How NDVI depends on LAI and vegetation cover ?
September 7, 2000
Kenlo Nishida (NTSG, School of Forestry, Univ. of Montana)
Introduction
NDVI is one of the most famous spectral vegetation indices observable with satellite sensors such as NOAA/AVHRR, Landsat/TM, SPOT/HRV, JERS1/OPS, Terra/MODIS, and so on. In this simulation study, I tested the relationship between NDVI and canopy structure, say, LAI and vegetation cover.
Model
For a rigorous study, threedimensional canopy transfer model may be necessary especially for checking BRDF. However, in this study, I focused on heterogeneity of canopy which may be complicated for three dimensional modeling. Hence, I adopted a simple 1dimensional radiative transfer model.
Suppose n layers of horizontal leaves on a soil. Another words, stack n leaves horizontally on a soil. If we denote the reflectance of this “canopy” as R_{n}, we can easily get the following formula:
Where, r_{leaf} and t_{leaf} are reflectance and transmittance of each leaf, respectively. If the reflectance of earth surface beneath the canopy is given (and denoted as R_{0}), R_{n} can be calculated with this equation.
Though some “clumping effect” is well known, I assumed spacially random distribution (Poisson Distribution) of leaves as a first approximation. It gives the following formula:
Where, P_{m} is the portion of canopy at which m layers of leaves are stacked on, and k is a coefficient which projects LAI perpendicularly onto the earth surface. It can be defined as:
where, L(theta) is the leaf angle distribution and theta is the angle between nadir and the normal vector of a leaf.
The reflectance of canopy can be expressed with the above equations as:
where, R is the canopy reflectance.
Parameter settings
I configured those parameters of leaf reflectance, leaf transmittance, earth reflectance, and kparameter based on the observed data in TERC grassland in 1999. The spectral bands for red and nearinfrared regions are taken on 580680nm and 7251073nm respectively. They mimic the NOAA/AVHRR CH1 and CH2.
Table 1 Parameters
Red 
NIR 

Leaf reflectance 
0.0983 
0.486 

Leaf transmittance 
0.0637 
0.335 

Earth reflectance (Case 1) 
0.0808 
0.1634 

Earth reflectance (Case 2) 
0.2795 
0.3684 

Earth reflectance (Case 3) 
0.4 
0.5 

k 
0.596 
Here, I tested 3 cases. The first case gives small reflectance of earth surface, second one is a middle reflectance, and the third one is high reflectance. The first 2 cases stand for actual observations of dead grass materials.
Results
Fig. 1, 2, and 3 represents the results of simulation with case 1, 2, and 3. The most notable thing is that the relation between NDVI and vegetation cover changed greatly between the cases. Some studies assume that this relation can be represented with square function (i.e., vegetation cover is linearly related to the square of NDVI). However, this relation can be linear when the albedo of leaf and earth get close to each other.