A Physiological Model of Unbalanced Algal Growth
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:
low molecular weight carbohydrates (LMW), the product of photosynthesis,
storage molecules (RESERVE) and
the biosynthetic and photosynthetic apparatus (PROTEINS).
All algal state variables are expressed in 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 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.
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).
In another version, the light is imposed as a forcing function data set.
This model is written in FORTRAN.
aquaphy(times, y, parms, PAR = NULL, ...)
times |
time sequence for which output is wanted; the first value of times must be the initial time, |
y |
the initial (state) values ("DIN", "PROTEIN", "RESERVE", "LMW"), in that order, |
parms |
vector or list with the aquaphy model parameters; see the example for the order in which these have to be defined. |
PAR |
a data set of the photosynthetically active radiation
(light intensity), if |
... |
any other parameters passed to the integrator |
The model is implemented primarily to demonstrate the linking of FORTRAN with R-code.
The source can be found in the ‘doc/examples/dynload’ subdirectory of the package.
Karline Soetaert <karline.soetaert@nioz.nl>
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.
ccl4model, the CCl4 inhalation model.
## ======================================================
##
## 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))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.