# File dr.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 2008-2024 Mauricio Zambrano-Bigiarini
# Distributed under GPL 2 or later
########################################
# 'dr': Refined Index of Agreement #
########################################
# December 18th, 2008; 06-Sep-09 #
# 28-Feb-2016 #
# Updates: 20-Jul-2022 ; 29-Jul-2022 #
########################################
# 1) Willmott, C.J., Robeson, S.M. and Matsuura, K. (2012). A refined index of model performance. International Journal of climatology, 32(13), pp.2088-2094. doi:10.1002/joc.2419.
# 2) Willmott, C.J., Robeson, S.M., Matsuura, K. and Ficklin, D.L. (2015). Assessment of three dimensionless measures of model performance. Environmental Modelling & Software, 73, pp.167-174. doi:10.1016/j.envsoft.2015.08.012
# 3) Willmott, C.J. 1981. On the validation of models. Physical Geography, 2, 184-194
# 4) Willmott, C. J. (1984). "On the evaluation of model performance in physical geography." Spatial Statistics and Models, G. L. Gaile and C. J. Willmott, eds., 443-460.
# 5) Legates, D. R., and G. J. McCabe Jr. (1999), Evaluating the Use of "Goodness-of-Fit" Measures in Hydrologic and Hydroclimatic Model Validation, Water Resour. Res., 35(1), 233-241.
# In contrast to the Index of Agreement (Willmott et al., 1984), which ranges from 0 to 1.0,
# the Refined Index of Agreement is bounded by -1.0 and 1.0. The closer to 1 the better
# the performance of the model.
# In geneeral, dr is "more rationally related to model accuracy than are other existing
# indices" (MSE, NSE, d, rd) (Willmott et a., 2012; Willmott et al., 2015)
# 'obs' : numeric 'data.frame', 'matrix' or 'vector' with observed values
# 'sim' : numeric 'data.frame', 'matrix' or 'vector' with simulated values
# 'Result': Index of Agreement between 'sim' and 'obs'
dr <-function(sim, obs, ...) UseMethod("dr")
################################################################################
# Author: Mauricio Zambrano-Bigiarini #
################################################################################
# Started: 20-Jul-2022 #
# Updates: 29-Jul-2022 #
################################################################################
dr.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
# 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)
# Constant 'c' value
c <- 2
# Components of the denominator
A <- sum( abs(sim - obs) )
B <- c*sum( abs(obs - Om) )
if (A <= B) {
dr <- 1 - A / B
} else dr <- 1 - B / A
} else {
dr <- NA
warning("There are no pairs of 'sim' and 'obs' without missing values !")
} # ELSE end
return(dr)
} # 'dr.default' end
################################################################################
# Author: Mauricio Zambrano-Bigiarini #
################################################################################
# Started: 20-Jul-2022 #
# Updates: 29-Jul-2022 #
################################################################################
dr.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="") )
dr <- rep(NA, ncol(obs))
dr <- sapply(1:ncol(obs), function(i,x,y) {
dr[i] <- dr.default( x[,i], y[,i], na.rm=na.rm, ... )
}, x=sim, y=obs, na.rm=na.rm, fun=fun, ...,
epsilon.type=epsilon.type, epsilon.value=epsilon.value)
names(dr) <- colnames(obs)
return(dr)
} # 'dr.matrix' end
dr.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)
dr.matrix(sim, obs, na.rm=na.rm, fun=fun, ...,
epsilon.type=epsilon.type, epsilon.value=epsilon.value)
} # 'dr.data.frame' end
################################################################################
# Author: Mauricio Zambrano-Bigiarini #
################################################################################
# Started: 20-Jul-2022 #
# Updates: 29-Jul-2022 #
################################################################################
dr.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)) {
dr.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)
} # 'dr.zoo' end
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