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\name{aquaphy}
\alias{aquaphy}
\title{A Physiological Model of Unbalanced Algal Growth}
\description{A phytoplankton model with uncoupled carbon and nitrogen
assimilation as a function of light and Dissolved Inorganic Nitrogen
(DIN) concentration.
Algal biomass is described via 3 different state variables:
\itemize{
\item low molecular weight carbohydrates (LMW), the product of
photosynthesis,
\item storage molecules (RESERVE) and
\item the biosynthetic and photosynthetic apparatus (PROTEINS).
}
All algal state variables are expressed in
\eqn{\rm mmol\, C\, m^{-3}}{mmol C / m^3}.
Only proteins contain nitrogen and
chlorophyll, with a fixed stoichiometric ratio. As the relative
amount of proteins changes in the algae, so does the N:C and the Chl:C
ratio.
An additional state variable, dissolved inorganic nitrogen (DIN) has
units of \eqn{\rm mmol\, N\, m^{-3}}{mmol N / m^3}.
The algae grow in a dilution culture (chemostat): there is constant
inflow of DIN and outflow of culture water, including DIN and algae,
at the same rate.
Two versions of the model are included.
\itemize{
\item In the default model, there is a day-night illumination regime, i.e.
the light is switched on and off at fixed times (where the sum of
illuminated + dark period = 24 hours).
\item In another version, the light is imposed as a forcing function data
set.
}
This model is written in \code{FORTRAN}.
}
\usage{aquaphy(times, y, parms, PAR = NULL, ...)}
\arguments{
\item{times}{time sequence for which output is wanted; the first value
of times must be the initial time,}
\item{y}{the initial (state) values ("DIN", "PROTEIN", "RESERVE",
"LMW"), in that order,}
\item{parms }{vector or list with the aquaphy model parameters; see
the example for the order in which these have to be defined.}
\item{PAR }{a data set of the photosynthetically active radiation
(light intensity), if \code{NULL}, on-off PAR is used, }
\item{...}{any other parameters passed to the integrator \code{ode}
(which solves the model).}
}
\author{Karline Soetaert <karline.soetaert@nioz.nl>}
\examples{
## ======================================================
##
## Example 1. PAR an on-off function
##
## ======================================================
## -----------------------------
## the model parameters:
## -----------------------------
parameters <- c(maxPhotoSynt = 0.125, # mol C/mol C/hr
rMortPHY = 0.001, # /hr
alpha = -0.125/150, # uEinst/m2/s/hr
pExudation = 0.0, # -
maxProteinSynt = 0.136, # mol C/mol C/hr
ksDIN = 1.0, # mmol N/m3
minpLMW = 0.05, # mol C/mol C
maxpLMW = 0.15, # mol C/mol C
minQuotum = 0.075, # mol C/mol C
maxStorage = 0.23, # /h
respirationRate= 0.0001, # /h
pResp = 0.4, # -
catabolismRate = 0.06, # /h
dilutionRate = 0.01, # /h
rNCProtein = 0.2, # mol N/mol C
inputDIN = 10.0, # mmol N/m3
rChlN = 1, # g Chl/mol N
parMean = 250., # umol Phot/m2/s
dayLength = 15. # hours
)
## -----------------------------
## The initial conditions
## -----------------------------
state <- c(DIN = 6., # mmol N/m3
PROTEIN = 20.0, # mmol C/m3
RESERVE = 5.0, # mmol C/m3
LMW = 1.0) # mmol C/m3
## -----------------------------
## Running the model
## -----------------------------
times <- seq(0, 24*20, 1)
out <- as.data.frame(aquaphy(times, state, parameters))
## -----------------------------
## Plotting model output
## -----------------------------
par(mfrow = c(2, 2), oma = c(0, 0, 3, 0))
col <- grey(0.9)
ii <- 1:length(out$PAR)
plot(times[ii], out$Chlorophyll[ii], type = "l",
main = "Chlorophyll", xlab = "time, hours",ylab = "ug/l")
polygon(times[ii], out$PAR[ii]-10, col = col, border = NA); box()
lines(times[ii], out$Chlorophyll[ii], lwd = 2 )
plot (times[ii], out$DIN[ii], type = "l", main = "DIN",
xlab = "time, hours",ylab = "mmolN/m3")
polygon(times[ii], out$PAR[ii]-10, col = col, border = NA); box()
lines(times[ii], out$DIN[ii], lwd = 2 )
plot (times[ii], out$NCratio[ii], type = "n", main = "NCratio",
xlab = "time, hours", ylab = "molN/molC")
polygon(times[ii], out$PAR[ii]-10, col = col, border = NA); box()
lines(times[ii], out$NCratio[ii], lwd = 2 )
plot (times[ii], out$PhotoSynthesis[ii],type = "l",
main = "PhotoSynthesis", xlab = "time, hours",
ylab = "mmolC/m3/hr")
polygon(times[ii], out$PAR[ii]-10, col = col, border = NA); box()
lines(times[ii], out$PhotoSynthesis[ii], lwd = 2 )
mtext(outer = TRUE, side = 3, "AQUAPHY, PAR= on-off", cex = 1.5)
## -----------------------------
## Summary model output
## -----------------------------
t(summary(out))
## ======================================================
##
## Example 2. PAR a forcing function data set
##
## ======================================================
times <- seq(0, 24*20, 1)
## -----------------------------
## create the forcing functions
## -----------------------------
ftime <- seq(0,500,by=0.5)
parval <- pmax(0,250 + 350*sin(ftime*2*pi/24)+
(runif(length(ftime))-0.5)*250)
Par <- matrix(nc=2,c(ftime,parval))
state <- c(DIN = 6., # mmol N/m3
PROTEIN = 20.0, # mmol C/m3
RESERVE = 5.0, # mmol C/m3
LMW = 1.0) # mmol C/m3
out <- aquaphy(times, state, parameters, Par)
plot(out, which = c("PAR", "Chlorophyll", "DIN", "NCratio"),
xlab = "time, hours",
ylab = c("uEinst/m2/s", "ug/l", "mmolN/m3", "molN/molC"))
mtext(outer = TRUE, side = 3, "AQUAPHY, PAR=forcing", cex = 1.5)
# Now all variables plotted in one figure...
plot(out, which = 1:9, type = "l")
par(mfrow = c(1, 1))
}
\references{
Lancelot, C., Veth, C. and Mathot, S. (1991). Modelling ice-edge
phytoplankton bloom in the Scotia-Weddel sea sector of the Southern
Ocean during spring 1988. Journal of Marine Systems 2, 333--346.
Soetaert, K. and Herman, P. (2008). A practical guide to ecological
modelling. Using R as a simulation platform. Springer.
}
\details{
The model is implemented primarily to demonstrate the linking of
FORTRAN with \R-code.
The source can be found in the \file{doc/examples/dynload} subdirectory of the package.
}
\seealso{
\code{\link{ccl4model}}, the CCl4 inhalation model.
}
\keyword{models}
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