Calculates photosynthetic-irradiance (PE) parameters (alpha, ek) and fit statistics for PE
or rapid light curve data using the model of Webb et al. 1974.
Boolean. Default is FALSE. Set to TRUE if y is PSII quantum efficiency. See Details.
lowerlim
Lower limits of parameter estimates (alpha,ek).
upperlim
Upper limits of parameter estimates (alpha,ek).
fitmethod
The method to be used, one of "Marq", "Port", "Newton", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Pseudo". Default is "Nelder-Mead" - see details.
Details
This function passes the data to the function modFIT in the package FME that, through minimization via the specified 'fitmethod' algorithm, determines the optimal model parameters.
See the help on modFit algorithms. "Nelder-Mead" is fast and works well for two parameter models, "SANN" is slow and works well for three parameter models.
If normalize is set to FALSE, then data is fit to the equation:
y = alpha ek (1 - exp (-x / ek) )
If normalize is set to TRUE, then data is fit to the same equation but normalized to irradiance:
y = 1 / x alpha ek (1-exp (-x / ek) )
Fitting an irradiance-normalized PE model is useful for modeling the irradiance-dependency of PSII quantum yield, as discussed in Silsbe and Kromkamp 2012. If normalize is set to TRUE, x values eqaul to 0 are set to 1e-6.
Value
alpha
Parameter estimate, standard error, t-value and p-value
ek
Parameter estimate, standard error, t-value and p-value
ssr
Sum of square residuals of fit
residuals
Residuals of fit
model
Webb
normalize
Boolean. TRUE or FALSE as passed to the function
Note
Parameter units are dependent on the input.
If normalize=FALSE, then alpha has unit of y/x and ek has units of x.
If normalize=TRUE, then alpha has unit of y and ek has units of x.
Author(s)
Greg M. Silsbe
Sairah Y. Malkin
References
Silsbe, G.M., and Kromkamp, J.C. 2012 Modeling the irradiance dependency of the quantum efficiency of photosynthesis. Limnology and Oceanography: Methods. 10, 642–652.
Webb, W.L., Newton, M., and Starr, D. 1974 Carbon dioxide exchange of Alnus rubra: A mathematical model. Oecologia. 17, 281–291.
See Also
fitJP, fitPGH, fitEP
Examples
#### Single PE dataset example ####
PAR <- c(5,10,20,50,100,150,250,400,800,1200) #umol m-2 s-1
Pc <- c(1.02,1.99,3.85,9.2,15.45,21.3,28.8,34.5,39.9,38.6) #mg C m-3 hr-1
#Call function
myfit <- fitWebb(PAR, Pc)
#Plot input data
plot(PAR, Pc, xlim=c(0,1500), ylim=c(0,40), xlab="PAR", ylab="Pc")
#Add model fit
E <- seq(0,1500,by=1)
with(myfit, {
P <- alpha[1] * ek[1] * (1 - exp (-E / ek[1]))
lines(E,P)
})
#### Multiple RLC dataset example ####
data('rlcs')
names(rlcs) #id is unique to a given RLC
id <- unique(rlcs$id) #Hold unique ids
n <- length(id) #5 unique RLCs
#Setup arrays and vectors to store data
#All RLCs in example have the same 11 PAR steps in the same order
alpha <- array(NA,c(n,4))
ek <- array(NA,c(n,4))
ssr <- rep(NA,n)
residuals <- array(NA,c(n,11))
#Loop through individual RLCs
for (i in 1:n){
#Get ith data
PAR <- rlcs$PAR[rlcs$id==id[i]]
FqFm <- rlcs$FqFm[rlcs$id==id[i]]
#Call function
myfit <- fitWebb(PAR,FqFm,normalize=TRUE)
#Store data
alpha[i,] <- myfit$alpha
ek[i,] <- myfit$ek
ssr[i] <- myfit$ssr
residuals[i,] <- myfit$residuals
}