NPZriver: Nutrient Phytoplankton Zooplankton (NPZ) Model in a River

In simecolModels: Model collection for the simecol package

Description

Model describing the dynamics of Nutrients Phytoplankton and Zooplankton in a river. (Soetaert and Herman, 2008).

The model describes

• nutrients (N),

• phytoplankton (P),

• zooplankton (Z).

The physical component consists of an advective transport term (river flow, velocity v) only.

The river has constant cross-sectional surface and is 100 km long. It is subdivided in 100 boxes.

The equations are:

dN/dt=-v*dN/dx - mu*N/(N+kn)*P+g*P/(P+kp)*Z*(1-gamma)+m*Z

dP/dt=-v*dP/dx + mu*N/(N+kn)*P-g*P/(P+kp)*Z

dZ/dt=-v*dZ/dx + g*P/(P+kp)*Z*gamma -m*Z

where, for the nutrients, the first term is transport, the second term uptake by phytoplankton growth, the third term is excreted fraction due to zooplankton grazing and the last term is zooplankton mortality.

For the numerical approximation of the partial differential equations, see Soetaert and Herman, 2008.

Usage

NPZriver()

Format

An S4 object according to the odeModel specification.

The object contains the following slots:

• main model specifications.

• parms vector with the named parameters of the model - see code.

• times simulation time and integration interval (if dynamic simulation); not used if the steady-state is estimated.

• solver user supplied solver function that calls steady.1D with appropriate simulation control parameters and re-arranges output data.

• initfunc function that initialises the state variables and calculates the box lenghts.

The model is solved to steady-state using steady-state solver steady.1D from package rootSolve.

Author(s)

Karline Soetaert

References

Chapter 7.9.5 from the book:

Soetaert K and PMJ Herman, 2009. A practical guide to ecological Modelling - using R as a simulation platform. Springer.

See Also

R-package simecol for a description of the simObj class

Examples

# create an instance of the model
myNPZriver <- NPZriver()

# show model code, parameter settings,...
print(myNPZriver)

# Note that the model has a specialized solver function built in:
solver(myNPZriver)

# Alternative way: 
#   use standard solver and pass additional parameters through sim
# solver(myNPZriver) <- "NPZ_steady.1D"
# myNPZriver <- sim(myNPZriver, nspec=3, pos=TRUE)


#====================#
# 3 Model runs       #
#====================#

# steady-state solution, v=1 km d-1
outp       <- out(sim(myNPZriver))
N <- outp$N
P <- outp$P
Z <- outp$Z

# steady-state solution, v=5 km d-1
parms(myNPZriver)["flow"]     <- 5        # river flow, km/day
outp       <- out(sim(myNPZriver))
N <- cbind(N, outp$N)
P <- cbind(P, outp$P)
Z <- cbind(Z, outp$Z)


# steady-state solution, v=10 km d-1
parms(myNPZriver)["flow"]     <- 10     
outp       <- out(sim(myNPZriver))
N <- cbind(N, outp$N)
P <- cbind(P, outp$P)
Z <- cbind(Z, outp$Z)

#====================#
# plotting           #
#====================#
par(mfrow=c(2, 2))
parms <- as.list(parms(myNPZriver)) 
delx  <- parms$riverlen / parms$Nb        # box length
Dist  <- seq(delx/2, parms$riverlen, by=delx)
          
matplot(Dist, N, ylab="mmolN/m3", main="DIN", type="l",
        lwd=2, ylim=c(0,110), xlab="Distance, km")
matplot(Dist, P, ylab="mmolN/m3", main="Phytoplankton", type="l",
        lwd=2, ylim=c(0,110), xlab="Distance, km")
matplot(Dist, Z, ylab="mmolN/m3", main="Zooplankton", type="l",
        lwd=2, ylim=c(0,110), xlab="Distance, km")

plot(0, type="n", xlab="", ylab="", axes=FALSE)
legend("center", lty=c(1, 1, 2), lwd=c(2, 1, 1), col=1:3,
        title="river flowrate",
       c(expression(v==1~km~d^{-1}), expression(v==5~km~d^{-1}),
         expression(v==10~km~d^{-1}))
) 

mtext(side=3, outer=TRUE, "NPZ model in a river", line=-1.5, cex=1.5)	

simecolModels documentation built on May 2, 2019, 4:59 p.m.