Title: Dynamic Stem Profile Models, AKA Tree Taper Equations
Version: 1.1
Description: Performs calculations with tree taper (or stem profile) equations, including model fitting. The package implements the methods from García, O. (2015) "Dynamic modelling of tree form" http://mcfns.net/index.php/Journal/article/view/MCFNS7.1_2. The models are parsimonious, describe well the tree bole shape over its full length, and are consistent with wood formation mechanisms through time.
License: MIT + file LICENSE
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.2.1
Depends: R (≥ 2.10)
VignetteBuilder: knitr
Suggests: knitr, lattice
URL: https://github.com/ogarciav/dyntaper
BugReports: https://github.com/ogarciav/dyntaper/issues
NeedsCompilation: no
Packaged: 2022-08-12 03:55:06 UTC; oscar
Author: Oscar Garcia ORCID iD [cre, aut]
Maintainer: Oscar Garcia <garcia@dasometrics.net>
Repository: CRAN
Date/Publication: 2022-08-14 08:00:02 UTC

dyntaper: Dynamic Stem Profile Models, AKA Tree Taper Equations

Description

Performs calculations with tree taper (or stem profile) equations, including model fitting. The package implements the methods from García, O. (2015) "Dynamic modelling of tree form" http://mcfns.net/index.php/Journal/article/view/MCFNS7.1_2. The models are parsimonious, describe well the tree bole shape over its full length, and are consistent with wood formation mechanisms through time.

Details

The main functions relevant to the user are

The package includes a small example dataset, brink.

For a tutorial, see the vignette: vignette("dyntaper", package="dyntaper").

Author(s)

Maintainer: Oscar Garcia garcia@dasometrics.net (ORCID)

References

García, O. (2015) "Dynamic modelling of tree form". Mathematical and Computational Forestry & Natural-Resource Sciences (MCFNS) 7(1), 9–15. (http://mcfns.net/index.php/Journal/article/view/MCFNS7.1_2).

Koirala, A., Montes, C. R., Bullock, B. P. and Wagle, B. H. (2021) "Developing taper equations for planted teak (Tectona grandis L. f.) trees of central lowland Nepal". Trees, Forests and People 5. (doi:10.1016/j.tfp.2021.100103).

See Also

Useful links:

Examples

   dfir <- c(2.569, 0, 1.042, 0.3012, -1)  # params. for D.fir in B.C.
   height <- 32; dbh <- 24;  k <- 0.956  # k is a bark conversion factor
   # Plot a taper curve (inside-bark diameter over height levels):
   curve(
     taper(h, height, k*dbh, dfir, 1.3),  # 1.3 m is the breast height
   from = 0, to = 32, xname = "h")
   # Height level for a diameter of 10 cm (i.b.):
   (h10 <- hlevel(10, height, k*dbh, dfir, 1.3))
   # Volume from a 30 cm stump to a 10 cm diameter limit:
   volume(0.3, h10, height, k*dbh, dfir, 1.3, 100)

Integral of decay function.

Description

Integral of decay function.

Usage

Id(x, p)

Arguments

x

Input value(s), possibly a vector.

p

Parameter.

Value

Integral of the decay function between 0 and x.

Examples

   Id(2, 0)
   Id(1.5,0.5)
   Id(2.5, 0.5)
   Id(2.5, -0.5)
   for(p in seq(1, -1, -0.5)) curve(Id(x, p), 0, 3, add=(p != 1))

Double integral of decay function.

Description

Double integral of decay function.

Usage

Idd(x, p)

Arguments

x

Input value(s), possibly a vector.

p

Parameter.

Value

Iterated integral of the decay function between 0 and x, that is, the integral of Id(x, p).

Examples

   Idd(2, 0)
   Idd(1.5,0.5)
   Idd(2.5, -1)
   Idd(2.5, -0.5)
   for(p in seq(1, -1, -0.5)) curve(Idd(x, p), 0, 3, add=(p != 1))

Small taper dataset from Brink and von Gadow (1986).

Description

Taper measurements on 10 Eucalyptus cloeziana trees.

