Functions
The R-package contains all relevant functions from the Fortran-library and uses vectorized evaluation. It is recommended to use the get*-functions, but for convenience wrapper functions using the names of the Fortan-subroutines are included so that older scripts can easily be adapted to the use of the R-package.
Beside the core-functions (buildTree, getDiameter, getHeight, getVolume, getAssortment, getBiomass, getBark, getForm and getSpeciesCode) there is a plotting function.
preliminary note
The use of the BDAT Fortran functions requires the preparation of the
data to conform with what Fortran is expecting to come. Within this
R-Package, this is implemented in two ways: either one can prepare all
necessary variables within a list or data frame and pass it over to the
respective function via the tree parameter or one can pass
a tree definition into parameter tree of each function and
use the second parameter (i.e. Dx, Hx,
AB or sort, here called vars) to
hand over the required - function specific - information. In the first
case, the function returns one result for each row given. In the second
case, a cross join / cartesian product between tree and
vars is calculated. If vars is of size one,
the results is the same as in the first case. If the size of
vars is bigger than one, the functions return one value for
each given tree (e.g. 3) and element of vars (e.g. 4), in
the example this is 12. For functions returning a scalar, a matrix is
returned with trees given in rows and vars
given in columns (e.g. 3x4-matrix). The assortment function, usually
returning a data frame, still returns a data frame, but now the order
(and naming) of trees is different from the given input
tree parameter, since internally the tree object is now
expanded. Hence, the first tree is repeated (length-of-vars) number of
times, before the second tree is process and returned and so on.
Getting started
In BDAT, a tree is specified at its minimum by its species code, dbh (diameter in breast height, i.e. 1.3m) and height. Implicitly, this defines a second diameter in 30% of three height according to the “Masse-Tafeln” (Volume-Tables) from Grundner und Schwappach (1921). For the possibility of more precisely specifying taper form see further below.
## This is rBDAT 1.0.0## Classes 'datBDAT' and 'data.frame': 1 obs. of 6 variables:
## $ spp: num 1
## $ D1 : num 30
## $ H : num 27
## $ H1 : num 1.3
## $ D2 : num 0
## $ H2 : num 0One can visualise the taper curve of a given tree using the plot-function:
Here, the taper curve over bark (black) and under bark (grey) is
drawn.
getting BDAT-species code
BDAT has been parameterised for 36 tree species, more or less common in Germany based on about 30.000 trees. These 36 tree species are index and each posesses its own BDAT-species code. This code and the respective species name (short and long format), english species name and scientific name can be retrieved by the getSpeciesCode-function:
