217: Implementation of a two-pool Michaelis-Menten model

In SoilR: Models of Soil Organic Matter Decomposition

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

An object of class NlModel that can be further queried.

Author(s)

Carlos A. Sierra, Markus Mueller

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.

Examples

  
  days=seq(0,1000,0.5)
  
  #Run the model with default parameter values
  MMmodel=TwopMMmodel(t=days,ival=c(100,10))
# fixme mm:
# the next line causes trouble on Rforge Windows patched build

#  Cpools=getC(MMmodel)
#  
#  #Time solution
#  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")
#  
#  #Microbial biomass over time
#  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")
  

SoilR documentation built on May 4, 2017, 9:08 p.m.