biometrics (version 1.0.3)

kozak.fx: Function to computes the stem diameter of a tree according to the Kozak (1988) taper equation.

Description

Function of the Kozak (1988) taper equation model, based upon the model parameters, and the tree variables: diameter, total height, and stem height. The mathematical expression is as follows $$ d_{l_{i}} = \alpha_0 d_i^{\alpha_1}\alpha_2^{d_i}X_{l_{i}}^{ \left[\beta_1 z_{l_{i}}^{2} +\beta_2 \ln{(z_{l_{i}} + 0.001)} + \beta_3\sqrt{z_{l_{i}}}+ \beta_4 \mathrm{e}^{z_{l_{i}}} +\beta_5 (d_i/h_i)\right] },$$ where: \(d_{l_{i}}\) is the stem diameter at stem-height \(h_{l_{i}}\) for the i-th tree; and \(d_i\) and \(h_i\) are the tree-level variables diameter at breast height and total height, respectively, for tje i-th tree. The other terms are $$z_{l_{i}}=\frac{h_{l_{i}}}{h_i},$$ $$X_{l_{i}}=\frac{ 1-\sqrt{ z_{l_{i}}} }{ 1-\sqrt{p} },$$ with p being the inflextion point.

Usage

kozak.fx(d, h, hl, paramod, p = 0.2, c0 = 0.001)

Value

Returns the diameter of the stem at the stem-height \(h_l\), thus \(d_l\), for the Kozak (1988) functional form, based upon tree diameter \(d\) and total height \(h\).

Arguments

d

is the diameter at breast height (1.3 m) of the tree. The measurement unit is cm in the metric system, but ultimately it will depend on how the model was previously fitted, because of the measurement unit of the variables included.

h

is total height of the tree.

hl

is stem height within the tree, thus \(h_l \leq h\).

paramod

is a vector having the eight coefficients of the taper model in the following order: \(\alpha_0,\alpha_1,\alpha_2,\beta_1,\beta_2,\beta_3,\beta_4\), and \(\beta_5\).

p

is the inflextion height. By default is set to 0.2

c0

is a constant build-in the model. By default is set to 0.001.

Author

Christian Salas-Eljatib.

References

Kozak A. 1988. A variable-exponent taper equation. Canadian Journal of Forest Research 18: 1363-1368. tools:::Rd_expr_doi("10.1139/x88-213")

Examples

# Parameters
a0<- 1.02453; a1<- 0.88809; a2<- 1.00035
b1<- 0.95086; b2<- -0.18090; b3<- 0.61407;
b4<- -0.35105; b5 <- 0.05686;
coefs<-c(a0,a1,a2,b1,b2,b3,b4,b5);p.coef <- 0.25
# Tree attributes
dbh <- 45; toth <- 27

# Using the function
hl.int <- c(0.3, 1.3, 5)
dl.hat <- kozak.fx(d=dbh,h=toth,hl=hl.int,paramod=coefs,p=p.coef)
cbind(hl.int,dl.hat)