R/TwopSeriesModel14.R

In SoilR: Models of Soil Organic Matter Decomposition

#
# vim:set ff=unix expandtab ts=2 sw=2:
TwopSeriesModel14<-structure(
  function #Implementation of a two-pool C14 model with series structure
  ### This function creates a model for two pools connected in series. 
  ### 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 radiocarbon fraction 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.
   a21,  ##<< A scalar with the value of the transfer rate from pool 1 to pool 2.
   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(length(In)==1) inputFluxes=BoundInFlux(
                                     function(t){matrix(nrow=2,ncol=1,c(In,0))},
                                     t_start,
                                     t_stop
                                     )
    if(class(In)=="data.frame"){
      x=In[,1]  
      y=In[,2]  
      inputFlux=function(t0){as.numeric(spline(x,y,xout=t0)[2])}
      inputFluxes=BoundInFlux(
                     function(t){matrix(nrow=2,ncol=1,c(inputFlux(t),0))},
                     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])}
    }
    
    A=-abs(diag(ks))
    A[2,1]=a21
    
    At=BoundLinDecompOp(
           function(t){
             fX(t)*A
           },
           t_start,
           t_stop
    ) 

    Fc=BoundFc(inputFc,lag=lag,format="Delta14C")
    
    mod=GeneralModel_14(t,At,ivList=C0,initialValF=ConstFc(F0_Delta14C,"Delta14C"),inputFluxes=inputFluxes,Fc,di=lambda,pass=pass)
    ### A Model Object that can be further queried 
    ##seealso<< \code{\link{TwopParallelModel14}}, \code{\link{TwopFeedbackModel14}} 
  }
  ,
  ex=function(){
    
    years=seq(1901,2009,by=0.5)
    LitterInput=700 
    
    Ex=TwopSeriesModel14(t=years,ks=c(k1=1/2.8, k2=1/35),
                         C0=c(200,5000), F0_Delta14C=c(0,0),
                         In=LitterInput, a21=0.1,inputFc=C14Atm_NH)
    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))
  }
  )