gof: Numerical Goodness-of-fit measures
In hydroGOF: Goodness-of-Fit Functions for Comparison of Simulated and Observed Hydrological Time Series
gof R Documentation
Numerical Goodness-of-fit measures
Description
Numerical goodness-of-fit measures between sim and obs, with treatment of missing values. Several performance indices for comparing two vectors, matrices or data.frames
Usage
gof(sim, obs, ...)
## Default S3 method:
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
j=1, lambda=0.95, norm="sd", s=c(1,1,1), method=c("2009", "2012", "2021"),
lQ.thr=0.6, hQ.thr=0.1, start.month=1, digits=2, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'matrix'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
j=1, lambda=0.95, norm="sd", s=c(1,1,1), method=c("2009", "2012", "2021"),
lQ.thr=0.6, hQ.thr=0.1, start.month=1, digits=2, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'data.frame'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
j=1, lambda=0.95, norm="sd", s=c(1,1,1), method=c("2009", "2012", "2021"),
lQ.thr=0.6, hQ.thr=0.1, start.month=1, digits=2, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'zoo'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
j=1, lambda=0.95, norm="sd", s=c(1,1,1), method=c("2009", "2012", "2021"),
lQ.thr=0.6, hQ.thr=0.1, start.month=1, digits=2, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
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.
do.spearman
logical. Indicates if the Spearman correlation has to be computed. The default is FALSE.
do.pbfdc
logical. Indicates if the Percent Bias in the Slope of the midsegment of the Flow Duration Curve (pbiasfdc) has to be computed. The default is FALSE.
j
argument passed to the mNSE and wsNSE functions.
lambda
argument passed to the wsNSE function.
norm
argument passed to the nrmse function
s
argument passed to the KGE, KGElf, sKGE and KGEkm functions.
method
argument passed to the KGE, KGElf, sKGE and KGEkm functions.
lQ.thr
[OPTIONAL]. Only used for the computation of the pbiasFDC % (with the pbiasfdc function) and the weighted seasonal Nash-Sutcliffe Efficiency (with the wsNSE function.
hQ.thr
[OPTIONAL]. Only used for the computation of the pbiasFDC % (with the pbiasfdc function), the high flow bias (HFB, with the HFB function) and the weighted seasonal Nash-Sutcliffe Efficiency (with the wsNSE function.
start.month
[OPTIONAL]. Only used for the computation of the split KGE (sKGE), annual peak flow bias (APFB) and high flow bias (HFB) when the (hydrological) year of interest is different from the calendar year.
numeric in [1:12] indicating the starting month of the (hydrological) year. Numeric values in [1, 12] represent months in [January, December]. By default start.month=1.
digits
decimal places used for rounding the goodness-of-fit indexes.
fun
function to be applied to sim and obs in order to obtain transformed values thereof before computing the all the goodness-of-fit functions.
The first argument MUST BE a numeric vector with any name (e.g., x), and additional arguments are passed using ....
...
arguments passed to fun, in addition to the mandatory first numeric vector.
epsilon.type
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 of epsilon.type are:
1) "none": sim and obs are used by FUN without the addition of any nummeric value.
2) "Pushpalatha2012": one hundredth (1/100) of the mean observed values is added to both sim and obs before applying FUN, as described in Pushpalatha et al. (2012).
3) "otherFactor": the numeric value defined in the epsilon.value argument is used to multiply the the mean observed values, instead of the one hundredth (1/100) described in Pushpalatha et al. (2012). The resulting value is then added to both sim and obs, before applying FUN.
4) "otherValue": the numeric value defined in the epsilon.value argument is directly added to both sim and obs, before applying FUN.
epsilon.value
-) when epsilon.type="otherValue" it represents the numeric value to be added to both sim and obs before applying fun.
-) when epsilon.type="otherFactor" it represents the numeric factor used to multiply the mean of the observed values, instead of the one hundredth (1/100) described in Pushpalatha et al. (2012). The resulting value is then added to both sim and obs before applying fun.
