of the United Kingdom at midsummer. The LAI and daily integrated values of P were fitted to eq. 2 using the 
Nelder-Mead simplex algorithm. The same divisions used for the LAI-VI data were used to create a suite of 
semi-empirical models linking P to LAI with the LAI-P data. 
2.4. Sensitivity of the VI-LAI and VI-P relationships 
The standard deviation of a VI at any given LAI (a VI ) is an expression of the sensitivity of the VI-LAI 
relationship to noise. In this case noise is taken to mean anything not explicitly accounted for in the semi- 
empirical models. It therefore includes the scatter of points around the fitted curve caused by uncontrolled 
variability in soil reflectance, average leaf angle, leaf optical properties and solar-view geometry. This scatter 
of points around a mean value (for any given LAI) can be expressed as relative equivalent noise (REN^), which 
has been defined as the product of a v , /LAI and the inverse of the local slope of the VI-LAI relationship (Baret 
and Guyot, 1991). The slope of the VI-LAI relationship is obtained by differentiating eq. 1 
dVI/dLAI = - k V] (VI, - VIJ exp(- k VI LAI) (4) 
and so REN^ is defined as: 
REN,* = o^, /LAI = (o VI /LAI) (dVI/dLAI)' 1 
= (a VI /LAI){ - k vt (VI, - VI m )exp(- k VI LAI))' 1 (5) 
The scatter around the VI-P relationship is derived in a similar manner and the relative equivalent noise of P 
(RENp) is defined as follows: 
RENp = a P / P = (Ov,/ P) (dP/dVI) 1 
= (o VI / P)(aP, (VI„ - VI) <“'> / (VI, - VI,) ° }‘(6) 
where dP/dVI is the slope of eq. 3 and a = kp/k vl . 
3. RESULTS 
3.1. The sensitivity of the relative equivalent noise of LAI signal to chlorosis distribution, ALA and soil 
reflectance 
Fig. la shows the REN^ of NDVI and TSAVI for a fixed ALA=55°. When LAI>2 the relative equivalent noise 
of both indices was significantly larger when the chlorosis distribution was unknown. This arises because the 
effect of slight differences in the leaf optical properties of the two components are greatly magnified when the 
optical thickness of the layers increase. At low LAI the relative equivalent noise of TSAVI was an order of 
magnitude less than that of NDVI. This difference arises because the NDVI is far more sensitive than the TSAVI 
to soil reflectance. At intermediate canopy densities (2<LAI<6) the REN^ of TSAVI was greater than that of 
NDVI because the TSAVI-LAI relationship saturated at a lower LAI than the NDVI-LAI relationship. When the 
chlorosis distribution was known REN W was similar for both indices at high LAI, but when the chlorosis 
distibution was unknown REN,^ was an order of magnitude greater for NDVI than for TSAVI. 
Fig. lb shows REN^ when soil reflectance = 20%. The relative equivalent noise for both indices only 
marginally increased when the chlorosis distribution was unknown. This implies that the variation in ALA was 
equally as important as the variation in the chlorosis distribution. The REN^ of TSAVI was virtually identical 
for the three chlorosis distributions over the complete range of LAI. However for the NDVI there were 
significant differences in the REN lai between the three chlorosis distributions when LAI>2. When the canopy was 
sparse the uncontrolled variation in ALA affected both indices equally. After canopy closure NDVI was initially 
more sensitive than TSAVI to increments in the LAI, therefore REN^ was smaller for NDVI than TSAVI at 
intermediate LAI. 
Fig. lc shows REN lai when both ALA and soil reflectance were unknown. The noise in both indices 
were dominated by the effects of soil reflectance when LAI<3 and by the effects of ALA or chlorosis distribution 
when LAI>3. In dense canopies the noise in both indices was only slightly larger than those when the soil 
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