TapeR (version 0.5.3)

resVar: Functions to put different size of uncertainty on given measurements

Description

When estimating a tree specific taper curve based on given measurements one can modify the assumed measurement uncertainty by these functions

Usage

resVar(relH, fn, sig2, par = NULL)

Value

vector of assumed residual variance

Arguments

relH

relative tree height for which the assumed residual variance should be calculated

fn

name of function to be applied as character string

sig2

residual variance from fitted model, cf. TapeR_FIT_LME.f

par

either NULL or a list with parameters to the different functions. See details.

Author

Christian Vonderach

Details

When estimating a tree specific taper curve based on given measurements the residual variance of the model is taken into account to estimate the tree specific random effects. Alternatively, it is possible to make assumptions about the measurement error, eventually at specific relative heights. With that, one can e.g. force the taper curve through the given measurements. Standard behaviour not necessarily leads to passing the measurements, if more than one is given.

Different functions are available. sig2 applies the model residual variance and hence is the default behaviour. zero means assuming no residual variance and forcing the taper curve through the given measurements. Care has to be taken in this case because forcing the taper curve through a lot of measurements might result in implausible results. linear interpolates between zero and the given residual variance along the stem, i.e. from bottom to tree top. bilinear puts zero variance not at zero but at a predefined location (can be given via par). Below and above a linear interpolation is done up to the given residual variance. If zero variance position is not given, it is set at 5% of tree height (approximately height of dbh). laglinear assumes zero variance up to a predefined location (defaults to 5% of tree height) and interpolates upwards to the given residual variance of the model. quadratic function distributes residual variance according to a quadratic function along the stem. It is build so that zero variance is put at a predefined location (defaults to 5% of tree height) and model residual variance (as a default) at tree top. dnorm and dlnorm put residual variance in form of an inverse normal or an inverse log-normal distribution along the stem with a zero-minimum at a predefined location (defaults to 5% of tree height). See examples for a visualisation.

For all functions (except zero and sig2) the point of zero residual variance is defined by par$zrv if given, otherwise set to 0.05. For dnorm one can additionally provide the parameter sd to determine standard deviation. By default it is set to zrv/3; in case of dlnorm one can define lsd (sdlog, cf. dlnorm), which is by default set to 1-sqrt(zrv). It is up to the user to define meaningful parameters and use the functions in appropriate context.

Examples

curve(resVar(relH=x, fn = "sig2", 0.5))
curve(resVar(relH=x, fn = "zero", 0.5))
curve(resVar(relH=x, fn = "linear", 0.5))
curve(resVar(relH=x, fn = "bilinear", 0.5))
curve(resVar(relH=x, fn = "laglinear", 0.5))
curve(resVar(relH=x, fn = "quadratic", 0.5))
curve(resVar(relH=x, fn = "dnorm", 0.5))
curve(resVar(relH=x, fn = "dnorm", 0.5, par=list(zrv=0.2, sd=0.2/3)))
curve(resVar(relH=x, fn = "dlnorm", 0.5))
curve(resVar(relH=x, fn = "dlnorm", 0.5, par=list(zrv=0.2)))
invisible(sapply(seq(0.01, 0.99, length.out=20), function(a){
  curve(resVar(relH=x, fn = "dlnorm", 0.5, par=list(zrv=a, lsd=(1-sqrt(a)))),
  n=1000)
}))