biometrics (version 1.0.3)

kozakln.fx: Function to computes the stem diameter of a tree according to the log-transformed Kozak (1988) taper equation.

Description

Function of the natural log-transformed 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 $$ \ln{d_{l_{i}}}=\alpha_0 + \alpha_1 \ln{d_i}+\alpha_2 {d_i}+ \beta_1 \ln{(X_{l_{i}})} z_{l_{i}}^{2} + \beta_2 \ln{(X_{l_{i}})} \ln{(z_{l_{i}}+0.001)} + \beta_3 \ln{(X_{l_{i}})} \sqrt{z_{l_{i}}} +\\ \beta_4 \ln{(X_{l_{i}})} e^{z_{l_{i}}} + \beta_5 \ln{(X_{l_{i}})} \frac{d_i}{h_i},$$ 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

kozakln.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 natural log-transformed Kozak (1988) functional form, based upon tree diameter \(d\) and total height \(h\). Therefore, the result applies the back-transformation by using the anti-log function, i.e., exp().

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<- 0.04338410; a1<- 0.88657485; a2<- 0.00446052;b1<- 1.978196;
b2<- -0.40676847; b3<- 3.50815520; b4<- -1.84177070;b5<- 0.19647175
coefs<-c(a0,a1,a2,b1,b2,b3,b4,b5);p.coef <- 0.25
# Tree attributes
dbh <- 40; toth <- 25

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