Passing Forcing Functions to Models Written in R or Compiled Code.
A forcing function is an external variable that is essential to the
model, but not explicitly modeled. Rather, it is imposed as a time-series.
Thus, if a model uses forcing variables, their value at each time point
needs to be estimated by interpolation of a data series.
The forcing functions are imposed as a data series, that contains
the values of the forcings at specified times.
Models may be defined in compiled C or FORTRAN code, as well as in R.
If the model is defined in R code, it is most efficient to:
1. define a function that performs the linear interpolation,
using R's approxfun. It is generally recommended to use
rule = 2, such as to allow extrapolation outside of the time interval,
especially when using the Livermore solvers, as these may exceed the last
time point.
2. call this function within the model's derivative function, to interpolate at the current timestep.
See first example.
If the models are defined in compiled C or FORTRAN code, it is possible to
use deSolves forcing function update algorithm. This is the
compiled-code equivalent of approxfun or approx.
In this case:
1. the forcing function data series is provided by means
of argument forcings,
2. initforc is the name of the forcing function initialisation function,
as provided in ‘dllname’, while
3. fcontrol is a list used to finetune how the forcing update should
be performed.
The fcontrol argument is a list that can supply any of the following components (conform the definitions in the approxfun function):
specifies the interpolation method to be used.
Choices are "linear" or "constant",
an integer describing how interpolation is to take place
outside the interval [min(times), max(times)].
If rule is 1 then an error will be triggered and the
calculation will stop if times extends the interval of the
forcing function data set. If it is 2, the default, the
value at the closest data extreme is used, a warning will be printed if
verbose is TRUE,
Note that the default differs from the approx default.
For method = "constant" a number between 0 and
1 inclusive, indicating a compromise between left- and
right-continuous step functions. If y0 and y1 are the
values to the left and right of the point then the value is
y0 * (1 - f) + y1 * f so that f = 0 is right-continuous and
f = 1 is left-continuous,
Handling of tied times values. Either a function
with a single vector argument returning a single number result or the
string "ordered".
Note that the default is "ordered", hence the existence of ties will
NOT be investigated; in the C code this will mean that -if ties
exist, the first value will be used; if the dataset is not ordered,
then nonsense will be produced.
Alternative values for ties are mean, min etc
The defaults are:
fcontrol = list(method = "linear", rule = 2, f = 0, ties = "ordered")
Note that only ONE specification is allowed, even if there is more than one forcing function data set.
More information about models defined in compiled code is in the package vignette ("compiledCode").
How to write compiled code is described in package vignette
"compiledCode", which should be referred to for details.
This vignette also contains examples on how to pass forcing functions.
Karline Soetaert,
Thomas Petzoldt,
R. Woodrow Setzer
events for how to implement events.
## =============================================================================
## FORCING FUNCTION: The sediment oxygen consumption example - R-code:
## =============================================================================
## Forcing function data
Flux <- matrix(ncol=2,byrow=TRUE,data=c(
1, 0.654, 11, 0.167, 21, 0.060, 41, 0.070, 73,0.277, 83,0.186,
93,0.140,103, 0.255, 113, 0.231,123, 0.309,133,1.127,143,1.923,
153,1.091,163,1.001, 173, 1.691,183, 1.404,194,1.226,204,0.767,
214, 0.893,224,0.737, 234,0.772,244, 0.726,254,0.624,264,0.439,
274,0.168,284 ,0.280, 294,0.202,304, 0.193,315,0.286,325,0.599,
335, 1.889,345, 0.996,355,0.681,365,1.135))
parms <- c(k=0.01)
times <- 1:365
## the model
sediment <- function( t, O2, k)
list (c(Depo(t) - k * O2), depo = Depo(t))
# the forcing functions; rule = 2 avoids NaNs in interpolation
Depo <- approxfun(x = Flux[,1], y = Flux[,2], method = "linear", rule = 2)
Out <- ode(times = times, func = sediment, y = c(O2 = 63), parms = parms)
## same forcing functions, now constant interpolation
Depo <- approxfun(x = Flux[,1], y = Flux[,2], method = "constant",
f = 0.5, rule = 2)
Out2 <- ode(times = times, func = sediment, y = c(O2 = 63), parms = parms)
mf <- par(mfrow = c(2, 1))
plot (Out, which = "depo", type = "l", lwd = 2, mfrow = NULL)
lines(Out2[,"time"], Out2[,"depo"], col = "red", lwd = 2)
plot (Out, which = "O2", type = "l", lwd = 2, mfrow = NULL)
lines(Out2[,"time"], Out2[,"O2"], col = "red", lwd = 2)
## =============================================================================
## SCOC is the same model, as implemented in FORTRAN
## =============================================================================
out<- SCOC(times, parms = parms, Flux = Flux)
plot(out[,"time"], out[,"Depo"], type = "l", col = "red")
lines(out[,"time"], out[,"Mineralisation"], col = "blue")
## Constant interpolation of forcing function - left side of interval
fcontrol <- list(method = "constant")
out2 <- SCOC(times, parms = parms, Flux = Flux, fcontrol = fcontrol)
plot(out2[,"time"], out2[,"Depo"], type = "l", col = "red")
lines(out2[,"time"], out2[,"Mineralisation"], col = "blue")
## Not run:
## =============================================================================
## show examples (see respective help pages for details)
## =============================================================================
example(aquaphy)
## show package vignette with tutorial about how to use compiled models
## + source code of the vignette
## + directory with C and FORTRAN sources
vignette("compiledCode")
edit(vignette("compiledCode"))
browseURL(paste(system.file(package = "deSolve"), "/doc", sep = ""))
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.