Once all trees were detected from the normalized point cloud and the tree list was generated, metrics and variables at stand level can be estimated. These estimations can be based on different plot designs, that are circular fixed area, k-tree and angle-count plots. The sizes of the plots can be regulated by defining the radius, k and the basal area factor (BAF) respectively.
In order to calculate metrics and variables at stand level, the
function metrics.variables is applied as
follows:
metrics <- metrics.variables(tree.tls = tree.list,
tree.ds = tree.ds, tree.field = tree.field,
plot.design = c("fixed.area", "k.tree", "angle.count"),
plot.parameters = data.frame(radius = 10, k = 10, BAF = 1),
scan.approach = "single", var.metr = NULL,
dbh.min = 4, h.min = 1.3, max.dist = Inf,
dir.data = dir.data, save.result = FALSE, dir.result = NULL)The input data frame is introduced in
tree.tls and should contain information
about the trees detected from TLS based data e.g., the output data frame
of the functions tree.detection.single.scan or
tree.detection.multi.scan. The path of the directory of the
.txt files containing the reduced point cloud data generated by the
function normalize can be specified in
dir.data otherwise the current working
directory will be assigned to this argument. If
save.result is set to
save.result = TRUE (default setting), the output files will
be saved to the directory indicated in
dir.result.
The scan approach, either TLS single-scan ("single") or
TLS multi-scan and SLAM point clouds approaches ("multi")
has to be specified in the argument
scan.approach. By default, the argument is
set to "multi".
If only a selection of metrics and variables should be calculated,
the metrics and variables of interest can be specified as a vector in
var.metr. If nothing is specified, the
argument is set to NULL and all possible metrics and
variables will be calculated.
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:
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$tree)
#> stratum id tree P.hn P.hn.cov P.hr P.hr.cov
#> 1 1 1 1 0.922808 0.9293580 0.9388107 0.9519734
#> 2 1 1 2 0.922808 0.8922843 0.9388107 0.9199997
#> 3 1 1 3 0.922808 0.9146826 0.9388107 0.9389643
#> 4 1 1 4 0.922808 0.9017652 0.9388107 0.9278849
#> 5 1 1 5 0.922808 0.9277925 0.9388107 0.9505678
#> 6 1 1 6 0.922808 0.9424095 0.9388107 0.9637861The data frame par shows the parameters
of the detection functions and AIC the
Akaike information criterion (AIC) for every detection function fit.
head(tree.ds$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 3375.123If 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 functionstree: number of the treeh.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 plotsdbh: 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).
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.
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.
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.
