Let’s calculate the section volume of felled trees using Smalian’s method, according to the formula: \[ V_{secao} = \frac{AS_{i} + AS_{i+1}}{2} . L \]
We’ll use the exfm7 dataframe as an exemple:
library(forestmangr)
data(exfm7)
data_ex <- exfm7
data_ex
#> # A tibble: 3,393 × 11
#> MAP PROJECT SPACING STRATA GENCODE TREE DBH TH hi di_wb bark_t
#> <chr> <fct> <fct> <int> <fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 FOREST1 PEQUI 3x3 4 FM00100 1 12.4 22.1 0.1 13.1 6
#> 2 FOREST1 PEQUI 3x3 4 FM00100 1 12.4 22.1 0.5 12.6 6
#> 3 FOREST1 PEQUI 3x3 4 FM00100 1 12.4 22.1 1 12.4 5
#> 4 FOREST1 PEQUI 3x3 4 FM00100 1 12.4 22.1 1.5 12.3 5
#> 5 FOREST1 PEQUI 3x3 4 FM00100 1 12.4 22.1 2 11.8 4
#> 6 FOREST1 PEQUI 3x3 4 FM00100 1 12.4 22.1 4 11.3 4
#> # ℹ 3,387 more rowsFirst we’ll calculate the volume with bark of each section with the
smalianwb function. In it we input the dataframe, and names
for the section diameter with bark, section height and tree
variables:
data_ex_sma <- smalianwb(data_ex,"di_wb", "hi","TREE")
head(as.data.frame(data_ex_sma))
#> MAP PROJECT SPACING STRATA GENCODE TREE DBH TH hi di_wb bark_t
#> 1 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 0.1 13.05071 6
#> 2 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 0.5 12.57324 6
#> 3 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 1.0 12.41409 5
#> 4 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 1.5 12.25493 5
#> 5 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 2.0 11.77747 4
#> 6 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 4.0 11.30000 4
#> CSA_WB VWB
#> 1 0.01337697 0.005158610
#> 2 0.01241607 0.006129952
#> 3 0.01210373 0.005974776
#> 4 0.01179537 0.005672382
#> 5 0.01089416 0.020922907
#> 6 0.01002875 0.018694737Now, we’ll calculate the volume without bark per secction, using the
smalianwb function. We’ll input the same variables as
before, and the variable name for the bark thickness. In our data, this
variable is in millimeters, so, we’ll use the bt_mm_to_cm
as TRUE to convert it to centimeters:
data_ex_sma <- smalianwob(data_ex_sma,"di_wb","hi","bark_t","TREE",bt_mm_to_cm=T)
head(as.data.frame(data_ex_sma))
#> MAP PROJECT SPACING STRATA GENCODE TREE DBH TH hi di_wb bark_t
#> 1 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 0.1 13.05071 0.6
#> 2 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 0.5 12.57324 0.6
#> 3 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 1.0 12.41409 0.5
#> 4 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 1.5 12.25493 0.5
#> 5 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 2.0 11.77747 0.4
#> 6 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 4.0 11.30000 0.4
#> CSA_WB VWB di_wob CSA_WOB VWOB
#> 1 0.01337697 0.005158610 11.85071 0.011030070 0.004237849
#> 2 0.01241607 0.006129952 11.37324 0.010159172 0.005097861
#> 3 0.01210373 0.005974776 11.41409 0.010232273 0.005045296
#> 4 0.01179537 0.005672382 11.25493 0.009948911 0.004853333
#> 5 0.01089416 0.020922907 10.97747 0.009464421 0.018123438
#> 6 0.01002875 0.018694737 10.50000 0.008659016 0.016363277This can be done directly using pipes (%>%):
data_ex_sma <- data_ex %>%
smalianwb("di_wb", "hi", "TREE") %>%
smalianwob("di_wb", "hi", "bark_t", "TREE", bt_mm_to_cm=T)
head(as.data.frame(data_ex_sma))
#> MAP PROJECT SPACING STRATA GENCODE TREE DBH TH hi di_wb bark_t
#> 1 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 0.1 13.05071 0.6
#> 2 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 0.5 12.57324 0.6
#> 3 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 1.0 12.41409 0.5
#> 4 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 1.5 12.25493 0.5
#> 5 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 2.0 11.77747 0.4
#> 6 FOREST1 PEQUI 3x3 4 FM00100 1 12.41409 22.1 4.0 11.30000 0.4
#> CSA_WB VWB di_wob CSA_WOB VWOB
#> 1 0.01337697 0.005158610 11.85071 0.011030070 0.004237849
#> 2 0.01241607 0.006129952 11.37324 0.010159172 0.005097861
#> 3 0.01210373 0.005974776 11.41409 0.010232273 0.005045296
#> 4 0.01179537 0.005672382 11.25493 0.009948911 0.004853333
#> 5 0.01089416 0.020922907 10.97747 0.009464421 0.018123438
#> 6 0.01002875 0.018694737 10.50000 0.008659016 0.016363277We can also visualize the mean curve form of the trees in the area,
using Kozak’s model with the average_tree_curve
function:
To calculate the volume of each tree, we’ll use the
vol_summarise function. We input the data, and dbhm height,
volume with bark, volume without bark and tree variables:
data_ex_vol_arvore <- vol_summarise(data_ex_sma, dbh = "DBH", th = "TH",
vwb="VWB",tree = "TREE",vwob="VWOB")
data_ex_vol_arvore
#> # A tibble: 197 × 10
#> TREE DBH TH CSA VWB VWOB FFWB FFWOB FFWB_mean FFWOB_mean
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 12.4 22.1 0.0121 0.131 0.113 0.489 0.424 0.468 0.412
#> 2 2 13.1 22.3 0.0134 0.145 0.126 0.487 0.423 0.468 0.412
#> 3 3 13.2 20 0.0137 0.126 0.108 0.459 0.393 0.468 0.412
#> 4 4 13.2 19.4 0.0137 0.139 0.123 0.521 0.463 0.468 0.412
#> 5 5 13.4 23.7 0.0140 0.156 0.133 0.470 0.401 0.468 0.412
#> 6 6 13.5 21.5 0.0144 0.139 0.124 0.450 0.401 0.468 0.412
#> # ℹ 191 more rowsNow to determine the most adequate volumetric model for this data,
we’ll fit two models, and compare them using plots for their residuals
with the resid_plot function.
Schumacher’s volumetric model: \[ Ln(V) = \beta_0 + \beta_1*Ln(dbh) + \beta_2*Ln(H) \]
Husch’s volumetric model: \[ Ln(V) = \beta_0 + \beta_1*Ln(dbh) \]
We’ll use the output “merge_est” from the lm_table
function. This will estimate the volume for the observed data
automatically. Then, we’ll use resid_plot to compare the
observed variable with the estimated ones:
data_ex_vol_arvore %>%
lm_table(log(VWB) ~ log(DBH) + log(TH),output="merge_est",est.name="Schumacher") %>%
lm_table(log(VWB) ~ log(DBH),output="merge_est",est.name="Husch") %>%
resid_plot("VWB", "Schumacher", "Husch")
Schumacher’s model was more symmetrical, and can be considered the better model for this dataset. To safe it’s coefficients in a dataframe, we’ll fit the model again, but with the standard output:
tabcoef_vwb <- lm_table(data_ex_vol_arvore, log(VWB) ~ log(DBH) + log(TH) )
tabcoef_vwb
#> b0 b1 b2 Rsqr Rsqr_adj Std.Error
#> 1 -9.595863 1.889372 0.9071631 0.9966646 0.9966303 0.04855508And do the same for the volume without bark: