rpcalc

An R package implementing the EPA Reasonable Potential (RP) Calculator for environmental compliance analysis. Given effluent monitoring data, the package determines whether a wastewater discharge has "reasonable potential" to cause or contribute to water quality standard exceedances.

Installation

# Install from source using devtools
devtools::install("path/to/rpcalc-master")

Overview

The RP analysis follows a 12-step EPA decision tree and produces one of three endpoints:

Endpoint	Meaning	Action Required
1	Definitive RP	Develop effluent limitations
2	No RP	Effluent limitations not required
3	Ambiguous	Retain existing limits; monitoring required

Decision Flow

Effluent data + mixing adjustment
        │
        ▼
Step 5: Naked exceedance? ──YES──► Endpoint 1
        │ NO
        ▼
Step 6: ≥ 3 detects AND c/n ≤ 80%?
        │ NO ──────────────────────────────────────► Step 11
        │ YES
        ▼
Steps 7–10: Parametric RPA (log-normal UCB)
   - All detects: use actual log data
   - Some non-detects (c/n ≤ 80%): use ROS-modeled data
        │
        ├── UCB > criteria ──► Endpoint 1
        └── UCB ≤ criteria ──► Endpoint 2
        
Step 11–12: Non-parametric RPA (> 80% non-detects)
   - Compute adjusted n (n minus ties above criteria)
        ├── adj n > 15 ──► Endpoint 2
        └── adj n ≤ 15 ──► Endpoint 3

Mixing Formula

Effluent concentrations are adjusted for receiving water dilution before comparison to criteria:

X = (Ce + Dm × Cs) / (Dm + 1)

• Ce = effluent concentration
• Dm = dilution factor
• Cs = background (receiving water) concentration

Statistical Methods

• Parametric (complete data): log-normal distribution; UCB = exp(mean_ln + SD_ln × g') where g' is the 95th-percentile/95%-confidence tolerance factor.
• ROS (some non-detects, c/n ≤ 80%): Regression on Order Statistics via the NADA package to model non-detect values before computing the UCB.
• Non-parametric (> 80% non-detects): adjusted sample size method.

Usage

Core function: rpcalc()

Runs the full RP analysis for a single parameter.

library(rpcalc)

result <- rpcalc(
  qual       = c("<", "", "", "<", ""),   # qualifier flags
  results    = c(5, 12, 8, 3, 15),        # effluent concentrations
  criteria   = 10,                         # water quality criterion
  dilution   = 10,                         # dilution factor (Dm)
  background = 1                           # background concentration (Cs)
)

result$endpoint     # 1, 2, or 3
result$test_value   # UCB or MEC used in the decision
result$reason       # which step produced the endpoint

The returned list contains:

Field	Description
endpoint	1, 2, or 3
reason	"Step 5", "Step 10", or "Step 12"
step_decision	Logical — whether RP was found
data_used	"Actual Data", "Inferred ROS Data"
results	Sorted mixed concentrations
test_value	MEC (Step 5) or UCB (Step 10)
criteria	The criterion used
censored_frac	Fraction of non-detects (c/n)
ML	Log mean (parametric only)
g_sharp	Tolerance factor g' (parametric only)
SD	Log standard deviation (parametric only)
adjusted_n	Adjusted n (non-parametric only)

Multi-parameter pipeline: run_rpa() and make_rpa_summary_table()

For analyzing multiple parameters at once using a combined data frame:

# 1. Prepare cleaned, merged data
data <- make_clean_data(
  effluent   = effluent_df,    # data frame with columns: parameter, qualifier, result
  criteria   = criteria_df,    # data frame with columns: parameter, criteria
  background = background_df,  # data frame with columns: parameter, background
  dilution   = 10
)

# 2. Apply mixing adjustment
data <- adjust_data(data)

# 3. Run the full RP analysis
data <- run_rpa(data)

# 4. Summarize results
summary_table <- make_rpa_summary_table(data)

Built-in datasets

data(background)   # Reference background concentrations
data(criteria)     # Regulatory water quality criteria
test_eff <- readRDS(system.file("data/test_eff.RDS", package = "rpcalc"))

Development

devtools::load_all()   # Load for interactive development
devtools::test()       # Run tests (Ctrl+Shift+T in RStudio)
devtools::check()      # Check package validity (Ctrl+Shift+E)
devtools::install()    # Install package (Ctrl+Shift+B)

Dependencies

• NADA — Regression on Order Statistics for censored data
• dplyr — Data manipulation
• readxl — Reading Excel input files
• janitor — Data cleaning
• here — Project-relative paths

References

• U.S. EPA (1991). Technical Support Document for Water Quality-based Toxics Control. EPA/505/2-90-001.
• Helsel, D.R. & Cohn, T.A. (1988). Estimation of descriptive statistics for multiply censored water quality data. Water Resources Research, 24(12), 1997–2004.