Misplaced Pages

#572427

43-402: FIRMs display areas that fall within the 100-year flood boundary. Areas that fall within the boundary are called special flood hazard areas (SFHAs) and they are further divided into insurance risk zones. The term 100-year flood indicates that the area has a one-percent chance of flooding in any given year, not that a flood will occur every 100 years. Such maps are used in town planning , in

86-404: A recurrence interval or repeat interval , is an average time or an estimated average time between events such as earthquakes , floods , landslides , or river discharge flows to occur. It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis. Examples include deciding whether a project should be allowed to go forward in

129-493: A 100-year flood downstream. During a time of flooding, news accounts necessarily simplify the story by reporting the greatest damage and largest recurrence interval estimated at any location. The public can easily and incorrectly conclude that the recurrence interval applies to all stream reaches in the flood area. Peak elevations of 14 floods as early as 1501 on the Danube River at Passau , Germany, reveal great variability in

172-453: A 100-year flood is generally expressed as a flood elevation or depth, and may include wave effects. For river systems, a 100-year flood is generally expressed as a flowrate. Based on the expected 100-year flood flow rate, the flood water level can be mapped as an area of inundation. The resulting floodplain map is referred to as the 100-year floodplain. Estimates of the 100-year flood flowrate and other streamflow statistics for any stream in

215-404: A 500-year event (if no comparable event occurs for a further 100 years). 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. Even if the historic return interval is a lot less than 1000 years, if there are a number of less-severe events of a similar nature recorded,

258-451: A 63.2% probability of a flood larger than the 50-year return flood to occur within any period of 50 year. If the return period of occurrence T {\textstyle T} is 243 years ( μ = 0.0041 {\textstyle \mu =0.0041} ) then the probability of exactly one occurrence in ten years is In a given period of n × τ {\displaystyle n\times \tau } for

301-434: A certain or greater magnitude happens with 1% probability, only that it has been observed exactly once in 100 years. That distinction is significant because there are few observations of rare events: for instance, if observations go back 400 years, the most extreme event (a 400-year event by the statistical definition) may later be classed, on longer observation, as a 200-year event (if a comparable event immediately occurs) or

344-542: A flood way. In the United States the FIRM for each town is occasionally updated. At that time a preliminary FIRM will be published, and available for public viewing and comment. FEMA sells the official FIRMs, called community kits , as well as an updating access service to the maps. There are also some companies that sell software to locate land parcels or real estate on digitized FIRMs. These FIRMs are used in identifying whether

387-420: A given flood threshold can be expressed, using the binomial distribution , as P e = 1 − [ 1 − ( 1 T ) ] n {\displaystyle P_{e}=1-\left[1-\left({\frac {1}{T}}\right)\right]^{n}} 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

430-539: A hydrologically similar region or from other hydrologic models . Similarly for coastal floods, tide gauge data exist for only about 1,450 sites worldwide, of which only about 950 added information to the global data center between January 2010 and March 2016. Much longer records of flood elevations exist at a few locations around the world, such as the Danube River at Passau , Germany, but they must be evaluated carefully for accuracy and completeness before any statistical interpretation. For an individual stream reach,

473-502: A land or building is in flood zone and, if so, which of the different flood zones are in effect. In 2004, FEMA began a project to update and digitize the flood plain maps at a yearly cost of $ 200 million. The new maps usually take around 18 months to go from a preliminary release to the final product. During that time period FEMA works with local communities to determine the final maps. In early 2014, two congressmen from Louisiana, Bill Cassidy and Steve Scalise , asked FEMA to consider

SECTION 10

#1732837568573

516-432: A single year is 100/X. A similar analysis is commonly applied to coastal flooding or rainfall data. The recurrence interval of a storm is rarely identical to that of an associated riverine flood, because of rainfall timing and location variations among different drainage basins . 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

559-480: A unit time τ {\displaystyle \tau } (e.g. τ = 1 year {\displaystyle \tau =1{\text{year}}} ), the probability of a given number r of events of a return period μ {\displaystyle \mu } is given by the binomial distribution as follows. This is valid only if the probability of more than one occurrence per unit time τ {\displaystyle \tau }

602-445: A zone of a certain risk or designing structures to withstand events with a certain return period. The following analysis assumes that the probability of the event occurring does not vary over time and is independent of past events. Recurrence interval = n + 1 m {\displaystyle ={n+1 \over m}} For floods, the event may be measured in terms of m /s or height; for storm surges , in terms of

