fasstr, the Flow Analysis Summary Statistics Tool for R, is a set of R functions to tidy, summarize, analyze, trend, and visualize streamflow data. This package summarizes continuous daily mean streamflow data into various daily, monthly, annual, and long-term statistics, completes trending and frequency analyses, with outputs in both table and plot formats.
This vignette is a guide on the various volume frequency analysis functions found in
fasstr to plot frequency data and determine frequency quantile statistics using the Log-Pearson Type III or Weibull distributions. In this vignette you’ll learn what functions to use for specific analyses, arguments to customize analyses, and what results and outputs are produced.
Computing a frequency analysis with
fasstr allows for options and customization of both the inputs and outputs. These functions plot probabilities of flow data using chosen plotting options and calculates frequency quantiles (ex. 7Q10) based on fitting data to either Log-Pearson Type III or Weibull distributions. There are four functions within
fasstr that conduct frequency analyses:
compute_annual_frequencies()- conduct an annual frequency analysis from daily streamflow data (analysis calculates minimums/maximums and subsequently ranks that data).
compute_frequency_quantile()- conduct an annual frequency analysis from daily streamflow data and return a specific quantile based on a duration (rolling mean days) and return period (analysis calculates minimums/maximums and subsequently ranks that data).
compute_HYDAT_peak_frequencies()- conduct an annual frequency analysis from instantaneous peak data (minimum or maximum) for stations from a HYDAT database.
compute_frequency_analysis()- conduct a frequency analysis with custom data (analysis ranks data provided; is the main frequency analysis function used within each of the frequency analysis functions).
With the exception of the
compute_frequency_quantile() function which only produces a quantile value, the frequency functions produce five outputs contained within a list. See the sections below for more information on each output and options. The five outputs include the following:
compute_frequency_analysis(), computed extremes in
compute_annual_frequencies(), or HYDAT extracted extremes in
fitdistplus::fitdistobject that contains information on the computed curve based on the selected distribution (Pearson Type III (or log of) or weibull) and fitting methods (methods of moments or maximum likelihood estimation).
To determine frequencies of annual daily minimum or daily maximum flows, or of any duration days, from a daily streamflow data set, the
compute_frequency_quantile() functions will take daily data, either from HYDAT using the
station_number argument or your own data frame of data using the
data argument to complete an analysis. As with most
fasstr functions, options for rolling days, missing values, and date filtering can be completed using the function arguments (roll_days, water_year_start, etc).
compute_annual_frequencies() function will produce all five outputs from the analysis, as listed above, including the plotting data, plot, and computed quantiles. If just the quantile is desired, and assuming your data fits the selected distributions, the
compute_frequency_quantile() function can be used. By supplying the desired duration (
roll_days argument) and the desired return period (
return_period argument) a single numeric quantile value will be returned from the data.
To determine frequencies of annual instantaneous minimum or maximum flows from stations from HYDAT, the
compute_HYDAT_peak_frequencies() function will extract the data, if available, and complete the analysis. As this data is extracted from HYDAT by listing the station using the
station_number argument and no pre-filtering is completed on the data, the
data argument and many of the filtering arguments are not available for this function. If you have a data frame of your own instantaneous maximums or minimums, a custom analysis can be completed using the
compute_frequency_analysis() function as described below.
To complete a frequency analysis using custom data, like peaks-over-threshold analyses, the
compute_frequency_analysis() function will take the provided data and complete the analysis. The data provided must contain three columns:
Here is an example of data the can be provided, wrangled from the annual lowflows function:
low_flows <- calc_annual_lowflows(station_number = "08NM116", start_year = 1980, end_year = 2000, roll_days = 7) low_flows <- dplyr::select(low_flows, Year, Value = Min_7_Day) low_flows <- dplyr::mutate(low_flows, Measure = "7-Day") low_flows
# A tibble: 21 x 3 Year Value Measure <dbl> <dbl> <chr> 1 1980 0.655 7-Day 2 1981 0.885 7-Day 3 1982 1.05 7-Day 4 1983 0.634 7-Day 5 1984 0.784 7-Day 6 1985 0.589 7-Day 7 1986 0.719 7-Day 8 1987 0.355 7-Day 9 1988 0.186 7-Day 10 1989 0.577 7-Day # ... with 11 more rows
This data can then be applied to the
compute_frequency_analysis() function. This example has the default column names in the data and this do not need to be listed, but are shown for demonstration.
