I am trying to figure out the relationship between the taper ratio and tree diameter (at breast height = dbh) at specific heights of the tree. Taper is a ratio between diameter at dbh and tree height in the same units (cm, m..). If the tree taper is 1:100, this means that with increasing 100 cm of height, tree looses 1 cm in diameter. So, if my tree has dbh diameter 10 cm, and height 10 m, the taper is 1:100, the diameters at other 1 m long sections:
taper = 1/100
h_dbh = 1.3
D_dbh = 10
H_max = 10
# Create a vector tree section of length 1 m
h = h_dbh + c(1: (H_max-h_dbh)) # segments: length = 100 cm
Logically, my diameters at individual heights should be:
d_h = c(10,9,8,7,6,5,4,3,2,1)
I guess that my formula should take into account something like compounded rate or some exponent:
d_h = D_dbh/1.1 # something like compounded rate?
d_h = D_dbh - exp(taper)
But I am unsure how to specify in formula my heights?
But, what if the ratio is 1:60 or 1:132 instead of 1:100? How to predict my diameters still at 1 m long segments (not at 60 or 132 as indicated by 1:132 ratio)? I am looking for some specific formula, where I can specify the ratio.
