R/ThreepFeedbackModel.R

In SoilR: Models of Soil Organic Matter Decomposition

#
# vim:set ff=unix expandtab ts=2 sw=2:
ThreepFeedbackModel<-structure(
    function #Implementation of a three pool model with feedback structure
    ### This function creates a model for three pools connected with feedback. It is a wrapper for the more general function \code{\link{GeneralModel}}.
    ##references<< Sierra, C.A., M. Mueller, S.E. Trumbore. 2012. Models of soil organic matter decomposition: the SoilR package version 1.0. Geoscientific Model Development 5, 1045-1060.
     (t,      ##<< A vector containing the points in time where the solution is sought.
      ks,	##<< A vector of lenght 3 containing the values of the decomposition rates for pools 1, 2, and 3.
      a21, ##<< A scalar with the value of the transfer rate from pool 1 to pool 2.
      a12, ##<< A scalar with the value of the transfer rate from pool 2 to pool 1.
      a32, ##<< A scalar with the value of the transfer rate from pool 2 to pool 3.
      a23, ##<< A scalar with the value of the transfer rate from pool 3 to pool 2.
      C0,	##<< A vector containing the initial concentrations for the 3 pools. The length of this vector is 3
      In,     ##<< A 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.
      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(ks)!=3) stop("ks must be of length = 3")
      if(length(C0)!=3) stop("the vector with initial conditions must be of length = 3")
      
      if(length(In)==1){
          inputFluxes=BoundInFlux(
            function(t){matrix(nrow=3,ncol=1,c(In,0,0))},
            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=3,ncol=1,c(inputFlux(t),0,0))},
          t_start,
          t_end
      )
      }
      A=-1*abs(diag(ks))
      A[2,1]=a21
      A[1,2]=a12
      A[3,2]=a32
      A[2,3]=a23
      
      if(length(xi)==1){
        fX=function(t){xi}
        Af=BoundLinDecompOp(function(t){fX(t)*A},t_start,t_end)
      }
	
      if(class(xi)=="data.frame"){
        X=xi[,1]
      	Y=xi[,2]
        fX=splinefun(X,Y)
        Af=BoundLinDecompOp(function(t){fX(t)*A},min(X),max(X))
       }
      Mod=GeneralModel(t=t,A=Af,ivList=C0,inputFluxes=inputFluxes,solver,pass)
     return(Mod)
### A Model Object that can be further queried 
      ##seealso<< \code{\link{ThreepParallelModel}}, \code{\link{ThreepSeriesModel}}
    }
    ,
    ex=function(){
      t_start=0 
      t_end=10 
      tn=50
      timestep=(t_end-t_start)/tn 
      t=seq(t_start,t_end,timestep) 
      ks=c(k1=0.8,k2=0.4,k3=0.2)
      C0=c(C10=100,C20=150, C30=50)
      In = 60
      
      Temp=rnorm(t,15,1)
      TempEffect=data.frame(t,fT.Daycent1(Temp))

      Ex1=ThreepFeedbackModel(t=t,ks=ks,a21=0.5,a12=0.1,a32=0.2,a23=0.1,C0=C0,In=In,xi=TempEffect)
      Ct=getC(Ex1)
      Rt=getReleaseFlux(Ex1)
      
      plot(
        t,
        rowSums(Ct),
        type="l",
        ylab="Carbon stocks (arbitrary units)",
        xlab="Time (arbitrary units)",
        lwd=2,
        ylim=c(0,sum(Ct[51,]))
      ) 
      lines(t,Ct[,1],col=2)
      lines(t,Ct[,2],col=4)
      lines(t,Ct[,3],col=3)
      legend(
        "topleft",
        c("Total C","C in pool 1", "C in pool 2","C in pool 3"),
        lty=c(1,1,1,1),
        col=c(1,2,4,3),
        lwd=c(2,1,1,1),
        bty="n"
      )

      plot(
        t,
        rowSums(Rt),
        type="l",
        ylab="Carbon released (arbitrary units)",
        xlab="Time (arbitrary units)",
        lwd=2,
        ylim=c(0,sum(Rt[51,]))
      ) 
      lines(t,Rt[,1],col=2)
      lines(t,Rt[,2],col=4)
      lines(t,Rt[,3],col=3)
      legend(
        "topleft",
        c("Total C release",
        "C release from pool 1",
        "C release from pool 2",
        "C release from pool 3"),
        lty=c(1,1,1,1),
        col=c(1,2,4,3),
        lwd=c(2,1,1,1),
        bty="n"
      )
      
      Inr=data.frame(t,Random.inputs=rnorm(length(t),50,10))
      plot(Inr,type="l")
      
      Ex2=ThreepFeedbackModel(t=t,ks=ks,a21=0.5,a12=0.1,a32=0.2,a23=0.1,C0=C0,In=Inr)
      Ctr=getC(Ex2)
      Rtr=getReleaseFlux(Ex2)
      
      plot(
        t,
        rowSums(Ctr),
        type="l",
        ylab="Carbon stocks (arbitrary units)",
        xlab="Time (arbitrary units)",
        lwd=2,
        ylim=c(0,sum(Ctr[51,]))
      ) 
      lines(t,Ctr[,1],col=2)
      lines(t,Ctr[,2],col=4)
      lines(t,Ctr[,3],col=3)
      legend("topright",c("Total C","C in pool 1", "C in pool 2","C in pool 3"),
             lty=c(1,1,1,1),col=c(1,2,4,3),lwd=c(2,1,1,1),bty="n")

      plot(t,rowSums(Rtr),type="l",ylab="Carbon released (arbitrary units)",
           xlab="Time (arbitrary units)",lwd=2,ylim=c(0,sum(Rtr[51,]))) 
      lines(t,Rtr[,1],col=2)
      lines(t,Rtr[,2],col=4)
      lines(t,Rtr[,3],col=3)
      legend(
        "topright",
        c("Total C release",
          "C release from pool 1",
          "C release from pool 2",
          "C release from pool 3"
        ),
        lty=c(1,1,1,1),
        col=c(1,2,4,3),
        lwd=c(2,1,1,1),
        bty="n")
}
)