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z(xi) 2 Pixel value pixel i, i e (1,..,6) 
2(Xi+n) = Pixel value pixel i + h 
h = distance 
y, = semivariance at distance h 
= number of pixel pairs 
  
  
b (z(xi) - Z(Xi+n)) 
6 
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ya x3 (z(x; )— 2x, ) 
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sill 
  
nugget 
  
  
range 
  
Figure 1. Determination of a variogram for the row of six pixels. For every distance h all pixel pairs are determined and the 
difference is entered in the formula to calculate the semivariance y, . Through these values the variogram is fitted, which results in 
the three characteristics sill, range and nugget. 
taken into account. The range indicates the maximum distance 
of spatial dependency; when points are further apart their values 
cannot be used to predict each other with a higher probability 
than predictions based on the overall variance. 
Woodcock et al. (1988a) determined variograms for artificial 
images to investigate how they are influenced by ground 
objects. The images consisted of a homogenous background and 
objects placed on it, and for different images the number and 
size of the objects varied, so they could study the response of 
variograms to different situations. They concluded that the sill 
is influenced by the density of the objects, while the range 
depends on their diameter. Furthermore variations in size 
distribution result in different shapes of the variogram close to 
the range. 
The next step was to determine variograms for real images and 
to interpret them using the results obtained from the artificial 
images (Woodcock et al., 1988b). Their findings from the first 
phase remained valid; density of objects influences the sill, and 
the size of objects and the variance in their size distribution 
affect the range and the shape of the variogram. 
2.2 Crop growth models 
Environmental impact from agriculture increased because 
agricultural intensity increased. Since the aim of agriculture is 
the production of food, the aim of increasing the intensity is to 
raise yields. The actual yield thus contains information on 
agricultural intensity and environmental impact. 
Three theoretical yield levels can be distinguished. The 
potential yield is the maximum yield and it can only be obtained 
under ideal circumstances. In practice it will never be reached 
because of limiting and reducing factors. Limiting factors are 
water and nutrients stress and they can be combated by 
fertilisation and drainage or irrigation. Examples of reducing 
factors are pests and plagues which are combated by pesticides. 
When no limiting factors are eliminated, but all reducing factors 
are, the limited yield will be obtained. When neither limiting 
nor reducing factors are eliminated, the reduced yield will be 
obtained. The actual yield will lie somewhere between the 
reduced and the potential yield. 
Values of theoretical yields can be calculated by crop growth 
simulation models. When data on limiting and reducing factors 
are available they can also estimate actual yields whose values 
are available through statistics as well. An example of a crop 
growth model is WOFOST (Hijmans et al, 1994), which 
simulates on the basis of eco-physiological processes. It uses 
soil, weather and crop characteristics as input and produces 
biomass weight as output, which can be converted into yield. 
The model has been applied to extensive areas (Hooijer and 
Wal, 1994). 
3. CONCEPTS OF THE METHOD 
The aim of the method (figure 2) is to give an up-to-date 
overview of locations where the overall environmental impact 
of agriculture changed and to indicate whether the situation. 
improved or deteriorated. In the current situation the state of the 
environment or the assumed environmental impact is 
determined and afterwards changes are located. In the proposed 
method this process is split into two steps: first regions where 
changes occurred are identified and second the overall 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 65