9.2: Activity 9A Recurrence Intervals and the Russian River
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 14559
Recall that a recurrence interval (or return period) is based on the probability that a given event, in this case a flood of specific magnitude, will be equaled or exceeded in any given year. For example, a “1 in 100year flood event” means on average, we can expect a flood of this size or greater to occur within any 100year period. However, we cannot predict it will occur in any particular year, only that each year has a 1 in 100 (1%) chance of occurring in any year.
Data for this activity was collected from the USGS peak streamflow for the Russian River, located in northern California south of Ukiah. The chart below includes the 20 largest discharge events for Russian River at USGS station 11467000 from February 28, 1940 – February 27, 2019.
Step 1: To create a flood frequency graph, we must calculate the recurrence interval. First, however, we need to rank the flood events on the chart below. The bigger the stream flow (cfs, read as cubic feet per second), the higher the discharge. A 1 signifies the highest discharge event and a 20 the lowest discharge event (see table below).
Date 
Stream flow (cfs) 
Flood Rank 
Recurrence Interval (years) 
Probability (%) 

Feb. 28, 1940 
88,400 

Feb. 06, 1942 
67,800 

Jan. 22, 1943 
69,200 

Dec. 23, 1955 
90,100 

Feb. 25, 1958 
68,700 

Feb. 01, 1963 
71,800 
1 
80 
1.25 
Dec. 23, 1964 
93,400 

Jan. 05, 1966 
77,000 

Jan. 21, 1967 
68,400 

Jan. 14, 1969 
68,600 

Jan. 24, 1970 
72,900 

Jan. 17, 1974 
74,000 

Feb. 13, 1975 
67,300 

Dec. 20, 1981 
67,200 

Jan. 27, 1983 
71,900 

Feb. 18, 1986 
102,000 

Jan. 09, 1995 
93,900 

Jan. 01, 1997 
82,100 

Jan. 01, 2006 
86,000 

Feb. 27, 2019 
72,000 
Step 2: Calculate the recurrence interval for each discharge event using the following equation:
\[RI = \dfrac{n+1}{m} \nonumber \]
Where,
RI = Recurrence Interval (in years)
n = number of years of record (in this case, 79)
m = rank of flood (see table)
Example: Feb. 18, 1986
RI = (79 + 1) / 1
RI = 80 (Note: It is ok to round to the nearest tenth)
Step 3: Calculate the probability of each discharge event:
\[Probability = \left( \frac{1}{RI} \right) \times100 \nonumber \]
Where,
RI = Recurrence Interval (from Step 2)
Example: Feb. 18, 1986
Probability = (1/80) * 100
Probability = 1.2% (Note: round to the nearest tenth)
What does this calculation signify? On average a flood event of this magnitude, discharge of 102,000 cfs (cubic feet per second), occurs every 80 years. This does not preclude the event from happening every year, but the probability of that is small (~1.25%).
Step 4: Now that the table has been completed, plot the discharge against the recurrence interval on the graph below. After plotting each point, use a ruler or other straightedge to draw a best fit line.
What is a best fit line? It is a straight line on a graph that shows the general direction that a group of points appear to be heading, however it does not connect all points on the graph.
Step 5: Answer the following questions based on Table 9.1 and Figure 9.14 from above.

On which date did a flood event have a recurrence interval of 10?

1/5/1966

1/17/1974

12/20/1981

2/18/1986

Of the following dated flood events, which one would you expect to happen more often?

12/23/1955

2/1/1958

2/18/1986

1/1/2006

Observe your best fit line. What approximate discharge would be associated with a 50year recurrence interval?

82,000 cfs

88,000 cfs

94,750 cfs

98,000 cfs

Is it possible that a flood with a similar discharge to that of the event from 2/27/2019 could happen again in the next 10 years?

Yes or no?

Why or why not?

Attributions

Table 9.1: “Peak Streamflow for the Russian River” (Public Domain; Chloe Branciforte and Emily Haddad via USGS/NWIS)

Figure 9.14: “Recurrence Interval Graph” (CCBY 4.0; Chloe Branciforte, own work)