Skip to contents

Flow Duration Curve with uncertainty bounds.

fdcu.Rd

Computes and plots the Flow Duration Curve (FDC) for the streamflows given by x and for two uncertainty bounds, with the possibility of plotting an additional FDC representing simulated streamflows for x, in order to compare them.

Usage

fdcu(x, lband, uband, ...)

# S3 method for default
fdcu(x, lband, uband, sim=NULL, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y", 
     main="Flow Duration Curve", xlab="% Time flow equalled or exceeded", 
     ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05), 
     col=c("black", "red"), pch=c(1, 15), lwd=c(1, 0.8), lty=c(1, 3), cex=0.2, 
     cex.axis=1.2, cex.lab=1.2, leg.txt= c("Qobs", "Qsim", "95PPU"), 
     leg.cex=1, leg.pos="auto", verbose= TRUE, thr.shw=TRUE, border=NA, 
     bands.col="lightcyan", bands.density=NULL, bands.angle=45, new=TRUE, ...)

# S3 method for matrix
fdcu(x, lband, uband, sim=NULL, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y", 
     main="Flow Duration Curve", xlab="% Time flow equalled or exceeded", 
     ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05), 
     col=matrix(c(rep("black", ncol(x)), 
     palette("default")[2:(ncol(x)+1)]), byrow=FALSE, ncol=2), 
     pch=matrix(rep(c(1, 15), ncol(x)), byrow=TRUE, ncol=2),
     lwd=matrix(rep(c(1, 0.8), ncol(x)), byrow=TRUE, ncol=2),
     lty=matrix(rep(c(1, 3), ncol(x)), byrow=TRUE, ncol=2),                        
     cex=rep(0.1, ncol(x)), cex.axis=1.2, cex.lab=1.2, 
     leg.txt=c("OBS", colnames(x), "95PPU"),  leg.cex=1, leg.pos="auto", 
     verbose= TRUE,  thr.shw=TRUE, border=rep(NA, ncol(x)), 
     bands.col=rep("lightcyan", ncol(x)), bands.density=rep(NULL, ncol(x)), 
     bands.angle=rep(45, ncol(x)), new=TRUE, ...)

# S3 method for data.frame
fdcu(x, lband, uband, sim=NULL, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y", 
     main="Flow Duration Curve", xlab="% Time flow equalled or exceeded", 
     ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05), 
     col=matrix(c(rep("black", ncol(x)), 
     palette("default")[2:(ncol(x)+1)]), byrow=FALSE, ncol=2),
     pch=matrix(rep(c(1, 15), ncol(x)), byrow=TRUE, ncol=2),
     lwd=matrix(rep(c(1, 0.8), ncol(x)), byrow=TRUE, ncol=2),
     lty=matrix(rep(c(1, 3), ncol(x)), byrow=TRUE, ncol=2),                        
     cex=rep(0.1, ncol(x)), cex.axis=1.2, cex.lab=1.2,
     leg.txt=c("OBS", colnames(x), "95PPU"), leg.cex=1, leg.pos="auto", 
     verbose= TRUE, thr.shw=TRUE, border=rep(NA, ncol(x)), 
     bands.col=rep("lightcyan", ncol(x)), bands.density=rep(NULL, ncol(x)), 
     bands.angle=rep(45, ncol(x)), new=TRUE, ...)

<!-- %% \method{fdcu}{zoo}(x, lband, uband, sim=NULL, lQ.thr=0.7, hQ.thr=0.2, plot=TRUE, log="y",  -->
<!-- %%      main="Flow Duration Curve", xlab="\% Time flow equalled or exceeded",  -->
<!-- %%      ylab="Q, [m3/s]", ylim, yat=c(0.01, 0.1, 1), xat=c(0.01, 0.025, 0.05),  -->
<!-- %%      col=matrix(c(rep("black", NCOL(x)),  -->
<!-- %%      palette("default")[2:(NCOL(x)+1)]), byrow=FALSE, ncol=2), -->
<!-- %%      pch=matrix(rep(c(1, 15), NCOL(x)), byrow=TRUE, ncol=2), -->
<!-- %%      lwd=matrix(rep(c(1, 0.8), NCOL(x)), byrow=TRUE, ncol=2), -->
<!-- %%      lty=matrix(rep(c(1, 3), NCOL(x)), byrow=TRUE, ncol=2),                         -->
<!-- %%      cex=rep(0.1, NCOL(x)), cex.axis=1.2, cex.lab=1.2, -->
<!-- %%      leg.txt=c("OBS", colnames(x), "95PPU"), leg.cex=1, leg.pos="auto",  -->
<!-- %%      verbose= TRUE, thr.shw=TRUE, border=rep(NA, NCOL(x)),  -->
<!-- %%      bands.col=rep("lightcyan", NCOL(x)), bands.density=rep(NULL, NCOL(x)),  -->
<!-- %%      bands.angle=rep(45, NCOL(x)), new=TRUE, ...) -->

Arguments

x

numeric, zoo, data.frame or matrix object with the observed streamflows for which the flow duration curve have to be computed.
Measurements at several gauging stations can be stored in a data.frame of matrix object, and in that case, each column of x represent the time series measured in each gauging station, and the column names of x have to correspond to the ID of each station (starting by a letter). When x is a matrix or data.frame, the flow duration curve is computed for each column.

