R/sunML.R

In serbinsh/biocro: Simulation of Energycane and Sugarcane

## BioCro/R/sunML.R by Fernando Ezequiel Miguez Copyright (C) 2007-2009
## 
## This program is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by the Free
## Software Foundation; either version 2 or 3 of the License (at your option).
## 
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
## more details.
## 
## A copy of the GNU General Public License is available at
## http://www.r-project.org/Licenses/
##' Sunlit shaded multi-layer model
##'
##' Simulates the light microenvironment in the canopy based on the
##' sunlit-shade model and the multiple layers.
##'
##'
##' @param I.dir direct light (quantum flux), (\eqn{\mu mol \; m^{-2} \;
##' s^{-1}}{micro mol /m2/s}).
##' @param I.diff indirect light (diffuse), (\eqn{\mu mol \; m^{-2} \;
##' s^{-1}}{micro mol /m2/s}).
##' @param LAI leaf area index, default 8.
##' @param nlayers number of layers in which the canopy is partitioned, default
##' 8.
##' @param kd extinction coefficient for diffuse light.
##' @param chi.l The ratio of horizontal:vertical projected area of leaves in
##' the canopy segment.
##' @param cos.theta cosine of \eqn{\theta}{theta}, solar zenith angle.
##' @export
##' @return a \code{\link{list}} structure with components
##'
##' Vectors size equal to the number of layers.
##' @returnItem I.solar direct solar radiation.
##' @returnItem I.diffuse difusse solar radiation.
##' @returnItem I.total total solar radiation.
##' @returnItem LAI.sun proportion of the leaf area in each layer which is in
##' direct light.
##' @returnItem LAI.shade proportion of the leaf area in each layer which is in
##' indirect light.
##' @returnItem Fsun total leaf area in each layer which is in direct light.
##' @returnItem Fshade total leaf area in each layer which is in indirect
##' light.
##' @keywords models
##' @examples
##'
##' res2 <- sunML(1500,200,3,10)
##'
##' xyplot(Fsun + Fshade ~ c(1:10), data=res2,
##'        ylab='LAI',
##'        xlab='layer',
##'        type='l',lwd=2,col=c('blue','green'),
##'        lty=c(1,2),
##'        key=list(text=list(c('Direct','Diffuse')),lty=c(1,2),
##'                 cex=1.2,lwd=2,lines=TRUE,x=0.7,y=0.5,
##'                 col=c('blue','green')))
##'
sunML <- function(I.dir, I.diff, LAI = 8, nlayers = 8, kd = 0.1, chi.l = 1, cos.theta = 0.5) {
    k0 <- cos.theta * sqrt(chi.l^2 + tan(acos(cos.theta))^2)
    k1 <- chi.l + 1.744 * (chi.l + 1.183)^-0.733
    k <- abs(k0/k1)
    LAI.sun <- numeric(nlayers)
    LAI.shade <- numeric(nlayers)
    F.sun <- numeric(nlayers)
    F.shade <- numeric(nlayers)
    LAI.i <- LAI/nlayers
    I.solar <- numeric(nlayers)
    I.diffuse <- numeric(nlayers)
    I.total <- numeric(nlayers)
    for (i in 0:nlayers) {
        CumLAI <- LAI.i * i
        if (i == 0) {
            Isolar <- I.dir
            Idiffuse <- I.diff
        } else {
            Isolar <- I.dir * exp(-k * CumLAI)
            Idiffuse <- I.diff * exp(-kd * CumLAI)
        }
        Itotal <- Isolar + Idiffuse
        Ls <- (1 - exp(-k * CumLAI))/k
        Ld <- CumLAI - Ls
        Ls2 <- (cos.theta * (1 - exp(-k * Ls/cos.theta)))/k
        Ld2 <- CumLAI - Ls2
        I.solar[i] <- Isolar
        I.diffuse[i] <- Idiffuse
        I.total[i] <- Itotal
        F.sun[i] <- Ls2/CumLAI
        F.shade[i] <- Ld2/CumLAI
        LAI.sun[i] <- LAI * F.sun[i]
        LAI.shade[i] <- LAI * F.shade[i]
    }
    list(I.solar = I.solar, I.diffuse = I.diffuse, I.total = I.total, LAI.sun = LAI.sun, 
        LAI.shade = LAI.shade, Fsun = F.sun, Fshade = F.shade)
}