CODEWITHSUNDEEP
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maycca
maycca

Reputation: 4090

Calculate diameters at specific heights based on taper ratio?

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.

enter image description here

Upvotes: 1

Views: 515

Answers (2)

GKi
GKi

Reputation: 39707

A h/d-ratio of 100 does not mean that increasing 100 cm of height a tree looses 1 cm in diameter, as the diameter is measured in 1.3m height. In case you assume a cone a tree with height = 11.3m and dbh = 10cm will loose 1cm dbh per 1m height. To get the diameter at specific height you can use:

D_dbh * (H_max - h) / (H_max - h_dbh)

Typical a stem is not a cone. To take this into consideration you can add an exponent like:

D_dbh * ((H_max - h) / (H_max - h_dbh)) ^ 0.6

In case you just have tapper and H_max or D_dbh you can get the other with:

taper = H_max / D_dbh
H_max = taper * D_dbh
D_dbh = H_max / taper

Upvotes: 1

ThomasIsCoding
ThomasIsCoding

Reputation: 102359

Not sure if this is the thing you are after

d_h <- D_dbh - taper*(h-h_dbh)*100

such that

> d_h
[1] 9 8 7 6 5 4 3 2

Upvotes: 1

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