| id | radius | n.pts | n.pts.est | n.pts.red | n.pts.red.est | P01 | P05 | P10 | P20 | P25 | P30 | P40 | P50 | P60 | P70 | P75 | P80 | P90 | P95 | P99 | mean.z | mean.q.z | mean.g.z | mean.h.z | median.z | mode.z | max.z | min.z | var.z | sd.z | CV.z | D.z | ID.z | kurtosis.z | skewness.z | p.a.mean.z | p.a.mode.z | p.a.2m.z | p.b.mean.z | p.b.mode.z | p.b.2m.z | CRR.z | L2.z | L3.z | L4.z | L3.mu.z | L4.mu.z | L.CV.z | median.a.d.z | mode.a.d.z | weibull_c.z | weibull_b.z | mean.rho | mean.q.rho | mean.g.rho | mean.h.rho | median.rho | mode.rho | max.rho | min.rho | var.rho | sd.rho | CV.rho | D.rho | ID.rho | kurtosis.rho | skewness.rho | p.a.mean.rho | p.a.mode.rho | p.b.mean.rho | p.b.mode.rho | CRR.rho | L2.rho | L3.rho | L4.rho | L3.mu.rho | L4.mu.rho | L.CV.rho | median.a.d.rho | mode.a.d.rho | weibull_c.rho | weibull_b.rho | mean.r | mean.q.r | mean.g.r | mean.h.r | median.r | mode.r | max.r | min.r | var.r | sd.r | CV.r | D.r | ID.r | kurtosis.r | skewness.r | p.a.mean.r | p.a.mode.r | p.b.mean.r | p.b.mode.r | CRR.r | L2.r | L3.r | L4.r | L3.mu.r | L4.mu.r | L.CV.r | median.a.d.r | mode.a.d.r | weibull_c.r | weibull_b.r |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 10 | 9788.667 | 1796.620 | 444.6667 | 322.3520 | 1.1763271 | 4.149327 | 5.984327 | 7.555327 | 7.824327 | 7.932327 | 8.176327 | 8.646327 | 9.357327 | 10.00233 | 10.32033 | 10.68533 | 11.39733 | 12.03533 | 13.43333 | 8.686622 | 8.991724 | 8.185912 | 6.949452 | 8.601327 | 7.935327 | 15.11633 | 0.2503271 | 5.393706 | 2.322435 | 0.2673577 | 14.866 | 2.423 | 4.535413 | -0.8176501 | 48.55133 | 69.29800 | 98.07203 | 51.44867 | 30.64412 | 1.927974 | 0.5746516 | 112023087 | 1088745309 | 10962245432 | -1830560027 | 23849979309 | 1e-07 | 1.223295 | 0.7512949 | 4.218465 | 9.554482 | 4.455202 | 5.325242 | 3.203021 | 1.745464 | 3.977145 | 0.1000033 | 9.999991 | 0.1000033 | 8.509383 | 2.917085 | 0.6547593 | 9.899988 | 5.068693 | 1.782223 | 0.2812223 | 46.60337 | 99.99993 | 53.39663 | 0 | 0.4455206 | 39291647 | 289779246 | 2301164191 | -235377229 | 1816420654 | 1e-07 | 2.562719 | 4.355199 | 1.560419 | 4.957027 | 10.17625 | 10.45033 | 9.878583 | 9.541126 | 10.03613 | 7.939957 | 18.04629 | 1.9854031 | 5.653233 | 2.377653 | 0.2336472 | 16.06089 | 3.486677 | 2.864220 | 0.0953509 | 48.15005 | 85.54384 | 51.84995 | 14.45609 | 0.5638970 | 151314734 | 1701009907 | 19924353576 | -2918437931 | 44702069599 | 1e-07 | 1.765318 | 2.2362936 | 4.892407 | 11.09717 |
| 2 | 10 | 11222.000 | 2815.061 | 611.1667 | 506.5021 | 1.0425898 | 4.121590 | 5.898590 | 7.335590 | 7.912590 | 8.448590 | 9.110590 | 9.663590 | 10.223590 | 10.64959 | 10.79059 | 10.87959 | 11.37959 | 11.90259 | 13.43459 | 9.052322 | 9.383953 | 8.475137 | 7.020125 | 9.605590 | 10.788590 | 16.82859 | 0.2505898 | 6.114052 | 2.472661 | 0.2731521 | 16.578 | 2.933 | 4.501117 | -1.0871433 | 60.10169 | 23.93897 | 97.82422 | 39.89831 | 75.97166 | 2.175783 | 0.5379133 | 101884570 | 