R/TwopParallelModel14.R

In SoilR: Models of Soil Organic Matter Decomposition

#' Implementation of a two-pool C14 model with parallel structure
#' 
#' This function creates a model for two independent (parallel) pools.  It is a
#' wrapper for the more general function \code{\link{GeneralModel_14}} that can
#' handle an arbitrary number of pools.
#' 
#' 
#' @param t A vector containing the points in time where the solution is
#' sought. It must be specified within the same period for which the Delta 14 C
#' of the atmosphere is provided. The default period in the provided dataset
#' \code{\link{C14Atm_NH}} is 1900-2010.
#' @param ks A vector of length 2 containing the decomposition rates for the 2
#' pools.
#' @param C0 A vector of length 2 containing the initial amount of carbon for
#' the 2 pools.
#' @param F0_Delta14C A vector of length 2 containing the initial amount of the
#' fraction of radiocarbon for the 2 pools as Delta14C values in per mil.
#' @param In A scalar or a data.frame object specifying the amount of litter
#' inputs by time.
#' @param gam A scalar representing the partitioning coefficient, i.e. the
#' proportion from the total amount of inputs that goes to pool 1.
#' @param xi A scalar or a data.frame specifying the external (environmental
#' and/or edaphic) effects on decomposition rates.
#' @param inputFc A Data Frame object containing values of atmospheric Delta14C
#' per time. First column must be time values, second column must be Delta14C
#' values in per mil.
#' @param lambda Radioactive decay constant. By default lambda=-0.0001209681
#' y^-1 . This has the side effect that all your time related data are treated
#' as if the time unit was year.
#' @param lag A positive scalar representing a time lag for radiocarbon to
#' enter the system.
#' @param solver A function that solves the system of ODEs. This can be
#' \code{\link{euler}} or \code{\link{deSolve.lsoda.wrapper}} or any other user
#' provided function with the same interface.
#' @param pass if TRUE Forces the constructor to create the model even if it is
#' invalid
#' @return A Model Object that can be further queried
#' @seealso There are other \code{\link{predefinedModels}} and also more
#' general functions like \code{\link{Model_14}}.
#' @examples
#' lag <- 2
#' years=seq(1901+lag,2009,by=0.5)
#' LitterInput=700 
#' Ex=TwopParallelModel14(t=years,ks=c(k1=1/2.8, k2=1/35),C0=c(200,5000), 
#' F0_Delta14C=c(0,0),In=LitterInput, gam=0.7,inputFc=C14Atm_NH,lag=lag)
#' R14m=getF14R(Ex)
#' C14m=getF14C(Ex)
#' C14t=getF14(Ex)
#' par(mfrow=c(2,1))
#' plot(C14Atm_NH,type="l",xlab="Year",ylab="Delta 14C (per mil)",xlim=c(1940,2010)) 
#' lines(years, C14t[,1], col=4)
#' lines(years, C14t[,2],col=4,lwd=2)
#' legend("topright",c("Delta 14C Atmosphere", "Delta 14C pool 1", "Delta 14C pool 2"),
#' lty=c(1,1,1),col=c(1,4,4),lwd=c(1,1,2),bty="n")
#' plot(C14Atm_NH,type="l",xlab="Year",ylab="Delta 14C (per mil)",xlim=c(1940,2010)) 
#' lines(years,C14m,col=4)
#' lines(years,R14m,col=2)
#' legend("topright",c("Delta 14C Atmosphere","Delta 14C SOM", "Delta 14C Respired"),
#' lty=c(1,1,1), col=c(1,4,2),bty="n")
#' par(mfrow=c(1,1))
TwopParallelModel14<- function 
     (t,			
     ks,	
     C0,	
     F0_Delta14C,  
     In,     
     gam,  
     xi=1,   
     inputFc,
     lambda=-0.0001209681, 
     lag=0, 
     solver=deSolve.lsoda.wrapper, 
     pass=FALSE  
    )	
    { 
      t_start=min(t)
      t_stop=max(t)
      if(length(ks)!=2) stop("ks must be of length = 2")
      if(length(C0)!=2) stop("the vector with initial conditions must be of length = 2")
      if(gam > 1 | gam < 0) stop("The the partitioning coefficient gam is outside the interval [0,1]")
      if(length(In)==1) inputrates=BoundInFluxes(
        function(t){matrix(nrow=2,ncol=1,c(gam*In,(1-gam)*In))},
        t_start,
        t_stop
      )
      if(inherits(In, "data.frame")){
         x=In[,1]  
         y=In[,2]  
         inputrate=function(t0){as.numeric(spline(x,y,xout=t0)[2])}
         inputrates=BoundInFluxes(
            function(t){
                matrix(nrow=2,ncol=1,
                    c(
                        gam*inputrate(t),
                        (1-gam)*inputrate(t)
                    )
                )
            },
            min(x),
            max(x)
         )   
        }
      if(length(xi)==1) fX=function(t){xi}
      if(inherits(xi, "data.frame")){
      X=xi[,1]
      Y=xi[,2]
      fX=function(t){as.numeric(spline(X,Y,xout=t)[2])}
      }
      At=BoundLinDecompOp(
             function(t){
               fX(t)*diag(-abs(ks))
             },
             t_start,
             t_stop
             ) 
      Fc=BoundFc(inputFc,lag=lag,format="Delta14C")
      mod=GeneralModel_14(t,At,ivList=C0,initialValF=ConstFc(F0_Delta14C,"Delta14C"),inputFluxes=inputrates,inputFc=Fc,di=lambda,pass=pass)
}