Flood frequency graph, 30-year flood, 1981-2000

Method. Arrange the data in descending order, assign the Weibull return period $T=(N+1)/m$ with N = 20, plot flood peak against T on semi-log paper (T on the log axis) and read the flood at T = 30 years from the extended line.

Graph. Plot Q (arithmetic scale) against T (log scale). The points lie approximately on a straight line for the Gumbel type of data. A best-fit line through the points has the equation

$$Q=88.2+167.2\log_{10}T \quad(\text{m}^3/\text{s})$$

 Q (m3/s)
 300 |                    o   (x at T=30 line)
 250 |              o  o
 200 |         o
 150 |    o o o
 100 | o o
     +--+-----+------+-------- T (yr, log)
      1.05     2     10  30

Reading at T = 30 years:

$$Q_{30}=88.2+167.2\times\log_{10}(30)=335 \text{ m}^3/\text{s}$$

Answer: the annual peak flood with a 30-year return period ≈ 335 m³/s. (Check by Gumbel's equation with mean 155.6 and standard deviation 60.6 m³/s, using $\bar y_n=0.5236$ and $S_n=1.0628$: 319 m³/s; the graph estimate depends on the line drawn through the points.)