1031348422 | 10753389699 | -1735525894 | 23502278857 | 1e-07 | 1.586268 | 1.7362678 | 4.119804 | 9.970272 | 5.443356 | 6.210808 | 4.027388 | 1.859293 | 5.913727 | 0.1000035 | 9.999995 | 0.1000035 | 8.944021 | 2.990656 | 0.5494140 | 9.899991 | 5.164815 | 1.754274 | -0.2467470 | 52.36865 | 99.99991 | 47.63135 | 0 | 0.5443358 | 44630617 | 347962930 | 2851615225 | -380857693 | 3209731874 | 1e-07 | 2.607957 | 5.343352 | 1.892479 | 6.133511 | 11.06990 | 11.25312 | 10.857815 | 10.592588 | 10.95586 | 10.778054 | 18.13256 | 1.1552180 | 4.090119 | 2.022404 | 0.1826941 | 16.97734 | 2.092208 | 4.720474 | -0.3191920 | 47.73584 | 57.02047 | 52.26416 | 42.97944 | 0.6104983 | 146515187 | 1723625155 | 20809992902 | -3142095776 | 52214652344 | 1e-07 | 1.040121 | 0.2918422 | 6.395220 | 11.89079 |
| 3 | 10 | 7931.000 | 3522.606 | 644.6667 | 676.3987 | 0.7535283 | 3.119528 | 5.446528 | 7.362528 | 7.852528 | 8.331528 | 8.914528 | 9.612528 | 10.219528 | 10.81653 | 11.00853 | 11.29753 | 12.37553 | 13.04753 | 14.07753 | 9.177116 | 9.598251 | 8.419140 | 6.533724 | 9.612528 | 10.845528 | 15.92853 | 0.2505283 | 7.906972 | 2.811934 | 0.3064071 | 15.678 | 3.156 | 3.930470 | -0.9284260 | 56.40392 | 29.20901 | 96.89650 | 43.59608 | 70.75913 | 3.103504 | 0.5761434 | 92236146 | 971093853 | 10589014798 | -1568290062 | 21550099741 | 1e-07 | 1.685412 | 1.6684122 | 3.627730 | 10.180048 | 6.672340 | 6.885693 | 6.452606 | 6.234672 | 6.568161 | 1.0608273 | 9.999985 | 1.0608273 | 2.892645 | 1.700778 | 0.2548997 | 8.939158 | 3.089093 | 1.845899 | 0.1775212 | 48.04518 | 99.99990 | 51.95482 | 0 | 0.6672350 | 47469238 | 356252676 | 2796808210 | -593939497 | 5968664998 | 1e-07 | 1.542566 | 5.611513 | 4.446252 | 7.316667 | 11.64407 | 11.81267 | 11.457447 | 11.243853 | 11.75383 | 1.180774 | 18.26309 | 1.1807736 | 3.954716 | 1.988647 | 0.1707862 | 17.08232 | 2.547107 | 3.769785 | -0.2945041 | 52.92946 | 99.99990 | 47.07054 | 0.00000 | 0.6375741 | 139705385 | 1716628700 | 21577086613 | -3163588038 | 55274110885 | 1e-07 | 1.274854 | 10.4633013 | 6.878014 | 12.45916 |
| 4 | 10 | 14815.833 | 2391.316 | 253.5000 | 228.6277 | 0.8293213 | 3.240321 | 5.588321 | 7.137321 | 7.584321 | 7.896321 | 8.796321 | 9.439321 | 9.999321 | 10.67532 | 11.14432 | 11.66732 | 13.05332 | 13.78632 | 15.08332 | 9.208836 | 9.676083 | 8.445007 | 6.697945 | 9.439321 | 9.490321 | 35.28932 | 0.2503213 | 8.823948 | 2.970513 | 0.3225720 | 35.039 | 3.560 | 3.513803 | -0.5324590 | 54.14860 | 48.89439 | 97.14021 | 45.85140 | 51.07578 | 2.859793 | 0.2609525 | 28567998 | 308407516 | 3490877952 | -480824942 | 6666412747 | 3e-07 | 1.767485 | 0.2814852 | 3.426340 | 10.246363 | 4.801007 | 5.401068 | 4.067086 | 3.284440 | 4.668175 | 0.6118197 | 9.999958 | 0.6118197 | 6.121887 | 2.474245 | 0.5153596 | 9.388139 | 3.940113 | 2.071634 | 0.2721649 | 47.95151 | 99.99967 | 52.04849 | 0 | 0.4801027 | 8901023 | 61927806 | 468289564 | -66273596 | 510018428 | 5e-07 | 2.021859 | 4.189187 | 2.031767 | 5.418747 | 10.78393 | 11.08143 | 10.423270 | 9.950309 | 10.50525 | 9.212659 | 35.48690 | 2.2008590 | 6.504908 | 2.550472 | 0.2365066 | 33.28604 | 3.332113 | 3.510630 | -0.3286589 | 44.53457 | 77.13968 | 55.46543 | 22.85999 | 0.3038850 | 37469021 | 445207961 | 5485056120 | -766979859 | 12425003393 | 3e-07 | 1.618794 | 1.5712744 | 4.827566 | 11.76894 |
