Floods: Recurrence intervals and 100-year floods

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How do we know or measure if a flood that could happen tomorrow is worse than one that happened 2, 10 or 50 years ago? If heavy rain is being forecasted does that mean that rivers are going to rise and spill over their banks and flood your neighborhood? These are some of the questions that many of us think about when flooding or heavy rain is forecast by the National Weather Service (NWS) or is trending in public media.

USGS Personnel taking samples off of a flooded bridge

USGS Scientist measuring the South Branch Rancocas Creek at Vincentown during flood conditions in 2004.

(Public domain.)

In general, the science and engineering community has categorized the severity of a flood by documenting the depth, extent of flood waters, and the total volume of water that passes a known reference point along a river or stream to estimate which floods are bigger or worse than others. Typically, those reference points are U.S. Geological Survey stream-gaging stations (or streamgages). No, a forecast of heavy rain does not necessarily mean that widespread flooding will occur. It usually takes a combination of higher than normal river flow conditions combined with heavy rain or snowmelt unless an extremely heavy rainfall or precipitation event is being forecast.

 

What does it mean when you hear or read the terms 100-year flood or 1-percent flood?

These terms are used to describe the extreme nature of the flood and help us to compare how common some floods are annually. When the media indicates that a recent flood was a 100-year flood, what they are really saying is that it is a statistically rare flood. USGS hydrologists for many years have preferred to use 100-year recurrence interval and are now moving to the term 1-percent annual exceedance probability (or 1-percent flood) to help clear up some of the confusion about relating this statistic to how many years it will be until the next flood.  These terms are not connected to the number of years between floods.

 

Annual Exceedance Probability vs. Recurrence Interval. How are they related?

For many years the USGS and other agencies often refer to flood frequency statistics in terms of recurrence interval (100-year flood). Recurrence-interval terminology tends to be more understandable for flood intensity comparisons. It’s easier to understand that a 100-year flood is greater than a 25-year flood.  In recent years the USGS and other agencies are more often referring to the percent chance of occurrence of a flood in terms of its Annual Exceedance Probability or AEP and not recurrence interval. An AEP is always a fraction of one. So a 0.2 AEP flood has a 20% chance of occurring in any given year, and this corresponds to a 5-year recurrence-interval flood. Although recurrence interval terminology tends to be more understandable, using AEP terminology reminds the observer that a rare flood occurring this year does not reduce the chances of another rare flood occurring again within a short time period.

 

There is a more detailed description of recurrence interval and annual exceedance probability below:

What is a recurrence interval?

"100-year floods can happen 2 years in a row"

Road Flooding at Delaware Water Gap

Old Mine Road flooded out at  the Delaware Water Gap

(Public domain.)

Statistical techniques, through a process called frequency analysis, are used to estimate the probability of the occurrence of a given precipitation event. The recurrence interval is based on the probability that the given event will be equaled or exceeded in any given year. For example, assume there is a 1 in 50 chance that 6.60 inches of rain will fall in a certain area in a 24-hour period during any given year. Thus, a rainfall total of 6.60 inches in a consecutive 24-hour period is said to have a 50-year recurrence interval.  

This principle can also be applied to streamflow. For example, using a frequency analysis (Interagency Advisory Committee on Water Data, 1982) let’s assume there is a 1 in 100 chance that a streamflow of 15,000 cubic feet per second (ft3/s) will occur during any year at a certain streamgage. Thus, a peak streamflow of 15,000 ft3/s at the example streamgage is said to have a 100-year recurrence interval (or it has a 1 percent chance of occurrence in any given year). Rainfall recurrence intervals are based on both the magnitude and the duration of a rainfall event, whereas streamflow recurrence intervals are based solely on the magnitude of the annual peak flow.

Ten or more years of data are required to perform a frequency analysis for the determination of recurrence intervals (or annual exceedance probabilities). Of course, the more years of historical data the better—a hydrologist will typically have more confidence on an analysis using 30 or more years of peak streamflow record than one based on 10 years of record.

Recurrence intervals (or annual exceedance probabilities) for the annual peak streamflow at a given location change as we collect more data to better define the probability of rare peak streamflows, and if there are significant changes in the flow patterns at that location, possibly caused by changes to control structures, an impoundment or diversion of flow. The effects of development (conversion of land from forested or agricultural uses to commercial, residential, or industrial uses) on peak flows is generally much greater for low-recurrence interval floods than for high-recurrence interval floods, such as 25- 50- or 100-year floods. During these larger floods, the soil is saturated and does not have the capacity to absorb additional rainfall. Under these conditions, essentially all the rain that falls, whether on paved surfaces or on saturated soil, runs off and becomes streamflow.

 

The 100-year flood or 1-percent Annual Exceedance Probability flood can change.

Since the peak streamflow with a 1-percent chance of occurrence in any given year (or 100-year recurrence interval) is a statistical calculation, collecting more current and historic data to better describe the flood conditions that occurred over time help to improve this statistic.  As more data are collected, or when a river basin is altered in a way that affects the flow of water in the river, scientists re-evaluate the frequency of flooding. Dams and urban development are examples of some man-made changes in a basin that affect floods, as shown in the charts below.

Graphs of urban development and changes in flood frequency

Graphs showing how urban developemnt can affect changes in flooding witin a basin.

(Public domain.)

How can we have two "100-year floods" in less than two years?

This question points out the importance of proper terminology. The term "100-year flood" is used in an attempt to simplify the definition of a flood that statistically has a 1-percent chance of occurring in any given year. Likewise, the term "100-year storm" is used to define a rainfall event that statistically has this same 1-percent chance of occurring. In other words, over the course of 1 million years, these events would be expected to occur 10,000 times. But, just because it rained 10 inches in one day last year doesn't mean it can't rain 10 inches in one day again this year.

Table of flood recurrence intervals

Flood recurrence intervals and probabilities of occurences

(Public domain.)

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Glossary of flood terms

Flood - A flood is any relatively high streamflow that overtops the natural or artificial banks of a river.

Discharge - Discharge is another term for streamflow; it is the measured volume of water that moves past a point in the river in a given amount of time. Discharge is usually expressed in cubic feet per second.

Cubic foot per second - One cubic foot per second (cfs) is about 450 gallons per minute. The average discharge of the Columbia River in September at The Dalles, Oregon, is about 120,000 cfs, which would fill the Seattle Kingdome in less than 10 minutes. The average discharge of the Puyallup River in September is about 1,700 cfs at Puyallup, Wash.

Floodplain - The floodplain is the relatively flat lowland that borders a river, usually dry but subject to flooding. Floodplain soils actually are former flood deposits.  The average number of years between floods of a certain size is the recurrence interval or return period. The actual number of years between floods of any given size varies a lot because of the naturally changing climate.

Recurrence interval - The average number of years between floods of a certain size is the recurrence interval or return period. The actual number of years between floods of any given size varies a lot because of the naturally changing climate

Hydrograph - A hydrograph is a graph that shows changes in discharge or river stage over time. The time scale may be in minutes, hours, days, months, years, or decades.

River stage - The river stage is the height of the water in the river, measured relative to an arbitrary fixed point.