phytotools (version 1.0)

fitJP: Fit PE or RLC data to Jassby and Platt 1976

Description

Calculates photosynthetic-irradiance (PE) parameters (alpha, ek) and fit statistics for PE or RLC data using the model of Jassby and Platt 1976

Usage

fitJP(x, y, normalize = FALSE, lowerlim = c(0, 1), upperlim = c(100, 1000), 
fitmethod=c("Nelder-Mead"))

Arguments

x

PAR data. Units of umol m-2 s-1

y

Photosynthetic rate or PSII quantum efficiency.

normalize

Boolean. Default is FALSE. Set to TRUE if fitting 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.

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

JP

normalize

Boolean. TRUE or FALSE as passed to the function

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:

$$y = alpha \times ek \times tanh(\frac{x}{ek})$$

If normalize is set to TRUE, then data is fit to the same equation but normalized to irradiance:

$$y = \frac{1}{x} \times alpha \times ek \times tanh(\frac{x}{ek})$$

Fitting an E-normalized PE model is useful for modeling the irradiance-dependency of PSII quantum yield, as discussed in Silsbe and Kromkamp 2012.

References

Jassby, A.D.and Platt, T. 1976 Mathematical formulation of the relationship between photosynthesis and light for phytoplankton. Limnology and Oceanography. 21, 540--547.

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.

See Also

fitWebb, 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

myfit <- fitJP(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]*tanh(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

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 <- fitJP(PAR,FqFm,normalize=TRUE)
  
  #Store data
  alpha[i,]     <- myfit$alpha
  ek[i,]        <- myfit$ek
  ssr[i]        <- myfit$ssr
  residuals[i,] <- myfit$residuals
  
}