forcings {deSolve} | R Documentation

## Passing Forcing Functions to Models Written in R or Compiled Code.

### Description

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.

### Details

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 `deSolve`s 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):

method

  specifies the interpolation method to be used. Choices are `"linear"` or `"constant"`,

rule

  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.

f

  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,

ties

  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").

### Note

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.

### Author(s)

Karline Soetaert,

Thomas Petzoldt,

R. Woodrow Setzer

### See Also

`approx` or `approxfun`, the R function,

`events` for how to implement events.

### Examples

    ## =============================================================================
    ## 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)

[Package deSolve version 1.24 Index]