## ID kurz lang short long scientific
## 1 1 Fi Fichte NS Norway spruce Picea abies
## 2 2 SF Sitka-Fichte SS Sitka spruce Picea sitchensis
## 3 3 Ta Tanne ESF European silver fir Abies alba
## 4 4 KT Kuestentanne GF Grand fir Abies grandis
## 5 5 Kie Kiefer SP Scotch pine Pinus sylvestris
## 6 6 SK Schwarzkiefer AUP Austrian pine Pinus nigra
## 7 7 WK Weymouthskiefer WEP Weymouth pine Pinus strobus
## 8 8 DG Douglasie DF Douglas fir Pseudotsuga menziesii
## 9 9 La Laerche XLA larch Larix spp.
## 10 10 EL Europ. Laerche ELA European larch Larix decidua
## 11 11 JL Jap. Laerche JLA Japanese larch Larix kaempferi
## 12 12 Th Thuja RC Western red cedar Thuja plicata
## 13 13 Ts Tsuga WH Western hemlock Tsuga heterophylla
## 14 14 SN sNB XC other conifers Coniferales trees
## 15 15 Bu Buche BE beech Fagus sylvatica
## 16 16 HB Hainbuche HBM hornbeam Carpinus betulus
## 17 17 Ei Eiche OK oak (robur/petraea) Quercus spp.
## 18 18 RE Roteiche ROK Red oak Quercus rubra
## 19 19 Pa Pappel XPO poplar Populus spp.
## 20 20 BP Balsampappel BPO Balsam poplar Populus balsamifera
## 21 21 Es Esche AH ash Fraxinus excelsior
## 22 22 Ah Ahorn XAH maple Acer spp.
## 23 23 BA Bergahorn SY sycamore Acer pseudoplatanus
## 24 24 SA Spitzahorn NOM Norway maple Acer platanoides
## 25 25 FA Feldahorn FM Field maple Acer campestre
## 26 26 Bi Birke XBI birch Betula spp.
## 27 27 Li Linde LI lime tree Tilia spp.
## 28 28 Er Erle AR alder Alnus spp.
## 29 29 Kir Kirsche WCH Wild cherry Prunus avium
## 30 30 Ul Ulme EM elm Ulmus spp.
## 31 31 Ro Robinie BL black locust Robinia pseudoacacia
## 32 32 El Elsbeere WST Wild service tree Sorbus torminalis
## 33 33 Ka Kastanie SC Sweet chestnut Castanea sativa
## 34 34 We Weide XWL willow Salix spp.
## 35 35 LB sLB XB other broadleaves Magnoliopsida trees
## 36 36 VB Vogelbeere ROW rowan Sorbus aucupariaIf the function is called without any parameter, a data.frame is
returned holding the information which can be retrieved. One can
alternatively specify the type of input and
output. Input must be one of the data entries,
output must be one of the column names.
## ID kurz lang short long scientific
## 1 1 Fi Fichte NS Norway spruce Picea abies## [1] 1## [1] 1## [1] "Picea abies"## [1] "NS" "SS" "ESF" "GF" "SP" "AUP" "WEP" "DF" "XLA" "ELA" "JLA" "RC"
## [13] "WH" "XC" "BE" "HBM" "OK" "ROK" "XPO" "BPO" "AH" "XAH" "SY" "NOM"
## [25] "FM" "XBI" "LI" "AR" "WCH" "EM" "BL" "WST" "SC" "XWL" "XB" "ROW"getting diameter in given height
The taper functions specify a curve being a function of height within tree and returns the respective diameter. Hence, one can evalutate this function at a given height and receive the diameter. There are fortran functions to return either diameter over bark and diameter under bark, but this package binds these functions together and uses a boolean parameter to switch between both.
## [1] 30As a default, diameter over bark is returned, but this can easily be changed:
## [1] 28.40971It is possible to request diameter in several heights at once:
## [1] 31.14922 28.44761 27.57622 26.92106 26.32229 25.76090 25.21790 24.67427
## [9] 24.11234 23.52139Using this kind of call to the functions, Hx is
evaluated for each given tree separately:
## [,1] [,2]
## [1,] 31.14922 28.44761
## [2,] 36.54927 32.92451Here, a matrix is returned with one row per tree and one column per requested Hx.
An alternative way is specifying Hx directly inside the
tree-object:
## spp D1 H Hx H1 D2 H2
## 1 1 30 27 1 1.3 0 0
## 2 1 35 27 2 1.3 0 0## [1] 31.14922 32.92451Here, tree2 consists of 2 rows, because the give list is internally
transformed into a data frame (common rules for building data.frames
apply). Finally, the object is evaluated row-wise. Because
Hx is already given, the parameter Hx can be
left empty.
getting double bark thickness
Double bark thickness is that part of a diameter over bark, which is considered to consist of bark tissue. The relation between wood and bark with respect to diameter can be expressed as {double bark thickness} + {diameter under bark} = {diameter over bark}. The implemented functions originate from the works of Altherr et al. (1974, 1975, 1976, 1978 and 1979).
dub <- getDiameter(tree, Hx=1.3, bark = FALSE)
dob <- getDiameter(tree, Hx=1.3, bark = TRUE)
dbt <- getBark(tree, Hx=1.3)
dub + dbt == dob## [1] TRUEAgain, it is possible to either include parameter Hx
into the tree-object or pass it separately. In the second case, an
matrix is returned if Hx is longer than one.
