knitr::opts_chunk$set(echo = TRUE)

BDAT: a Fortran library for taper curves

BDAT is a Fortran program library to estimate volume, diameter, height, bark thickness and assortments of a specified tree. Hence, it is a library about taper functions. It has been developed at FVA-BW on request of BMELV for the first german national forest inventory (BWI 1, 1987). Adjustements have been made for the BWI2 (2002). BDATPro is a version including these latest adjustments but also an additionaly GUI. The latest version includes biomass functions and form parameters for NFI3 (=BWI3). Here the latest version was implemented.

Colloquially the library is called BDAT.

The Fortran library has been extensively used in several application, of which the most important might be WEHAM (WaldEntwicklungs- and HolzAufkommensModell: forest developement and timber stock prediction model) but also in other forest inventories. At that time, R was not emerged, yet, later direct calls to the Windows-DLL were used. With the present R-package, the usage of BDAT in R was highly simplified, ported to other operating systems (32bit and 64bit) and better documented. There are some original documents on my gitlab repository about the methodology and application, but all have been written in German.

The BDAT library is based on a spline representation of the taper function of different tree species. A methodological improvement has been made using B-Splines and mixed-modelling, see Kublin et al. 2013 and the R-package TapeR. Still, BDAT is in use and keeps being used since the library offers more than just the taper form itself: estimation of diameters, height, double bark thickness, volume of sections defined by height and/or diameter, assortments given parameters and all already parameterised for a whole bunch of tree species including deciduous tree species with their complex tree crowns. It is based on approximately 30.000 measured trees and studies on bark thickness and tree crown volume.

further references

Further references like BDAT Documentations, related articles and reports can be found at especially at, unfortunately these resources are all written in German.


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.

tree <- buildTree(tree = list(spp=1, D1=30, H=27))

One 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:


If 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.

getSpeciesCode("NS") # english abbreviation of Norway spruce
getSpeciesCode(1, "scientific")
getSpeciesCode(c(1:36), "short")

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.

getDiameter(tree, Hx = 1.3) # return dbh

As a default, diameter over bark is returned, but this can easily be changed:

getDiameter(tree, Hx = 1.3, bark = FALSE) # return d.u.b. at 1.3m

It is possible to request diameter in several heights at once:

getDiameter(tree, Hx = c(1:10))

Using this kind of call to the functions, Hx is evaluated for each given tree separately:

tree2 <- buildTree(list(spp=1, D1=c(30, 35), H=27))
getDiameter(tree2, Hx = c(1, 2))

Here, 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:

tree2 <- buildTree(list(spp=1, D1=c(30, 35), H=27, Hx=c(1, 2)))

Here, 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

Again, 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.

getBark(tree2, Hx = 1:5)

getting 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.

getHeight(tree, Dx=30) # height of diameter over bark
getHeight(tree, Dx=30, bark = FALSE) # height of diameter under bark == 30

Again, 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.

getHeight(tree2, Dx=c(30, 20, 10)) # returns value in meters
tree2$Dx = c(30, 20)

As 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):

getVolume(tree) # get coarse wood, which is the same as next line
getVolume(tree, AB = list(A=0, B=7), iAB=c("H", "Dob"), bark = T) 

One can precisely specify the section for which volume under or over bark is required:

# volume including bark between height 1m and 2m
getVolume(tree2, AB=list(A=1, B=2)) 
# volume excluding bark between 30 and 7cm in diameter over bark
getVolume(tree2, AB=list(A=30, B=7), iAB="dob", bark = F) 

The 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:

# again: coarse wood volume
# identical
getVolume(tree, AB=list(A=0.27, B=7, sl=2), iAB=c("H", "Dob"), bark=F) 
# 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) 

If 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:

getVolume(tree, AB=list(A=0:9, B=1:10))
getVolume(tree = tree2, AB=list(A=0:9, B=1:10))

getting 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:

getBiomass(list(spp=1, D1=30, H=27, D2=c(23, 24, 25))) 

getting 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:

getAssortment(tree2) # using standard assortment parameters

By 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':

getAssortment(tree2, value = "raw") # usually of little interest...

Other 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:

getAssortment(tree, sort=list(Az=15)) # minimum diameter o.b. for assortments
getAssortment(tree, sort=list(Az=15, Hsh=10)) # Hsh= max. height of sawlog quality

Additionally 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)) 

In case the considered tree exhibits rotten/decaying wood at stem foot, this can also be specified (in german termed X-Holz):

getAssortment(tree, sort=list(lX=1.4)) # remove 1.4m from stump upwards

Additionally, 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:

getAssortment(tree, sort = list(Az=c(10, 7)))
getAssortment(tree2, sort = list(Az=c(10, 7)))

Here, 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))
getDiameter(tree) # Hx specified beforehand being 30% of tree height

With 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:

getForm(tree[1,], inv=c(1, 2, 3, 4))

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rBDAT documentation built on March 16, 2021, 5:07 p.m.