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Dees, Matthias 
  
proportional to the area of the strata, provided that the sample size comprises the number of strata several times over. 
The exact localisation of the samples during field work allows all sample points to be clearly assigned to stands. 
These requirements are fulfilled in the forest inventories in the public forest enterprises. A further requirement is the 
exact delineation of the forest stands. This can be done at little economic expense by registering the stand borders using 
aerial photos (Duvenhorst & Niehaus-Übel, 1996). Figure 2 shows the mapping of forest stands carried out within the 
framework of the study on the basis of CIR aerial photos. 
3.2 Statistical methods 
In the sample inventory estimates are needed for a large number of attributes. Statistically, they can be primarily 
derived from estimates of sums, mean values, and ratios. The forest area is known in inventories of forest enterprises. If 
the attributes are determined per area with reference to the single plot size and as quantities per ha, sums can be 
determined from the product of the characteristics mean values and the overall area in ha. The following examples 
should make this clear: 
Attributes volume per ha (e.g. 250 m?/ha) 
volume spruce per ha (e.g. 60 m*/ha) 
area spruce per ha (eg. 0,12 ha/ha = 0,12) 
Estimation of corresponding totals: 
Volume = total area x mean[volume per ha] 
Volume spruce - total area x mean[volume spruce per ha] 
Species area = total Area x mean[area spruce per ha] 
Estimation of corresponding ratios: 
Volume spruce per area spruce = mean[volume spruce per ha] / mean[area spruce per ha] 
Thus it is sufficient to derive estimators for means with the corresponding variances of the estimation of the mean and 
to derive estimators for ratios with the 
corresponding variances of the estimation of the 
ratios. An alternative is to derive estimators for 
totals and ratios instead of means and ratios as 
described by e.g. Dees (1996), but since the 
means and totals defined above differ only by 
the factor of the known area, the two 
approaches are equivalent. 
The combination of a systematic grid with a 
partition of the area into strata can be viewed 
approximately as an independent systematic 
sampling within each strata. The estimation of 
overall estimates is based on the estimation of 
means, variances and covariances inside the 
strata. The estimation inside the strata is done 
assuming simple random sampling inside the 
strata. Thus the resulting variances will 
overestimate the true values resulting in 
conservative estimates of the errors and derived 
confidence statements. 
To evaluate the benefits of a stratified estimate, 
an estimate is calculated without stratification. 
These estimates are calculated using estimators 
for simple random sampling, again resulting in 
conservative estimates of the errors. This is 
common practice in forest inventories in order 
to be on the safe side. Since the finite 7 p. : 4 
population correction can be neglected in forest ) À 
inventories for forest enterprises, the following 
estimators do not include a finite population 
correction. 
  
  
Figure 2. Registering of the stand borders based on aerial CIR photos 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 357