| 5 | 10 | 13582.333 | 4682.324 | 574.6667 | 445.8058 | 0.8972930 | 4.469293 | 7.796293 | 8.695293 | 9.044293 | 9.561293 | 10.514293 | 10.960293 | 11.478293 | 12.07729 | 12.46029 | 12.85829 | 13.79829 | 14.36229 | 15.39429 | 10.584187 | 10.963716 | 9.863618 | 7.785157 | 10.964293 | 10.945293 | 16.88629 | 0.2502930 | 8.178051 | 2.859729 | 0.2701888 | 16.636 | 3.426 | 5.038409 | -1.1877711 | 58.91270 | 50.64919 | 97.66575 | 41.08730 | 49.31287 | 2.334252 | 0.6267916 | 151746390 | 1789588757 | 21722917667 | -3028745442 | 47953862766 | 1e-07 | 1.718894 | 0.3611058 | 4.169715 | 11.649419 | 5.359885 | 6.080607 | 4.037565 | 2.053025 | 5.693991 | 0.1000073 | 9.999996 | 0.1000073 | 8.245425 | 2.871485 | 0.5357363 | 9.899989 | 4.844945 | 1.909141 | -0.2794109 | 54.17449 | 99.99992 | 45.82551 | 0 | 0.5359887 | 46676336 | 353412044 | 2820930172 | -397127026 | 3289545553 | 1e-07 | 2.451160 | 5.259878 | 1.946119 | 6.044389 | 12.22845 | 12.53702 | 11.850902 | 11.333547 | 12.47152 | 11.346734 | 18.43135 | 0.8785378 | 7.641773 | 2.764376 | 0.2260609 | 17.55282 | 4.173565 | 2.992009 | -0.5124616 | 53.34442 | 63.06284 | 46.65558 | 36.93708 | 0.6634594 | 198422726 | 2648674843 | 36436151565 | -4630530899 | 84906244333 | 1e-07 | 2.160321 | 0.8817201 | 5.072474 | 13.30724 |
| 6 | 10 | 6254.500 | 1674.809 | 448.0000 | 364.1714 | 0.6060312 | 3.035031 | 6.009031 | 8.205031 | 8.697031 | 9.233031 | 10.052031 | 10.662031 | 11.199031 | 11.60703 | 11.80803 | 12.04303 | 12.86603 | 13.40603 | 14.68603 | 9.948021 | 10.370678 | 9.078045 | 6.626844 | 10.662031 | 11.459031 | 16.45303 | 0.2500312 | 8.587836 | 2.930501 | 0.2945813 | 16.203 | 3.111 | 4.773276 | -1.3195711 | 61.54501 | 33.64629 | 96.60452 | 38.45499 | 66.31770 | 3.395478 | 0.6046315 | 85730909 | 962580012 | 11098719111 | -1595976775 | 23700818001 | 1e-07 | 1.688990 | 1.5110099 | 3.789572 | 11.008726 | 6.594068 | 6.949814 | 6.180656 | 5.719248 | 6.507049 | 0.9677901 | 9.999993 | 0.9677901 | 4.818198 | 2.195039 | 0.3328809 | 9.032203 | 3.993594 | 1.867432 | -0.0993663 | 48.84616 | 99.99987 | 51.15384 | 0 | 0.6594072 | 38500784 | 303690374 | 2521537499 | -457939362 | 4555795906 | 2e-07 | 1.978972 | 5.626277 | 3.308526 | 7.350166 | 12.25927 | 12.48402 | 11.988194 | 11.639040 | 12.45260 | 1.071134 | 18.74465 | 1.0711337 | 5.561109 | 2.358200 | 0.1923605 | 17.67352 | 2.645716 | 4.167097 | -0.6340967 | 54.22377 | 99.99987 | 45.77623 | 0.00000 | 0.6540144 | 124231693 | 1625048934 | 21779500092 | -2943918051 | 54116275529 | 1e-07 | 1.326611 | 11.1881392 | 6.047834 | 13.20862 |
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.
