R/TwopParallelModel14.R

In SoilR: Models of Soil Organic Matter Decomposition

#
# vim:set ff=unix expandtab ts=2 sw=2:
TwopParallelModel14<-structure(
    function #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.
     (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.
     ks,	##<< A vector of length 2 containing the decomposition rates for the 2 pools. 
     C0,	##<< A vector of length 2 containing the initial amount of carbon for the 2 pools.
     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.
     In,     ##<< A scalar or a data.frame object specifying the amount of litter inputs by time.
     gam,  ##<< A scalar representing the partitioning coefficient, i.e. the proportion from the total amount of inputs that goes to pool 1.
     xi=1,   ##<< A scalar or a data.frame specifying the external (environmental and/or edaphic) effects on decomposition rates. 
     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.
     lambda=-0.0001209681, ##<< 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.
     lag=0, ##<< A positive scalar representing a time lag for radiocarbon to enter the system. 
     solver=deSolve.lsoda.wrapper, ##<< A function that solves the system of ODEs. This can be \code{\link{euler}} or \code{\link{ode}} or any other user provided function with the same interface.
     pass=FALSE  ##<< if TRUE Forces the constructor to create the model even if it is invalid 
    )	
    { 
      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=BoundInFlux(
        function(t){matrix(nrow=2,ncol=1,c(gam*In,(1-gam)*In))},
        t_start,
        t_stop
      )
      if(class(In)=="data.frame"){
         x=In[,1]  
         y=In[,2]  
         inputrate=function(t0){as.numeric(spline(x,y,xout=t0)[2])}
         inputrates=BoundInFlux(
            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(class(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,Fc,di=lambda,pass=pass)
      ### A Model Object that can be further queried 
      ##seealso<< \code{\link{TwopSeriesModel14}}, \code{\link{TwopFeedbackModel14}}  
    }
    ,
    ex=function(){
      
      years=seq(1901,2009,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=2)
      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))
}
)