# fdcu: Flow Duration Curve with uncertainty bounds. In hydroTSM: Time Series Management and Analysis for Hydrological Modelling

 fdcu R Documentation

## Flow Duration Curve with uncertainty bounds.

### Description

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, ...)

## Default S3 method:
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 class '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 class '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, ...)

``````

### 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)

### 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.

### Author(s)

Mauricio Zambrano-Bigiarini, mzb.devel@gmail

### 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.

`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)
``````

hydroTSM documentation built on May 29, 2024, 8:36 a.m.