To describe the tendencies and distribution of the spherical
coordinates z, \(\rho\)
(horizontal distance, rho) and r (euclidean
distance), the following statistics are calculated:
mean.arit.z/rho/r), quadratic
(mean.qua.z/rho/r), geometric
(mean.geom.z/rho/r) and harmonic means
(mean.harm.z/rho/r)median.z/rho/r)mode.z/rho/r)var.z/rho/r)sd.z/rho/r)CV.z/rho/r)D.z/rho/r)ID.z/rho/r)max.z/rho/r)min.z/rho/r)kurtosis.z/rho/r)skewness.z/rho/r)p.a.mean.z/rho/r) and the mode
(p.a.mode.z/rho/r)p.b.mean.z/rho/r) and the mode
(p.b.mode.z/rho/r)p.a.2m.z,
only for the \(z\) coordinate)p.b.2m.z,
only for the \(z\) coordinate)L2.z/rho/r,
L3.z/rho/r and L4.z/rho/r)L3.mu.z/rho/r and
L4.mu.z/rho/r)L.CV.z/rho/r)median.a.d.z/rho/r)mode.a.d.z/rho/r)mean.z/rho/r to
max.z/rho/r (CRR.z/rho/r)weibull_c.z/rho/r,
weibull_b.z/rho/r)| id | radius | N.tls | N.hn | N.hr | N.hn.cov | N.hr.cov | N.sh | G.tls | G.hn | G.hr | G.hn.cov | G.hr.cov | G.sh | V.tls | V.hn | V.hr | V.hn.cov | V.hr.cov | V.sh | d.tls | dg.tls | dgeom.tls | dharm.tls | h.tls | hg.tls | hgeom.tls | hharm.tls | d.0.tls | dg.0.tls | dgeom.0.tls | dharm.0.tls | h.0.tls | hg.0.tls | hgeom.0.tls | hharm.0.tls |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 10 | 222.8169 | 241.4554 | 237.3396 | 239.9341 | 234.2128 | 230.5601 | 12.83139 | 13.90472 | 13.66770 | 13.81712 | 13.48764 | 13.27729 | 72.26462 | 78.30949 | 76.97464 | 77.81611 | 75.96057 | 74.77589 | 26.63218 | 27.07807 | 26.17896 | 25.72557 | 11.98963 | 12.02086 | 11.95768 | 11.92508 | 31.50910 | 31.60757 | 31.40772 | 31.30362 | 12.77989 | 12.78591 | 12.77382 | 12.76769 |
| 2 | 10 | 350.1409 | 379.4298 | 372.9622 | 374.9814 | 366.2799 | 364.2843 | 18.91537 | 20.49762 | 20.14823 | 20.25731 | 19.78724 | 19.67943 | 101.80664 | 110.32268 | 108.44214 | 109.02925 | 106.49921 | 105.91896 | 25.75150 | 26.22655 | 25.29375 | 24.86175 | 11.59380 | 11.66199 | 11.51966 | 11.43902 | 32.68378 | 32.75790 | 32.60870 | 32.53280 | 12.41950 | 12.44332 | 12.39576 | 12.37212 |
| 3 | 10 | 381.9719 | 413.9235 | 406.8678 | 414.2445 | 403.9974 | 392.6248 | 23.55858 | 25.52924 | 25.09407 | 25.54904 | 24.91703 | 24.21562 | 115.70695 | 125.38573 | 123.24843 | 125.48298 | 122.37892 | 118.93393 | 27.86976 | 28.02296 | 27.71227 | 27.55093 | 11.38201 | 11.44246 | 11.32332 | 11.26633 | 31.17303 | 31.20949 | 31.13698 | 31.10141 | 11.78541 | 11.93916 | 11.62884 | 11.47255 |
| 4 | 10 | 254.6479 | 275.9490 | 271.2452 | 274.7699 | 268.1497 | 265.5833 | 22.15673 | 24.01012 | 23.60084 | 23.90752 | 23.33151 | 23.10820 | 124.40696 | 134.81348 | 132.51548 | 134.23744 | 131.00320 | 129.74938 | 32.71822 | 33.28417 | 32.14873 | 31.58609 | 12.69636 | 12.81602 | 12.56975 | 12.43597 | 38.69937 | 38.87412 | 38.53131 | 38.37101 | 12.55974 | 12.57650 | 12.54186 | 12.52257 |
