KGEnp | R Documentation |
Non-parametric Kling-Gupta efficiency between sim
and obs
, with treatment of missing values.
This goodness-of-fit measure was developed by Pool et al. (2018), as a non-parametric alternative to the original Kling-Gupta efficiency (KGE) proposed by Gupta et al. (2009). See Details.
KGEnp(sim, obs, ...)
## Default S3 method:
KGEnp(sim, obs, na.rm=TRUE, out.type=c("single", "full"), fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'data.frame'
KGEnp(sim, obs, na.rm=TRUE, out.type=c("single", "full"), fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'matrix'
KGEnp(sim, obs, na.rm=TRUE, out.type=c("single", "full"), fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'zoo'
KGEnp(sim, obs, na.rm=TRUE, out.type=c("single", "full"), 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. |
out.type |
character, indicating the whether the output of the function has to include each one of the three terms used in the computation of the Kling-Gupta efficiency or not. Valid values are: -) single: the output is a numeric with the Kling-Gupta efficiency only. -) full: the output is a list of two elements: the first one with the Kling-Gupta efficiency, and the second is a numeric with 3 elements: the Spearman rank correlation coefficient (‘rSpearman’), the ratio between the mean of the simulated values to the mean of observations (‘Beta’), and the variability measure (‘Alpha’). |
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 |
This non-paramettric verison of the Kling-Gupta efficiency keeps the bias term Alpha (mean(sim) / mean(obs)), but for correlation uses the Spearman rank coefficient instead of the Pearson product-moment coefficient; and for variability it uses the normalized flow-duration curve instead of the standard deviation (or coefficient of variation).
The proposed non-parametric based multi-objective function can be seen as a useful alternative to existing performance measures when aiming at acceptable simulations of multiple hydrograph aspects (Pool et al., 2018).
KGE_{np} = 1 - ED
ED = \sqrt{ ((\rho-1)^2 + (\alpha-1)^2 + (\beta-1)^2 }
\rho = \textrm{Spearman rank correlation coefficient}
\alpha = 1 - 0.5*sum( sim(I(k)) / (n*\mu_s) - obs(J(k)) / (n*\mu_o) )
\beta = \mu_s/\mu_o
Traditional Kling-Gupta efficiencies (Gupta et al., 2009; Kling et al., 2012) range from -Inf to 1, and therefore KGEnp should do so. Essentially, the closer to 1, the more similar sim
and obs
are.
Knoben et al. (2019) showed that traditional Kling-Gupta (Gupta et al., 2009; Kling et al., 2012) values greater than -0.41 indicate that a model improves upon the mean flow benchmark, even if the model's KGE value is negative.
numeric with the non-parametric Kling-Gupta efficiency between sim
and obs
.
If sim
and obs
are matrices, the output value is a vector, with the non-parametric Kling-Gupta 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
Mauricio Zambrano-Bigiarini <mzb.devel@gmail.com>
Pool, S.; Vis, M.; Seibert, J. (2018). Evaluating model performance: towards a non-parametric variant of the Kling-Gupta efficiency. Hydrological Sciences Journal, 63(13-14), pp.1941-1953. doi:/10.1080/02626667.2018.1552002.
Garcia, F.; Folton, N.; Oudin, L. (2017). Which objective function to calibrate rainfall-runoff models for low-flow index simulations?. Hydrological sciences journal, 62(7), 1149-1166. doi:10.1080/02626667.2017.1308511.
Gupta, H. V.; Kling, H.; Yilmaz, K. K.; Martinez, G. F. (2009). Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. Journal of hydrology, 377(1-2), 80-91. doi:10.1016/j.jhydrol.2009.08.003. ISSN 0022-1694.
Kling, H.; Fuchs, M.; Paulin, M. (2012). Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios. Journal of Hydrology, 424, 264-277, doi:10.1016/j.jhydrol.2012.01.011.
Santos, L.; Thirel, G.; Perrin, C. (2018). Pitfalls in using log-transformed flows within the KGE criterion. doi:10.5194/hess-22-4583-2018.
Knoben, W.J.; Freer, J.E.; Woods, R.A. (2019). Inherent benchmark or not? Comparing Nash-Sutcliffe and Kling-Gupta efficiency scores. Hydrology and Earth System Sciences, 23(10), 4323-4331. doi:10.5194/hess-23-4323-2019.
KGE
, KGElf
, sKGE
, gof
, ggof
# Example1: basic ideal case
obs <- 1:10
sim <- 1:10
KGEnp(sim, obs)
obs <- 1:10
sim <- 2:11
KGEnp(sim, obs)
##################
# Example2: Looking at the difference between 'method=2009' and 'method=2012'
# Loading daily streamflows of the Ega River (Spain), from 1961 to 1970
data(EgaEnEstellaQts)
obs <- EgaEnEstellaQts
# Simulated daily time series, initially equal to twice the observed values
sim <- 2*obs
# KGE 2009
KGE(sim=sim, obs=obs, method="2009", out.type="full")
# KGE 2012
KGE(sim=sim, obs=obs, method="2012", out.type="full")
# KGEnp (Pool et al., 2018):
KGEnp(sim=sim, obs=obs)
##################
# Example3: KGEnp for simulated values equal to observations plus random noise
# on the first half of the observed values
# 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 <- obs
sim[1:1826] <- obs[1:1826] + rnorm(1826, mean=10)
# Computing the new 'KGEnp'
KGEnp(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 'KGEnp'
KGEnp(sim=sim, obs=obs)
##################
# Example 4: KGEnp 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.
KGEnp(sim=sim, obs=obs, fun=log)
# Verifying the previous value:
lsim <- log(sim)
lobs <- log(obs)
KGEnp(sim=lsim, obs=lobs)
##################
# Example 5: KGEnp 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
KGEnp(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)
KGEnp(sim=lsim, obs=lobs)
##################
# Example 6: KGEnp 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
KGEnp(sim=sim, obs=obs, fun=log, epsilon.type="otherValue", epsilon.value=eps)
# Verifying the previous value:
lsim <- log(sim+eps)
lobs <- log(obs+eps)
KGEnp(sim=lsim, obs=lobs)
##################
# Example 7: KGEnp 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
KGEnp(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)
KGEnp(sim=lsim, obs=lobs)
##################
# Example 8: KGEnp 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)}
KGEnp(sim=sim, obs=obs, fun=fun1)
# Verifying the previous value, with the epsilon value following Pushpalatha2012
sim1 <- sqrt(sim+1)
obs1 <- sqrt(obs+1)
KGEnp(sim=sim1, obs=obs1)
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