Low Flow Calculations

1. Low Flow Calculations In NPDES permits the permitted industry or municipality must meet certain requirements with regards to the toxicity of their effluent. The percent of the effluent being discharged to the receiving stream that must not be toxic is based on the historically based low flow conditions of the receiving system. For example, if under low flow conditions in freshwater the effluent can occupy 65% of the flow of the stream, in the biomonitoring toxicity tests (Short-term Chronic, 7-day Ceriodaphnia dubia survival and reproduction test and the Pimephales promelas survival and growth test) must reveal that the effluent is not toxic at a dilution of 65% or lower. The rationale is that under low flow conditions the effluent cannot occupy more than 65% of the stream but can constitute that much of the flow or lower. Therefore, the effluent cannot be toxic when diluted to 65% by upstream or laboratory water.

2. Depending on the State and the EPA Region, what constitutes the historic low flow conditions can vary. Most often the low flow is based on the 7Q10 flow. In Texas the low flow is based on the 7Q2 flow. The definition of 7Q10 is, the lowest average discharge over a period of one week with a recurrence interval of 10 years. Since the value of N for the 7Q10 is 10 years, there is only a 10% probability that there will be a lower flow in any given year. There is a 90% probability that the flow will be greater than the 7Q10 value. The definition of 7Q2 is the lowest average discharge over a period of one week with a recurrence interval of 2 years. Since the value of N for the 7Q2 is 2 years, there is a 50% probability that there will be a lower flow in any given year. Or, in other words, there is a 50% probability that there will be a flow greater than the 7Q2 in any given year.

3. Given the following record of stream flow data, estimate the 7Q10 flow for the stream. Year Lowest Seven-Day Average Flow, m3/s 1980 4.4 1981 2.8 1982 4.0 1983 3.4 1984 5.2 Solution: First arrange the flow data in decreasing order of magnitude and assign a “rank” or m value to each flow, beginning with 1 and increasing sequentially. In the case of “ties” assign the tied scores the average of the tied ranks.

4. For example, the following data 2.6, 3.2, 3.2 3.2 and 4.5 m3/s would be ranked 1 for 4.5, and 3 for each of the 3.2 values and 5 for the 2.6 value. Had there only been two 3.2 values the average rank would have been 2.5 for each of these values. The probability of observing an equal or higher flow in any given year is estimated by dividing the rank m by the number of years of record plus 1 (n+1); in this example n = 5. In formula form the probability P = m/(n+1). Low Flow, m3/s Rank Probability 5.2 1 1/6=0.167 4.4 2 2/6=0.333 4.0 3 3/6=0.500 3.4 4 4/6=0.667 2.8 5 5/6=0.833

5. Plot the data on log probability paper with the y-axis as the Yearly 7-Consecutive Day Low Flow, m3/s, and the x-axis as the Probability of a Larger Flow.

7. If an industry is discharging 2.53 m3 into the receiving system represented by the calculations we just made i.e. a 7Q10 of 2.72 and a 7Q2 of 4.0 m3/sec at what percent effluent does the industry have to pass the WET requirements in their NPDES permit? Calculations: 7Q10 2.53 m3 + 2.72 m3 = 5.25 m3 2.53/5.22 = 48% under low flow conditions the effluent could not occupy more than 48% the flow of the receiving system. 7Q2 2.53 m3 + 4.0 m3/sec = 6.53 m3/sec 2.53/6.53 m3/sec = 39% under low flow conditions the effluent could not occupy more than 39% of the flow of the receiving system.

8. Using the methodology given above determine both the 7Q10 and the 7Q2 flow for the data shown in the Table on the next page. The data represent the lowest seven-day average flow m3/s for the year shown. How is this determined? Generally the USGS defines a water year as the period from October 1 to September 30. Low flow calculations (e.g. 7Q10) are calculated based on data collected between April 1 and March 31.