Science

Theory of Operation

Calculating Leaf Area Index (LAI) with the LAI-2200C requires certain assumptions about the plant canopy. This allows accurate measurements without the need to destructively sample the canopy. The LAI-2200C relies upon four assumptions: all light is absorbed by the foliage, the foliage is randomly distributed, the foliage orientation is random, and the foliage elements are limited by the view ring.

No real canopy conforms exactly to these assumptions. Foliage is never random, but is clumped along stems and branches, and is not "black." Many species exhibit some degree of heliotropism, which violates the azimuthal randomness assumption. However, many canopies can be considered random, and living foliage does have low transmittance and reflectance below 490 nm. Also, it is now possible to correct for errors caused by any transmittance or reflectance that does affect readings.

Offsetting errors are common, such as when leaves are grouped along stems (transmittance higher than the random model). In practice, most violations of the assumptions can be overcome with the proper measurement technique, and the model still works well even if all the assumptions are not met exactly.

All light is absorbed by the foliage

It is assumed that the below-canopy readings do not include radiation that has been reflected or transmitted by foliage. Note: this assumption is removed when you apply scattering corrections, thus accounting for foliage reflectance and transmittance in post-processing.

Foliage is randomly distributed

These envelopes might be parallel tubes (a row crop), a single ellipsoid (an isolated bush), an infinite box (turf grass), or a finite box with holes (deciduous forest with gaps).

Foliage orientation is random

That is, it does not matter how the foliage is inclined, but the leaves should be facing all compass directions.

Foliage elements are limited by the view ring

This is ensured when the distance from the optical sensor to the nearest foliage element, such as a leaf, is at least four times the element width.

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.

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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.

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;

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 LAI=μ*z, so Equation 2 may be rewritten

The LAI‑2200C implements this equation by numerical integration using the 5 measured view angles. The detector geometry fixes the value of sinθdθ for each ring, allowing computation of a constant weighting factor w(θi) for each ring. The numerical integration then becomes quite simple:

where the subscript i refers to each of the detector rings with view angle centered at θi.

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).

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Gap Fractions

The gap fraction technique is at present the most powerful and practical tool available for indirect sensing of canopy structure. It can be applied not only to continuous canopies, but also to discrete foliage-containing envelopes, such as row structure or individual trees.

Canopy structure information, including amount and orientation of foliage, can be estimated from measurements of gap fractions.

The gap fraction of a canopy is the fraction of view in some direction from beneath a canopy that is not blocked by foliage. The fractional sunfleck area is equivalent to the gap fraction in the solar direction.

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Light Scattering Correction

One of the traditional underlying assumptions of the LAI‑2000 and LAI‑2200 has been that foliage absorbs all the radiation in the blue waveband seen by the sensor (320-490 nm). This is usually a good assumption under diffuse light conditions such as uniform overcast, just before sunrise, or just after sunset. In direct sunlight, however, reflectance off foliage causes a much greater overestimation of the gap fraction and underestimation of leaf area index.