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Flow Duration Curve

fdc.Rd

Computes and plots the Flow Duration Curve (FDC) corresponding to a given time series of streamflow discharges.

Usage

fdc(x, ...)

# S3 method for default
fdc(x,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="black", 
    pch=1, lwd=1, lty=1, cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL, leg.cex=1, 
    leg.pos="topright", verbose= TRUE, thr.shw=TRUE, new=TRUE, ...)

# S3 method for matrix
fdc(x, 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=palette("default")[1:ncol(x)], pch=1:ncol(x), lwd=rep(1, ncol(x)), 
    lty=1:ncol(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL, 
    leg.cex=1, leg.pos="topright",verbose=TRUE, thr.shw=TRUE, new=TRUE, ...)

# S3 method for data.frame
fdc(x, 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=palette("default")[1:ncol(x)], pch=1:ncol(x), lwd=rep(1, ncol(x)), 
     lty=1:ncol(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL, 
     leg.cex=1, leg.pos="topright", verbose=TRUE, thr.shw=TRUE, new=TRUE, ...)
     
# S3 method for zoo
fdc(x, 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=palette("default")[1:NCOL(x)], pch=1:NCOL(x), lwd=rep(1, NCOL(x)), 
     lty=1:NCOL(x), cex=0.4, cex.axis=1.2, cex.lab=1.2, leg.txt=NULL, 
     leg.cex=1, leg.pos="topright", verbose=TRUE, thr.shw=TRUE, 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.

lQ.thr

numeric, low-flow 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 should be deemed as low flows. Default value is 0.7.

hQ.thr

numeric, high-flow 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 should br deemed as high flows. Default value is 0.2.

plot

logical. Indicates if the flow duration curve should be plotted or not. Default value is TRUE.

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

A title for the x axis. See plot.

ylab

A title for the y axis. See plot.

ylim

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

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

The colors to be used 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. See plot.default.

pch

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

lwd

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

lty

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

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.

verbose

logical; if TRUE, progress messages are printed (when x is a matrix or data.frame).

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.

new

logical, if TRUE (default), a new plotting window is created.

...

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

Value

numeric, matrix or data.frame whose columns contains the % of time each one of the streamflow magnitudes given as input was equalled or exceeded. The resulting values have to be multiplied by 100 to get a percentage.

When plot is TRUE (default), the resulting flow duration curve is plotted in a new window.

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

See also

fdcu

Examples

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

## Daily Flow Duration Curve
fdc(OcaEnOnaQts)

###################
# Getting the streamflow values corresponding to 5 and 95% of time equalled or 
# exceeded (and also the first streamflow value in 'x' just for verification)
x  <- OcaEnOnaQts

# First streamflow value (x1=42.1 m3/s)
x1 <- x[1]

# Daily FDC for 'x'
y <- fdc(x)

# value of the FDC for x1 (y1=0.002739726)
y1 <- y[1]

# Performing cubic (or Hermite) spline interpolation of 'x' and 'y'
f <- splinefun(y,x)

# Getting the (known) streamflow value for 'y1'
f(y1) # 42.1 m3/s, equal to the known 'x1'

# Streamflow values corresponding to 5 and 95% of time equalled or exceeded
f(c(.05, .95))

###################
## Getting 
data(OcaEnOnaQts)

## Daily Flow Duration Curve
fdc(OcaEnOnaQts)