hydroGOF (version 0.5-4)

gof: 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, ...)

# S3 method for default 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, start.month=1, digits=2, fun=NULL, ..., epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), epsilon.value=NA) # S3 method for 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, start.month=1, digits=2, fun=NULL, ..., epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), epsilon.value=NA) # S3 method for 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, start.month=1, digits=2, fun=NULL, ..., epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), epsilon.value=NA) # S3 method for 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, start.month=1, digits=2, fun=NULL, ..., epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), epsilon.value=NA)

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% <= nrms <= 100% )

PBIAS

Percent Bias

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 )

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 <= PI <= 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 )

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 )

sKGE

Split Kling-Gupta Efficiency between sim and obs
( -Inf <= sKGE <= 1 ). Only computed when both sim and obs are zoo objects

VE

Volumetric efficiency between sim and obs
( -Inf <= VE <= 1)

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

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

start.month

[OPTIONAL]. Only used for the computation of the split KGE (sKGE) 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.

Author

Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>

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 Base 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

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

ggof, me, mae, mse, rmse, ubRMSE, nrmse, pbias, rsr, rSD, NSE, mNSE, rNSE, wNSE, d, dr, md, rd, cp, rPearson, R2, br2, KGE, KGElf, KGEnp, sKGE, VE, rSpearman, pbiasfdc

Examples

Run this code
##################
# 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 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)

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",]

if (FALSE) {
# 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)
}

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