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#' Implementation of a two-pool C14 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_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 a12 A scalar with the value of the transfer rate from pool 2 to pool
#' 1.
#' @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 integer 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 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=TwopFeedbackModel14(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,a12=0.01,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))
TwopFeedbackModel14<- function
(t,
ks,
C0,
F0_Delta14C,
In,
a21,
a12,
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
A[1,2]=a12
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)
}
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