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.636124 1.527308 1.491416 1.464177 1.439089
## [2,] 1.842470 1.705602 1.661812 1.629562 1.600471getting height for given diameter
The diameter-height-relation from above, where we evaluated the function for a given height-value, can also be evaluated for a given diameter. The internal function is an iterative procedure to determine height. Diameter can be specified over and under bark. Default is bark = TRUE.
## [1] 1.3## [1] 0.8916153Again, it is possible to vary passing of the
Dx-parameter: it can take one or several values, but can
also be included to the tree parameter. In the first case, a cross join
/ cartesian product between tree and Dx is
created, in the second case the tree object is processed
as is.
## [,1] [,2] [,3]
## [1,] 1.300000 14.82080 22.65465
## [2,] 5.370549 17.27376 23.05898## [1] 1.30000 17.27376As one can see, in the first case a matrix with one row per tree and
one column per Dx is returned and in the second call, a
vector with one element for each row in tree2.
getting volume
The maybe most interesting function is the one returning volume. The
function includes a switch to return volume with (the default) or
without bark volume as well. Volume is calculated using
middiameter-formula (in Germany called “Huber’sche Formel”) from
2m-sections (default), but section lengths can be varied. Additionally,
it is necessary to specify the section for which volume is required.
This can be done either using diameters or heights, or a mixture of
both. If parameter AB is not given, i.e. NULL, then the
function assumes coarse wood volume over bark is required (i.e. from
forest floor up to diameter over bark of 7cm):
## [1] 0.9168622## [1] 0.9168622One can precisely specify the section for which volume under or over bark is required:
## [1] 0.06184182 0.08197092# volume excluding bark between 30 and 7cm in diameter over bark
getVolume(tree2, AB=list(A=30, B=7), iAB="dob", bark = F) ## [1] 0.7153726 0.6583801The section length for which middiameter-formula is applied is 2m as
a default. It is possible to change that behaviour by setting parameter
sl inside the AB-argument:
## [1] 0.9168622## [1] 0.7892534# using sl=0.1, that is section length for volume calculation set to be 0.1m
getVolume(tree, AB=list(A=0.27, B=7, sl=0.1), iAB=c("H", "Dob"), bark=F) ## [1] 0.7971188If one wants to get the volume for several sections of a tree, one
could either build a suited data.frame on its own, repeating the tree
attributes and adjusting the Aand B values as
needed. The more elegant way is to let the functions do that work for
you. In the easiest case, we saw that already in the example above,
specifying one tree and one section, where the function returns exactly
one volume. Internally, the AB data is merged to the tree
data by a cross join (or cartesion product), hence we can make use of
that behaviour by defining several sections at once:
## [1] 0.09056835 0.06184182 0.06128590 0.05816483 0.05563769 0.05319688
## [7] 0.05102357 0.04886994 0.04674566 0.04458112## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.09056835 0.06184182 0.06128590 0.05816483 0.05563769 0.05319688
## [2,] 0.12786366 0.08197092 0.08171326 0.07714033 0.07358742 0.07018656
## [,7] [,8] [,9] [,10]
## [1,] 0.05102357 0.04886994 0.04674566 0.04458112
## [2,] 0.06725162 0.06435400 0.06151795 0.05862010getting biomass
Beside getting volume section information, there is a function to get total aboveground biomass. These biomass-functions were fitted independently of the parameterisation of BDAT and were developed in preparation of the german NFI3. These functions are based on 983 analysed trees of a subset of species only. The other species are either fit at a synthetical data set or in worst case subsumed to other species. These functions are the official ones used during reporting of results of the NFI3.
