100-year flood

A 100-year flood, also called a 1% flood, or High Probability in the UK, is a flood event for a defined location at a level reached or exceeded once per hundred years, on average, but as there are many locations there are multiple independent 100-year floods within the same year. In the US, it is estimated on past records as having a 1 in 100 chance of being equaled or exceeded in any given year.
The estimated boundaries of inundation in a 100-year or 1% flood are marked on flood maps.
UK planning guidance defines Flood Zone 3a "High Probability" as Land having a 1% or greater annual probability of river flooding; or Land having a 0.5% or greater annual probability of sea.

Maps, elevations and flow rates

For coastal flooding and lake flooding, a 100-year flood is generally expressed as a water level elevation or depth, and includes a combination of tide, storm surge, and waves.
For river systems, a 100-year flood can be expressed as a flow rate, from which the flood elevation is derived. The resulting area of inundation is referred to as the 100-year floodplain. Estimates of the 100-year flood flow rate and other streamflow statistics for any stream in the United States are available.
A 100-year storm may or may not cause a 100-year flood, because of rainfall timing and location variations among different drainage basins, and independent causes of floods, such as snow melt and ice dams.
In the UK, the Environment Agency publishes a comprehensive map of all areas at risk of a 100-year flood. In the US, the Federal Emergency Management Agency publishes maps of the 100-year and 500-year floodplains.
Maps of the riverine or coastal 100-year floodplain may figure importantly in building permits, environmental regulations, and flood insurance. These analyses generally represent 20th-century climate and may underestimate the effects of climate change.

Risk

A common misunderstanding is that a 100-year flood happens once in a 100-year period. On average one happens per 100 years, five per 500 years, ten per thousand years. Any average hides variations. In any particular 100 years at one spot, there is a 37% chance that no 100-year flood happens, 37% chance that exactly one happens, and 26% chance that two or more happen. On the Danube River at Passau, Germany, the actual intervals between 100-year floods during 1501 to 2013 ranged from 37 to 192 years.
A related misunderstanding is that floods bigger than 100-year floods are too rare to be of concern. The 1% chance per year accumulates to 10% chance per decade, 26% chance during a 30-year mortgage, and 55% chance during an 80-year human lifetime. It is common to refer to 100-year floods as floods with 1% chance per year. It is equally true to refer to them as floods with 10% chance per decade.
Over a large diverse area, such as a large country or the world, in an average year 1% of watersheds have 100-year floods or bigger, and 0.1% of watersheds have 1,000-year floods or bigger. There are more in wet years, fewer in dry years. Of 1.6 million kilometers of coastline in the world,
in an average year 1,600 kilometers have 1,000-year floods or bigger, more in stormy years, fewer in calmer years.
The US flood insurance program, starting in the 1960s, chose to foster rules in, and insure buildings in, 100-year floodplains, as "a fair balance between protecting the public and overly stringent regulation."
After the North Sea flood of 1953, the United Kingdom mapped 1,000-year floods and the Netherlands raised its flood defenses to protect against up to 10,000 year floods.
In 2017 the Netherlands designed some areas against million-year floods.
The American Society of Civil Engineers recommends designing some structures for up to 1,000-year floods,
while it recommends designing for up to 3,000-year winds.
Per century, any one area has a 63% chance of a 100-year flood or worse, 10% chance of a 1,000-year flood, 1% chance of a 10,000-year flood, and 0.01% chance of a million-year flood.
As David van Dantzig, working on the government response to the 1953 flood, said, "One will surely be willing to spend a multiple of the amount that would be lost by a flood if the flood can thereby be prevented."

Flood insurance

In the United States, the 100-year flood provides the risk basis for flood insurance rates. A regulatory flood or base flood is routinely established for river reaches through a science-based rule-making process targeted to a 100-year flood at the historical average recurrence interval. In addition to historical flood data, the process accounts for previously established regulatory values, the effects of flood-control reservoirs, and changes in land use in the watershed. Coastal flood hazards have been mapped by a similar approach that includes the relevant physical processes. Most areas where serious floods can occur in the United States have been mapped consistently in this manner. On average nationwide, those 100-year flood estimates are sufficient for the purposes of the National Flood Insurance Program and offer reasonable estimates of future flood risk, if the future is like the past. Approximately 3% of the U.S. population lives in areas subject to the 1% annual chance coastal flood hazard.
In theory, removing homes and businesses from areas that flood repeatedly can protect people and reduce insurance losses, but in practice it is difficult for people to retreat from established neighborhoods.

