kozak_hi {timbeR}

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).

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)))))

Value

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

Examples

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)