ThreepFeedbackModel14 {SoilR}

Implementation of a three-pool C14 model with feedback structure

Description

This function creates a model for three pools connected with feedback. It is a wrapper for the more general function GeneralModel_14 that can handle an arbitrary number of pools with arbitrary connections. GeneralModel_14 can also handle input data in different formats, while this function requires its input as Delta14C. Look at it as an example how to use the more powerful tool GeneralModel_14 or as a shortcut for a standard task!

Usage

ThreepFeedbackModel14(
  t,
  ks,
  C0,
  F0_Delta14C,
  In,
  a21,
  a12,
  a32,
  a23,
  xi = 1,
  inputFc,
  lambda = -0.0001209681,
  lag = 0,
  solver = deSolve.lsoda.wrapper,
  pass = FALSE
)

Arguments

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 C14Atm_NH is 1900-2010.

ks

A vector of length 3 containing the decomposition rates for the 3 pools.

C0

A vector of length 3 containing the initial amount of carbon for the 3 pools.

F0_Delta14C

A vector of length 3 containing the initial fraction of radiocarbon for the 3 pools in Delta14C format. The format will be assumed to be Delta14C, so please take care that it is.

In

A scalar or a data.frame object specifying the amount of litter inputs by time.

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.

xi

A scalar or a data.frame specifying the external (environmental and/or edaphic) effects on decomposition rates.

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.

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.

lag

A positive scalar representing a time lag for radiocarbon to enter the system.

solver

A function that solves the system of ODEs. This can be euler or deSolve.lsoda.wrapper or any other user provided function with the same interface.

pass

if TRUE forces the constructor to create the model even if it is invalid. This is sometimes useful when SoilR is used by external packages for parameter estimation.

See Also

There are other predefinedModels and also more general functions like Model_14.

Examples

#years=seq(1901,2009,by=0.5)
years=seq(1904,2009,by=0.5)
LitterInput=100
k1=1/2; k2=1/10; k3=1/50
a21=0.9*k1
a12=0.4*k2
a32=0.4*k2
a23=0.7*k3

Feedback=ThreepFeedbackModel14(
t=years,
ks=c(k1=k1, k2=k2, k3=k3),
C0=c(100,500,1000),
F0_Delta14C=c(0,0,0),
In=LitterInput,
a21=a21,
a12=a12,
a32=a32,
a23=a23,
inputFc=C14Atm_NH
)
F.R14m=getF14R(Feedback)
F.C14m=getF14C(Feedback)
F.C14t=getF14(Feedback)

Series=ThreepSeriesModel14(
t=years,
ks=c(k1=k1, k2=k2, k3=k3),
C0=c(100,500,1000),
F0_Delta14C=c(0,0,0),
In=LitterInput,
a21=a21,
a32=a32,
inputFc=C14Atm_NH
)
S.R14m=getF14R(Series)
S.C14m=getF14C(Series)
S.C14t=getF14(Series)

Parallel=ThreepParallelModel14(
t=years,
ks=c(k1=k1, k2=k2, k3=k3),
C0=c(100,500,1000),
F0_Delta14C=c(0,0,0),
In=LitterInput,
gam1=0.6,
gam2=0.2,
inputFc=C14Atm_NH,
lag=2
)
P.R14m=getF14R(Parallel)
P.C14m=getF14C(Parallel)
P.C14t=getF14(Parallel)

par(mfrow=c(3,2))
plot(
C14Atm_NH,
type="l",
xlab="Year",
ylab=expression(paste(Delta^14,"C ","(per mille)")),
xlim=c(1940,2010)
) 
lines(years, P.C14t[,1], col=4)
lines(years, P.C14t[,2],col=4,lwd=2)
lines(years, P.C14t[,3],col=4,lwd=3)
legend(
"topright",
c("Atmosphere", "Pool 1", "Pool 2", "Pool 3"),
lty=rep(1,4),
col=c(1,4,4,4),
lwd=c(1,1,2,3),
bty="n"
)

plot(C14Atm_NH,type="l",xlab="Year",
ylab=expression(paste(Delta^14,"C ","(per mille)")),xlim=c(1940,2010)) 
lines(years,P.C14m,col=4)
lines(years,P.R14m,col=2)
legend("topright",c("Atmosphere","Bulk SOM", "Respired C"),
lty=c(1,1,1), col=c(1,4,2),bty="n")

plot(C14Atm_NH,type="l",xlab="Year",
ylab=expression(paste(Delta^14,"C ","(per mille)")),xlim=c(1940,2010)) 
lines(years, S.C14t[,1], col=4)
lines(years, S.C14t[,2],col=4,lwd=2)
lines(years, S.C14t[,3],col=4,lwd=3)
legend("topright",c("Atmosphere", "Pool 1", "Pool 2", "Pool 3"),
lty=rep(1,4),col=c(1,4,4,4),lwd=c(1,1,2,3),bty="n")

plot(C14Atm_NH,type="l",xlab="Year",
ylab=expression(paste(Delta^14,"C ","(per mille)")),xlim=c(1940,2010)) 
lines(years,S.C14m,col=4)
lines(years,S.R14m,col=2)
legend("topright",c("Atmosphere","Bulk SOM", "Respired C"),
lty=c(1,1,1), col=c(1,4,2),bty="n")

plot(C14Atm_NH,type="l",xlab="Year",
ylab=expression(paste(Delta^14,"C ","(per mille)")),xlim=c(1940,2010)) 
lines(years, F.C14t[,1], col=4)
lines(years, F.C14t[,2],col=4,lwd=2)
lines(years, F.C14t[,3],col=4,lwd=3)
legend("topright",c("Atmosphere", "Pool 1", "Pool 2", "Pool 3"),
lty=rep(1,4),col=c(1,4,4,4),lwd=c(1,1,2,3),bty="n")

plot(C14Atm_NH,type="l",xlab="Year",
ylab=expression(paste(Delta^14,"C ","(per mille)")),xlim=c(1940,2010)) 
lines(years,F.C14m,col=4)
lines(years,F.R14m,col=2)
legend("topright",c("Atmosphere","Bulk SOM", "Respired C"),
lty=c(1,1,1), col=c(1,4,2),bty="n")


par(mfrow=c(1,1))