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

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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?