Site index is the most commonly used method of assessing site quality in North America and is defined as the height of a tree at a base or index age, usually 50 years. Trees that are measured to determine site index should be over 30 years old and be in a dominant or codominant canopy position.
Below in Figure 1 are site index curves for red pine that have withstood the test of time (Benzie 1977).

Figure 1. Site index curves for red pine from different regions of North America 
Carmean et al. (1989) provided seven sets of site index curves for red pine using various index ages. Although an index age of 50 is commonly used, some of them use younger index ages. These curves are representative of height growth patterns for red pine based on total tree age, plantation age, and age measured at breast height (measured at 4.5 ft or 1.3 m above the ground) for specific regions across North America.
Figures 2 and 3 are graphical comparisons of these published site index curves from distinctly different regions, grouping the curves according to a total or breast height index age. Below in Table 1 are the equations to reproduce these curves.
(enlarge)
Figure 2. Comparison of site index curves based on total age from Minnesota, Vermont, Wisconsin, and Ontario. Site indices of 50, 60, and 70 are presented for each group of curves. Equation form: H = b 1S b2[1 ‑ exp(b 3A)] b4 (S^b5), where H = total height in feet, S = site index, A = total age, and b i designates parameter estimates provided in Table 1.
(enlarge)
Figure 3. Comparison of site index curves based on breast height age from New York, Illinois, and Ontario. Site indices of 40, 50, and 60 are presented for each group of curves. Equation form: H = 4.5 + b 1S b2[1 ‑ exp(b 3Abh)] b4 (S^b5), where H = total height in feet, S = site index, Abh = breast height age measured at 4.5 ft, and b i designates parameter estimates provided in Table 1.
Table 1. Parameter estimates for the equations used to create Figures 2 and 3. See Carmean and others (1989) for details on the derivation of the parameters and citations for original references.
Region 
b 1 
b 2 
b 3 
b 4 
b 5 
Reference 
Total age 






Minnesota Natural stands 
1.8900

1.0000

0.0198

1.3892

0.0000

Gevorkiantz 1957

Vermont Plantations (index age of 30 yrs) 
2.0401

1.0003

0.0361

1.7914

0.0090

Hannah 1971

Wisconsin Plantations 
2.6359

0.8259

0.0389

21.5578

0.6271

Wilde et al. 1965

Eastern Ontario Plantations 
2.0434

0.9978

0.0147

1.0937

0.0035

Stiell and Berry 1973

Breast height age 






New York Natural stands (index age = 20 yrs bh) 
19.0635

0.5885

0.0111

3.3922

0.3418

Richards et al. (1962)

Illinois Plantations (index age = 25 yrs bh) 
0.7666

1.0909

0.0733

3.2335

0.2947

Gilmore (1957)

Central Ontario Natural stands 
13.6713

0.5404

0.0283

8.7720

0.5308

Thrower (1986)

The
curves
using
a total
age for
Minnesota,
Wisconsin,
and Ontario
are based
on site
indices
of 50,
60, and
70 at
an index
age of
50. Site
indices
from Vermont
are based
on site
indices
of 40,
50, and
60 at
an index
age of
30. Curves
from Vermont
indicate
a more
rapid
early
height.
The Minnesota
and Ontario
curves
have a
similar
form.
The curves
from Wisconsin
suggest
lower
productivity,
in terms
of height
growth,
relative
to other
regions
for red
pine.
The site index curves based on a bh index age for Ontario are based on site indices of 50, 60, and 70 at an index age of 50 years at breast height. Site indices from Illinois are based on site indices of 30, 40, and 50 at 25 years at breast height. Site indices from New York are based on site indices of 20, 30, and 40 at an index age of 20 years at breast height. Curves from Vermont indicate a more rapid early height. The curves from Ontario indicate greater early height growth and greater productivity, in terms of height growth, than those from New York and Illinois. The curves from Illinois suggest similar productivity to the Ontario sites and younger ages but low productivity at older ages. The curves from New York indicate less productivity than those from Ontario but greater productivity than Illinois at older ages.