biometrics (version 1.0.3)

taperpoly.fx: Carrasco polynomial function

Description

Polynomial function of Carrasco (1986)

Usage

taperpoly.fx(hl = hl, hcc = hcc, paramod = paramod, n = (length(paramod) - 1))

Value

Returns the diameter of the stem at the stem-height \(h_l\), thus \(d_l\), divided by the diameter at breast height (1.3). This is $$ \frac{d_{l_i}}{d_i} $$

Arguments

hl

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

hcc

is height to crown base.

paramod

is a vector having the coefficients of the taper model in the following order up to n: \(\beta_0, \beta_1, \beta_2, ... , \beta_n\)

n

degree of the polynomic function

Author

Christian Salas-Eljatib and Nicolás Campos

Details

This function takes the form of

$$\frac{d_{l_{i}}}{d_i} = \beta_0 + \beta_1 X + \beta_2 X^2 + \beta_3 X^3 + \cdots + \beta_n X^{n}, $$ where: \(d_{l_{i}}\) is the stem diameter at stem-height \(h_{l_{i}}\) for the i-th tree; \(d_i\) and \(h_i\) are the tree-level variables diameter at breast height and total height respectively for the i-th tree, and $n$ is the degree of the polynomial. The other term is

$$X = \frac{hcc_i - h_{l_i}}{hcc_i - 1.3}, $$

References

• Carrasco, J. 1986. Estudio Comparativo de dos Métodos para Evaluar la Calidad a árboles en pie y para representar la Forma del Fuste en el Bosque Siempreverde valdiviano. Tesis Ingeniero Forestal. Universidad Austral de Chile. Valdivia, Chile. 117 p.

Examples

dl <- seq(40, 0, -5)
hl <- seq(0, 16, 2)
d <- 30
hcc <- 12
h <- max(hl)
df <- data.frame(dl = dl,
                 hl = hl,
                 d = d,
                 hcc = hcc,
                 h = h)
df

myparams <- c(0.3, 0.8, 0.00003)

taperpoly.fx(hl = df$hl, hcc = df$hcc, paramod = myparams, n = 2)

df$y <- taperpoly.fx(hl = df$hl, hcc = df$hcc, paramod = myparams, n = 2)
## the n parameter is not necesary
df$y2 <- taperpoly.fx(hl = df$hl, hcc = df$hcc, paramod = myparams)
df$dl.h <- df$y * df$d
df