# tyearsS: Calculate Low-Flow Quantiles for given Return Periods In lfstat: Calculation of Low Flow Statistics for Daily Stream Flow Data

## Description

Fits an extreme value distribution using L-moments to the dry spells of a time series of discharges and subsequently estimates quantiles (the so called T-years event) for given return periods. In the presence of zero flow observations a mixed distribution is fitted.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```tyearsS(lfobj, event = 1/probs, probs = 0.01, pooling = NULL, dist = "wei", check = TRUE, zeta = NULL, plot = TRUE, col = 1, log = TRUE, legend = TRUE, rp.axis = "bottom", rp.lab = "Return period", freq.axis = TRUE, freq.lab = expression(paste("Frequency " *(italic(F)), " = Non-Exceedance Probability P ", (italic(X) <= italic(x)))), xlab = expression("Reduced variate, " * -log(-log(italic(F)))), ylab = "Quantile", variable = c("volume", "duration"), aggr = "max", hyearstart = hyear_start(lfobj), ...) ```

## Arguments

 `lfobj` An object of class lfobj or an object which can be coerced to class xts. Either with a single column or with a column named 'discharge'. `event` numeric vector specifying the return periods. E.g. `event = 100` will yield the 100 years extreme low flow event. `probs` Alternate way to specify the return period of the event. `pooling` a pooling function, see `pooling`. `dist` A character vector of distributions to fit. Basically all distributions provided by Hosking's `lmom-package` and their reversed counterparts can be chosen. `check` logical, should `check_distribution` get called? `zeta` numeric vector of length one for manually setting a lower bound. Only a few distributions allow for a lower bound, namely `'gpa'`, `'ln3'`, `'wak'` and `'wei'`. The default value of `NULL` results in not bounding the distribution, therefore the parameter `zeta` is estimated. `plot` logical. If `TRUE`, sample observations as well as estimated quantile functions are plotted. `col` numeric or character vector of length one or as long as `dist`, specifying the color used for plotting. `log` logical. If `TRUE` probabilities will be plotted on a double logarithmic scale. `legend` logical, should a legend be added to the plot? `rp.axis` vector of length one, specifying if and how an additional scale bar for the return periods is drawn. Possible choices are `'bottom'`, `'top'` and `'none'`. Alternatively, the position of the scale bar can be specified as an real number between 0 and 1, indicating the y-position of the legend. `rp.lab` character vector, text above the scale bar for return periods `freq.axis` logical, should an additional abscissa showing the probabilities be drawn on top of the plot? `freq.lab` character vector, text above the probability axis `xlab` character vector, a label for the x axis `ylab` character vector, a label for the y axis `variable` character vector of length one. Either `'v'` to calculate volumes or `'d'` for durations. `aggr` function like `max` or `sum` used for aggregating volumes or durations of a hydrological year. `hyearstart` vector of length one, providing the start of the hydrological year. This is evaluated by `water_year`. The default is, to retrieve the values stored in the attributes of the `lfobj`. `...` arguments passed on to `find_droughts`, e.g. `threshold`.

## Details

This function is vectorised over `dist` and `event`.

According to paragraph 7.4.2 of the WMO manual, special care has to be taken in the presence of zero flow observations. A cdf called G(x) is fitted to the non-zero values of the original time series

If a distribution is fitted which allows for finite lower bound (`zeta`), and `zeta` is estimated being negative, estimation is repeated constraining `zeta = 0`. If this behavior is not desired, the parameter `zeta` has to be set explicitly.

## Value

An object of class evfit, see `evfit`.

Gregor Laaha

## References

Gustard, A. & Demuth, S. (2009) (Eds) Manual on Low-flow Estimation and Prediction. Operational Hydrology Report No. 50, WMO-No. 1029, 136p.

`evfit`
 ```1 2 3 4 5 6``` ```data("ngaruroro") rp <- c(1.3, 3, 5, 35) sumD <- tyearsS(ngaruroro, event = rp, dist = "wei", variable = "d", aggr = sum) sumD summary(sumD) ```