Value
The output of the gof function is a matrix with one column only, and the following rows:
ME
Mean Error
MAE
Mean Absolute Error
MSE
Mean Squared Error
RMSE
Root Mean Square Error
ubRMSE
Unbiased Root Mean Square Error
NRMSE
Normalized Root Mean Square Error ( -100% <= NRMSE <= 100% )
PBIAS
Percent Bias ( -Inf <= PBIAS <= Inf [%] )
RSR
Ratio of RMSE to the Standard Deviation of the Observations, RSR = rms / sd(obs). ( 0 <= RSR <= +Inf )
rSD
Ratio of Standard Deviations, rSD = sd(sim) / sd(obs)
NSE
Nash-Sutcliffe Efficiency ( -Inf <= NSE <= 1 )
mNSE
Modified Nash-Sutcliffe Efficiency ( -Inf <= mNSE <= 1 )
rNSE
Relative Nash-Sutcliffe Efficiency ( -Inf <= rNSE <= 1 )
wNSE
Weighted Nash-Sutcliffe Efficiency ( -Inf <= wNSE <= 1 )
wsNSE
Weighted Seasonal Nash-Sutcliffe Efficiency ( -Inf <= wsNSE <= 1 )
d
Index of Agreement ( 0 <= d <= 1 )
dr
Refined Index of Agreement ( -1 <= dr <= 1 )
md
Modified Index of Agreement ( 0 <= md <= 1 )
rd
Relative Index of Agreement ( 0 <= rd <= 1 )
cp
Persistence Index ( 0 <= cp <= 1 )
r
Pearson Correlation coefficient ( -1 <= r <= 1 )
R2
Coefficient of Determination ( 0 <= R2 <= 1 )
bR2
R2 multiplied by the coefficient of the regression line between sim and obs
( 0 <= bR2 <= 1 )
VE
Volumetric efficiency between sim and obs
( -Inf <= VE <= 1)
KGE
Kling-Gupta efficiency between sim and obs
( -Inf <= KGE <= 1 )
KGElf
Kling-Gupta Efficiency for low values between sim and obs
( -Inf <= KGElf <= 1 )
KGEnp
Non-parametric version of the Kling-Gupta Efficiency between sim and obs
( -Inf <= KGEnp <= 1 )
KGEkm
Knowable Moments Kling-Gupta Efficiency between sim and obs
( -Inf <= KGEnp <= 1 )
The following outputs are only produced when both sim and obs are zoo objects:
sKGE
Split Kling-Gupta Efficiency between sim and obs
( -Inf <= sKGE <= 1 ). Only computed when both sim and obs are zoo objects
APFB
Annual Peak Flow Bias ( 0 <= APFB <= Inf )
HBF
High Flow Bias ( 0 <= HFB <= Inf )
r.Spearman
Spearman Correlation coefficient ( -1 <= r.Spearman <= 1 ). Only computed when do.spearman=TRUE
pbiasfdc
PBIAS in the slope of the midsegment of the Flow Duration Curve
Note
obs and sim has to have the same length/dimension.
Missing values in obs and/or sim can be removed before the computations, depending on the value of na.rm.
Although r and r2 have been widely used for model evaluation, these statistics are over-sensitive to outliers and insensitive to additive and proportional differences between model predictions and measured data (Legates and McCabe, 1999)
Author(s)
Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>
References
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See Also
ggof, me, mae, mse, rmse, ubRMSE,
nrmse, pbias, rsr, rSD, NSE, mNSE,
rNSE, wNSE, wsNSE, d, dr, md,
rd, cp, rPearson, R2, br2, VE,
KGE, KGElf, KGEnp, , KGEkm, sKGE, APFB,
HFB, rSpearman, pbiasfdc
Examples
##################
# Example 1: basic ideal case
obs <- 1:10
sim <- 1:10
gof(sim, obs)
obs <- 1:10
sim <- 2:11
gof(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 'gof' for the "best" (unattainable) case
gof(sim=sim, obs=obs)
##################
# Example 3: gof 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 low 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)
gof(sim=sim, obs=obs)
