Graphical Goodness of Fit

Graphical comparison between two vectors (numeric, ts or zoo), with several numerical goodness of fit printed as a legend.
Missing values in observed and/or simulated values can removed before the computations.

Usage

ggof(sim, obs, na.rm = TRUE, dates, date.fmt = "%Y-%m-%d", 
     pt.style = "ts", ftype = "o",  FUN, 
     stype="default", season.names=c("Winter", "Spring", "Summer", "Autumn"),
     gof.leg = TRUE,  digits=2, 
     gofs=c( "ME",  "MAE",  "RMSE", "NRMSE", "PBIAS", "NSE",   "d",    
             "dr",    "r",    "R2",   "KGE",  "LCE", "JDKGE", "VE"),
     legend, leg.cex=1,
     tick.tstep = "auto", lab.tstep = "auto", lab.fmt=NULL,
     cal.ini=NA, val.ini=NA,
     main, xlab = "Time", ylab=c("Q, [m3/s]"),  
     col = c("blue", "black"), 
     cex = c(0.5, 0.5), cex.axis=1.2, cex.lab=1.2,
     lwd = c(1, 1), lty = c(1, 3), pch = c(1, 9), ...)

Arguments

sim: numeric or zoo object with with simulated values
obs: numeric or zoo object 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.
dates: character, factor, Date or POSIXct object indicating how to obtain the dates for the corresponding values in the sim and obs time series
If dates is a character or factor, it is converted into Date/POSIXct class, using the date format specified by date.fmt
date.fmt: OPTIONAL. character indicating the format in which the dates are stored in dates, cal.ini and val.ini. See format in as.Date. Default value is %Y-%m-%d
ONLY required when class(dates)=="character" or class(dates)=="factor" or when cal.ini and/or val.ini is provided.
pt.style: Character indicating if the 2 ts have to be plotted as lines or bars. When ftype is NOT o, it only applies to the annual values. Valid values are:
-) ts : (default) each ts is plotted as a lines along the 'x' axis
-) bar: both series are plotted as barplots.
ftype: Character indicating how many plots are desired by the user. Valid values are:
-) o : only the original sim and obs time series are plotted
-) dm : it assumes that sim and obs are daily time series and Daily and Monthly values are plotted
-) ma : it assumes that sim and obs are daily or monthly time series and Monthly and Annual values are plotted
-) dma : it assumes that sim and obs are daily time series and Daily, Monthly and Annual values are plotted
-) seasonal: seasonal values are plotted. See stype and season.names
FUN: OPTIONAL, ONLY required when ftype is in c('dm', 'ma', 'dma', 'seasonal'). Function that have to be applied for transforming teh original ts into monthly, annual or seasonal time step (e.g., for precipitation FUN MUST be sum, for temperature and flow time series, FUN MUST be mean)
stype: OPTIONAL, only used when ftype=seasonal.
character, indicating whath weather seasons will be used for computing the output. Possible values are:
-) default => "winter"= DJF = Dec, Jan, Feb; "spring"= MAM = Mar, Apr, May; "summer"= JJA = Jun, Jul, Aug; "autumn"= SON = Sep, Oct, Nov
-) FrenchPolynesia => "winter"= DJFM = Dec, Jan, Feb, Mar; "spring"= AM = Apr, May; "summer"= JJAS = Jun, Jul, Aug, Sep; "autumn"= ON = Oct, Nov
season.names: OPTIONAL, only used when ftype=seasonal.
character of length 4 indicating the names of each one of the weather seasons defined by stype.These names are only used for plotting purposes
gof.leg: logical, indicating if several numerical goodness of fit have to be computed between sim and obs, and plotted as a legend on the graph. If leg.gof=TRUE, then x is considered as observed and y as simulated values (for some gof functions this is important).
digits: OPTIONAL, only used when leg.gof=TRUE. Numeric, representing the decimal places used for rounding the goodness-of-fit indexes.
gofs: character, with one or more strings indicating the goodness-of-fit measures to be shown in the legend of the plot when gof.leg=TRUE.
Possible values when ftype!='seasonal' are in c("ME", "MAE", "MSE", "RMSE", "NRMSE", "PBIAS", "RSR", "rSD", "NSE", "mNSE", "rNSE", "d", "md", "rd", "cp", "r", "R2", "bR2", "KGE", "VE")
Possible values when ftype='seasonal' are in c("ME", "RMSE", "PBIAS", "RSR", "NSE", "d", "R2", "KGE", "VE")
legend: character of length 2 to appear in the legend.
leg.cex: OPTIONAL. ONLY used when leg.gof=TRUE. Character expansion factor for drawing the legend, *relative* to current 'par("cex")'. Used for text, and provides the default for 'pt.cex' and 'title.cex'. Default value = 1
tick.tstep: character, indicating the time step that have to be used for putting the ticks on the time axis. Valid values are: auto, years, months,weeks, days, hours, minutes, seconds.
lab.tstep: character, indicating the time step that have to be used for putting the labels on the time axis. Valid values are: auto, years, months,weeks, days, hours, minutes, seconds.
lab.fmt: Character indicating the format to be used for the label of the axis. See lab.fmt in drawTimeAxis.
cal.ini: OPTIONAL. Character, indicating the date in which the calibration period started.
When cal.ini is provided, all the values in obs and sim with dates previous to cal.ini are SKIPPED from the computation of the goodness-of-fit measures (when gof.leg=TRUE), but their values are still plotted, in order to examine if the warming up period was too short, acceptable or too long for the chosen calibration period. In addition, a vertical red line in drawn at this date.
val.ini: OPTIONAL. Character, the date in which the validation period started.
ONLY used for drawing a vertical red line at this date.
main: character representing the main title of the plot.
xlab: label for the 'x' axis.
ylab: label for the 'y' axis.
col: character, representing the colors of sim and obs
cex: numeric, representing the values controlling the size of text and symbols of 'x' and 'y' with respect to the default
cex.axis: numeric, representing the magnification to be used for the axis annotation relative to 'cex'. See par.
cex.lab: numeric, representing the magnification to be used for x and y labels relative to the current setting of 'cex'. See par.
lwd: vector with the line width of sim and obs
lty: numeric with the line type of sim and obs
pch: numeric with the type of symbol for x and y. (e.g., 1: white circle; 9: white rhombus with a cross inside)
...: further arguments passed to or from other methods.

