R/SeriesLinearModel14.R

In SoilR: Models of Soil Organic Matter Decomposition

#
# vim:set ff=unix expandtab ts=2 sw=2:
SeriesLinearModel14<-structure(
  function #General m-pool linear C14 model with series structure
  ### This function creates a radiocarbon model for m number of pools connected in series. It is a wrapper for the more general function \code{\link{GeneralModel_14}}.
  ##references<< Sierra, C.A., M. Mueller, S.E. Trumbore. 2014. Modeling radiocarbon dynamics in soils: SoilR version 1.1. Geoscientific Model Development 7, 1919-1931.
  (t,      ##<< A vector containing the points in time where the solution is sought.
   m.pools, ##<< An integer with the total number of pools in the model.
   ki,	##<< A vector of lenght m containing the values of the decomposition rates for each pool i.
   Tij, ##<< A vector of length m-1 with the transfer coefficients from pool j to pool i. The value of these coefficients must be in the range [0, 1].
   C0,	##<< A vector of length m containing the initial amount of carbon for the m pools.
   F0_Delta14C,  ##<< A vector of length m containig the initial amount of the radiocarbon fraction for the m pools.
   In,    ##<< A scalar or data.frame object specifying the amount of litter inputs by time. 
   xi=1,  ##<< A scalar or data.frame object 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_end=max(t)
    if(length(ki)!=m.pools) stop("ki must be of length = m.pools")
    if(length(C0)!=m.pools) stop("the vector with initial conditions must be of length = m.pools")
    
    if(length(In)==1){
      inputFluxes=BoundInFlux(
        function(t){matrix(nrow=m.pools,ncol=1,c(In,rep(0,m.pools-1)))},
        t_start,
        t_end
      )
    }
    if(class(In)=="data.frame"){
      x=In[,1]  
      y=In[,2]  
      inputFlux=splinefun(x,y)
      inputFluxes=BoundInFlux(
        function(t){matrix(nrow=m.pools,ncol=1,c(inputFlux(t),rep(0,m.pools-1)))},
        min(x),
        max(x)
      )
    }
    
    A=-1*abs(diag(ki))
    a=abs(ki[-length(ki)])*Tij
    ij=matrix(c((2:m.pools),(1:(m.pools-1))),ncol=2)
    A[ij]=a
    
    if(length(xi)==1) fX=function(t){xi}
    if(class(xi)=="data.frame"){
      X=xi[,1]
      Y=xi[,2]
      fX=splinefun(X,Y)
    }
    Af=BoundLinDecompOp(
      function(t){fX(t)*A},
      t_start,
      t_end
    )

    Fc=BoundFc(inputFc,lag=lag,format="Delta14C")
    
    
    Mod=GeneralModel_14(t=t,A=Af,ivList=C0,initialValF=ConstFc(F0_Delta14C,"Delta14C"),inputFluxes=inputFluxes,Fc,di=lambda,pass=pass)
    return(Mod)
    ### A Model Object that can be further queried 
    ##seealso<< \code{\link{GeneralModel_14}}, \code{\link{SeriesLinearModel}} 
  }
  ,
  ex=function(){
    
    years=seq(1901,2009,by=0.5)
    LitterInput=700 
    
    Ex=SeriesLinearModel14(
      t=years,ki=c(k1=1/2.8, k2=1/35, k3=1/100), m.pools=3,
      C0=c(200,5000,500), F0_Delta14C=c(0,0,0),
      In=LitterInput, Tij=c(0.5, 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)
    lines(years, C14t[,3],col=4,lwd=3)
    legend(
      "topright",
      c("Delta 14C Atmosphere", "Delta 14C pool 1", "Delta 14C pool 2", "Delta 14C pool 3"),
      lty=rep(1,4),col=c(1,4,4,4),lwd=c(1,1,2,3),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))
  }
)