R/SeriesLinearModel.R

In SoilR: Models of Soil Organic Matter Decomposition

#
# vim:set ff=unix expandtab ts=2 sw=2:
SeriesLinearModel<-structure(
    function #General m-pool linear model with series structure
    ### This function creates a model for m number of pools connected in series. 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.
      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.
      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.
      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}
        #assume the whole time interval for the date
        tAs=t_start
        tAe=t_end
      }
      if(class(xi)=="data.frame"){
        X=xi[,1]
        Y=xi[,2]
        fX=splinefun(X,Y)
        tAs=min(X)
        tAe=max(X)
       }
      Af=BoundLinDecompOp(
            function(t){fX(t)*A},
            tAs,
            tAe
      )
      Mod=GeneralModel(t=t,A=Af,ivList=C0,inputFluxes=inputFluxes,pass=pass)
     return(Mod)
### A Model Object that can be further queried 
      ##seealso<< \code{\link{GeneralModel}}, \code{\link{ThreepFeedbackModel}}, \code{\link{ParallelModel}} 
    }
    ,
    ex=function(){
      #A five-pool model
      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, k4=0.1,k5=0.05)
      Ts=c(0.5,0.2,0.2,0.1)
      C0=c(C10=100,C20=150, C30=50, C40=50, C50=10)
      In = 50
      
      Ex1=SeriesLinearModel(t=t,m.pools=5,ki=ks,Tij=Ts,C0=C0,In=In,xi=fT.Q10(15))
      Ct=getC(Ex1)
      
      matplot(t,Ct,type="l",col=2:6,lty=1,ylim=c(0,sum(C0)))
      lines(t,rowSums(Ct),lwd=2)
      legend("topright",c("Total C","C in pool 1", "C in pool 2","C in pool 3",
                          "C in pool 4","C in pool 5"),
             lty=1,col=1:6,lwd=c(2,rep(1,5)),bty="n")

}
)