TwopMMmodel {SoilR}

Implementation of a two-pool Michaelis-Menten model

Description

This function implements a two-pool Michaelis-Meneten model with a microbial biomass and a substrate pool.

Usage

TwopMMmodel(
  t,
  ks = 1.8e-05,
  kb = 0.007,
  Km = 900,
  r = 0.6,
  Af = 1,
  ADD = 3.2,
  ival
)

Arguments

t

vector of times (in days) to calculate a solution.

ks

a scalar representing SOM decomposition rate (m3 d-1 (gCB)-1)

kb

a scalar representing microbial decay rate (d-1)

Km

a scalar representing the Michaelis constant (g m-3)

r

a scalar representing the respired carbon fraction (unitless)

Af

a scalar representing the Activity factor; i.e. a temperature and moisture modifier (unitless)

ADD

a scalar representing the annual C input to the soil (g m-3 d-1)

ival

a vector of length 2 with the initial values of the SOM pool and the microbial biomass pool (g m-3)

Details

This implementation is similar to the model described in Manzoni and Porporato (2007).

Value

Microbial biomass over time

References

Manzoni, S, A. Porporato (2007). A theoretical analysis of nonlinearities and feedbacks in soil carbon and nitrogen cycles. Soil Biology and Biochemistry 39: 1542-1556.

See Also

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

Examples

days=seq(0,1000,0.5)
MMmodel=TwopMMmodel(t=days,ival=c(100,10))
Cpools=getC(MMmodel)
matplot(days,Cpools,type="l",ylab="Concentrations",xlab="Days",lty=1,ylim=c(0,max(Cpools)*1.2))
legend("topleft",c("SOM-C", "Microbial biomass"),lty=1,col=c(1,2),bty="n")
ks=0.000018
kb=0.007
r=0.6
ADD=3.2
#Analytical solution of fixed points
#Cs_=kb/((1-r)*ks) wrong look at the sympy test print twopMModel.pdf
Km=900
Af=1
Cs=kb*Km/(Af*ks*(1-r)-kb)
abline(h=Cs,lty=2)
Cb=(ADD*(1-r))/(r*kb)
abline(h=Cb,lty=2,col=2)
#State-space diagram
plot(Cpools[,2],Cpools[,1],type="l",ylab="SOM-C",xlab="Microbial biomass")
plot(days,Cpools[,2],type="l",col=2,xlab="Days",ylab="Microbial biomass")

#The default parameterization exhaust the microbial biomass.
#A different behavior is obtained by increasing ks and decreasing kb
MMmodel=TwopMMmodel(t=days,ival=c(972,304) ,Af=3,kb=0.0000001)
Cpools=getC(MMmodel)

matplot(days,Cpools,type="l",ylab="Concentrations",xlab="Days",lty=1,ylim=c(0,max(Cpools)*1.2))
legend("topleft",c("SOM-C", "Microbial biomass"),lty=1,col=c(1,2),bty="n")

plot(Cpools[,2],Cpools[,1],type="l",ylab="SOM-C",xlab="Microbial biomass")

plot(days,Cpools[,2],type="l",col=2,xlab="Days",ylab="Microbial biomass")