biocro: Simulation of Energycane and Sugarcane

##' Radiation use efficiency based model
##'
##' Simulates leaf area index, biomass and light interception.  Based on the
##' Monteith (1973) equations, adapted for Miscanthus by Clifton Brown et
##' al.(2001) (see references).
##'
##'
##' @param Rad Daily solar radiation (MJ \eqn{ha^{-2}}).
##' @param T.a Daily average temperature (Fahrenheit).
##' @param doy.s first day of the growing season, default 91.
##' @param doy.f last day of the growing season, default 227.
##' @param lai.c linear relationship between growing degree days and leaf area
##' index.
##' @param rue radiation use efficiency, default 2.4.
##' @param T.b base temperature for calculating growing degree days, default
##' 10.
##' @param k light extinction coefficient, default 0.68.
##' @export
##' @return a \code{\link{list}} structure with components
##' @returnItem doy day of the year.
##' @returnItem lai.cum cumulative leaf area index.
##' @returnItem AG.cum cumulative above ground dry biomass (Mg \eqn{ha^{-1}}).
##' @returnItem AGDD cumulative growing degree days.
##' @returnItem Int.e Intercepted solar radiation.
##' @note This empirical model is useful but it has limitations.
##' @seealso \code{\link{RUEmodMY}}
##' @references Monteith (1973) \emph{Principles of Environmental Physics}.
##' Edward Arnold, London. UK.
##'
##' Clifton-Brown, J.C., Long, S.P. and Jorgensen, U. with contributions from
##' S.A. Humphries, Schwarz, K.-U. and Schwarz, H. (2001) \emph{Miscanthus
##' Productivity}. Ch 4. In: Miscanthus for Energy and Fibre. Edited by: Jones,
##' Michael B. and Walsh, Mary. James & James (Science Publishers), London, UK.
##' @keywords models
##' @examples
##'
##'
##' ## See RUEmodMY
##'
##'
RUEmod <- function(Rad, T.a, doy.s = 91, doy.f = 227, lai.c = 0.0102, rue = 2.4, 
    T.b = 10, k = 0.68) {
    T.a <- (T.a - 32) * (5/9)
    PAR <- Rad/2
    T.a <- T.a[doy.s:doy.f]
    Rad <- Rad[doy.s:doy.f]
    deltTemp <- ifelse(T.a - T.b > 0, T.a - T.b, 0)
    AGDD <- apply(as.matrix(deltTemp), 2, FUN = cumsum)
    lai0 <- deltTemp * lai.c
    lai.cum <- apply(as.matrix(lai0), 2, FUN = cumsum)
    # lai.cum.mo <- ifelse(lai.cum > 15, 15 , lai.cum)
    e.i <- 1 - exp(-k * lai.cum)
    int.Rad <- Rad * e.i
    AGBiomass <- rue * int.Rad
    AG.cum.g <- apply(as.matrix(AGBiomass), 2, FUN = cumsum)  ## This is in grams
    AG.cum <- AG.cum.g/100  ## This is used to convert g m-2 to Mg ha-1.
    doy <- c(doy.s:doy.f)
    list(doy = doy, lai.cum = lai.cum, AG.cum = AG.cum, AGDD = AGDD, Int.e = e.i)
}