R/TwopSeriesModel14.R

In SoilR: Models of Soil Organic Matter Decomposition

#' 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.
#' 
#' 
#' @param 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.
#' @param ks A vector of length 2 containing the decomposition rates for the 2
#' pools.
#' @param C0 A vector of length 2 containing the initial amount of carbon for
#' the 2 pools.
#' @param 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.
#' @param In A scalar or a data.frame object specifying the amount of litter
#' inputs by time.
#' @param a21 A scalar with the value of the transfer rate from pool 1 to pool
#' 2.
#' @param xi A scalar or a data.frame specifying the external (environmental
#' and/or edaphic) effects on decomposition rates.
#' @param 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.
#' @param lambda 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.
#' @param lag A (positive) scalar representing a time lag for radiocarbon to
#' enter the system.
#' @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_14}}.
#' @examples
#' 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))
TwopSeriesModel14<- function 
  (t,  		
   ks,	
   C0,	
   F0_Delta14C,  
   In,     
   a21,  
   xi=1,   
   inputFc,
   lambda=-0.0001209681, 
   lag=0, 
   solver=deSolve.lsoda.wrapper, 
 pass=FALSE  
   )	
  { 
    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=BoundInFluxes(
                                     function(t){matrix(nrow=2,ncol=1,c(In,0))},
                                     t_start,
                                     t_stop
                                     )
    if(inherits(In, "data.frame")){
      x=In[,1]  
      y=In[,2]  
      inputFlux=function(t0){as.numeric(spline(x,y,xout=t0)[2])}
      inputFluxes=BoundInFluxes(
                     function(t){matrix(nrow=2,ncol=1,c(inputFlux(t),0))},
                     min(x),
                     max(x)
                     )   
    }
    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])}
    }
    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,inputFc=Fc,di=lambda,pass=pass)
}