Details

Plots observed and simulated values in the same graph.

If gof.leg=TRUE, it computes the numerical values of:
'me', 'mae', 'rmse', 'nrmse', 'PBIAS', 'RSR, 'rSD', 'NSE', 'mNSE', 'rNSE', 'd', 'md, 'rd', 'cp', 'r', 'r.Spearman', 'R2', 'bR2', 'KGE', 'VE'

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

References

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Author

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

Examples

obs <- 1:10
sim <- 2:11

if (FALSE) { # \dontrun{
ggof(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)
#>         [,1]
#> ME         0
#> MAE        0
#> MSE        0
#> RMSE       0
#> ubRMSE     0
#> NRMSE %    0
#> PBIAS %    0
#> RSR        0
#> rSD        1
#> NSE        1
#> mNSE       1
#> rNSE       1
#> wNSE       1
#> wsNSE      1
#> d          1
#> dr         1
#> md         1
#> rd         1
#> cp         1
#> r          1
#> R2         1
#> bR2        1
#> VE         1
#> KGE        1
#> KGElf      1
#> KGEnp      1
#> KGEkm      1
#> JDKGE      1
#> LME        1
#> LCE        1
#> sKGE       1
#> APFB       0
#> HFB        0

# 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 measures
gof(sim=sim, obs=obs)
#>          [,1]
#> ME       5.47
#> MAE      5.47
#> MSE     55.21
#> RMSE     7.43
#> ubRMSE   5.03
#> NRMSE % 37.10
#> PBIAS % 34.60
#> RSR      0.37
#> rSD      1.04
#> NSE      0.86
#> mNSE     0.57
#> rNSE    -0.57
#> wNSE     0.97
#> wsNSE    0.72
#> d        0.97
#> dr       0.78
#> md       0.78
#> rd       0.63
#> cp       0.42
#> r        0.97
#> R2       0.86
#> bR2      0.76
#> VE       0.65
#> KGE      0.65
#> KGElf    0.49
#> KGEnp    0.61
#> KGEkm    0.63
#> JDKGE    0.64
#> LME      0.65
#> LCE      0.65
#> sKGE     0.63
#> APFB     0.03
#> HFB      0.12

# Getting the graphical representation of 'obs' and 'sim' along with the numeric 
# goodness-of-fit measures for the daily and monthly time series 
if (FALSE) { # \dontrun{
ggof(sim=sim, obs=obs, ftype="dm", FUN=mean)
} # }

# Getting the graphical representation of 'obs' and 'sim' along with some numeric 
# goodness-of-fit measures for the seasonal time series 
if (FALSE) { # \dontrun{
ggof(sim=sim, obs=obs, ftype="seasonal", FUN=mean)
} # }

# Computing the daily residuals 
# even if this is a dummy example, it is enough for illustrating the capability
r <- sim-obs

# Summarizing and plotting the residuals
if (FALSE) { # \dontrun{
library(hydroTSM)

# summary
smry(r) 

# daily, monthly and annual plots, boxplots and histograms
hydroplot(r, FUN=mean)

# seasonal plots and boxplots
hydroplot(r, FUN=mean, pfreq="seasonal")
} # }