bi_hi {timbeR}

Estimate the height at which a given diameter occurs in a tree, based on a fitted Bi (2000) 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 Bi taper function.

Usage

bi_hi(dbh, h, di, coef)

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 seven coefficients of the Bi taper equation

Details

the Bi (2000) variable-form taper function is represented mathematically by the following expression

di ~ dbh * (log(sin((pi/2) * (hi/h)))/(log(sin((pi/2) * (1.3/h)))))^(b0 + b1 * sin((pi/2) * (hi/h)) + b2 * cos((3 * pi/2) * (hi/h)) + b3 * (sin((pi/2) * (hi/h))/(hi/h)) + b4 * dbh + b5 * (hi/h) * dbh^0.5 + b6 * (hi/h) * h^0.5)

Value

a 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)

bi <-  nlsLM(di ~ taper_bi(dbh, h, hih, b0, b1, b2, b3, b4, b5, b6),
data=tree_scaling,
start=list(b0=1.8,b1=-0.2,b2=-0.04,b3=-0.9,b4=-0.0006,b5=0.07,b6=-.14))

coef_bi <- coef(bi)

dbh <- 25
h <- 20
di <- 5

bi_hi(dbh, h, di, coef_bi)