The call is identical to the already shown pattern:
## [1] 406.1523## [1] 350.5038 375.2445 400.5624getting assortments
One very nice feature of the BDAT program library is its ability to
use the presented functions to simulate roundwoods from given trees. For
that purpose a separate function was written, which is called via
getAssortment(). Similarly to other functions, it requires
data of one or more trees and optionally parameters to control the
sorting process. There are quite a few parameters to be specified. It’s
easiest to show that using some examples:
## tree No Sort height length midD topD Vol
## 1 1 1 X 0.00 0.000000 0.000000 0.000000 0.00000000
## 2 1 2 Sth 0.27 20.000000 21.250875 12.429831 0.70937115
## 3 1 3 Ab 0.00 0.000000 0.000000 0.000000 0.00000000
## 4 1 4 Ind 20.47 1.000000 11.460602 10.725959 0.01031584
## 5 1 5 nvDh 21.47 2.717499 8.529173 5.998856 0.01552648
## 6 2 1 X 0.00 0.000000 0.000000 0.000000 0.00000000
## 7 2 2 Sth 0.27 20.000000 24.499969 13.956373 0.94286811
## 8 2 3 Ab 0.00 0.000000 0.000000 0.000000 0.00000000
## 9 2 4 Ind 20.47 1.000000 12.778620 11.893189 0.01282501
## 10 2 5 nvDh 21.47 2.904999 9.106683 5.990857 0.01892153By default, a data.frame is returned with one row for each tree and roundwood piece. It keeps information about the roundwood foot position inside the stem, its length (without add-on), mid-diameter under bark (midD), top-diameter under bark (topD) and the respective volume under bark. The standard assortments comprise stem-wood (Sth), second length stem wood (Ab, after optionally specified cutting diameter for Sth or after transportation-cut, i.e. 20m), industrial roundwood (Ind) and residual coarse wood (nvDh, between cutting diameter for Ind and 7cm over bark). Assortment X is unusuable wood at the stem foot.
If one is interested in raw BDAT return, one can specify
value='raw':
## $n
## [1] 2
##
## $BDATArtNr
## [1] 1 1
##
## $D1
## [1] 30 35
## attr(,"Csingle")
## [1] TRUE
##
## $H1
## [1] 1.3 1.3
## attr(,"Csingle")
## [1] TRUE
##
## $D2
## [1] 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $H2
## [1] 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $H
## [1] 27 27
## attr(,"Csingle")
## [1] TRUE
##
## $lX
## [1] 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $Hkz
## [1] 0 0
##
## $Skz
## [1] 0 0
##
## $Az
## [1] 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $Hsh
## [1] 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $Zsh
## [1] 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $Zab
## [1] 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $Sokz
## [1] 1 1
##
## $Skl
## [1] 0 0 2 0 0 0 0 0 2 0 0 0
##
## $Vol
## [1] 0.91686225 0.00000000 0.70937115 0.00000000 0.01031584 0.01552648
## [7] 0.18164879 1.21056700 0.00000000 0.94286811 0.00000000 0.01282501
## [13] 0.01892153 0.23595232
## attr(,"Csingle")
## [1] TRUE
##
## $LDSort
## [1] 0.000000 0.000000 0.000000 0.000000 0.270000 20.000000 21.250875
## [8] 12.429831 0.000000 0.000000 0.000000 0.000000 20.470001 1.000000
## [15] 11.460602 10.725959 21.470001 2.717499 8.529173 5.998856 0.000000
## [22] 0.000000 0.000000 0.000000 0.270000 20.000000 24.499969 13.956373
## [29] 0.000000 0.000000 0.000000 0.000000 20.470001 1.000000 12.778620
## [36] 11.893189 21.470001 2.904999 9.106683 5.990857
## attr(,"Csingle")
## [1] TRUE
##
## $BHD
## [1] 30 35
## attr(,"Csingle")
## [1] TRUE
##
## $Ifeh
## [1] 0 0
##
## $FixLngDef
## [1] 0 0 0 0 0 0 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $NMaxFixLng
## [1] 0 0
##
## $FixLng
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [149] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [186] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [223] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [260] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [297] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [334] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## attr(,"Csingle")
## [1] TRUE
##
## $NFixLng
## [1] 0 0Other options are also available like ‘Vol’ (Volume), ‘Skl’ (Stärkeklassen, i.e. diameter classes), ‘Fix’ (fixed length assortments, if specified) and ‘LDSort’ (an added feature w.r.t. the original BDAT Fortran code, keeping length and diameter of the assortments, which was missing in the original BDAT library, hence only available in rBDAT!), which return a subset of the raw BDAT return value. The default is ‘merge’ which produces an aggregated data.frame of relevant information about the roundwoods produced for each tree.
