R/TwopFeedbackModel.R

In SoilR: Models of Soil Organic Matter Decomposition

#' Implementation of a two pool model with feedback structure
#' 
#' This function creates a model for two pools connected with feedback. It is a
#' wrapper for the more general function \code{\link{GeneralModel}}.
#' 
#' 
#' @param t A vector containing the points in time where the solution is
#' sought.
#' @param ks A vector of length 2 with the values of the decomposition rate for
#' pools 1 and 2.
#' @param a21 A scalar with the value of the transfer rate from pool 1 to pool
#' 2.
#' @param a12 A scalar with the value of the transfer rate from pool 2 to pool
#' 1.
#' @param C0 A vector of length 2 containing the initial amount of carbon for
#' the 2 pools.
#' @param In A data.frame object specifying the amount of litter inputs by
#' time.
#' @param xi A scalar or data.frame object specifying the external
#' (environmental and/or edaphic) effects on decomposition rates.
#' @param solver A function that solves the system of ODEs. This can be
#' \code{\link{euler}} or \code{\link{deSolve.lsoda.wrapper}} or any other user
#' provided function with the same interface.
#' @param pass if TRUE forces the constructor to create the model even if it is
#' invalid
#' @return A Model Object that can be further queried
#' @seealso There are other \code{\link{predefinedModels}} and also more
#' general functions like \code{\link{Model}}.
#' @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.
#' @examples
#' #This example show the difference between the three types of two-pool models  
#' times=seq(0,20,by=0.1)
#' ks=c(k1=0.8,k2=0.00605)
#' C0=c(C10=5,C20=5)
#' 
#' Temp=rnorm(times,15,2)
#' WC=runif(times,10,20)
#' TempEffect=data.frame(times,fT=fT.Daycent1(Temp))
#' MoistEffect=data.frame(times, fW=fW.Daycent2(WC)[2])
#' 
#' Inmean=1
#' InRand=data.frame(times,Random.inputs=rnorm(length(times),Inmean,0.2))
#' InSin=data.frame(times,Inmean+0.5*sin(times*pi*2))
#' 
#' Parallel=TwopParallelModel(t=times,ks=ks,C0=C0,In=Inmean,gam=0.9,
#' xi=(fT.Daycent1(15)*fW.Demeter(15)))
#' Series=TwopSeriesModel(t=times,ks=ks,a21=0.2*ks[1],C0=C0,In=InSin,
#' xi=(fT.Daycent1(15)*fW.Demeter(15)))
#' Feedback=TwopFeedbackModel(t=times,ks=ks,a21=0.2*ks[1],a12=0.5*ks[2],C0=C0,
#' In=InRand,xi=MoistEffect)
#' 
#' CtP=getC(Parallel)
#' CtS=getC(Series)
#' CtF=getC(Feedback)
#' 
#' RtP=getReleaseFlux(Parallel)
#' RtS=getReleaseFlux(Series)
#' RtF=getReleaseFlux(Feedback)
#' 
#' par(mfrow=c(2,1),mar=c(4,4,1,1))
#' plot(times,rowSums(CtP),type="l",ylim=c(0,20),ylab="Carbon stocks (arbitrary units)",xlab=" ")
#' lines(times,rowSums(CtS),col=2)
#' lines(times,rowSums(CtF),col=3)
#' legend("topleft",c("Two-pool Parallel","Two-pool Series","Two-pool Feedback"),
#' lty=c(1,1,1),col=c(1,2,3),bty="n")
#' 
#' plot(times,rowSums(RtP),type="l",ylim=c(0,3),ylab="Carbon release (arbitrary units)", xlab="Time")
#' lines(times,rowSums(RtS),col=2)
#' lines(times,rowSums(RtF),col=3)
#' par(mfrow=c(1,1))
TwopFeedbackModel<- function 
     (t,    	
      ks,	
      a21, 
      a12, 
      C0,	
      In,     
      xi=1,  
      solver=deSolve.lsoda.wrapper,  
      pass=FALSE  
    )	
    { 
      t_start=min(t)
      t_end=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=BoundInFluxes(
            function(t){matrix(nrow=2,ncol=1,c(In,0))},
            t_start,
            t_end
          )
      }
      if(inherits(In, "data.frame")){
         x=In[,1]  
         y=In[,2]  
         inputFlux=splinefun(x,y)
         inputFluxes=BoundInFluxes(
            function(t){matrix(nrow=2,ncol=1,c(inputFlux(t),0))},
            min(x),
            max(x)
         )
        }
      A=-1*abs(diag(ks))
      A[2,1]=a21
      A[1,2]=a12
      if(length(xi)==1) fX=function(t){xi}
      if(inherits(xi, "data.frame")){
        X=xi[,1]
        Y=xi[,2]
        fX=function(t){as.numeric(spline(X,Y,xout=t)[2])}
       }
      Af=BoundLinDecompOp(
        function(t){fX(t)*A},
        t_start,
        t_end
      )
      Mod=GeneralModel(t=t,A=Af,ivList=C0,inputFluxes=inputFluxes,solver,pass)
     return(Mod)
}