compute_frequency_analysis(data = low_flows, events = Year, values = Value, measures = Measure)
The returned Freq_Analysis_Data object provides the raw data used in the frequency analyses. Based on the selected frequency function used, this tibble will contain the respective data; the provided values with the custom analysis, the computed extremes with the annual analysis, and the HYDAT extreme peaks from HYDAT in the peak analysis. See each functions’ documentation for more information. This tibble object provides the analysis data as the annual and HYDAT peak data are calculated or extracted from HYDAT.
To provide examples of the outputs, an annual analysis will be completed on a Mission Creek HYDAT station (the
plot_curve argument is set to
FALSE for the start of this example):
freq_analysis <- compute_annual_frequencies(station_number = "08NM116", start_year = 1981, end_year = 2010, roll_days = 7, plot_curve = FALSE)
The following is an example of the returned Freq_Analysis_Data tibble:
# A tibble: 30 x 3 Year Measure Value <dbl> <fct> <dbl> 1 1981 7-Day 0.885 2 1982 7-Day 1.05 3 1983 7-Day 0.634 4 1984 7-Day 0.784 5 1985 7-Day 0.589 6 1986 7-Day 0.719 7 1987 7-Day 0.355 8 1988 7-Day 0.186 9 1989 7-Day 0.577 10 1990 7-Day 0.958 # ... with 20 more rows
Based on the analysis data in the Freq_Analysis_Data object, the data is ranked, by default for low-flow frequencies, from low to high with the lowest flow value ranked at 1. To complete high-flow analyses and rank the data from high to low, set the
use_max argument to
TRUE. The probabilities of each event are then determined using the following generalize plotting equation:
The probability plotting positions (A and B constants) are selected using the
prob_plot_position argument, listing
'weibull' where A and B are 0,
'median' where A and B are 0.3, or
'hazen' where A and B are 0.5. The selected plotting position does not have an effect on the final computed curve. To plot the data on a logarithmic scale, set the
use_log argument to
With these options set, the data used for plotting is returned in the Freq_Plot_Data tibble object. The events are sorted by measure, and ranked by the event value, and provides the probability and the return period for each event, used for plotting. See the following for an example of this output:
# A tibble: 30 x 5 Year Measure Value Probability `Return Period` <dbl> <fct> <dbl> <dbl> <dbl> 1 1988 7-Day 0.186 0.0323 31 2 1993 7-Day 0.298 0.0645 15.5 3 2002 7-Day 0.331 0.0968 10.3 4 1987 7-Day 0.355 0.129 7.75 5 2003 7-Day 0.363 0.161 6.2 6 2010 7-Day 0.454 0.194 5.17 7 2007 7-Day 0.454 0.226 4.43 8 2008 7-Day 0.463 0.258 3.88 9 1994 7-Day 0.465 0.290 3.44 10 2009 7-Day 0.502 0.323 3.1 # ... with 20 more rows
This data is then used for plotting and returned in the Freq_Plot
ggplot2 object. See the example below. To change the probabilities/vertical lines shown on the x-axis, change the values using the
prob_scale_points argument to list the breaks.
fasstr functions also compute frequency quantiles, like commonly used 7Q5, 7Q10, 5Q30, etc. Calculating frequency quantiles requires fitting historical event data (annual minimums, maximums or others) to a probability distribution (i.e. Log-Pearson Type III or Weibull in
fasstr). The flow quantiles are then extracted from the distribution for given probabilities (and equivalent return periods). In the
fasstr frequency analysis functions, this is done so by choosing a probability distribution and method of fitting to fit the data (may require data exploration for determining most appropriate distribution). Results from this fitting are found in 3 objects:
fitdistplus::fitdistobject that contains information about the fitting, including various parameter estimates, fitting statistics, and various plots.
