HD models {lmfor}

Available 2- and 3- parameter H-D model functions to be used by function fithd.

Description

Nonlinear functions for modeling tree height on diameter. Usually called using fithd.

Usage

HDnaslund(d, a, b, bh=1.3) 
HDcurtis(d, a, b, bh=1.3) 
HDmichailoff(d, a, b, bh=1.3) 
HDmeyer(d, a, b, bh=1.3) 
HDpower(d, a, b, bh=1.3)
HDnaslund2(d, a, b, bh=1.3)
HDnaslund3(d, a, b, bh=1.3)
HDnaslund4(d, a, b, bh=1.3)
HDmicment(d, a, b, bh=1.3) 
HDmicment2(d, a, b, bh=1.3) 
HDwykoff(d, a, b, bh=1.3) 


HDprodan(d, a, b, c, bh=1.3) 
HDlogistic(d, a, b, c, bh=1.3) 
HDrichards(d, a, b, c, bh=1.3) 
HDweibull(d, a, b, c, bh=1.3) 
HDgomperz(d, a, b, c, bh=1.3) 
HDsibbesen(d, a, b, c, bh=1.3) 
HDkorf(d, a, b, c, bh=1.3) 
HDratkowsky(d, a, b, c, bh=1.3) 
HDhossfeldIV(d, a, b, c, bh=1.3)

startHDnaslund(d, h, bh=1.3) 
startHDcurtis(d, h, bh=1.3) 
startHDmichailoff(d, h, bh=1.3) 
startHDmeyer(d, h, bh=1.3) 
startHDpower(d, h, bh=1.3)
startHDnaslund2(d, h, bh=1.3) 
startHDnaslund3(d, h, bh=1.3) 
startHDnaslund4(d, h, bh=1.3) 
startHDmicment(d, h, bh=1.3) 
startHDmicment2(d, h, bh=1.3) 
startHDwykoff(d, h, bh=1.3) 

startHDprodan(d, h, bh=1.3) 
startHDlogistic(d, h, bh=1.3) 
startHDrichards(d, h, bh=1.3, b=0.04) 
startHDweibull(d, h, bh=1.3) 
startHDgomperz(d, h, bh=1.3) 
startHDsibbesen(d, h, bh=1.3, a=0.5) 
startHDkorf(d, h, bh=1.3) 
startHDratkowsky(d, h, bh=1.3, c=5) 
startHDhossfeldIV(d, h, bh=1.3, c=5)

Arguments

d

A vector of tree diameters, usually in cm

h

A vector of tree heights, usually in m. The observed heights should be always above or equal to bh.

a, b, c

Parameters a, b (and c for 3- parameter functions) of the applied function. See details for expressions of different functions.

bh

The applied height for the measurement of tree diameter (so called breast height). Of the same unit as h.

Details

The available 2- parameter functions are

• Naslund: h(d) = bh + \frac{d^2}{(a + bd)^2}

• Curtis: h(d) = bh + a \left(\frac{d}{1 + d}\right)^b

• Michailoff: h(d) = bh + a e^{-b d^{-1}}

• Meyer: h(d) = bh + a (1-e^{-b d})

• Power: h(d) = bh + a d^b

• Naslund2: h(d) = bh + \frac{d^2}{\left(a + e^b d\right)^2}

• Naslund3: h(d) = bh + \frac{d^2}{(e^a + b d)^2}

• Naslund4: h(d) = bh + \frac{d^2}{(e^a + e^b d)^2}

• Michaelis-Menten: h(d) = bh + \frac{a d}{b + d}

• Michaelis-Menten2: h(d) = bh + \frac{d}{a + b * d}

• Wykoff: h(d) = bh + \exp\left(a + \frac{b}{d + 1}\right)

The available 3- parameter functions are

• Prodan: h(d) = bh + \frac{d^2}{a + bd + c d^2}

• Logistic: h(d) = bh + \frac{a}{1 + b e^{-c d}}

• Chapman-Richards: h(d) = bh + a (1 - e^{-bd})^c

• Weibull: h(d) = bh + a (1 - e^{-b d^c})

• Gomperz: h(d) = bh + a \exp(-b \exp(-c d))

• Sibbesen: h(d) = bh + a d^{b d^{-c}}

• Korf: h(d) = bh + a \exp(-b d^{-c})

• Ratkowsky: h(d) = bh + a \exp\left(\frac{-b}{d + c}\right)

• Hossfeld IV: h(d) = bh + \frac{a}{1 + \frac{1}{bd^c}}

For each model, two functions are provided: one computing the value of the H-D model for given diameters using given values of parameters a, b (and c), and another returning the initial guesses of a, b (and c) for given h-d data.

The initial guesses are in most cases computed by fitting a linearized version of the model into the provided h-d data using lm. For some 3- parameter versions, no straightforward linearization is possible and one of the parameters is set to a fixed sensible constant. Those values can be seen as additional arguments in the corresponding startHD - functions. Details can be seen directly from the function definitions.

The user can define her own functions to be used with fithd. The case-sensitive naming of the functions should follow exactly the naming convention shown above. In addition, the names of the of arguments, as well as their order, should be the same as in the functions above.

The models are named according to references in

• Zeide, B. 1993. Analysis of growth equations. Forest Science 39(3):594-616. doi:10.1093/forestscience/39.3.594

• Huang, S., Titus, S.J., and Wiens, D.P. 1992. Comparison of nonlinear height-diameter functiond for major Alberta tree species. Can J. For. Res. 22: 1297-1304. doi:10.1139/x92-172

Suggestions on naming and references on the functions are welcome.

Value

For functions HDxxx, a vector of tree heights corresponding diameters d is returned. For functions startHDxxx, a named vector of initial estimates of a, b and (c).

Author(s)

Lauri Mehtatalo <[e-mail]>

References

Mehtatalo, L., Gregoire, T.G., and de Miguel, S. Modeling Height-diameter curves for height prediction. Canadian Journal of Forest Research, 45(7): 826-837, doi:10.1139/cjfr-2015-0054

Examples

data(spati)
theta<-startHDnaslund(spati$d,spati$h)
plot(spati$d,spati$h)
d<-seq(0,50)
lines(d,HDnaslund(d,a=theta[1],b=theta[2]),col="red",lwd=5)