As said before, assortment rules can be specified using several parameters, which in detail are given in the help file. Some examples follow:
## tree No Sort height length midD topD Vol
## 1 1 1 X 0.000 0.000000 0.00000 0.000000 0.00000000
## 2 1 2 Sth 0.270 19.100000 21.51180 13.584801 0.69418710
## 3 1 3 Ab 0.000 0.000000 0.00000 0.000000 0.00000000
## 4 1 4 Ind 0.000 0.000000 0.00000 0.000000 0.00000000
## 5 1 5 nvDh 19.561 4.626499 10.10419 5.998856 0.03709757## Warning in getAssortment.datBDAT(tree, sort = list(Az = 15, Hsh = 10)): error indication in subroutine BDAT20:
## tree 1: Top-shafted coniferous tree with positive stem height: Skz = 0|1 and Hsh > 0; spp < 15## tree No Sort height length midD topD Vol
## 1 1 1 X NA NA NA NA NA
## 2 1 2 Sth NA NA NA NA NA
## 3 1 3 Ab NA NA NA NA NA
## 4 1 4 Ind NA NA NA NA NA
## 5 1 5 nvDh NA NA NA NA NAAdditionally one can specify a fixed length assortment at stem foot, which is cut before sawlogs.
## fixN = number of roundwood pieces
## fixL = length of roundwood pieces in m
## fixA = absolute length addition (good for measure) in cm
## fixR = relative length addition in %
## fixZ = minimum cutting diameter for this assortment (Z=Zopf) in cm
getAssortment(tree, sort=list(Az=15, fixN=2, fixL=4, fixA=10, fixZ=20)) ## tree No Sort height length midD topD Vol
## 1 1 1 X 0.000000 0.0000 0.00000 0.000000 0.0000000
## 2 1 2 Sth 8.470001 10.9000 19.04127 13.584801 0.3103904
## 3 1 3 Ab 0.000000 0.0000 0.00000 0.000000 0.0000000
## 4 1 4 Ind 0.000000 0.0000 0.00000 0.000000 0.0000000
## 5 1 5 nvDh 19.479000 4.7085 10.16843 5.998856 0.0382367
## 6 1 6 Fix01 0.270000 4.0000 25.86922 24.547409 0.2102405
## 7 1 7 Fix02 4.370000 4.0000 23.40202 22.309429 0.1720507In case the considered tree exhibits rotten/decaying wood at stem foot, this can also be specified (in german termed X-Holz):
## tree No Sort height length midD topD Vol
## 1 1 1 X 0.27 1.400000 28.892862 26.715826 0.09179077
## 2 1 2 Sth 1.67 20.000000 20.387375 10.421552 0.65289372
## 3 1 3 Ab 0.00 0.000000 0.000000 0.000000 0.00000000
## 4 1 4 Ind 0.00 0.000000 0.000000 0.000000 0.00000000
## 5 1 5 nvDh 21.87 2.317499 8.178885 5.998856 0.01217580Additionally, one can plot the taper curve and include the assortments:
assort <- getAssortment(tree, sort=list(Az=15, fixN=2, fixL=4, fixA=10, fixZ=20))
plot(tree, assort=assort)
using more than one assortment specification
buildTree uses the parameters tree and
vars which are merged by a cross join / cartesian product.
