The goal of rpnc250 is to provide R functions that produce height, volume, and biomass estimates using the equations and coefficients from USFS Research Paper NC-250: Tree volume and biomass equations for the Lake States.
Citation for publication: Hahn, Jerold T. 1984. Tree volume and biomass equations for the Lake States. Research Paper NC-250. St. Paul, MN: U.S. Dept. of Agriculture, Forest Service, North Central Forest Experiment Station
The original publication can be accessed from the U.S. Forest Service.
The equations and species-specific coefficients were copied out of the PDF version of the publication by Henry Rodman in January 2021. The tables are stored in csv format in the R package and have been translated into package data objects for use in the internal functions.
The functions for estimating height, volume, and biomass have been tested to align with the examples provided in the original publication.
You can install the latest version of rpnc250 from Github with:
remotes::install_github("SilviaTerra/rpnc250", ref = "main")Here are some examples to show a few ways to work with the functions:
First, load a few packages.
library(rpnc250)
library(magrittr)The package has a set of test trees pulled from some FIA data in northern Minnesota (source code).
head(test_trees)
#> cn plt_cn statuscd spcd common_name dbh tpa_unadj ht
#> 1 65340991010661 65340894010661 1 95 black spruce 1.5 74.96528 NA
#> 2 65340995010661 65340894010661 1 95 black spruce 1.5 74.96528 NA
#> 3 65340999010661 65340894010661 1 95 black spruce 2.8 74.96528 NA
#> 4 65341003010661 65340894010661 1 95 black spruce 1.9 74.96528 NA
#> 5 65341007010661 65340894010661 1 95 black spruce 2.7 74.96528 NA
#> 6 65341011010661 65340894010661 1 95 black spruce 2.0 74.96528 NA
#> volcfgrs
#> 1 NA
#> 2 NA
#> 3 NA
#> 4 NA
#> 5 NA
#> 6 NAThe height equation includes stand basal area as a covariate, so we can summarize FIA plot-level (four subplots combined) basal area to use for that purpose. For simplicity, we will assume that site index is constant for all of the plot locations.
# summarize plot-level basal area
plot_ba <- test_trees %>%
dplyr::filter(
!is.na(dbh),
!is.na(tpa_unadj),
statuscd == 1
) %>%
dplyr::group_by(
plt_cn # FIA plot IDs
) %>%
dplyr::summarize(
bapa = sum(tpa_unadj * 0.005454 * dbh^2),
.groups = "drop"
)
# filter the trees and join to plot basal area table
trees_prepped <- test_trees %>%
dplyr::filter(
!is.na(dbh),
statuscd == 1, # only live trees
!is.na(tpa_unadj)
) %>%
dplyr::left_join(
plot_ba,
by = "plt_cn"
)The height equation in the publication generates estimates of height to a given top diameter (outside bark) provided species, DBH (inches), site index, and stand basal area.
To estimate height to 4" top we can apply the function
estimate_height:
# clone prepped tree dataframe
ht_trees <- trees_prepped
ht_trees$height_4 <- estimate_height(
spcd = ht_trees$spcd,
dbh = ht_trees$dbh,
site_index = 65,
top_dob = 4,
stand_basal_area = ht_trees$bapa
)It is also possible to use the functions within dplyr::mutate calls
which facilitates clean data wrangling workflows.
ht_trees <- trees_prepped %>%
dplyr::mutate(
height_4 = estimate_height(
spcd = spcd,
dbh = dbh,
site_index = 65,
top_dob = 4,
stand_basal_area = bapa
)
)We can summarize total merchantable volume up to 4" top very easily. First, join the plot-level basal area table to the tree table, then estimate height to 4" top for each stem. Using those estimates as inputs to the volume equations we can estimate stem-level volumes.
merch_cuft_4 <- trees_prepped %>%
dplyr::mutate(
height_4 = estimate_height(
spcd = spcd,
dbh = dbh,
site_index = 65,
top_dob = 4,
stand_basal_area = bapa
),
gross_cuft_vol = estimate_volume(
spcd = spcd,
dbh = dbh,
height = height_4,
vol_type = "cuft"
)
)
# plot relationship between diameter and gross volume
merch_cuft_4 %>%
ggplot2::ggplot(
ggplot2::aes(
x = dbh,
y = gross_cuft_vol,
color = common_name
)
) +
ggplot2::geom_point() +
ggplot2::labs(
x = "DBH (inches)",
y = "gross volume to 4\" top (cubic ft)",
color = "species"
)
#> Warning: Removed 106 rows containing missing values (geom_point).
To get merchantable volume in board feet (Int’l 1/4) we can set the merchantable height to 9" for softwood trees, and 10" for hardwood trees. You and I both know that the large aspen are probably not destined for sawtimber products, but we can dream.
# make table of spcd and hardwood/softwood assignment
spp_groups <- tidyFIA::ref_tables[["species"]] %>%
dplyr::transmute(
spcd,
class = dplyr::case_when(
major_spgrpcd %in% c(1, 2) ~ "softwood",
major_spgrpcd %in% c(3, 4) ~ "hardwood"
)
)
merch_bdft <- trees_prepped %>%
dplyr::left_join(
spp_groups,
by = "spcd"
) %>%
dplyr::mutate(
top_dob = dplyr::case_when(
class == "hardwood" ~ 10,
class == "softwood" ~ 9
)
) %>%
dplyr::filter(
dbh >= top_dob + 1 # make sure dbh is at least as big as top dob
) %>%
dplyr::mutate(
merch_height = estimate_height(
spcd = spcd,
dbh = dbh,
site_index = 65,
top_dob = top_dob,
stand_basal_area = bapa
),
gross_bdft_vol = estimate_volume(
spcd = spcd,
dbh = dbh,
height = merch_height,
vol_type = "bdft"
)
)
merch_bdft %>%
ggplot2::ggplot(
ggplot2::aes(
x = dbh,
y = gross_bdft_vol,
color = common_name
)
) +
ggplot2::geom_point() +
ggplot2::labs(
x = "DBH (inches)",
y = "gross volume (board ft)",
color = "species"
)
The publication outlines a process for obtaining estimates of green tons of biomass. This method differs from the methods used by FIA so keep that in mind if you are attempting to immitate the FIA methodology. The FIA methods use the gross cubic foot volume equations and coefficients from this publication but use a different process for converting the bole volume estimate into biomass.
trees_with_biomass <- trees_prepped %>%
dplyr::mutate(
biomass = estimate_biomass(
spcd = spcd,
dbh = dbh,
site_index = 65,
stand_basal_area = bapa
)
)
trees_with_biomass %>%
ggplot2::ggplot(
ggplot2::aes(
x = dbh,
y = biomass,
color = common_name
)
) +
ggplot2::geom_point() +
ggplot2::labs(
x = "DBH (inches)",
y = "biomass (green tons)",
color = "species"
)