# computeG: Foliage projection ratio G(theta). In AMAPVox: LiDAR Data Voxelisation

 computeG R Documentation

## Foliage projection ratio G(theta).

### Description

Compute the mean projection of unit leaf area on the plane perpendicular to beam direction, namely, G(theta) parameter. Assumption of symmetric distribution of leaf azimuth angle. When estimating G for large amount of theta values, it is advised to enable the lookup table for speeding up the calculation.

### Usage

``````computeG(
theta,
pdf = "spherical",
chi,
mu,
nu,
with.lut = length(theta) > 100,
lut.precision = 0.001
)
``````

### Arguments

 `theta` a numeric vector, theta, the incident beam inclination, in radian, ranging `⁠[0, pi/2]⁠`. `pdf` the name of the probability density function of the leaf angle distribution. One of "uniform", "spherical", "planophile", "erectophile", "plagiophile", "extremophile", "ellipsoidal", "twoParamBeta". Refer to section "Leaf Angle Distribution functions" for details. `chi` a float, parameter of the ellipsoidal leaf angle distribution. The ratio the ratio horizontal axis over vertical axis. See section "Leaf Angle Ditribution functions" for details. `mu` a float, parameter controlling the Beta distribution. See section "Leaf Angle Distribution functions" for details. `nu` a float, parameter controlling the Beta distribution. See section "Leaf Angle Distribution functions" for details. `with.lut` a Boolean, whether to estimate G with a lookup table (LUT). By default the lookup table is automatically generated when length of theta vector is greater than 100. `lut.precision` a float, the increment of the theta sequence ranging from 0 to pi/2 for computing the lookup table.

### Details

Leaf Angle Distribution functions

• de Wit’s leaf angle distribution functions:

• uniform, proportion of leaf angle is the same at any angle

• spherical, relative frequency of leaf angle is the same as for surface elements of a sphere

• planophile, horizontal leaves most frequent

• erectophile, vertical leaves most frequent

• plagiophile, oblique leaves most frequent

• extremophile, oblique leaves least frequent

• ellipsoidal distribution function, generalization of the spherical distribution over an ellipsoid. Relative frequency of leaf angle is the same as for surface elements of an ellipsoid. Takes one parameter `chi` the ratio horizontal axis over vertical axis. For `chi = 1` the distribution becomes spherical. For `chi < 1`, the ellipsoid is a prolate spheroid (like a rugby ball). For `chi > 1` the ellipsoid is an oblate spheroid (a sphere that bulges at the equator and is somewhat squashed at the poles).

• two parameters Beta distribution. Most generic approach from Goal and Strebel (1984) to represent large variety of leaf angle distribution. Takes two parameters `mu` and `nu` that control the shape of the Beta distribution.

### References

Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.

`plotG()` for plotting G(theta) profiles

### Examples

``````# G(theta) == 0.5 for spherical distribution
all(computeG(theta = runif(10, 0, pi/2)) == 0.5) # returns TRUE
# ellipsoidal distribution
computeG(theta = runif(10, 0, pi/2), pdf = "ellipsoidal", chi = 0.6)
``````

AMAPVox documentation built on July 9, 2023, 5:32 p.m.