Hence, if assortment specifications are extended to a length bigger one,
the function should return an estimated assortment for each tree and
specified assortment. Let’s check that:
## tree No Sort height length midD topD Vol
## 1 1 1 X 0.00 0.0000000 0.000000 0.000000 0.000000000
## 2 1 2 Sth 0.27 20.0000000 21.250875 12.429831 0.709371150
## 3 1 3 Ab 0.00 0.0000000 0.000000 0.000000 0.000000000
## 4 1 4 Ind 20.47 2.0000000 10.725959 9.139494 0.018071413
## 5 1 5 nvDh 22.47 1.7174988 7.639552 5.998856 0.007872671
## 6 2 1 X 0.00 0.0000000 0.000000 0.000000 0.000000000
## 7 2 2 Sth 0.27 20.0000000 21.250875 12.429831 0.709371150
## 8 2 3 Ab 0.00 0.0000000 0.000000 0.000000 0.000000000
## 9 2 4 Ind 20.47 3.0000000 9.953113 7.379699 0.023341509
## 10 2 5 nvDh 23.47 0.7174988 6.702212 5.998856 0.002531322## tree No Sort height length midD topD Vol
## 1 1 1 X 0.00 0.0000000 0.000000 0.000000 0.000000000
## 2 1 2 Sth 0.27 20.0000000 21.250875 12.429831 0.709371150
## 3 1 3 Ab 0.00 0.0000000 0.000000 0.000000 0.000000000
## 4 1 4 Ind 20.47 2.0000000 10.725959 9.139494 0.018071413
## 5 1 5 nvDh 22.47 1.7174988 7.639552 5.998856 0.007872671
## 6 2 1 X 0.00 0.0000000 0.000000 0.000000 0.000000000
## 7 2 2 Sth 0.27 20.0000000 24.499969 13.956373 0.942868114
## 8 2 3 Ab 0.00 0.0000000 0.000000 0.000000 0.000000000
## 9 2 4 Ind 20.47 2.0000000 11.893189 10.009459 0.022218592
## 10 2 5 nvDh 22.47 1.9049988 8.071947 5.990857 0.009748576
## 11 3 1 X 0.00 0.0000000 0.000000 0.000000 0.000000000
## 12 3 2 Sth 0.27 20.0000000 21.250875 12.429831 0.709371150
## 13 3 3 Ab 0.00 0.0000000 0.000000 0.000000 0.000000000
## 14 3 4 Ind 20.47 3.0000000 9.953113 7.379699 0.023341509
## 15 3 5 nvDh 23.47 0.7174988 6.702212 5.998856 0.002531322
## 16 4 1 X 0.00 0.0000000 0.000000 0.000000 0.000000000
## 17 4 2 Sth 0.27 20.0000000 24.499969 13.956373 0.942868114
## 18 4 3 Ab 0.00 0.0000000 0.000000 0.000000 0.000000000
## 19 4 4 Ind 20.47 3.0000000 10.970320 7.971595 0.028356308
## 20 4 5 nvDh 23.47 0.9049988 6.997648 5.990857 0.003480503Here, the first call returns the estimated assortments for both assortment specifications, the tree order inside the resulting object is clear: tree 1 uses Az=10 and tree 2 uses Az=7. In the second call, the order is the same, although this is not as clear as in the first example.
more advanced specification of trees
As shown, a tree is specified by its species code, its dbh and height. If done so, this assumes a predefined diameter in 30% of tree height, which in turn defines the taper form or the relation between diameter in 30% and 5% of the tree height. But easily, this can be changed: the BWI-equivalent taper form can be specified using H2=50. The D2 and H2 parameter can take a very flexible parameterisation being diameter and heights but also quantiles of the q03-distribution (H2) or the q03-parameter itself (D2). q03 is the quotient of diameter in 30% of three height and in 5% of tree height. Hence, quite a variety of taper forms can be represented. All BDAT-functions respond sensitively to this fourth parameter.
tree <- buildTree(tree = list(spp=1, D1=30, H=27, H2=c(30, 50, 99, 0),
D2=c(0, 0, 0, -0.8), Hx=0.3*27))
str(tree)## Classes 'datBDAT' and 'data.frame': 4 obs. of 7 variables:
## $ spp: num 1 1 1 1
## $ D1 : num 30 30 30 30
## $ H : num 27 27 27 27
## $ H2 : num 30 50 99 0
## $ D2 : num 0 0 0 -0.8
## $ Hx : num 8.1 8.1 8.1 8.1
## $ H1 : num 1.3 1.3 1.3 1.3## [1] 23.19664 24.00090 27.59044 23.84774With the getForm-function, one can specify trees mimicking the mean sample trees from different inventories. This function returns the expected q03 of a given diameter-height-class, here of dbh=30 and h=27:
## [1] 0.8049681 0.7996023 0.7913954 0.8107125