jabiol, 1995. The supports of the possibility
12 P. Lagacherie et al. Agriculture, Ecosystems and Environment 81 2000 5–16
Fig. 6. Estimations of mean hard wheat yield over the period 1984-1991 for three representative climate situations B´eziers, Aniane, P´ezenas, as a function of the soil awc. Correlation coefficients of curves fitted to the data are shown on the graph Wassenaar et al., 1999.
distributions were defined according to the maximum admitted errors Table 1. The qualitative descriptions
of STUs do not include any information about the bulk density of the soil. Consequently, a unique pos-
sibility distribution was defined for the region from a set of soil bulk density measurements. The core
and the support of this distribution are given by the intervals 1.35, 1.60 and 1.15, 1.85, respectively.
Second, awc was mapped over the region follow- ing the scheme presented in Fig. 3. Available water
capacities of the 96 STUs were determined accord- ing to Section 2.2. The points of the water retention
curve involved in expressing awc were estimated by pedotransfer functions derived from dataset containing
372 measurements of hydraulic properties of soil hori- zons located in the Languedoc-Roussillon Bastet et
al., 1997. Different pedotransfer functions were cal- culated for four classes of substratum to increase the
Table 1 The maximum errors used for defining supports of possibility
distributions Variable
Maximum error Clay, silt, sand
100 g kg
− 1
Depth 10 cm
Stoniness 100 g kg
− 1
Organic matter content 10 g kg
− 1
lower classes 50 g kg
− 1
upper classes Slope gradient
2 cm m
− 1
lower classes 5 cm m
− 1
upper classes
precision of estimations. A similar technique was ap- plied to determine the relation between the two points
of the retention curve last equation of system 1. For each of these statistical relations, the error term
was converted into possibility distributions. As stated in Section 2.2.1, the CSP solver CON’FLEX was used
for calculating the final possibility distribution of awc per STU.
The presence of STUs was determined in terms of possibility at each node of a 100 m×100 m grid cov-
ering the region according to Section 2.2. Additional geographical information involved in this step was as
follows: 1 a slope gradient map derived from digi- tal elevation model at scale 1:25,000; 2 a 1:50,000
geological map and 3 a land use map derived from the 1:25,000 topographical map. The error terms as-
sociated with 1 and the positional uncertainty of the boundaries of the map units of 2 and 3 were
determined statistically by comparing with more pre- cise information which was available in some limited
areas in the region like air-photograph-derived DEM, detailed soil maps Cazemier, 1999. The possibil-
ity theory algorithms required for calculating the possibility of presence of STUs Section 2.2 were
implemented in the macro language of ArcInfo
TM
. Finally, distributions of possibility of awc were ob-
tained over the region by merging the two previous steps according to the disjunctive combination oper-
ation mentioned in Section 1.2. This algorithm was also implemented in the ArcInfo
TM
macro-language.
P. Lagacherie et al. Agriculture, Ecosystems and Environment 81 2000 5–16 13
3.3.3. Applying agrotransfer functions with fuzzy estimates of available water capacity
The application of the agrotransfer functions amounts to a fuzzy calculus as presented in Section
2.3. Prior to this, each node of the grid covering the region was allocated to one of the three considered
typical climate situations in view to select the adequate agrotransfer function. This was done by a nearest-
neighbour algorithm. All these operations were per- formed within the GIS ArcInfo
TM
. 3.4. Results and discussion
The evaluation of the estimates of awc by the pro- posed spatial procedure addressed two questions: 1
do the estimates match reality?, and 2 are they in- formative?
To answer the first question, a validation set of 111 sites with measured Euro-Access 2 soil inputs was
considered in the study region. At each site, a mean annual wheat yield for the period 1984–1991 was cal-
culated by an Euro-Access 2 simulation. To use these validation data for evaluating the spatial procedure,
the estimated possibility distributions of wheat yield were first traduced into a set of crisp prediction inter-
vals each defined by the two values of yield having a given possibility level Fig. 7. The prediction inter-
vals were then evaluated at each site by determining whether they include or not the calculated yields.
Finally prediction errors were defined for each pos- sibility level by calculating over the set of validation
sites the percentage of wrong predictions provided by intervals defined at the considered possibility level.
Fig. 8 shows the prediction errors calculated from the different levels of possibility. It reveals that the
Fig. 7. The definition of prediction intervals black arrows for possibility levels 0.1, 0.5 and 1 from estimated possibility distri-
bution of yields grey line. Fig. 8. Prediction errors of yield estimates according to possibility
levels p at which are defined prediction intervals.
proposed spatial procedure provided very reliable estimates since the error was never higher than 12
possibility level=1. For possibility levels lower than 0.8, the predicted points were all included in the
prediction intervals.
To determine whether the predictions are infor- mative or not, the widths of the prediction intervals
derived from the estimated possibility distributions calculated over the whole region were considered.
The larger the interval is, the less informative the pre- diction. For example, predicting that wheat yield is
in the interval 3.5–4.8 Mg ha
− 1
, is more informative than predicting yield in the interval 1.5–4.8 Mg ha
− 1
. Fig. 9 illustrates the width of the predicted inter-
vals over the region. The mean width the black dots
Fig. 9. Mean width of yield prediction intervals black dots and range of variations over the region grey vertical bars according
to the selected possibility levels. Ranges of variation are defined by 5 confidence intervals.
14 P. Lagacherie et al. Agriculture, Ecosystems and Environment 81 2000 5–16
Fig. 10. Proportions of areas with the different possible answers given by the spatialisation procedure for different user-fixed thresh-
olds of yield.
ranged between 4.4 and 8 Mg ha
− 1
. These values de- note that the predictions were, in general, not very
informative. The width of intervals for the lower lev- els of possibility 0.6, was even larger than the total
range of variations observed in the validation dataset 0.67–7.42 Mg ha
− 1
. However, as shown by the con- fidence intervals of the highest level of possibility
the grey vertical bars, the interval width exhibited a substantial variation around the mean, suggesting
that more informative predictions could be found for limited areas in the study region.
In order to evaluate this, Fig. 10 presents the evo- lution of the areas covered by each decision unit de-
scribed in Section 2.4 with respect to a yield threshold value. This figure demonstrates clearly that the ability
to provide an informative result depends strongly on the query, i.e. of the considered threshold value. When
the threshold ranged between 2–5.5 Mg ha
− 1
, the pro- portion of areas for which no decision can be made
undecided predominated. However, an informative answer could be given for most locations when ex-
treme threshold values were considered. As expected, the proportion of undoubted answers remained low,
whatever the threshold value considered. On the other hand, for all threshold values, it was possible to
identify small but significant areas that have extreme behaviour with regard to the question posed. For
example, the spatial procedure identified within the region 127 km
2
where hard wheat yields were likely to be greater than 3.5 Mg ha
− 1
, and 21 km
2
where hard wheat yields were likely to be less than this
threshold value. The corresponding map is provided in Fig. 11.
Fig. 11. An example of hard wheat yield map over the region for the threshold 3.5 t ha
− 1
.
4. Conclusions
