Stand-level

Distance sampling (distance.sampling function)

The distance sampling method is used for the correction of occlusion effects. When the distance.sampling function was applied, the list with tree detection probabilities (i.e., the output file of the mentioned function) can be introduced in tree.ds. By default, this argument is set to NULL and metrics using distance sampling corrections will not be calculated. The distance.sampling is applied as follows:

tree.ds <- distance.sampling(tree.tls = tree.list,
                             id.plots = NULL,
                             strata.attributes = NULL)

The distance.sampling function computes the probability of detection of trees depending on their distance to the TLS device. Detection functions are fitted to the histogram representing the distribution of the trees relative to their horizontal distances. The computation of the detection functions is based on the data frame of the detected trees, i.e. the output file of the tree.detection.single.scan or tree.detection.multi.scan (here tree.list), which is introduced in the argument tree.tls. The plots to be analysed can be specified in id.plots by inserting a vector containing the plot identification numbers. If not specified, this argument is set to id.plots = NULL and all plots will be considered.

Two detection functions are fitted, that are the half normal and hazard rate functions, with and without \(dbh\) as covariate. These functions describe the decreasing detection probability with increasing distance. The probabilities are used for correcting estimation bias of the stand-level variables caused by the lack of detection of trees due to occlusion.

A list with three elements is generated by the distance.sampling function. The data frame tree represents the detection probabilities for each tree of all plots according to the four different detection functions. The columns P.hn and P.hn.cov show the detection probabilities calculated by the half normal function without and with \(dbh\) as covariate, while P.hr and P.hr.cov contain the probabilities according to the hazard rate function without and with covariate respectively.

head(tree.ds$tree)
#>   stratum id tree     P.hn  P.hn.cov      P.hr  P.hr.cov
#> 1       1  1    1 0.922808 0.9293580 0.9388107 0.9519734
#> 2       1  1    2 0.922808 0.8922843 0.9388107 0.9199997
#> 3       1  1    3 0.922808 0.9146826 0.9388107 0.9389643
#> 4       1  1    4 0.922808 0.9017652 0.9388107 0.9278849
#> 5       1  1    5 0.922808 0.9277925 0.9388107 0.9505678
#> 6       1  1    6 0.922808 0.9424095 0.9388107 0.9637861

The data frame par shows the parameters of the detection functions and AIC the Akaike information criterion (AIC) for every detection function fit.

head(tree.ds$par)
#>              P.hn.scale P.hn.cov.scale.intercept P.hn.cov.dbh P.hr.scale
#> X.Intercept.   35.84341                 64.17593    -2.231185   21.85271
#>              P.hr.shape P.hr.cov.scale.intercept P.hr.cov.dbh P.hr.cov.shape
#> X.Intercept.   3.544516                 26.38362   -0.7110327       3.832857

head(tree.ds$AIC)
#>       P.hn P.hn.cov     P.hr P.hr.cov
#> 1 3375.162 3376.521 3374.114 3375.123

Additional information about trees through field data

If supplementary field data is available for the sample plots, a data frame containing this information can be included in tree.field. Each row of the data frame must represent a tree and the data frame must contain at least the following columns:

• id: plot identification number (character string or numeric), which must coincide with those in the id column of the tree.tls argument i.e., the list of trees yielded by the tree detection functions
• tree: number of the tree
• h.dist: horizontal distance (in m) of the tree’s center to the plot’s center, which must coincide with the centers of their corresponding TLS plots
• dbh: tree diameter (in cm) at breast height (1.3 m)
• h: total tree height (in m)
• dead: integer value indicating whether the tree is dead (1) or not (NA)

Further optional columns are h.blc (height based live crown, in m), h.bdc (height based dead crown, in m), v.user (tree volume, in m\(^3\)) and w.user (tree biomass, in Mg).

Selecting trees to be included in the calculations

The arguments dbh.min, h.min and max.dist are used to determine the trees that are included in the calculations. The minimum diameter at breast height (\(dbh\)) and the minimum tree height can be specified in dbh.min (in cm) and h.min (in m) and are set to 4 cm and 1.3 m respectively by default. In max.dist, the maximal horizontal distance (in m) of a tree from the plot’s center to be included in the calculations can be defined. If not specified, no trees are discarded because of their distance.

Plot design and parameters

The metrics and variables can be computed for different plot designs which are specified by plot.design and plot.parameters. There are three different plot designs, which are similar to the procedure used in conventional forest inventories. The plot design, which is to be used can be specified in plot.design. By default, all plot designs will be considered.

As the name implies, circular fixed area plots ("fixed.area") are plots with a circular area defined by the plot radius (in m). The size of k-tree plots ("k.tree") is determined by the number of trees (k) that enter the plot. The basal area factor (BAF in m\(^2\)/ha) defines the size of angle-count plots ("angle.count"). The parameters radius, k and BAF have to be specified as data frame in plot.parameters. If one of these parameters is not specified, the corresponding plot design will not be considered in the calculations. To calculate the dominant height and diameter, the number of dominant trees per ha (trees/ha) can be indicated by the argument num.tree. By default, the number of dominant trees is set to 100 trees/ha.

Output files

The function metrics.variables generates a list in which each element represents one of the considered plot designs (fixed area, k-tree and angle-count plots). These elements are data frames containing the estimated metrics and variables at stand-level as columns (described below). Further columns include information about the plot, such as the identification number (id) and the stratum identification (stratum) both coinciding with the respective columns in the output file of the tree.detection functions. Each row represents a simulated plot i.e., a plot with a certain size (defined by the values for radius, k and BAF shown in the respective columns).

If save.result = TRUE, the data frames will be saved as seperate .csv files (one for each plot design) to the directory indicated in dir.result (or if not specified to the working directory). The .csv files (without row names) will be created using the write.csv function from the utils package.

Stand-level metrics

metrics[1:6, -c(3:36)]

The stand-level metrics are statistical descriptive values, such as percentiles, standard deviation or means, as well as the number of points belonging to the normal section of the point cloud.

The values n.pts, n.pts.est, n.pts.red and n.pts.red.est indicate the number of points and the estimated number of points respectively that belong to the tree’s normal section (1.3 m +/- 0.05 m). This is calculated for the original point cloud (n.pts, n.pts.est) and the reduced point cloud (n.pts.red, n.pts.red.est).

Furthermore, the height percentiles (P01, P05, P10, P20, P25, P30, P40, P50, P60, P70, P75, P80, P90, P95, P99, numbers indicating the k-th percentile) are calculated for the \(z\) coordinate of the TLS point cloud. Therefore they denominate the height (in m) above ground level.

Stand-level variables

metrics[1:6, 1:36]

The variables are estimated based on the tree attributes of the detected trees from the point cloud data (output of the functions tree.deteection.single.scan and tree.deteection.multi.scan) similar to the procedure of conventional forest inventories. The values are computed at stand-level and are therefore extended to an area of one ha.