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###############################################
## Soetaert and Herman (2008) ##
## A practical guide to ecological modelling ##
## Chapter 5. ##
## Model solution - analytical methods ##
## Chapter 5.5.2. Project ##
## Oxygen dynamics in sediment ##
###############################################
par(mfrow=c(2,2))
###################################
# 1-dimensional oxygen model
###################################
BW <- 200 # mmol/m3 bottom water conc
Ds <- 1 # cm2/d diffusion coeff
O2conc <- function(Ds,k,BW,x) BW*exp(-sqrt(k/Ds)*x)
O2flux <- function(Ds,k,BW) Ds*sqrt(k/Ds)*BW
O2depth <- function(Ds,k,BW) log(BW/0.1)/sqrt(k/Ds)
#======================================
# vertical profiles, different k-values
#======================================
x <- seq(0,2,length=200)
plot (O2conc(Ds,k=10 ,BW,x),x,lty=1,ylim=rev(range(x)),
xlab="ľmol/l",ylab="cm",main="O2",type="l",lwd=2)
lines(O2conc(Ds,k=1 ,BW,x),x,lty=2,lwd=2)
lines(O2conc(Ds,k=100,BW,x),x,lty=3,lwd=2)
legend("right",c("k=10","k=1","k=100"),lty=1:3,lwd=2)
writelabel("A")
# plot flux and penetration depth to screen:
O2flux(Ds,c(1,10,100),BW)
O2depth(Ds,c(1,10,100),BW)
#======================================
# Flux versus oxygen penetration depth
#======================================
# sequence of k-values
kseq <- exp(seq(log(1),log(1000),length=200))
flux <- O2flux(Ds,kseq,BW)/100
OPD <- O2depth(Ds,kseq,BW)*10
plot(flux,OPD,type="l",ylab="Oxygen Penetration depth,mm",xlab="oxygen flux,mmol/m2/d",main="sediment oxygen",lwd=2)
writelabel("B")
#======================================
# calibration
#======================================
# input data
depth <- c(0,0.1,0.2,0.3,0.4,0.5,1.0)
O2 <- c(300,65.52,14.31,3.13,0.68,0.59,0.27)
profiledepth <- c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 1)
O2measured <- c(300, 65.52, 14.31, 3.13, 0.68, 0.59, 0.27)
BW <- 300
Ds <- 1
plot( O2,depth,lty=1,ylim=c(1,0),pch=15,cex=2,
xlab="ľmol/l",ylab="cm",main="O2")
writelabel("C")
fit <- nls(O2 ~ O2conc(Ds,k,BW,depth),start=c(k=100))
k <- coef(fit)
x <-seq(from=0,to=1,length.out=100)
lines(O2conc(Ds,k,BW,x),x)
k
O2flux(Ds,k,BW)/100
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