Computing frequency quantiles in
fasstr requires choosing a probability distribution to fit the data, either Log-Pearson Type III,
"PIII" (default), or Weibull,
"weibull", distributions with the
fit_dist argument. When using the
"PIII" distribution, data provided is log-transformed (base 10) before being fit to a Pearson Type III distribution. The method of fitting data to distributions is selected using the
fit_distr_method argument with either
"MLE" for ‘maximum likelihood estimation’ or
"MOM" (default) for ‘method of moments’. For the
"PIII" distribution, the data will be fit using
"weibull" can only use
"MOM". Internally, these arguments are passed on to the
fitdistrplus::fitdist function from the ‘fitdistrplus’ package (see for more information). Fitting results from the
fitdistrplus::fitdist function are returned in the Freq_Fitting object in the list and contain information regarding the fitting process, including the parameter estimates (e.g. shape, location, and scale), AIC statistics, Q-Q and density plots, amongst other statistics. As per the
fitdistrplus::fitdist documentation, there are several ways to view the
fitdist object, three of these including using the generic
plot() functions. See the following examples for how to view some of the fitting information.
Fitting of the distribution ' PIII ' by matching moments Parameters: estimate shape 21.71135693 location 0.58975205 scale -0.03836902
Fitting of the distribution ' PIII ' by matching moments Parameters : estimate shape 21.71135693 location 0.58975205 scale -0.03836902 Loglikelihood: 9.973448 AIC: -13.9469 BIC: -9.743303
plot_curve argument is set to
TRUE (default) the computed frequency curves are plotted against the events data in the Freq_Plot object:
freq_analysis <- compute_annual_frequencies(station_number = "08NM116", roll_days = 7, plot_curve = TRUE) freq_analysis$Freq_Plot
Based on the fitted distribution, flow events with specific probabilities/return periods (quantiles) can be extracted from the computed curves. The desired quantiles are selected by listing the probabilities in the
fit_quantiles argument (defaults to
c(.975, .99, .98, .95, .90, .80, .50, .20, .10, .05, .01),). The results are returned in the Freq_Fitted_Quantiles tibble in the list. In the example below of the quantiles, the 7Q5 value would be the 7-day flow value with a 5-year return period, so 0.409 cms in this example.
# A tibble: 11 x 4 Distribution Probability `Return Period` `7-Day` <chr> <dbl> <dbl> <dbl> 1 PIII 0.01 100 0.194 2 PIII 0.05 20 0.280 3 PIII 0.1 10 0.334 4 PIII 0.2 5 0.409 5 PIII 0.5 2 0.578 6 PIII 0.8 1.25 0.772 7 PIII 0.9 1.11 0.881 8 PIII 0.95 1.05 0.972 9 PIII 0.975 1.03 1.05 10 PIII 0.98 1.02 1.08 11 PIII 0.99 1.01 1.14
As noted, when using the
"PIII" distribution in
fasstr, the provided data is log-transformed (log base 10 using
log10()) before being fit to a Pearson Type III distribution. These log-transformed values are what are seen as the ‘Data’ and ‘quantiles’ axes when plotting the Freq_Fitting
fitdist objects (as seen above). The resulting quantiles are then transformed back to the original scale when computing the final quantiles returned in the Fitted_Quantiles object and the plotted computed curves in the Freq_Plot object. To use the natural log (using
log()) instead of the base 10 log, set
use_log = TRUE. Since the log of zero or negative numbers cannot be computed, data provided with these values (e.g. data with minimums of zero flow) will not be accepted into the functions.