Probability

The probability P_e that one or more floods occurring during any period will exceed a given flood threshold can be expressed, using the binomial distribution, as
where T is the threshold mean recurrence interval, greater than 1. If T is in years, then n is the number of years in the period, and P is the chance per year, Annual Exceedance Probability.
The formula can be understood as:

Chance per year of a T-year flood is 1/T for example 1/100 = 0.01
Chance per year of no such flood is 1 − 1/T for example 1 − 0.01 = 0.99
Chance that n independent years have no such flood, by multiplying, is for example 0.99 = 0.366
Chance of at least one flood in n years is 1 − for example 1 − 0.99 = 0.634 = 63.4%

The probability of exceedance P_e is also described as the natural, inherent, or hydrologic risk of failure. However, the expected value of the number of 100-year floods occurring in any 100-year period is 1.
Ten-year floods have a 10% chance of occurring in any given year ; 500-year floods have a 0.2% chance of occurring in any given year ; etc. The percent chance of a T-year flood occurring in a single year is 100/T, where T is bigger than 1.

Storm with chance shown below, of being equaled or exceeded each year	1 year	10 years	30 years	50 years	80 years	100 years	200 years
1/100	1.0%	9.6%	26.0%	39.5%	55.2%	63.4%	86.6%
1/500	0.2%	2.0%	5.8%	9.5%	14.8%	18.1%	33.0%
1/1,000	0.1%	1.0%	3.0%	4.9%	7.7%	9.5%	18.1%
1/10,000	0.0%	0.10%	0.30%	0.50%	0.80%	1.00%	1.98%
1/1,000,000	0.0001%	0.001%	0.003%	0.005%	0.008%	0.010%	0.020%

The same formula above can give the chance of occurrence in less than a year. A 1-year flood is a 12-month flood, with a 1/12 chance each month, and the formula in months shows 65% chance each year.
The field of extreme value theory was created to model rare events such as 100-year floods for the purposes of civil engineering. This theory is most commonly applied to the maximum or minimum observed stream flows of a given river. In desert areas where there are only ephemeral washes, this method is applied to the maximum observed flow over a given period of time. The extreme value analysis only considers the most extreme event observed in a given year. So, between the large spring runoff and a heavy summer rain storm, whichever resulted in more runoff would be considered the extreme event, while the smaller event would be ignored in the analysis.

Statistical assumptions

There are a number of assumptions that are made to complete the analysis that determines the 100-year flood. First, the extreme events observed in each year must be independent from year to year. In other words, the maximum river flow rate from 1984 cannot be found to be significantly correlated with the observed flow rate in 1985, which cannot be correlated with 1986, and so forth. The second assumption is that the observed extreme events must come from the same probability density function. The third assumption is that the probability distribution relates to the largest storm that occurs in any one year. The fourth assumption is that the probability distribution function is stationary, meaning that the mean, standard deviation and maximum and minimum values are not increasing or decreasing over time. This concept is referred to as stationarity.
The first assumption is often but not always valid and should be tested on a case-by-case basis. The second assumption is often valid if the extreme events are observed under similar climate conditions. For example, if the extreme events on record all come from late summer thunderstorms, or from snow pack melting, then this assumption should be valid. If, however, there are some extreme events taken from thunder storms, others from snow pack melting, and others from hurricanes, then this assumption is most likely not valid. The third assumption is only a problem when trying to forecast a low, but maximum flow event. Since this is not typically a goal in extreme analysis, or in civil engineering design, then the situation rarely presents itself.
The final assumption about stationarity is difficult to test from data for a single site because of the large uncertainties in even the longest flood records. More broadly, substantial evidence of climate change strongly suggests that the probability distribution is also changing and that managing flood risks in the future will become even more difficult. The simplest implication of this is that most of the historical data represent 20th-century climate and might not be valid for extreme event analysis in the 21st century.