| gof {hydroGOF} | 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 |
|
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)