% 
470 
VI 
= a 
(lb * e~ rMAI ) 
cence data. 
In the monomolecular function the three 
parameters determine a physical 
relationship between a VI and LAI. 
-Parameter a is the asymptote. 
- Parameter b controls the value of the 
VI if LAI=0. 
- Parameter c controls the rate of 
ascent of the asymptotic 
relationship. Low c values point to a 
better suited model. 
Mon-linear regression procedures 
involve the use of arbitrary starting 
values to estimate the parameter 
values from the set of observational 
data. 
However, since the parameters of the 
monomolecular function do have a 
physical meaning, appropriate starting 
values can easily be selected. 
The largest VI value of the training 
set can serve as initial estimate of a. 
Parameter b can be understood as an 
approximate of (1 - VInoii) (Wiegand 
and Hatfield 1988). Parameter c is a 
scattering/absorption coefficient and 
is smaller than 1. 
The monomolecular function has also 
been used by others (e.g. Baret and 
Major 1988) and has been proposed as a 
standard function in the SAMMA project 
(Wiegand and Hatfield 1988). 
3.2. Calibration results and discussion 
senes 
2. The values for parameter b 
effectively control the model for the 
situation LAI=0, both for bare soil 
situations as for completely senesced 
vegetation. For instance, for the 
models PVI/LAI and GRS/LAI, the b 
values are approximately equal to 1. 
3. R 2 values, indicating how close the 
calibration data fit to the proposed 
model are larger than .84. In all cases 
there is a lower R 2 value for the post 
senescence models as compared to the 
pre-senescence data. The ND, NDIV and 
TSAVI indices display the least scatter 
around the model, which is probably due 
to their strong asymptotic behaviour 
with respect to LAI. 
4. As for the corrections for solar 
zenith angle, the blanket corrected 
Vi's (bcor) show higher R 2 and is 
followed consistently by 'lcor', 
'nocor' and 'vocor' . This is the case 
for pre-senescence data as well as for 
post-senescence data. 
It can be concluded at this stage that 
the proposed monomolecular model 
appears to provide a suitable 
description of Vi’s and winter wheat 
LAI. 
The differences of the b and c 
parameters between the pre-senescence 
and post-senescence models warrant the 
use of two different models during the 
winter wheat growth cycle. 
A randomly selected 50 % subsample of 
the 1986 winter wheat data was retained 
for the calibration of the model. The 
training data were a priori divided in 
pre-senescence data and post-senescence 
data. The time boundary taken was 
Feekes stage 10.5 (all ears out of 
sheath). 
The estimation of the monomolecular 
parameters was different for both data 
sets: the asymptotic value a from the 
estimation of the pre-senescence data 
was assumed to be valid for the post 
senescence data case, leaving only b 
and c to be estimated. This approach 
makes the choice of the time boundary 
to separate both data sets less 
critical. 
This rationale is based on experimental 
evidence reported by Asrar et al. 
(1984), whereby the VI/LAI relationship 
reaches an asymptotic value at maximum 
LAI and migrates back, according to 
different b and c values. 
In the pre-senescence regressions, for 
each Julian date, a data pair for bare 
soil was included to tune the model for 
the boundary condition LAI=0, i.e. 
properly estimate the b parameter. 
From the model calibration following 
results can be highlighted: 
3.3. Validation results and discussion 
In order to test how effective a model 
is as a predictive tool, it is 
necessary to subject an independent 
test data set to the obtained 
prediction equations. All data from 
1904, 1985 and 1988, as well as the 
remaining 50% of the 1986 data served 
as test data. 
The model validation exercise was 
expected to provide answers to the 
following questions: 
-Are the VI/LAI relationships stable, 
i.e. do they apply to several 
cultivars and growing seasons? 
-Which VI is the best estimator of 
LAI? 
-Is a correction 
angle necessary, 
correction type is 
for solar 
and if so, 
the best? 
zenith 
which 
All calibration models were inverted, 
to yield, after input of measured VI, 
estimated winter wheat LAI (LAIesi). 
The general form of the inverted model 
is 
LAIn n t = ln((l - (Vl/a))/b)/-c 
The limitations of an inverted 
monomolecular model are obvious: 
1. The higher rate of ascent of the ND 
and TSAVI with increasing LAI, as often 
reported in literature is mirrored by 
the large c values (approximately .7, 
as opposed to .4 for SR) . NDIV follows 
the same pattern. However, this trend 
is less differentiated for the post- 
1. If VI values are larger than the 
model asymptote a, there is no solution 
for LAIrh i . If VI values are only 
slightly smaller than a, 
unrealistically high LAI«*t values may 
result. In both cases this problem was 
met by replacing the LAIer.t value by