gof: Numerical Goodness-of-fit measures

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

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, norm="sd", s=c(1,1,1), method=c("2009", "2012"), lQ.thr=0.7, 
             hQ.thr=0.2, digits=2,...)
## S3 method for class 'matrix'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
             j=1, norm="sd", s=c(1,1,1), method=c("2009", "2012"), lQ.thr=0.7, 
             hQ.thr=0.2, digits=2,...)
## S3 method for class 'data.frame'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
             j=1, norm="sd", s=c(1,1,1), method=c("2009", "2012"), lQ.thr=0.7, 
             hQ.thr=0.2, digits=2,...)
## S3 method for class 'zoo'
gof(sim, obs, na.rm=TRUE, do.spearman=FALSE, do.pbfdc=FALSE,
             j=1, norm="sd", s=c(1,1,1), method=c("2009", "2012"), lQ.thr=0.7, 
             hQ.thr=0.2, digits=2,...)                                       

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 function
norm	argument passed to the nrmse function
s	argument passed to the KGE function
method	argument passed to the KGE function
lQ.thr	argument passed to the (optional) pbiasfdc function
hQ.thr	argument passed to the (optional) pbiasfdc function
digits	decimal places used for rounding the goodness-of-fit indexes.
...	further arguments passed to or from other methods.

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
nrmse	Normalized Root Mean Square Error ( -100% <= nrms <= 100% )
PBIAS	Percent Bias
pbiasfdc	PBIAS in the slope of the midsegment of the Flow Duration Curve
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
rNSE	Relative Nash-Sutcliffe Efficiency
d	Index of Agreement ( 0 <= d <= 1 )
d1	Modified Index of Agreement
rd	Relative Index of Agreement
cp	Persistence Index ( 0 <= PI <= 1 )
r	Pearson Correlation coefficient ( -1 <= r <= 1 )
r.Spearman	Spearman Correlation coefficient ( -1 <= r.Spearman <= 1 )
R2	Coefficient of Determination ( 0 <= R2 <= 1 ). Gives the proportion of the variance of one variable that is predictable from the other variable
bR2	R2 multiplied by the coefficient of the regression line between sim and obs ( 0 <= bR2 <= 1 )
KGE	Kling-Gupta efficiency between sim and obs ( 0 <= KGE <= 1 )
VE	Volumetric efficiency between sim and obs ( -Inf <= VE <= 1)

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 <[e-mail]>

References

Legates, D. R., and G. J. McCabe Jr. (1999), Evaluating the Use of "Goodness-of-Fit" Measures in Hydrologic and Hydroclimatic Model Validation, Water Resour. Res., 35(1), 233–241

Krause P., Boyle D.P., and B\"ase F., Comparison of different efficiency criteria for hydrological model assessment, Advances in Geosciences 5 (2005), pp. 89–97

Moriasi, D.N., Arnold, J.G., Van Liew, M.W., Bingner, R.L., Harmel, R.D., Veith, T.L. 2007. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations
Transactions of the ASABE. 50(3):885-900

Boyle, D. P., H. V. Gupta, and S. Sorooshian (2000), Toward Improved Calibration of Hydrologic Models: Combining the Strengths of Manual and Automatic Methods, Water Resour. Res., 36(12), 3663–3674

Kitanidis, P. K., and R. L. Bras (1980), Real-Time Forecasting With a Conceptual Hydrologic Model 2. Applications and Results, Water Resour. Res., 16(6), 1034–1044

J.E. Nash and J.V. Sutcliffe, River flow forecasting through conceptual models. Part 1: a discussion of principles, J. Hydrol. 10 (1970), pp. 282–290

Yapo P. O., Gupta H. V., Sorooshian S., 1996. Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data. Journal of Hydrology. v181 i1-4. 23–48

Yilmaz, K. K., H. V. Gupta, and T. Wagener (2008), A process-based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model, Water Resour. Res., 44, W09417, doi:10.1029/2007WR006716

Hoshin V. Gupta, Harald Kling, Koray K. Yilmaz, Guillermo F. Martinez. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. Journal of Hydrology, Volume 377, Issues 1-2, 20 October 2009, Pages 80-91. DOI: 10.1016/j.jhydrol.2009.08.003. ISSN 0022-1694

Criss, R. E. and Winston, W. E. (2008), Do Nash values have value? Discussion and alternate proposals. Hydrological Processes, 22: 2723-2725. doi: 10.1002/hyp.7072

See Also

me, mae, rmse, nrmse, pbias, pbiasfdc, rSD, NSE, mNSE, rNSE, d, md, rd, cp, br2, KGE, VE

Examples

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

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

##################
# 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 

# Getting the numeric goodness of fit for the "best" (unattainable) case
gof(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)

# Getting the new numeric goodness of fit
gof(sim=sim, obs=obs)

# 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 March 14, 2020, 1:07 a.m.