Question 13.SQ.7: The data below are the minimum instantaneous discharges reco......
The data below are the minimum instantaneous discharges recorded at a gauging station during a period of 10 consecutive years. There is a proposal to abstract water from just above the gauging station. Determine in how many years on average the flow is likely to be less than 1.50 m³/s. Comment upon the accuracy of the result.
Hint: rank the data with the highest flow = 1; calculate P% = 100r/(N + 1) and then plot logQ against P% on log-normal probability paper. Extrapolate the line to 1.50 m³/s and determine the corresponding probability (P) that this flow will be exceeded. The probability that the flow will be less than this is (1 – P) and the return period is 1/(1 – P) years.
Table STQ13.7 shows the ranked data and calculated percentage probabilities, which are plotted in Fig. STQ13.7. It is apparent from the bottom scale that the probability of a flow of 1.5 m³/s being exceeded is 98%, which means that the probability that the flow will be less than 1.5 m³/s is 2% (this value can be read directly off the top scale). Thus on average the flow will be less than required once every 50 years. With only 10 years of data, extrapolation to 50 years is not recommended. Additionally in this range the answer is affected significantly by only a small change in gradient, e.g. the line could be drawn to give a probability of 1% or 1 in 100 years, so doubling the calculated return period.
| Table STQ13.7 | |||
| Year | Min. flow (m³/s) | Rank (r) | P % = 100 r/(N+1) |
| 5 | 4.37 | 1 | 9.1 % |
| 1 | 3.97 | 2 | 18.2 % |
| 4 | 2.90 | 3 | 27.3% |
| 2 | 2.77 | 4 | 36.4 % |
| 9 | 2.73 | 5 | 45.5 % |
| 8 | 2.69 | 6 | 54.5 % |
| 10 | 2.54 | 7 | 63.6 % |
| 3 | 2.42 | 8 | 72.7 % |
| 7 | 2.11 | 9 | 81.8 % |
| 6 | 1.99 | 10 | 90.9 % |