Usage

brink

Format

A data frame with 108 rows and 5 variables:

Tree

tree identification number (factor)

h

height level, meters

dib

diameter inside bark, centimeters

Dob

dbh outside bark, cm (breast height is 1.35 m)

H

total height, meters

Source

Brink, C. and von Gadow, K. (1986) "On the use of growth and decay functions for modelling stem profiles". EDV in Medizin und Biologi 17, 20-27

Decay function delta

Description

Calculates (1 - p*x)_+^{1/p}, or its limit exp(-x) when p tends to 0.

Usage

decay(x, p)

Arguments

x

Input value(s), possibly a vector.

p

Parameter.

Details

Perhaps overkill, but uses log1p() function for better accuracy than the more obvious formula.

Value

Decay function value(s).

Examples

   decay(2, 0) == exp(-2)
   decay(1.5, 0.5)
   decay(2.5, 0.5)
   decay(2.5, -0.5)
   for(p in seq(1, -1, -0.5)) curve(decay(x, p), 0, 3, add=(p != 1))

Height level for given diameter or area.

Description

Find the height level at which the tree reaches a given diameter (if area == FALSE, default) or a given cross-sectional area (if area == TRUE). That is, the inverse of taper(), except that a vector argument is not allowed.

Usage

hlevel(ds, H, D, b, bh, area = FALSE)

Arguments

ds

The given diameter or area.

H

Tree total height.

D

Tree diameter at breast height.

b

Vector with the 5 parameters.

bh

Breast height. Typically 1.2, 1.3 or 1.4 m, or 4.5 ft.

area

If TRUE, 'ds' is a cross-sectional area, otherwise a diameter. Default is FALSE.

Value

Height level corresponding to 'ds' if any, otherwise NA.

Examples

   b <- c(2.569, 0, 1.042, 0.3012, -1)  # parameters
   Dib <- 0.956 * 24  # convert dbh outside bark to inside bark 
   hlevel(15, 32, Dib, b, 1.3)  # height where the diameter is 15
   hlevel(24, 32, Dib, b, 1.3)  # breast height
   hlevel(35, 32, Dib, b, 1.3)  # height where the diameter is 35

Tree taper (or profile) equation.

Description

Returns the diameter or cross-sectional area at one or more hight levels.

Usage

taper(h, H, D, b, bh, area = FALSE)

Arguments

h

Height level(s), possibly a vector.

H

Tree total height.

D

Tree diameter at breast height (dbh).

b

Vector with the 5 parameters.

bh

Breast height. Typically 1.2, 1.3 or 1.4 m, or 4.5 ft.

area

If TRUE, returns cross-sectional areas, otherwise returns diameters. Default is FALSE.

Value

Diameter(s) at level(s) 'h' if 'area' is FALSE, otherwise cross-sectional area(s).

Note

Diameters or areas are either all outside bark, or all inside bark. A dbh outside bark can be used with an inside-bark taper equation through a substitution D -> k * D, where k is an outside to inside bark conversion factor.

Examples

  curve(taper(x, 32, 0.956*24, c(2.569, 0, 1.042, 0.3012, -1), 1.3), 0, 32)

Unscaled base taper curve of cross-sectional area vs height level.

Description

Unscaled base taper curve of cross-sectional area vs height level.

Usage

tbase(h, H, b)

Arguments

h

Height level(s), possibly a vector.

H

Tree total height.

b

Vector with the 5 parameters.

Value

Value(s) proportional to the area(s) at the level(s) h.

Examples

    tbase(16, 32, c(2.569, 0, 1.042, 0.3012, -1))

Volume between two height levels.

Description

Volume between two height levels.

Usage

volume(h1, h2, H, D, b, bh, rhd)

Arguments

h1, h2

The two height levels.

H

Tree total height.

D

Tree diameter at breast height.

b

Vector with the 5 parameters.

bh

Breast height. Typically 1.2, 1.3 or 1.4 m, or 4.5 ft.

rhd

Ratio between the height and diameter units. E.g., 100 for m and cm, or 12 for feet and inches.

Value

Volume between h1 and h2.

Examples

   b <- c(2.569, 0, 1.042, 0.3012, -1)  # parameters
   Dib <- 0.956 * 24  # convert dbh outside bark to inside bark 
   volume(0, 32, 32, Dib, b, 1.3, 100)  # total volume
   h15 <- hlevel(15, 32, Dib, b, 1.3)  # height for diameter 15
   volume(0.3, h15, 32, Dib, b, 1.3, 100)  # volume between stump and h15