wNSE | R Documentation |
Weighted Nash-Sutcliffe efficiency between sim
and obs
, with treatment of missing values.
This goodness-of-fit measure was proposed by Hundecha and Bardossy (2004) to put special focus on high values.
wNSE(sim, obs, ...)
## Default S3 method:
wNSE(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'data.frame'
wNSE(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'matrix'
wNSE(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'zoo'
wNSE(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
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. |
fun |
function to be applied to The first argument MUST BE a numeric vector with any name (e.g., |
... |
arguments passed to |
epsilon.type |
argument used to define a numeric value to be added to both It is was designed to allow the use of logarithm and other similar functions that do not work with zero values. Valid values of 1) "none": 2) "Pushpalatha2012": one hundredth (1/100) of the mean observed values is added to both 3) "otherFactor": the numeric value defined in the 4) "otherValue": the numeric value defined in the |
epsilon.value |
-) when |
wNSE = 1 -\frac { \sum_{i=1}^N O_i * ( S_i - O_i )^2 } { \sum_{i=1}^N O_i * ( O_i - \bar{O} )^2 }
Weighted Nash-Sutcliffe efficiency between sim
and obs
.
If sim
and obs
are matrixes, the returned value is a vector, with the relative Nash-Sutcliffe efficiency between each column of sim
and obs
.
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
If some of the observed values are equal to zero (at least one of them), this index can not be computed.
sluedtke (github user)
Nash, J.E. and J.V. Sutcliffe, River flow forecasting through conceptual models. Part 1: A discussion of principles, J. Hydrol. 10 (1970), pp. 282-290. doi:10.1016/0022-1694(70)90255-6.
Hundecha, Y., Bardossy, A. (2004). Modeling of the effect of land use changes on the runoff generation of a river basin through parameter regionalization of a watershed model. Journal of hydrology, 292(1-4), 281-295. doi:10.1016/j.jhydrol.2004.01.002.
Hundecha, Y., Ouarda, T. B., Bardossy, A. (2008). Regional estimation of parameters of a rainfall-runoff model at ungauged watersheds using the 'spatial' structures of the parameters within a canonical physiographic-climatic space. Water Resources Research, 44(1). doi:10.1029/2006WR005439.
Hundecha, Y. and Merz, B. (2012), Exploring the Relationship between Changes in Climate and Floods Using a Model-Based Analysis, Water Resour. Res., 48(4), 1-21, doi:10.1029/2011WR010527..
NSE
, rNSE
, mNSE
, KGE
, gof
, ggof
##################
# Example 1: basic ideal case
obs <- 1:10
sim <- 1:10
wNSE(sim, obs)
obs <- 1:10
sim <- 2:11
wNSE(sim, obs)
##################
# Example 2:
# 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 'wNSE' for the "best" (unattainable) case
wNSE(sim=sim, obs=obs)
##################
# Example 3: wNSE for simulated values equal to observations plus random noise
# on the first half of the observed values.
# This random noise has more relative importance for ow flows than
# for medium and high flows.
# Randomly changing the first 1826 elements of 'sim', by using a normal distribution
# with mean 10 and standard deviation equal to 1 (default of 'rnorm').
sim[1:1826] <- obs[1:1826] + rnorm(1826, mean=10)
ggof(sim, obs)
wNSE(sim=sim, obs=obs)
##################
# Example 4: wNSE for simulated values equal to observations plus random noise
# on the first half of the observed values and applying (natural)
# logarithm to 'sim' and 'obs' during computations.
wNSE(sim=sim, obs=obs, fun=log)
# Verifying the previous value:
lsim <- log(sim)
lobs <- log(obs)
wNSE(sim=lsim, obs=lobs)
##################
# Example 5: wNSE for simulated values equal to observations plus random noise
# on the first half of the observed values and applying (natural)
# logarithm to 'sim' and 'obs' and adding the Pushpalatha2012 constant
# during computations
wNSE(sim=sim, obs=obs, fun=log, epsilon.type="Pushpalatha2012")
# Verifying the previous value, with the epsilon value following Pushpalatha2012
eps <- mean(obs, na.rm=TRUE)/100
lsim <- log(sim+eps)
lobs <- log(obs+eps)
wNSE(sim=lsim, obs=lobs)
##################
# Example 6: wNSE for simulated values equal to observations plus random noise
# on the first half of the observed values and applying (natural)
# logarithm to 'sim' and 'obs' and adding a user-defined constant
# during computations
eps <- 0.01
wNSE(sim=sim, obs=obs, fun=log, epsilon.type="otherValue", epsilon.value=eps)
# Verifying the previous value:
lsim <- log(sim+eps)
lobs <- log(obs+eps)
wNSE(sim=lsim, obs=lobs)
##################
# Example 7: wNSE for simulated values equal to observations plus random noise
# on the first half of the observed values and applying (natural)
# logarithm to 'sim' and 'obs' and using a user-defined factor
# to multiply the mean of the observed values to obtain the constant
# to be added to 'sim' and 'obs' during computations
fact <- 1/50
wNSE(sim=sim, obs=obs, fun=log, epsilon.type="otherFactor", epsilon.value=fact)
# Verifying the previous value:
eps <- fact*mean(obs, na.rm=TRUE)
lsim <- log(sim+eps)
lobs <- log(obs+eps)
wNSE(sim=lsim, obs=lobs)
##################
# Example 8: wNSE for simulated values equal to observations plus random noise
# on the first half of the observed values and applying a
# user-defined function to 'sim' and 'obs' during computations
fun1 <- function(x) {sqrt(x+1)}
wNSE(sim=sim, obs=obs, fun=fun1)
# Verifying the previous value, with the epsilon value following Pushpalatha2012
sim1 <- sqrt(sim+1)
obs1 <- sqrt(obs+1)
wNSE(sim=sim1, obs=obs1)
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