Calculate annualized load duration curve — calc_annual

Calculates the median annual ldc with confidence intervals.

Usage

calc_annual_ldc(
  .tbl,
  Q = NULL,
  C = NULL,
  Date = NULL,
  allowable_concentration = NULL,
  breaks = c(1, 0.8, 0.4, 0),
  labels = c("High Flows", "Medium Flows", "Low Flows"),
  conf_level = 0.9,
  estimator = 6,
  n = 500
)

Arguments

.tbl: data frame with at least three columns Q (discharge or flow), C (associated pollutant concentration), and Date.
Q: variable name in .tbl for discharge or flow. This must be of class `units`, typically with a units value of "ft^3/s".
C: variable name in .tbl for associated pollutant concentration at a given flow value. This must be of class `units`, typically with a units value of "mg/L" or "cfu/100mL".
Date: variable name in .tbl for the event Date. This variable must be of class `Date`.
allowable_concentration: an object of class units specifying the allowable pollutant concentration.
breaks: a numeric vector of break points for flow categories. Must be of length of labels + 1. defaults to c(1, 0.8, 0.4, 0).
labels: labels for the categories specified by breaks.
conf_level: numeric, confidence level (default is 0.9) of the median interval at given exceedance probability.
estimator: one of c(5,6,7,8,9,"hd"). 6 is the default method correponding to the Weibull plotting position. Further details are provided in quantile. "hd" uses the Harrell-Davis Distribution-Free Quantile Estimator (see: hdquantile).
n: numeric, the length of generated probability points. Larger n may result in a slightly smoother curve at a cost of increased processing time. The probability points are used to generate the continuous sample quantiles types 5 to 9 (see quantile).

Value

list of two tibbles (Q and C). Includes variables in .tbl and Daily_Flow_Volume (discharge volume), Daily_Load (pollutant sample volume), P_Exceedance (exeedance probability), Flow_Category (as defined by breaks and labels).

Details

The median annual ldc is calculated by computing the flow duration curve for each individual year in the dataset. Exceedance probabilities are calculated from the descending order of Daily Flows. By default, the Weibull plotting position is used: $$p = P(Q > q_i) = \frac{i}{n+1}$$ where $q_i, i = 1, 2, ... n$, is the i-th sorted streamflow value.

The median streamflow +/- chosen confidence interval is calculated at each exceedance probability. The load duration curve is calculated by multiplying the median streamflow by the allowable concentration and appropriate conversions.

References

Vogel, Richard M., and Neil M. Fennessey. "Flow-duration curves. I: New interpretation and confidence intervals." Journal of Water Resources Planning and Management 120, no. 4 (1994): 485-504. doi: 10.1061/(ASCE)0733-9496(1994)120:4(485)

Examples

# Basic example using built in Tres Palacios data
library(dplyr)
#> 
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#> 
#>     filter, lag
#> The following objects are masked from ‘package:base’:
#> 
#>     intersect, setdiff, setequal, union
library(units)
#> udunits database from /usr/share/xml/udunits/udunits2.xml
# Format data
install_unit("cfu")
df <- as_tibble(tres_palacios) %>%
  ## filter data so this run quicker
  filter(!is.na(Indicator_Bacteria)) %>%
  ## flow must have units, here is is in cfs
  mutate(Flow = set_units(Flow, "ft^3/s")) %>%
  ## pollutant concentration must have units
  mutate(Indicator_Bacteria = set_units(Indicator_Bacteria, "cfu/100mL"))
# Calculate LDC

## specify the allowable concentration
allowable_concentration <- 126
## set the units
units(allowable_concentration) <- "cfu/100mL"
df_ldc <- calc_annual_ldc(df,
                   Q = Flow,
                   C = Indicator_Bacteria,
                   Date = Date,
                   allowable_concentration = allowable_concentration,
                   estimator = 5,
                   n = 1000)
df_ldc$Q
#> # A tibble: 1,000 × 11
#>    P_Exceedance median_Q lwr.ci_Q upr.ci_Q median_Daily_Flow_V… lwr.ci_Daily_Fl…
#>           <dbl> [ft^3/s] [ft^3/s] [ft^3/s]            [100mL/d]        [100mL/d]
#>  1     0.000500     29.3     23.8     66.5           716846635.       582284980.
#>  2     0.00150      29.3     23.8     66.5           716846635.       582284980.
#>  3     0.00250      29.3     23.8     66.5           716846635.       582284980.
#>  4     0.00350      29.3     23.8     66.5           716846635.       582284980.
#>  5     0.00450      29.3     23.8     66.5           716846635.       582284980.
#>  6     0.00550      29.3     23.8     66.5           716846635.       582284980.
#>  7     0.00650      29.3     23.8     66.5           716846635.       582284980.
#>  8     0.00750      29.3     23.8     66.5           716846635.       582284980.
#>  9     0.00850      29.3     23.8     66.5           716846635.       582284980.
#> 10     0.00950      29.3     23.8     66.5           716846635.       582284980.
#> # … with 990 more rows, and 5 more variables:
#> #   upr.ci_Daily_Flow_Volume [100mL/d], median_Allowable_Daily_Load [cfu/d],
#> #   lwr.ci_Allowable_Daily_Load [cfu/d], upr.ci_Allowable_Daily_Load [cfu/d],
#> #   Flow_Category <fct>

## cleanup
remove_unit("cfu")