Aigner, Edgar 
maximum of the NDVI usually is not one sharp peak, but is situated within a more or less broad plateau of 
high NDVI values (see figure 1). The plateau very well corresponds to the grainfilling stage of wheat, when 
green leaf biomass is at a maximum (i.e. NDVI is at a maximum) and all the photosynthetical production is 
used for filling up the ears (N.A. QUARMBY et al. (1993)). The GF parameter has a negative correlation with 
yield. The earlier it starts, the longer it can last, and the more grain yield can be expected. The commencement 
of the grainfilling stage was approximated by the first day, when the NDVI was greater than 0.5. GSR (Fig. 2c) 
has a positive correlation with yield. The offset can be interpreted as the minimum rainfall necessary for yield 
greater than O0 in the growing season, assuming a strict linear regression. The SDD water stress index is 
calculated as the difference between surface temperature (here: from AVHRR measurements) and air 
temperature (here: as measured at 3 pm). This index was first described by R.D. JACKSON et al. (1977). 
Negative values correspond to a surface temperature lower than the air temperature due to the transpiration of 
plants. When transpiration is reduced because of drought, the surface temperature increases and so does the 
SDD. Positive values are interpreted as water stress. Figure 2d shows the negative correlation of SDD with 
crop yield. The relationship in this case is not 
very strong, but yet significant. It becomes Table 2: Squared Pearson correlation coefficients for 
stronger with late prediction dates (not shown different parameters to yield of wheat at three prediction 
     
   
here). dates using data from 1995 to 1997. GF generally appears 
Table 2 shows the squared correlation. after mber, 10". 
coefficients for all prediction dates examined 95-97 
for wheat. All correlations were found to be Date NDVI SDD 
significant on a 95 % level. Nevertheless, none 10. Se o. Wa 0.87200 
NDVI max 0. 0. ; 0.217 
Oct. 0. 0. . 0. 
of the regressions for themselves are reliable 
enough to allow accurate and reliable yield 
estimations. 
3.3. Multiple Linear Regressions with Crop Yield 
A multiple linear regression model for yield for example of wheat using the parameters described above as 
independent variables, can be formulated mathematically as: 
Yieldyneat = bo + b1*NDVI(t) + b.*GSR(t) + b,*GF + b,*SDD(t) (2), 
where Yieldyhea is the vector of all measured wheat-yield data, NDVI, GSR, GF and SDD are the 
corresponding vectors of the derived parameters, and t is the prediction date. This leads to a set of regression 
coefficients (bobi,b»,bs,b4), which then can be used for predicting crop yield on other wheat-paddocks. Table 
3 shows the squared correlation coefficients for wheat using a multiple linear regression of yield to different 
combinations of independent variables and for the three prediction dates examined. 
One can see from table 3, that adding parameters generally improves correlation. Considering all examined 
crops, certain parameter combinations can be identified, that deliver “optimum” results for the three prediction 
dates examined. For “10. Sep.” that is {NDVI, GSR}, as the GF parameter is not available that early in the 
growing season. For the other dates the 
combinations are {NDVI, GSR, GF} for Table 3: Squared correlation coefficients for different 
“NDVInax”, and all of the parameters examined combinations of independent variables to yield of wheat at 
for “31. Oct.”. The correlation figures for three prediction dates using a multiple linear regression. 
  
  
  
  
  
  
  
  
  
  
  
canola and cereals (wheat and barley) all lie in 95-97 
a similar range. However, the correlation NDVI,GSR, | NDVI,GSR, 
coefficient does not give information on the Date NOV, oi NDVLOSR GE SESDD 
; . s 10. Sep. 0,420 0,558|n/a n/a 
actual quality of a prediction using the set of NDVI max 0,633 0,681 0,723 0,733 
derived regression coefficients [bo bi... b.l. 31. Oct. 0,497 0,720 0,720 0,737 
The prediction model was then evaluated. 
  
  
  
22 : International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 
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