Tabic 3: Regression equations for the northern and southern quarter scene. 
The standard errors of the coefficients arc between brackets. 
North: 
xl = 2,681 + 0.014*yl - 0.018*y2 - 0.006*y3 - 0.036*y4 
(0.308) 
(0.024) 
(0.009) 
(0.008) 
(0.014) 
x2 = -2.238 + 
0.014*yl 
+ 0.022* y2 
+ 0.003*y3 
+ 0.025 *y4 
(0.240) 
(0.018) 
(0.007) 
(0.007) 
(0.011) 
x3 = 0.564 + 
0.029*yl 
+ 0.003*y2 
+ 0.003*y3 
+ 0.011 *y4 
(0.197) 
(0.015) 
(0.006) 
(0.005) 
(0.009) 
(n = 30) 
Middle/South: 
xl = 2.962 + 
0.027*yl 
+ 0.023*y2 
+ 0.025*y3 
+ 0.013*y4 
(0.162) 
(0.015) 
(0.005) 
(0.006) 
(0.014) 
x2 = -1.777 - 
0.044*yl 
+ 0.025 *y2 
+ 0.023*y3 
+ 0.020*y4 
(0.155) 
(0.014) 
(0.004) 
(0.006) 
(0.013) 
x3 = -0.178 + 
0.016*yl 
+ 0.002* y2 
+ 0.002* y3 
+ 0.007*y4 
(0.058) 
(0.005) 
(0.002) 
(0.002) 
(0.005) 
(n = 65) 
where 
xl = fraction 
heather per pixel 
yl = pixel 
value band 3 
x2 = fraction ; 
grass per pixel 
y2 = pixel 
value band 4 
x3 = fraction 
bare soil per pixel 
y3 = pixel 
value band 5 
y4 = pixel 
value band 7 
CONCLUSIONS 
Using multivariate inverse linear regression it 
is possible to calibrate Landsat TM images of 
Dutch hcathland with ground cover data. 
Three cover types were used: heather species, 
grass species and bare soil. An important 
Feature of the method is that ground elements 
arc arranged in a linear array to enable the 
localization of ground data in the image with 
subpixel accuracy. This method yielded quan 
titative cover predictions with an estimated 
prediction error of +/- 15%. 
DISCUSSION 
In this study several cover types were com 
bined to three main groups. An important 
source of residual variance is the spectral 
variability with the groups. Heather, for exam 
ple, consists of two species in various life 
stages, from young to dead plants. Redefinition 
of these groups might reduce residual variance 
and thus prediction error. 
Further improvements could be made by 
using a simple or stratified random sampling 
method for selecting training pixels. In this 
way, the conditions for applying regression 
techniques arc more formally met. 
Instead of linear arrays of ground elements 
other set-ups could be used, in which the 
elements arc not consecutive, but distributed 
over the field. As long as the position of the 
elements relative to each other is known, the 
same optimization procedure that was applied 
here could be used. When ground elements 
are not consecutive, the possible negative 
effects of spatial autocorrelation between the 
elements are avoided. 690 
Selecting pixels that contain only the cover 
types under study out of the whole TM image 
is a cumbersome procedure. Dutch heathlands 
arc scattered over the country in a few big 
and many small nature reserves. When the 
measurements have to be carried out more 
frequently, as in a monitoring system, the 
location of relevant cover types should be 
stored in a CHS. On aerial photographs is it 
usually very easy to discern areas to which the 
calibration models apply. Photo interpretation 
could also be used to mark out objects within 
heathlands that would increase the prediction 
error, like roads, water bodies, and woodland. 
To make the regression models comparable 
in time, the images should be radiometricly 
corrected to radiance or reflectance values. 
REFERENCES 
Berdowski, 1987. The catastrophic death 
of Calluna vulgaris in Dutch heathlands. The 
sis, University of Utrecht, The Netherlands. 
Gates, C.E., 1979. Line transects and related 
issues. In: Sampling Biological Populations, 
edited by R.M. Cormack, G.P. Patil and D.S. 
Robson (International Co-operative Publishing 
House, Fairland, Maryland, USA). 
Hcil, G.W., 1984. Nutrients and the species 
composition of hcathland. Thesis, University of 
Utrecht, The Netherlands. 
Lwin, T. and J.S. Maritz, 1982. An analysis of 
the linear-calibration controversy from the 
perspective of compound estimation. Techno- 
metrics, 24: 235-242.