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

  • Page ID
    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 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.

    9.14.png
    Figure 9.14: Graph to use for Activity 9A: Recurrence Intervals and the Russian River.

    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?

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

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