lband

numeric, zoo, data.frame or matrix object with the streamflows representing the the lower uncertainty bound of x, for which the flow duration curve have to be computed.
Measurements at several gauging stations can be stored in a data.frame of matrix object. When lband is a matrix or data.frame, the flow duration curve is computed for each column.

uband

numeric, zoo, data.frame or matrix object with the streamflows representing the the upper uncertainty bound of x, for which the flow duration curve have to be computed.
Measurements at several gauging stations can be stored in a data.frame of matrix object. When uband is a matrix or data.frame, the flow duration curve is computed for each column.

sim

OPTIONAL.
numeric, zoo, data.frame or matrix object with the streamflows simulated for x, for which the flow duration curve have to be computed.
Measurements at several gauging stations can be stored in a data.frame of matrix object. When sim is a matrix or data.frame, the flow duration curve is computed for each column.

lQ.thr

numeric, low flows separation threshold. If this value is different from 'NA', a vertical line is drawn in this value, and all the values to the left of it are deemed low flows.

hQ.thr

numeric, high flows separation threshold. If this value is different from 'NA', a vertical line is drawn in this value, and all the values to the right of it are deemed high flows

plot

logical. Indicates if the flow duration curve should be plotted or not.

log

character, indicates which axis has to be plotted with a logarithmic scale. Default value is y.

main

See plot. An overall title for the plot: see title.

xlab

See plot. A title for the x axis: see title.

ylab

See plot. A title for the y axis: see title.

ylim

See plot.default. The y limits of the plot.

yat

Only used when log="y".
numeric, with points at which tick-marks will try to be drawn in the Y axis, in addition to the defaults computed by R. See the at argument in Axis.

xat

Only used when log="x".
numeric, with points at which tick-marks will try to be drawn in the x axis, in addition to the defaults computed by R. See the at argument in Axis.

col

See plot.default. The colors for lines and points. Multiple colors can be specified so that each point can be given its own color. If there are fewer colors than points they are recycled in the standard fashion. Lines will all be plotted in the first colour specified.

pch

See plot.default. A vector of plotting characters or symbols: see points.

lwd

See plot.default. The line width, see par.

lty

See plot.default. The line type, see par.

cex

See plot.default. A numerical vector giving the amount by which plotting characters and symbols should be scaled relative to the default. This works as a multiple of par("cex"). 'NULL' and 'NA' are equivalent to '1.0'. Note that this does not affect annotation.

cex.axis

magnification of axis annotation relative to 'cex'.

cex.lab

Magnification to be used for x and y labels relative to the current setting of 'cex'. See '?par'.

leg.txt

vector with the names that have to be used for each column of x.

leg.cex

numeric, indicating the character expansion factor for the legend, *relative* to current par("cex"). Default value = 1

leg.pos

keyword to be used to position the legend. One of the list ‘"bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right", "center"’. This places the legend on the inside of the plot frame at the given location. See legend.
When leg.pos="auto", the legend provided by leg.txt is located on the ‘bottomleft’ when log="y" and on the ‘topright’ otherwise

verbose

logical; if TRUE, progress messages are printed

thr.shw

logical, indicating if the streamflow values corresponding to the user-defined thresholds lQ.thr and hQ.thr have to be shown in the plot.
When leg.pos="auto", the legend with the threshold values is located on the ‘topright’ when log="y" and on the ‘bottomleft’ otherwise

border

See polygon. The color to draw the border of the polygon with the uncertainty bounds. The default, 'NA', means to omit borders.

bands.col

See polygon. The color for filling the polygon. The default, 'NA', is to leave polygons unfilled, unless bands.density is specified. If bands.density is specified with a positive value this gives the color of the shading lines.

bands.density

See polygon. The density of shading lines for the polygon with the uncertainty bounds, in lines per inch. The default value of 'NULL' means that no shading lines are drawn. A zero value of bands.density means no shading nor filling whereas negative values (and 'NA') suppress shading (and so allow color filling).

bands.angle

See polygon. The slope of shading lines for the polygon with the uncertainty bounds, given as an angle in degrees (counter-clockwise).

new

logical, if TRUE, a new plotting window is created.

...

further arguments passed to or from other methods (to the plotting functions)

References

Vogel, R., and N. M. Fennessey (1994), Flow duration curves I: A new interpretation and confidence intervals, ASCE, Journal of Water Resources Planning and Management, 120(4).

Vogel, R., and N. Fennessey (1995), Flow duration curves II: A review of applications in water resources planning, Water Resources Bulletin, 31(6), 1029-1039, doi:10.1111/j.1752-1688.1995.tb03419.x.

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.

Author

Mauricio Zambrano-Bigiarini, mzb.devel@gmail

Note

If you do not want to use logarithmic scale for the streamflow axis, you can do it by passing the log=" " to the ... argument.

See also

fdc

Examples

## Loading daily streamflows at the station Oca en Ona (Ebro River basin, Spain) ##
data(OcaEnOnaQts)
q <- OcaEnOnaQts

# Creating a fictitious lower uncertainty band
lband <- q - min(q, na.rm=TRUE)

# Giving a fictitious upper uncertainty band
uband <- q + mean(q, na.rm=TRUE)

# Plotting the flow duration curve corresponding to 'q', with two uncertainty bounds
fdcu(q, lband, uband)