Recurrence Intervals of Floods

Natural hazard events like earthquakes, volcanic eruptions, floods, and hurricanes are repetitive.
Understanding the relationship between the frequency and magnitude of these events is important.
Small magnitude earthquakes occur more frequently, while large ones are rare.
Long-term monitoring helps determine the Return Period or Recurrence Interval (RI) for geological and weather events.
Recurrence Interval (RI) is useful in forecasting the probability of an event of a given magnitude.
RI refers to the past occurrence of events, while forecasting refers to the future likelihood.
Floods occur when the discharge increases, causing water to overflow onto the floodplain.
Stage refers to the height of the water with reference to a certain level (e.g., sea level).
Bankfull stage (or Flood Stage) is when water overflows the banks, causing inundation of land and roads, and threatening life and property.
Annual Peak Discharge is the highest discharge (and stage) reached over a year.
Stream flooding causes billions of dollars in losses annually in the United States.
These losses can be minimized by constructing structures outside high-risk zones.
Planners need to know the expected frequency and magnitude of future flooding events.
Discharge and stage are continuously monitored for major rivers/streams in most countries.

Flood recurrence interval (RI) represents the "return period" of a flood event of a given magnitude (discharge and stage).
Example: A river with 25 years of annual peak discharge data.
The data suggests that the river's annual peak discharge (in cubic feet per second or cfs) varies year-to-year.
Some years have low discharge, while others have high discharge, causing floods.

Step 1: Note the number of observations (N) in the dataset. Example: 25 years of data from 1974 to 1998.
Step 2: Sort the discharge data by magnitude from highest to lowest discharges. Can be done manually or using a spreadsheet.
Step 3: Assign a rank (M) to each annual peak discharge event. The highest discharge gets a rank of 1, the second highest gets 2, and so on.
Step 4: Calculate the RI of any given discharge event using the equation: $RI = (N + 1) / M$
N represents total number of observations (= 25 in the example) and M is the rank of the annual peak discharge.
Example: Calculating the RI of the 13th highest annual peak discharge, RI = (25 + 1) / 13 = 2 years.
N+1 = 26 remains constant, and M changes in the denominator.

Recurrence interval refers to the past occurrence of events, and forecasting refers to the future likelihood of such events.
Probability (P) is the chance that a particular event will occur on a scale from 0 (impossible) to 1 (absolutely certain) or as a percentage from 0 to 100%.
Example: The probability that pigs will fly is 0 (0%), and the sun will rise tomorrow is 1 (100%).
To determine the chance of occurrence of a flood of a given recurrence interval in any given year, take the inverse of the recurrence interval and multiply by 100.
$(1/RI) * 100 = percentage$
Example: Finding the chance that a flood of magnitude equal or greater than M = 13 (i.e., Recurrence interval of 2 years) in any given year, (1/2) * 100 = 50%.
There is an approximately 50% chance that a flood of this magnitude can happen next year.

Table 1 lists annual peak discharge for the Ogeechee River in coastal plain of Georgia. N = 25.
Columns in the table:
- (1) Year
- (2) Annual Peak Discharge (cfs)
- (3) Rank (M)
- (4) Recurrence Interval (RI) = $(N+1)/M$
- (5) Probability $(1/RI)*100$
Instructions:
- Examine the data and enter the rank of each annual discharge value in column 3. The highest discharge is ranked as 1.
- Determine the RI of each annual peak discharge event and enter them in column 4.
- Determine the probability of each peak discharge event using the RI and enter it in column 5.
- Use the completed Table 1 to answer questions on CANVAS Assignment #4.