| 5 | 10 | 318.3099 | 344.9362 | 339.0565 | 360.7488 | 349.0381 | 334.1288 | 21.34794 | 23.13368 | 22.73934 | 24.19417 | 23.40878 | 22.40886 | 117.11494 | 126.91149 | 124.74819 | 132.72937 | 128.42070 | 122.93514 | 28.64160 | 29.22187 | 27.98239 | 27.23715 | 12.77420 | 12.99329 | 12.47878 | 12.08340 | 34.98638 | 35.05872 | 34.91178 | 34.83518 | 13.39910 | 13.40467 | 13.39359 | 13.38812 |
| 6 | 10 | 254.6479 | 275.9490 | 271.2452 | 276.1346 | 269.3076 | 260.6298 | 15.96468 | 17.30011 | 17.00522 | 17.31175 | 16.88375 | 16.33971 | 89.59139 | 97.08563 | 95.43073 | 97.15093 | 94.74903 | 91.69596 | 28.06921 | 28.25304 | 27.88269 | 27.69453 | 12.82381 | 12.84689 | 12.80020 | 12.77611 | 31.41186 | 31.44841 | 31.37513 | 31.33830 | 12.79379 | 12.81666 | 12.77130 | 12.74923 |
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.
The stand density (N.tls, trees/ha) is
calculated by the following equations. For the circular fixed area and
k-tree plots, N.tls is calculated by
\[ N.tls=\frac{10000}{\pi R^2}\cdot n \]
with \(R\) being the radius of the plot (in m) and \(n\) the number of detected trees. The density of angle-count plots is calculated by
\[ N.tls=\sum_{i=1}^{n} \frac{BAF}{g_i} \]
with \(BAF\) being the basal area factor (in m\(^2\)/ha) and \(g_i\) the basal area of the tree \(i\) (in m\(^2\)).
The basal area (G.tls, in m\(^2\)/ha) is estimated for circular fixed
area and k-tree plots by the following equation:
\[ G.tls=\frac{10000}{\pi R^2}\sum_{i=1}^{n} g_i \]
and for angle-count plots, the following equation is applied:
\[ G.tls=BAF \cdot n \]
The stem volume (V.tls, in m\(^3\)/ha) is estimated by modelling the stem
profile as a paraboloid. The volume is calculated as the volume of the
revolution of the paraboloid function. The total heights of the detected
trees are estimated as the 99th percentile of the points of the \(z\) coordinate delimited by Voronoi
polygons (\(h_{P_{99}i}\), in m). The
equation used for the calculation for circular fixed area and k-tree
plots is
\[ V.tls=\frac{10000}{\pi R^2}\sum_{i=1}^{n} \pi \cdot \frac{h_{P_{99}i}^2}{2} \cdot \frac{(\frac{1}{2} \cdot dbh_i)^2}{(h_{P_{99}i} - 1.3)^2} \]
and for angle-count plots is
\[ V.tls=\sum_{i=1}^{n} \frac{BAF}{g_i} \cdot \pi \cdot \frac{h_{P_{99}i}^2}{2} \cdot \frac{(\frac{1}{2} \cdot dbh_i)^2}{(h_{P_{99}i} - 1.3)^2} \]
The above mentioned calculations of the stand-level variables \(N\), \(V\) and \(G\) do not consider possible occlusions of trees. Therefore, different occlusion correction approaches are included in the function.
