timbeR (version 2.0.1)

kozak_hi: Estimate the height at which a given diameter occurs in a tree, based on a fitted Kozak (2004) taper equation.

Description

Estimates the height at which a given diameter occurs in a tree, from the diameter at breast height, total height and coefficients of the Kozak (2004) taper function.

Usage

kozak_hi(dbh, h, di, coef, p)

Arguments

dbh

tree diameter at breast height, in centimeters.

h

total tree height, in meters.

di

diameter whose height of occurrence will be estimated, in centimeters.

coef

numerical vector containing nine coefficients of the Kozak taper equation

p

numerical value representing the first inflection point calculated in the segmented model of Max and Burkhart (1976).

Value

as numeric value indicating the height at which the given diameter occurs.

Details

the Kozak (2004) variable-form taper function is represented mathematically by the following expression

di ~b0*(dbh^b1)(h^b2)((1-(hi/h)^(1/4))/(1-(p^(1/3))))^(b3*(hi/h)^4+b4*(1/exp(dbh/h))+b5*((1-(hi/h)^(1/4))/(1-(p^(1/3))))^0.1+b6*(1/dbh)+b7*(h^(1-(hi/h)^(1/3)))+b8*((1-(hi/h)^(1/4))/(1-(p^(1/3)))))

Examples

# NOT RUN {
library(dplyr)
library(minpack.lm)
library(timbeR)

tree_scaling <- tree_scaling %>%
mutate(did = di/dbh,
       hih = hi/h)

kozak <- nlsLM(di ~ taper_kozak(dbh, h, hih, b0, b1, b2, b3, b4, b5, b6, b7, b8, p),
               start=list(b0=1.00,b1=.97,b2=.03,b3=.49,b4=-
                            0.87,b5=0.50,b6=3.88,b7=0.03,b8=-0.19, p = .1),
               data = tree_scaling,
               control = nls.lm.control(maxiter = 1000, maxfev = 2000)
)

coef_kozak <- coef(kozak)[-10]
p_kozak <- coef(kozak)[10]

h <- 20
dbh <- 25
hi <- 15

kozak_hi(dbh, h, hi, coef_kozak, p_kozak)

# }