##################
# Example 4: gof 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.
gof(sim=sim, obs=obs, fun=log)
# Verifying the previous value:
lsim <- log(sim)
lobs <- log(obs)
gof(sim=lsim, obs=lobs)
##################
# Example 5: gof 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
gof(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)
gof(sim=lsim, obs=lobs)
##################
# Example 6: gof 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
gof(sim=sim, obs=obs, fun=log, epsilon.type="otherValue", epsilon.value=eps)
# Verifying the previous value:
lsim <- log(sim+eps)
lobs <- log(obs+eps)
gof(sim=lsim, obs=lobs)
##################
# Example 7: gof 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
gof(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)
gof(sim=lsim, obs=lobs)
##################
# Example 8: gof 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)}
gof(sim=sim, obs=obs, fun=fun1)
# Verifying the previous value, with the epsilon value following Pushpalatha2012
sim1 <- sqrt(sim+1)
obs1 <- sqrt(obs+1)
gof(sim=sim1, obs=obs1)
# Storing a matrix object with all the GoFs:
g <- gof(sim, obs)
# Getting only the RMSE
g[4,1]
g["RMSE",]
## Not run:
# Writing all the GoFs into a TXT file
write.table(g, "GoFs.txt", col.names=FALSE, quote=FALSE)
# Getting the graphical representation of 'obs' and 'sim' along with the
# numeric goodness of fit
ggof(sim=sim, obs=obs)
## End(Not run)
hydroGOF documentation built on Nov. 4, 2024, 5:08 p.m.
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| gof | R Documentation |
Numerical Goodness-of-fit measures
Description
Numerical goodness-of-fit measures between sim and obs, with treatment of missing values. Several performance indices for comparing two vectors, matrices or data.frames
Usage
gof(sim, obs, ...)
## Default S3 method:
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
j=1, lambda=0.95, norm="sd", s=c(1,1,1), method=c("2009", "2012", "2021"),
lQ.thr=0.6, hQ.thr=0.1, start.month=1, digits=2, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'matrix'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
j=1, lambda=0.95, norm="sd", s=c(1,1,1), method=c("2009", "2012", "2021"),
lQ.thr=0.6, hQ.thr=0.1, start.month=1, digits=2, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'data.frame'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
j=1, lambda=0.95, norm="sd", s=c(1,1,1), method=c("2009", "2012", "2021"),
lQ.thr=0.6, hQ.thr=0.1, start.month=1, digits=2, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'zoo'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
j=1, lambda=0.95, norm="sd", s=c(1,1,1), method=c("2009", "2012", "2021"),
lQ.thr=0.6, hQ.thr=0.1, start.month=1, digits=2, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
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. |
do.spearman |
logical. Indicates if the Spearman correlation has to be computed. The default is FALSE. |
do.pbfdc |
logical. Indicates if the Percent Bias in the Slope of the midsegment of the Flow Duration Curve ( |
j |
argument passed to the |
lambda |
argument passed to the |
norm |
argument passed to the |
s |
argument passed to the |
method |
argument passed to the |
lQ.thr |
[OPTIONAL]. Only used for the computation of the |
hQ.thr |
[OPTIONAL]. Only used for the computation of the |
start.month |
[OPTIONAL]. Only used for the computation of the split KGE ( numeric in [1:12] indicating the starting month of the (hydrological) year. Numeric values in [1, 12] represent months in [January, December]. By default |
digits |
decimal places used for rounding the goodness-of-fit indexes. |
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 |
Value
The output of the gof function is a matrix with one column only, and the following rows:
ME |
Mean Error |
MAE |
Mean Absolute Error |
MSE |
Mean Squared Error |
RMSE |
Root Mean Square Error |
ubRMSE |
Unbiased Root Mean Square Error |
NRMSE |
Normalized Root Mean Square Error ( -100% <= NRMSE <= 100% ) |
PBIAS |
Percent Bias ( -Inf <= PBIAS <= Inf [%] ) |
RSR |
Ratio of RMSE to the Standard Deviation of the Observations, RSR = rms / sd(obs). ( 0 <= RSR <= +Inf ) |
