One Day of Sewage at 5x the Limit Can Still Pass the Permit

A sewage plant can discharge suspended solids at five times its permit concentration on one day and report no violation of the secondary treatment standard. I did not expect the arithmetic to be this plain. Here it is, with a warning first: I could not find a published analysis of national discharge monitoring data that shows peak-day exceedances clustering in storms. I changed my thesis because of that. I will say what I could and could not show.

Question

Does a plant that meets its average limit still fail on its worst day, and does that worst day come with the storm?

I split this in two. The first part is about rules and arithmetic, and I can answer it. The second part is about data, and I can only partly answer it.

What the rules say

For continuous dischargers, federal rules set the limit format by type of plant. Non-municipal dischargers get a maximum daily limit and an average monthly limit. Publicly owned treatment works (POTWs) get an average weekly and an average monthly limit [1]. So the premise in my working title needs a correction. A POTW under the basic secondary standard has no daily maximum from that rule. Many permits add daily limits for other pollutants, such as ammonia or disinfectant residual, but the standard itself does not.

The secondary standard for BOD5 and suspended solids is 30 mg/L as a 30-day average and 45 mg/L as a 7-day average, with at least 85 percent removal over 30 days [2]. EPA recommends that permit writers apply these as the monthly and weekly limits [3]. The permit writers' manual also says the weekly limit may be 1.5 times the monthly limit, which matches 45 and 30 [3].

Mass limits matter too. Rules require pollutants to be limited in mass, with exceptions such as pH [1]. The manual gives the formula: mass (lb/day) equals concentration (mg/L) times design flow (mgd) times 8.34 [3]. The design flow is fixed. The storm flow is not. I come back to that below.

Method

I used no Lab run. Every number below comes from a formula and inputs I state, and a reader can repeat it with a calculator. The plant cases are hypothetical. They are not data from any real plant.

Test 1: how much can one day hide?

Take a plant that discharges 20 mg/L TSS on normal days. Add one bad day at S mg/L. Which S breaks each test?

• Monthly (30 days, 29 normal): $(29 \times 20 + S)/30 > 30$ gives S above 320 mg/L.
• Weekly (7 days, 6 normal): $(6 \times 20 + S)/7 > 45$ gives S above 195 mg/L.

So a single day at 150 mg/L passes both tests. The weekly average is 38.6 mg/L and the monthly average is 24.3 mg/L. That day is 5 times the monthly limit and 3.3 times the weekly limit. Nothing is reported as a violation.

This assumes daily sampling. Many plants sample a few days each week. A spike on an unsampled day leaves no trace at all.

Test 2: how long must the bad period be?

If the bad period lasts two days at 120 mg/L, the weekly average is $(5 \times 20 + 2 \times 120)/7 = 48.6$ mg/L. That fails 45. The monthly average is $(28 \times 20 + 240)/30 = 26.7$ mg/L. That passes 30. One event fails the weekly test and passes the monthly one. A report that shows only the monthly figure shows a pass.

Test 3: the variability allowance

EPA sets a maximum daily limit at the 99th percentile of a lognormal distribution and a monthly limit at the 95th percentile of monthly averages, with a default CV of 0.6 [4]. I rebuilt the multipliers. For a lognormal with coefficient of variation CV, the 99th percentile over the long-term average (LTA) is

$\exp(z\sigma - \sigma^2/2), \quad \sigma^2 = \ln(1 + CV^2)$

with z = 2.326. For CV 0.6, σ is 0.555 and the multiplier is 3.1. For a monthly average of 4 samples at the 95th percentile (z = 1.645), the same formula with $\sigma_4^2 = \ln(1 + CV^2/4)$ gives 1.55. The ratio of daily maximum to monthly average is about 2.0.

The consequence is a design fact, not a defect. A plant that holds exactly the LTA has a 1 in 100 chance of exceeding the daily maximum on any day, if days are independent. That is about 3.7 days a year. Storms break the independence assumption. Wet days are not random draws from the dry-day distribution.

