Return period

recurrence interval1-in-100 year event1 in 100 year1 in 50 year1-in-50 year event1 in 200 year event1-in-1000-year eventrainfall rates1 in 10 year1 in 10 year flooding
A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, landslides, or a river discharge flows to occur.wikipedia
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Flood

floodingfloodsflood control
A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, landslides, or a river discharge flows to occur.
A series of annual maximum flow rates in a stream reach can be analyzed statistically to estimate the 100-year flood and floods of other recurrence intervals there.

100-year flood

100 year flood100-year500-year flood
where T is the threshold return period (e.g. 100-yr, 50-yr, 25-yr, and so forth), and n is the number of years in the period.

Earthquake

earthquakesseismic activityseismic
A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, landslides, or a river discharge flows to occur.

Landslide

landslideslandslipdebris avalanche
A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, landslides, or a river discharge flows to occur.

Discharge (hydrology)

dischargeflow rateoutflow
A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, landslides, or a river discharge flows to occur.

Frequency of exceedance

probability of exceedanceexceedance frequencyexceeded
For example, a 10-year flood has a 1/10 = 0.1 or 10% chance of being exceeded in any one year and a 50-year flood has a 0.02 or 2% chance of being exceeded in any one year.

Statistic

sample statisticempiricalmeasure
Also, the estimated return period below is a statistic: it is computed from a set of data (the observations), as distinct from the theoretical value in an idealized distribution.

Statistical model

modelprobabilistic modelstatistical modeling
Further, one cannot determine the size of a 1000-year event based on such records alone but instead must use a statistical model to predict the magnitude of such an (unobserved) event.

Poisson distribution

PoissonPoisson-distributedPoissonian
The most logical interpretation for this is to take the return period as the counting rate in a Poisson distribution since it is the expectation value of the rate of occurrences. The probability mass function of the Poisson distribution is

Bernoulli trial

Bernoulli trialsBernoulli random variablesBernoulli-distributed
An alternative interpretation is to take it as the probability for a yearly Bernoulli trial in the binomial distribution.

Binomial distribution

binomialbinomial modelBinomial probability
An alternative interpretation is to take it as the probability for a yearly Bernoulli trial in the binomial distribution.

Probability mass function

mass functionprobability massmass
The probability mass function of the Poisson distribution is

Tropical Storm Domoina

DomoinaCyclone DemoinaCyclone Domoina
Severe Tropical Storm Domoina in 1984 caused 100 year floods in South Africa and record rainfall in Swaziland.

Tōkai earthquakes

Tōkai earthquakeTokai earthquakelarge earthquakes
The Tōkai earthquakes are major earthquakes that have occurred regularly with a return period of 100 to 150 years in the Tōkai region of Japan.

Effects of Hurricane Dennis in Jamaica

Passing northeast of the island, impact from Dennis stemmed primarily from rainfall—accumulations peaked at 24.54 in and reached 1-in-50 year event levels.

October 2015 North American storm complex

nor'eastercatastrophic floodingFlash flooding
Some areas of the state saw rainfall equivalent to a 1-in-1000-year event.

Great Storm of 1987

Great Storm16 October 19871987
Among the most damaged areas were Greater London, the East Anglian coast, the Home Counties, the west of Brittany and the Cotentin Peninsula of Normandy, all of which weathered gusts typically with a return period of 1 in 200 years.

1985 Election Day floods

flood of 19851985 Cheat River flooddeadly flood event
In Roanoke, the Roanoke River rose 18.57 ft in ten hours to a peak of 23.35 ft, considered a 1 in 200 year event.

2016 West Virginia flood

floodsevere floodingflooding
According to meteorologists at the National Weather Service, this rainfall qualifies as a 1,000 year event for parts of Kanawha, Fayette, Nicholas, Summers and Greenbrier counties.

1962 Atlantic hurricane season

1962tropical depression1962 season
The second of three formed off the west coast of Florida and flooded widespread areas after 1 in 100 year rainfall.

Lake Tahoe

Lake Tahoe, CaliforniaTahoeLake Tahoe, Nevada
Subsequent studies revealed submarine landslides in Fallen Leaf Lake and Lake Tahoe that are thought to have been triggered by earthquakes on the West Tahoe fault and the timing of these events suggests a recurrence interval of 3,000–4,000 years.

October 1999 Mexico floods

1999 Mexico floodsextreme flooding in MexicoTropical Depression Eleven
The floods were estimated as a 1 in 67 year event in one location, although such floods are expected to affect eastern Mexico twice per century, the last time being 1944.