# Calculating Leaf Area Index

Leaf Area Index (LAI) is the ratio of foliage area to ground area. The LAI‑2200C computes LAI from measurements made above the canopy and below the canopy, which are used to determine canopy light interception at 5 angles. These data are fit to a well-established model of radiative transfer inside vegetative canopies to compute leaf area index, mean tilt angle, and canopy gap fraction.

The optical sensor of the LAI‑2200C consists of a fisheye lens and an optical system. The fisheye lens “sees” a hemispherical image, which the optical system focuses onto the photodiode optical sensor, which is made up of five concentric rings.

Each detector ring views a different portion of the canopy or sky centered on one of the 5 view angles. The fraction of diffuse incident radiation that passes through a plant canopy, for each view angle, can be expressed as

*T*(*θ*) is the probability of diffuse non-interceptance for a given view angle (ring) called the gap fraction; it is analogous to a transmittance. *T*(*θ*) depends on foliage orientation, foliage density, and pathlength through the canopy in the same way that light transmittance through a solution depends upon the extinction coefficient, absorber concentration and pathlength, *i.e.*, according to the Beer-Lambert Law.

(1)

— or —

where *G*(*θ*) is the fraction of foliage projected toward view angle *θ* (view ring), *μ* is the foliage density (m² foliage per m³ canopy; analogous to concentration) and *S*(*θ*) is the pathlength through the canopy for each view angle, *θ*. Miller (1983) gives an exact solution for foliage density, *μ*;

(2)

The ratio *ln*(*T*(*θ*))/*S*(*θ*) is called the contact number (m^{-1}). Equation 2 can be applied to any general canopy shape (rows, isolated plants, etc.) as long as *S*(*θ*) is known. For full cover canopy of height *z*, *S*(*θ*) =*z*/*cosθ*; and LA*I=μ***z*, so Equation 2 may be rewritten

(3)

The LAI‑2200C implements this equation by numerical integration using the 5 measured view angles. The detector geometry fixes the value of *sin _{θ}d_{θ}* for each ring, allowing computation of a constant weighting factor

*w*(

*θ*) for each ring. The numerical integration then becomes quite simple:

_{i}(4)

where the subscript *i* refers to each of the detector rings with view angle centered at *θ _{i}*.

## Clumping

Usually multiple canopy transmittance measurements are taken for computing LAI. The individual transmittances can either be averaged before computing LAI, or more appropriately, the logs of the individual transmittances should be averaged before computing canopy LAI, as this accounts for clumping on spatial scales that are larger than the field of view of the sensor. The LAI‑2200C computes LAI in both ways but reports the values based on the latter method. The ratio of the LAI values calculated using the two methods is used to estimate an Apparent Clumping Factor (Ryu et al, 2010; Leblanc et al 2005; van Gardingen et al 1999; Nilson 1999; and Nilson and Kuusk 2004).

## Foliage Orientation

The LAI‑2200C calculates mean tilt angle (MTA) after Lang (1986). Alternative orientation information, such as gap fraction in various angle classes can be calculated using FV2200C PC software (included).