rSD |
Ratio of Standard Deviations, rSD = sd(sim) / sd(obs) |
NSE |
Nash-Sutcliffe Efficiency ( -Inf <= NSE <= 1 ) |
mNSE |
Modified Nash-Sutcliffe Efficiency ( -Inf <= mNSE <= 1 ) |
rNSE |
Relative Nash-Sutcliffe Efficiency ( -Inf <= rNSE <= 1 ) |
wNSE |
Weighted Nash-Sutcliffe Efficiency ( -Inf <= wNSE <= 1 ) |
wsNSE |
Weighted Seasonal Nash-Sutcliffe Efficiency ( -Inf <= wsNSE <= 1 ) |
d |
Index of Agreement ( 0 <= d <= 1 ) |
dr |
Refined Index of Agreement ( -1 <= dr <= 1 ) |
md |
Modified Index of Agreement ( 0 <= md <= 1 ) |
rd |
Relative Index of Agreement ( 0 <= rd <= 1 ) |
cp |
Persistence Index ( 0 <= cp <= 1 ) |
r |
Pearson Correlation coefficient ( -1 <= r <= 1 ) |
R2 |
Coefficient of Determination ( 0 <= R2 <= 1 ) |
bR2 |
R2 multiplied by the coefficient of the regression line between |
VE |
Volumetric efficiency between |
KGE |
Kling-Gupta efficiency between |
KGElf |
Kling-Gupta Efficiency for low values between |
KGEnp |
Non-parametric version of the Kling-Gupta Efficiency between |
KGEkm |
Knowable Moments Kling-Gupta Efficiency between |
The following outputs are only produced when both sim and obs are zoo objects:
sKGE |
Split Kling-Gupta Efficiency between |
APFB |
Annual Peak Flow Bias ( 0 <= APFB <= Inf ) |
HBF |
High Flow Bias ( 0 <= HFB <= Inf ) |
r.Spearman |
Spearman Correlation coefficient ( -1 <= r.Spearman <= 1 ). Only computed when |
pbiasfdc |
PBIAS in the slope of the midsegment of the Flow Duration Curve |
Note
obs and sim has to have the same length/dimension.
Missing values in obs and/or sim can be removed before the computations, depending on the value of na.rm.
Although r and r2 have been widely used for model evaluation, these statistics are over-sensitive to outliers and insensitive to additive and proportional differences between model predictions and measured data (Legates and McCabe, 1999)
Author(s)
Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>
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See Also
ggof, me, mae, mse, rmse, ubRMSE,
nrmse, pbias, rsr, rSD, NSE, mNSE,
rNSE, wNSE, wsNSE, d, dr, md,
rd, cp, rPearson, R2, br2, VE,
KGE, KGElf, KGEnp, , KGEkm, sKGE, APFB,
HFB, rSpearman, pbiasfdc
Examples
##################
# Example 1: basic ideal case
obs <- 1:10
sim <- 1:10
gof(sim, obs)
obs <- 1:10
sim <- 2:11
gof(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 'gof' for the "best" (unattainable) case
gof(sim=sim, obs=obs)
##################
# Example 3: gof 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 low 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)
gof(sim=sim, obs=obs)
##################
# Example 4: gof 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.
gof(sim=sim, obs=obs, fun=log)
# Verifying the previous value:
lsim <- log(sim)
lobs <- log(obs)
gof(sim=lsim, obs=lobs)
##################
# Example 5: gof 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
gof(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)
gof(sim=lsim, obs=lobs)
##################
# Example 6: gof 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
gof(sim=sim, obs=obs, fun=log, epsilon.type="otherValue", epsilon.value=eps)
# Verifying the previous value:
lsim <- log(sim+eps)
lobs <- log(obs+eps)
gof(sim=lsim, obs=lobs)
##################
# Example 7: gof 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
gof(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)
gof(sim=lsim, obs=lobs)
##################
# Example 8: gof 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)}
gof(sim=sim, obs=obs, fun=fun1)
# Verifying the previous value, with the epsilon value following Pushpalatha2012
sim1 <- sqrt(sim+1)
obs1 <- sqrt(obs+1)
gof(sim=sim1, obs=obs1)
# Storing a matrix object with all the GoFs:
g <- gof(sim, obs)
# Getting only the RMSE
g[4,1]
g["RMSE",]
## Not run:
# Writing all the GoFs into a TXT file
write.table(g, "GoFs.txt", col.names=FALSE, quote=FALSE)
# Getting the graphical representation of 'obs' and 'sim' along with the
# numeric goodness of fit
ggof(sim=sim, obs=obs)
## End(Not run)
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