R/NSE.R

In hydroGOF: Goodness-of-Fit Functions for Comparison of Simulated and Observed Hydrological Time Series

# File NSE.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 2008-2023 Mauricio Zambrano-Bigiarini
# Distributed under GPL 2 or later

################################################################################
# 'NSE': Nash-Sutcliffe Efficiency                                             #
################################################################################
# 15-Dic-2008   ; 06-Sep-09                                                    #
# 29-Jun-2017                                                                  #
# 11-Jul-2022 ; 12-Jul-2022 ; 13-Jul-2022                                      #
# 20-Jan-2024                                                                  #
################################################################################
# Nash-Sutcliffe efficiencies (Nash and Sutcliffe, 1970) range from -Inf to 1. 
# An efficiency of 1 (NSE = 1) corresponds to a perfect match of modeled to the observed data. 
# An efficiency of 0 (NSE = 0) indicates that the model predictions are as accurate
# as the mean of the observed data, whereas 
# an efficiency less than zero (-Inf < NSE < 0) occurs when the observed mean is a better predictor than the model.
# Essentially, the closer the model efficiency is to 1, the more accurate the model is.  

# 'obs'   : numeric 'data.frame', 'matrix' or 'vector' with observed values
# 'sim'   : numeric 'data.frame', 'matrix' or 'vector' with simulated values
# 'Result': Nash-sutcliffe Efficiency between 'sim' and 'obs'

NSE <-function(sim, obs, ...) UseMethod("NSE")

NSE.default <- function (sim, obs, na.rm=TRUE, fun=NULL, ..., 
                         epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
                         epsilon.value=NA){ 

  # Checking 'epsilon.type'
  epsilon.type <- match.arg(epsilon.type) 

  if ( is.na(match(class(sim), c("integer", "numeric", "ts", "zoo", "xts"))) |
       is.na(match(class(obs), c("integer", "numeric", "ts", "zoo", "xts")))
  ) stop("Invalid argument type: 'sim' & 'obs' have to be of class: c('integer', 'numeric', 'ts', 'zoo', 'xts')")      

  # index of those elements that are present both in 'sim' and 'obs' (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     
     
    denominator <- sum( (obs - mean(obs))^2 )
     
    if ( (denominator != 0) & (!is.na(denominator)) ) {      
      NS <- 1 - ( sum( (obs - sim)^2 ) / denominator )     
    } else {
        NS <- NA
        warning("'sum((obs - mean(obs))^2)=0' => it is not possible to compute 'NSE'")  
      } 
  } else {
       NS <- NA
       warning("There are no pairs of 'sim' and 'obs' without missing values !")
    } # ELSE end
     
  return(NS)
     
} # 'NSE' end


NSE.matrix <- function(sim, obs, na.rm=TRUE, fun=NULL, ..., 
                       epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
                       epsilon.value=NA){ 

  # Checking 'epsilon.type'
  epsilon.type <- match.arg(epsilon.type)  

  # 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="") )
 
  NS <- rep(NA, ncol(obs))       
          
  NS <- sapply(1:ncol(obs), function(i,x,y) { 
                 NS[i] <- NSE.default( x[,i], y[,i], na.rm=na.rm, fun=fun, ..., 
                                       epsilon.type=epsilon.type, epsilon.value=epsilon.value)
               }, x=sim, y=obs )    
                     
  names(NS) <- colnames(obs)
  
  return(NS)
     
} # 'NSE.matrix' end


NSE.data.frame <- function(sim, obs, na.rm=TRUE, fun=NULL, ..., 
                           epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
                           epsilon.value=NA){ 
 
  # Checking 'epsilon.type'
  epsilon.type <- match.arg(epsilon.type)  

  sim <- as.matrix(sim)
  obs <- as.matrix(obs)
   
  NSE.matrix(sim, obs, na.rm=na.rm, fun=fun, ..., 
             epsilon.type=epsilon.type, epsilon.value=epsilon.value)
     
} # 'NSE.data.frame' end


NSeff <-function(sim, obs, ...) UseMethod("NSE")


################################################################################
# Author: Mauricio Zambrano-Bigiarini                                          #
################################################################################
# Started: 22-Mar-2013                                                         #
# Updates: 12-Jul-2022 ; 13-Jul-2022                                           #
#          18-Jan-2024 ; 19-Jan-2024                                           #
################################################################################
NSE.zoo <- function(sim, obs, na.rm=TRUE, fun=NULL, ..., 
                    epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
                    epsilon.value=NA){ 
    
    # Checking 'epsilon.type'
    epsilon.type <- match.arg(epsilon.type) 

    sim <- zoo::coredata(sim)
    if (is.zoo(obs)) obs <- zoo::coredata(obs)
    
    if (is.matrix(sim) | is.data.frame(sim)) {
       NSE.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)
     
  } # 'NSE.zoo' end