NSE: Nash-Sutcliffe Efficiency

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

Description

Nash-Sutcliffe efficiency between sim and obs, with treatment of missing values.

Usage

NSE(sim, obs, ...)

## Default S3 method:
NSE(sim, obs, na.rm=TRUE, FUN=NULL, 
                      epsilon=c(0, "Pushpalatha2012", "other"), epsilon.value=NA, ...)

## S3 method for class 'data.frame'
NSE(sim, obs, na.rm=TRUE, FUN=NULL, 
                      epsilon=c(0, "Pushpalatha2012", "other"), epsilon.value=NA, ...)

## S3 method for class 'matrix'
NSE(sim, obs, na.rm=TRUE, FUN=NULL, 
                      epsilon=c(0, "Pushpalatha2012", "other"), epsilon.value=NA, ...)

## S3 method for class 'zoo'
NSE(sim, obs, na.rm=TRUE, FUN=NULL, 
                      epsilon=c(0, "Pushpalatha2012", "other"), epsilon.value=NA, ...)

Arguments

sim	numeric, zoo, matrix or data.frame with simulated values
obs	numeric, zoo, matrix or data.frame with observed values
na.rm	a logical value indicating whether 'NA' should be stripped before the computation proceeds. When an 'NA' value is found at the i-th position in obs OR sim, the i-th value of obs AND sim are removed before the computation.
FUN	function to be applied to sim and obs in order to obtain transformed values thereof before computing the Nash-Sutcliffe efficiency.
epsilon	argument used to define a numeric value to be added to both sim and obs before applying FUN. It is was designed to allow the use of logarithm and other similar functions that do not work with zero values. Valid values are: 1) 0: zero is added to both sim and obs. 2) "Pushpalatha2012": one hundredth of the mean observed values is added to both sim and obs, as described in Pushpalatha et al., (2012). 3) "other": the numeric value defined in the epsilon.value argument is added to both sim and obs
epsilon.value	numeric value to be added to both sim and obs when epsilon="other".
...	further arguments passed to FUN.

Details

NSE = 1 - ( sum( (obs - sim)^2 ) / sum( (obs - mean(obs))^2 )

The Nash-Sutcliffe efficiency (NSE) is a normalized statistic that determines the relative magnitude of the residual variance ("noise") compared to the measured data variance ("information") (Nash and Sutcliffe, 1970).

NSE indicates how well the plot of observed versus simulated data fits the 1:1 line.

Nash-Sutcliffe efficiencies range from -Inf to 1. Essentially, the closer to 1, the more accurate the model is.
-) NSE = 1, corresponds to a perfect match of modelled to the observed data.
-) NSE = 0, indicates that the model predictions are as accurate as the mean of the observed data,
-) -Inf < NSE < 0, indicates that the observed mean is better predictor than the model.

Value

Nash-Sutcliffe efficiency between sim and obs.

If sim and obs are matrixes, the returned value is a vector, with the Nash-Sutcliffe efficiency between each column of sim and obs.

Note

obs and sim has to have the same length/dimension

The missing values in obs and sim are removed before the computation proceeds, and only those positions with non-missing values in obs and sim are considered in the computation

Author(s)

Mauricio Zambrano Bigiarini <[e-mail]>

References

Nash, J. E. and J. V. Sutcliffe (1970), River flow forecasting through conceptual models part I -A discussion of principles, Journal of Hydrology, 10 (3), 282-290

http://en.wikipedia.org/wiki/Nash%E2%80%93Sutcliffe_model_efficiency_coefficient

Pushpalatha, R., Perrin, C., Le Moine, N. and Andreassian, V. (2012). A review of efficiency criteria suitable for evaluating low-flow simulations. Journal of Hydrology, 420, 171-182. DOI: 10.1016/j.jhydrol.2011.11.055

See Also

mNSE, rNSE, KGE, gof, ggof

Examples

obs <- 1:10
sim <- 1:10
NSE(sim, obs)

obs <- 1:10
sim <- 2:11
NSE(sim, obs)

#################
# Computing NSE on the (natural) logarithm of simulated and observed values
obs <- 1:10/10
sim <- 2:11/10
NSE(sim=sim, obs=obs, FUN=log)

##################
# Loading daily streamflows of the Ega River (Spain), from 1961 to 1970
data(EgaEnEstellaQts)
obs <- EgaEnEstellaQts

# Generating a simulated daily time series, initially equal to the observed series
sim <- obs 

# Computing the 'NSE' for the "best" (unattainable) case
NSE(sim=sim, obs=obs)

# Randomly changing the first 2000 elements of 'sim', by using a normal distribution 
# with mean 10 and standard deviation equal to 1 (default of 'rnorm').
sim[1:2000] <- obs[1:2000] + rnorm(2000, mean=10)

# Computing the new 'NSE'
NSE(sim=sim, obs=obs)

Example output

Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

[1] 1
[1] 0.8787879
[1] 0.8167253
[1] 1
[1] 0.8624802

hydroGOF documentation built on March 14, 2020, 1:07 a.m.