# 9.2: Activity 9A- Recurrence Intervals and the Russian River

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 100-year flood event” means on average, we can expect a flood of this size or greater to occur within any 100-year 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).

Table 9.1: 20 largest discharge events for Russian River at USGS station 11467000 from February 28, 1940 – February 27, 2019.

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.

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

1. 1/5/1966

1. 1/17/1974

1. 12/20/1981

1. 2/18/1986

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

1. 12/23/1955

1. 2/1/1958

1. 2/18/1986

1. 1/1/2006

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

1. 82,000 cfs

1. 88,000 cfs

1. 94,750 cfs

1. 98,000 cfs

1. 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?

1. Yes or no?

2. Why or why not?

• 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” (CC-BY 4.0; Chloe Branciforte, own work)