Result: the bad day in mass

Take a hypothetical 10 mgd plant. Its TSS mass limit at 30 mg/L is $30 \times 10 \times 8.34 = 2{,}502$ lb/day [3]. That is 1,135 kg/day. If the plant serves people at 100 gallons per person per day (my assumption), the allowance is about 11 g of solids per person per day.

Case	Flow (mgd)	Effluent TSS (mg/L)	Out (lb/day)	Against limit of 2,502 lb/day
Dry day, plant works	10	20	1,668	67% of limit
Same effluent, storm flow	25	20	4,170	167% of limit
Storm flow, solids wash out of clarifiers	25	60	12,510	500% of limit

To stay inside the mass limit at 25 mgd, effluent must be 12 mg/L. The plant must treat better at 2.5 times the flow. Shorter detention time and higher solids loading push the other way. Guidance from Maine, as I read it in a search excerpt, says uncontrolled solids loss from secondary clarifiers at high flow can violate the permit [6]. The 60 mg/L case is my illustration of that, not a measurement.

The weekly concentration test would not necessarily catch the third row either. One day at 60 mg/L in a week of 20 mg/L days averages 25.7 mg/L. Concentration limits pass. The mass limit does not. Which limit binds depends on the permit, and I did not check any specific permit.

What the data show, and what they do not

The empirical claim in my working title is that exceedances cluster in storm-driven high flow. Here is the evidence I read.

McMahan compared two Florida plants using rainfall and plant data. The plant operating below capacity, with a nutrient removal process, handled peak wet weather flow better than the plant at or above capacity [5]. The abstract gives no violation counts. That supports the direction of the claim. Two plants are not a distribution, and I did not read the full thesis.

Several other PDFs, including an EPA wet weather performance summary and state guides, would not open as text in this session. I used only the search excerpts for the Maine guide [6] and I do not cite numbers from the ones I could not read. I found no national analysis that joins daily-maximum exceedances to rainfall.

The public data exist. EPA publishes the ICIS-NPDES effluent violation dataset [7]. The test is simple: for each daily-maximum exceedance, was there rain that day or the day before, and how does that compare with the base rate of wet days? I have not run it. So the clustering claim is a hypothesis that fits plant physics, not a result.

Sensitivity: which assumption moves the answer most

The spike size that hides depends on the baseline.

Normal-day TSS (mg/L)	One-day spike needed to fail weekly	One-day spike needed to fail monthly
10	255	600
20	195	320
28	147	88

A plant that runs well below its limit hides the biggest spikes. A plant that runs near its limit (28 mg/L) has almost no room, and the monthly test becomes the tighter one. The baseline matters more than the averaging rule, and it is the number a permit report rarely shows.

The second largest effect is the CV. At CV 0.3 the daily multiplier is 1.9. At 0.6 it is 3.1. At 1.0 it is 4.9. A plant with erratic effluent gets a loose daily limit. Wet-weather flow raises CV, so a limit built from dry-weather data is too tight on storm days and the plant fails it, while one built from erratic data is loose on dry days.

The third effect is sample frequency, which I cannot size without the permit.

What I conclude

I think permits and public reports should show the peak next to the mean: the highest daily value, the highest weekly value, and the daily flow for that day. This is opinion. The arithmetic only shows that the mean is a weak guard. I also distrust a plain pass or fail count, because it hides how far a day went over.

The trade-off nobody mentions: tighter daily limits push a plant to build for the storm. That means larger clarifiers, storage basins or wet-weather treatment, paid by ratepayers for a few days a year. I judge by cost per unit, and I may undervalue how a community weighs a rare, visible sewage release against a higher bill. I cannot price that here.

My current view is that the structural point holds with high confidence: averages can hide a failure day under the secondary standard. My confidence that failures cluster in storms is moderate, and it rests on physics and two plants. If a national DMR join showed wet days hold less than about 1.5 times their base-rate share of daily-maximum exceedances, I would drop the clustering claim.