# Evaluating yield and growth

First we load the packages and data:

library(forestmangr)
library(dplyr)
data(exfm16)

data_ex <- exfm16
data_ex
#> # A tibble: 139 x 7
#>   strata  plot   age    DH     N     V     B
#>    <int> <int> <dbl> <dbl> <int> <dbl> <dbl>
#> 1      1     1  26.4  12.4  1020  19.7   5.7
#> 2      1     1  38.4  17.2  1020  60.8   9.8
#> 3      1     1  51.6  19.1  1020 103.   13.9
#> 4      1     1  63.6  21.8  1020 136.   15.3
#> 5      1     2  26.4  15     900  27.3   6
#> 6      1     2  38.4  20.3   900  80    10.5
#> # ... with 133 more rows

The objetive of this vignette is to estimate future basal area and volume, using Clutter’s model.

$\left\{ \begin{array}{ll} Ln(B_2) = LnB_1\begin{pmatrix} \frac{I_1}{I_2} \end{pmatrix} + \alpha_0\begin{pmatrix} 1 - \frac{I_1}{I_2} \end{pmatrix} + \alpha_1\begin{pmatrix} 1 - \frac{I_1}{I_2} \end{pmatrix} S + ln(\varepsilon_2)\\ Ln(V_2) = \beta_0 + \beta_1 \begin{pmatrix} \frac{1}{I_2}\end{pmatrix} + \beta_2 S + \beta_3 Ln(B_2) + Ln(\varepsilon_1) \end{array} \right.$

To achieve this, first we need to estimate site. Let’s use Chapman & Richards’ model for this:

$DH = \beta_0 * (1 - exp^{-\beta_1 * Age})^{\beta_2}$

This is a non-linear model, thus, we’ll use the nls_table function to fit it, obtain it’s coefficients and estimate the site using it’s equation and the index age:

$S = DH* \frac{(1 - exp^{- \frac{ \beta_1}{Age} })^{\beta_2}} {(1 - exp^{- \frac{ \beta_1}{IndexAge}})^{\beta_2}}$

We’ll use an index age of 64 months.

index_age <- 64
data_ex <-  data_ex %>%
nls_table(DH ~ b0 * (1 - exp( -b1 * age )  )^b2,
mod_start = c( b0=23, b1=0.03, b2 = 1.3),
output = "merge" ) %>%
mutate(S = DH *( (  (1- exp( -b1/age ))^b2   ) /
(( 1 - exp(-b1/index_age))^b2 ))  ) %>%
select(-b0,-b1,-b2)
#>   strata plot  age   DH    N     V    B        S
#> 1      1    1 26.4 12.4 1020  19.7  5.7 22.48027
#> 2      1    1 38.4 17.2 1020  60.8  9.8 24.24290
#> 3      1    1 51.6 19.1 1020 103.4 13.9 22.07375
#> 4      1    1 63.6 21.8 1020 136.5 15.3 21.89203
#> 5      1    2 26.4 15.0  900  27.3  6.0 27.19388
#> 6      1    2 38.4 20.3  900  80.0 10.5 28.61226

Now that we’ve estimated the site variable, we can fit Clutter’s model:

coefs_clutter <- fit_clutter(data_ex, "age", "DH", "B", "V", "S", "plot")
coefs_clutter
#>         b0        b1        b2       b3       a0         a1
#> 1 1.398861 -28.84038 0.0251075 1.241779 1.883471 0.05012873

Now we can divide the data into classes, and calculate the production for each class with this model:

First, we classfy the data:

data_ex_class <- classify_site(data_ex, "S", 3, "plot")
#>   plot site_mean strata  age   DH    N    V    B       S interval category
#> 1   35   21.4510      2 44.4 18.8  740 40.6  6.5 24.0354 25.07877        1
#> 2   35   21.4510      2 55.2 19.1  720 50.4  7.4 21.0958 25.07877        1
#> 3   35   21.4510      2 68.4 20.1  720 62.2  8.5 19.2218 25.07877        1
#> 4   24   22.0728      2 30.0 13.5 1040 24.3  6.0 22.4604 25.07877        1
#> 5   24   22.0728      2 40.8 17.5 1040 54.8  8.9 23.6813 25.07877        1
#> 6   24   22.0728      2 52.8 19.0 1040 76.6 10.9 21.6216 25.07877        1
#>   category_
#> 1     Lower
#> 2     Lower
#> 3     Lower
#> 4     Lower
#> 5     Lower
#> 6     Lower

Now, we estimate basal area and volume with the est_clutter function. We’ll also calculate the Monthly Mean Increment (MMI) and Current Monthly Increment (CMI) values.

We input the data, a vector for the desired age range, and the basal area, site classification variables, and a vector with the Clutter function fitted coefficients, created previously:

data_ex_est <- est_clutter(data_ex_class, 20:125,"B", "S", "category_", coefs_clutter)
data_ex_est
#> # A tibble: 318 x 10
#> # Groups:   category_ [3]
#>   category_  Site G_mean   Age LN_B2_EST B2_EST V2_EST   CMI   MMI CMI_MMI
#>   <chr>     <dbl>  <dbl> <int>     <dbl>  <dbl>  <dbl> <dbl> <dbl>   <dbl>
#> 1 Lower      23.0   9.13    20      2.21   9.13   26.6 NA     1.33   NA
#> 2 Lower      23.0   9.13    21      2.25   9.48   29.8  3.24  1.42    1.82
#> 3 Lower      23.0   9.13    22      2.28   9.81   33.1  3.30  1.50    1.79
#> 4 Lower      23.0   9.13    23      2.31  10.1    36.4  3.33  1.58    1.75
#> 5 Lower      23.0   9.13    24      2.34  10.4    39.8  3.35  1.66    1.70
#> 6 Lower      23.0   9.13    25      2.37  10.7    43.2  3.36  1.73    1.64
#> # ... with 312 more rows

We can also create a plot for the technical age of cutting for each class:

est_clutter(data_ex_class, 20:125,"B", "S", "category_", coefs_clutter,output="plot")