# File rd.R
# Part of the hydroGOF R package, https://github.com/hzambran/hydroGOF ;
# https://cran.r-project.org/package=hydroGOF
# http://www.rforge.net/hydroGOF/
# Copyright 2010-2024 Mauricio Zambrano-Bigiarini
# Distributed under GPL 2 or later
########################################
# 'rd': Relative Index of Agreement #
########################################
# Started: April 15th, 2010 #
# Updates: 01-Jun-2011 #
# 20-Jul-2022 ; 29-Jul-2022 #
# 20-Jan-2024 #
########################################
# Ref
# 1) Krause, P., Boyle, D. P., and Base, F.:
# Comparison of different efficiency criteria for hydrological model assessment, Adv. Geosci., 5, 89-97, 2005
# Relative Index of Agreement (Willmott et al., 1984) range from 0.0 to 1.0
# and the closer to 1 the better the performance of the model
# 'obs' : numeric 'data.frame', 'matrix' or 'vector' with observed values
# 'sim' : numeric 'data.frame', 'matrix' or 'vector' with simulated values
# 'Result': Modified Index of Agreement between 'sim' and 'obs'
# This index was developed to be sensitive to systematic over- or
# under-prediction, in particular during low flow conditions.
# This index quantify the difference between simulated and observed values
# in a relative way, in order to significatively reduce the influence of
# the absolute differences of high flows and to give more weight to
# over- or under-prediction of low flows. At the same time, differences in
# low flows become more important, because they are looked in a relative way.
rd <-function(sim, obs, ...) UseMethod("rd")
rd.default <- function (sim, obs, na.rm=TRUE,
fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA){
if ( is.na(match(class(sim), c("integer", "numeric", "ts", "zoo"))) |
is.na(match(class(obs), c("integer", "numeric", "ts", "zoo")))
) stop("Invalid argument type: 'sim' & 'obs' have to be of class: c('integer', 'numeric', 'ts', 'zoo')")
epsilon.type <- match.arg(epsilon.type)
# index of those elements that are present both in 'x' and 'y' (NON- NA values)
vi <- valindex(sim, obs)
if (length(vi) > 0) {
# Filtering 'obs' and 'sim', selecting only those pairs of elements
# that are present both in 'x' and 'y' (NON- NA values)
obs <- obs[vi]
sim <- sim[vi]
if (!is.null(fun)) {
fun1 <- match.fun(fun)
new <- preproc(sim=sim, obs=obs, fun=fun1, ...,
epsilon.type=epsilon.type, epsilon.value=epsilon.value)
sim <- new[["sim"]]
obs <- new[["obs"]]
} # IF end
# Testing for zero values in obs, which leads to -Inf as result
zero.index <- which(obs==0)
if (length(zero.index > 0) )
warning("'rd' can not be computed: some elements in 'obs' are zero !", call.=FALSE)
# the next two lines are required for avoiding an strange behaviour
# of the difference function when sim and obs are time series.
if ( !is.na(match(class(sim), c("ts", "zoo"))) ) sim <- as.numeric(sim)
if ( !is.na(match(class(obs), c("ts", "zoo"))) ) obs <- as.numeric(obs)
# Mean of the observed values
Om <- mean(obs, na.rm=na.rm)
denominator <- sum( ( ( abs(sim - Om) + abs(obs - Om) ) / Om )^2 )
if ( (denominator != 0) & (!is.na(denominator)) ) {
rd <- 1 - ( sum( ( (obs - sim) / obs)^2 ) / denominator )
} else {
rd <- NA
warning("'sum( ( ( abs(sim-Om) + abs(obs-Om) ) / Om )^2 ) = 0', it is not possible to compute 'rd'")
} # ELSE end
} else {
rd <- NA
warning("There are no pairs of 'sim' and 'obs' without missing values !")
} # ELSE end
return(rd)
} # 'rd.default' end
rd.matrix <- function (sim, obs, na.rm=TRUE,
fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA){
# Checking that 'sim' and 'obs' have the same dimensions
if ( all.equal(dim(sim), dim(obs)) != TRUE )
stop( paste("Invalid argument: dim(sim) != dim(obs) ( [",
paste(dim(sim), collapse=" "), "] != [",
paste(dim(obs), collapse=" "), "] )", sep="") )
rd <- rep(NA, ncol(obs))
rd <- sapply(1:ncol(obs), function(i,x,y) {
rd[i] <- rd.default( x[,i], y[,i], na.rm=na.rm, fun=fun, ...,
epsilon.type=epsilon.type, epsilon.value=epsilon.value)
}, x=sim, y=obs )
names(rd) <- colnames(obs)
return(rd)
} # 'rd.matrix' end
rd.data.frame <- function (sim, obs, na.rm=TRUE,
fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA){
sim <- as.matrix(sim)
obs <- as.matrix(obs)
rd.matrix(sim=sim, obs=obs, na.rm=na.rm, fun=fun, ...,
epsilon.type=epsilon.type, epsilon.value=epsilon.value)
} # 'rd.data.frame' end
################################################################################
# Author: Mauricio Zambrano-Bigiarini #
################################################################################
# Started: 22-Mar-2013 #
# Updates: 20-Jul-2022 ; 29-Jul-2022 #
################################################################################
rd.zoo <- function(sim, obs, na.rm=TRUE,
fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA){
sim <- zoo::coredata(sim)
if (is.zoo(obs)) obs <- zoo::coredata(obs)
if (is.matrix(sim) | is.data.frame(sim)) {
rd.matrix(sim, obs, na.rm=na.rm, fun=fun, ...,
epsilon.type=epsilon.type, epsilon.value=epsilon.value)
} else NextMethod(sim, obs, na.rm=na.rm, fun=fun, ...,
epsilon.type=epsilon.type, epsilon.value=epsilon.value)
} # 'rd.zoo' end
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