Implementation of the Appendix III site-index equations from
Buckman et al. (2006) for red pine (PINU.RES) in the Lake States.
Appendix III presents this model as an improved version of the Lundgren and
Dolid red-pine height function implemented in [si_lundgrendolid1970()].
Buckman et al. note two imperfections in the earlier Lundgren-Dolid form:
height predicted at age 50 was slightly below site index rather than equal
to it exactly, and the curve overpredicted heights for young stands below
age 20. To address this, they refit the age-20+ equation with the constraint
that height at age 50 equals site index, and they replace the younger-age
portion with a separate polynomial curve that joins smoothly with the
older-age curve at age 20.
Value
A tibble with columns:
- height
Predicted total stand height (m), returned when input `si` is provided.
- si
Predicted site index (m at total age 50), returned when input `height` is provided.
Details
Species coverage: PINU.RES.
Geographic use: Ontario
Age definition note: `age` is stand age from seed (years)
Height definition note: `height` is total stand height (m).
Base-age note: site index is total height at 50 years.
Provide exactly one of `height` or `si`:
If `height` is provided, the function predicts `si`.
If `si` is provided, the function predicts `height`.
The source model is piecewise:
for `age < 20`: \(H = SI (k t^2 - m t^4)\)
for `age >= 20`: \(H = A SI (1 - e^{-Bt})^C\)
The constrained Buckman refit uses `A = 1.8604`, `B = 0.020928`, and `C = 1.4349`. The younger-age correction uses `k = 1.41876e-3` and `m = 1.05304e-6`, chosen so the two segments join smoothly at age 20.
Inputs and outputs are metric; the original equations are in imperial units, so the function converts internally.
References
Buckman, R. E., et al. (2006). Growth and yield of red pine in the Lake States. USDA Forest Service.
Lundgren, A. L., & Dolid, W. A. (1970). Biological growth functions describe published site index curves for Lake States timber species. Research Paper NC-36. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Forest Experiment Station.
Examples
# Predict site index from age + height
si_buckman2006(
age = c(15, 25, 50),
height = c(4, 10, 18)
)
#> # A tibble: 3 × 1
#> si
#> <dbl>
#> 1 15.0
#> 2 19.5
#> 3 18.0
# Predict height from age + site index
si_buckman2006(
age = c(15, 25, 50),
si = c(14, 16, 18)
)
#> # A tibble: 3 × 1
#> height
#> <dbl>
#> 1 3.72
#> 2 8.21
#> 3 18.0