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#' @name
#' funFU
#'
#' @title
#' Fu's function for relationship between precipitation and potential evapotranspiration
#'
#' @description It is a model based on the postulates of Budyko, which stated that not only does the actual
#' evapotranspiration depend on potential evapotranspiration, but it is also constrained by water availability
#' \cite{(Budyko, 1974)}.
#'
#' @param PET is the variable which will be inserted as the numerator in Fu's function. It can be a value or a numeric vector,
#' in which case it must have the same length as the denominator vector.
#' @param P is the variable which will be inserted as the numerator in Fu's function. It can be a value or a numeric vector,
#' in which case it must have the same length as the numerator vector.
#' @param alpha parameter of Fu's model which controls the evapotranspiration efficiency, yet it is named depending
#' on the variables used as numerator and denominator. It must be a unique value of type double.
#'
#' @return a value or a vector (depending on which kind of data was introduced for numerator and denominator).
#'
#' @author Nicolas Duque Gardeazabal <nduqueg@unal.edu.co> \cr
#' Pedro Felipe Arboleda Obando <pfarboledao@unal.edu.co> \cr
#' Carolina Vega Viviescas <cvegav@unal.edu.co> \cr
#' David Zamora <dazamoraa@unal.edu.co> \cr
#'
#' Water Resources Engineering Research Group - GIREH
#' Universidad Nacional de Colombia - sede Bogota
#'
#' @references
#' Zhang, L., Potter, N., Hickel, K., Zhang, Y., & Shao, Q. (2008).
#' "Water balance modeling over variable time scales based on the
#' Budyko framework – Model development and testing. Journal of Hydrology",
#' 360(1-4), 117–131.
#'
#' Budyko. (1974). "Climate and life". New York: Academic Press, INC.
#'
#' @export
#'
#' @examples
#' PET <- 1000
#' P <- 2000
#' alpha <- 0.69 # value used by Zhang et al. (2008)
#' funFU(PET, P, alpha)
#'
funFU <- function(PET, P, alpha){
F_FU <- 1 + PET/P - (1 + (PET/P)^(1/(1 - alpha)))^(1 - alpha)
F_FU[P == 0] <- 1 # it identifies where the limit of the function is not fulfilled and assigns the limit value
return(F_FU)
}
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