For angle-count plots, the occlusion correction is based on the
Poisson attenuation model. This approach calculates geometric gap
probabilities which decreases with increasing distance from the TLS
device and follow a Poisson distribution. The calculations of stand
density, volume and basal area are corrected with a factor accounting
for the gap probabilities and the corrected variables are called
N.pam, V.pam
and G.pam respectively. For further
details see Strahler et al. (20081) and Lovell et al. (20112).
For the other two plot designs (circular fixed area and k-tree plots)
different occlusion correction approaches are applied. One approach is
based on distance sampling data and can therefore only be used when the
function distance.sampling was used (i.e., when the
tree.ds argument is specified other than
NULL). Functions based on point transect sampling that
describe how the probability of tree detection decreases with increasing
distance from the TLS device are used for the calculation. These
functions are applied for the calculation of the variables
N.hn/V.hn/G.hn
and
N.hr/V.hr/G.hr
and are Half-Normal and Hazard-Rate respectively. Additionally,
N.hn.cov/V.hn.cov/G.hn.cov
and
N.hr.cov/V.hr.cov/G.hr.cov
are calculated with expanding the scale component of the function with
\(dbh\) as covariate.
The other approach corrects shadowing effects. Tthis method
calculates an expansion factor to correct the variables. The expansion
factor is based on the percentage of the shaded area i.e., unsample area
which is not seen from the TLS device due to masking by trees. The
corrected calculated variables are called
N.sh/V.sh/G.sh.
For more details see Seidel and Ammer (20143).
The mean heights (in m) and diameters (in cm) are calculated by the
arithmetic (h.tls,
d.tls), quadratic
(h.g, d.g),
geometric (h.geom,
d.geom) and harmonic means
(h.harm,
d.harm). To calculate the dominant heights
and diameters, only the \(n\) largest
trees per hectar are considered. If not otherwise specified in the
argument num.tree (see above), the number of dominant trees
per hectare is set to 100 trees/ha. Dominant heights and diameters are
also calculated as the arithmetic
(h.0.tls,
d.0.tls), quadratic
(h.0.g,
d.0.g), geometric
(h.0.geom,
d.0.geom) and harmonic means
(h.0.harm,
d.0.harm).
Strahler, A.H., Jupp, D.L.B., Woodcock, C.E., Schaaf, C.B., Yao, T., Zhao, F., Yang, X., Lovell, J., Culvenor, D., Newnham, G., Ni-Miester, W., Boykin-Morris, W., 2008. Retrieval of forest structural parameters using a ground-based lidar instrument (Echidna®). Can. J. Rem. Sens. 34 (Suppl. 2), S426–S440. https://doi.org/10.5589/m08-046.↩︎
Lovell, J.L., Jupp, D.L.B., Newnham, G.J., Culvenor, D.S., 2011. Measuring tree stem diameters using intensity profiles from ground-based scanning lidar from a fixed viewpoint. ISPRS J. Photogrammetry Remote Sens. 66 (1), 46–55. https://doi.org/10.1016/j.isprsjprs.2010.08.006.↩︎
Seidel, D., Ammer, C., 2014. Efficient measurements of basal area in short rotation forests based on terrestrial laser scanning under special consideration of shadowing. iFor. Biogeosci. For. 7 (4), 227–232. https://doi.org/10.3832/ifor1084-007.↩︎