645-443: Is where r {\displaystyle r} is the number of occurrences the probability is calculated for, t {\displaystyle t} the time period of interest, T {\displaystyle T} is the return period and μ = 1 / T {\displaystyle \mu =1/T} is the counting rate. The probability of no-occurrence can be obtained simply considering

688-474: 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 rainfall over a given period of time (24-hours, 6-hours, or 3-hours). 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

731-514: Is only a problem when trying to forecast a low, but maximum flow event (for example, an event smaller than a 2-year flood). 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 (see next section). More broadly, substantial evidence of climate change strongly suggests that

774-415: Is stationary, meaning that the mean (average), 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

817-415: Is that a 100-year flood is likely to occur only once in a 100-year period. In fact, there is approximately a 63.4% chance of one or more 100-year floods occurring in any 100-year period. On the Danube River at Passau , Germany, the actual intervals between 100-year floods during 1501 to 2013 ranged from 37 to 192 years. The probability P e that one or more floods occurring during any period will exceed

860-508: Is to take it as the probability for a yearly Bernoulli trial in the binomial distribution . That is disfavoured because each year does not represent an independent Bernoulli trial but is an arbitrary measure of time. This question is mainly academic as the results obtained will be similar under both the Poisson and binomial interpretations. The probability mass function of the Poisson distribution

903-432: Is zero. Often that is a close approximation, in which case the probabilities yielded by this formula hold approximately. If n → ∞ , μ → 0 {\displaystyle n\rightarrow \infty ,\mu \rightarrow 0} in such a way that n μ → λ {\displaystyle n\mu \rightarrow \lambda } then Take where Given that

SECTION 20

#1732837568573

946-423: 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. When these assumptions are violated, there is an unknown amount of uncertainty introduced into the reported value of what

989-494: The 100-year flood means in terms of rainfall intensity, or flood depth. When all of the inputs are known, the uncertainty can be measured in the form of a confidence interval. For example, one might say there is a 95% chance that the 100-year flood is greater than X, but less than Y. Direct statistical analysis to estimate the 100-year riverine flood is possible only at the relatively few locations where an annual series of maximum instantaneous flood discharges has been recorded. In

1032-606: The United States are available. In the UK, the Environment Agency publishes a comprehensive map of all areas at risk of a 1 in 100 year flood. Areas near the coast of an ocean or large lake also can be flooded by combinations of tide , storm surge , and waves . 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. A common misunderstanding

1075-745: The United States as of 2014, taxpayers have supported such records for at least 60 years at fewer than 2,600 locations, for at least 90 years at fewer than 500, and for at least 120 years at only 11. For comparison, the total area of the nation is about 3,800,000 square miles (9,800,000 km ), so there are perhaps 3,000 stream reaches that drain watersheds of 1,000 square miles (2,600 km ) and 300,000 reaches that drain 10 square miles (26 km ). In urban areas, 100-year flood estimates are needed for watersheds as small as 1 square mile (2.6 km ). For reaches without sufficient data for direct analysis, 100-year flood estimates are derived from indirect statistical analysis of flood records at other locations in

1118-463: 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

1161-485: The actual intervals between floods. Flood events greater than the 50-year flood occurred at intervals of 4 to 192 years since 1501, and the 50-year flood of 2002 was followed only 11 years later by a 500-year flood. Only half of the intervals between 50- and 100-year floods were within 50 percent of the nominal average interval. Similarly, the intervals between 5-year floods during 1955 to 2007 ranged from 5 months to 16 years, and only half were within 2.5 to 7.5 years. In

1204-411: The case for r = 0 {\displaystyle r=0} . The formula is Consequently, the probability of exceedance (i.e. the probability of an event "stronger" than the event with return period T {\displaystyle T} to occur at least once within the time period of interest) is Note that for any event with return period T {\displaystyle T} ,

1247-419: The connotations of the name "return period". In any given 100-year period, a 100-year event may occur once, twice, more, or not at all, and each outcome has a probability that can be computed as below. 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. One does not actually know that

1290-477: The extreme event, while the smaller event would be ignored in the analysis (even though both may have been capable of causing terrible flooding in their own right). 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

1333-409: The extreme events on record all come from late summer thunderstorms (as is the case in the southwest U.S.), or from snow pack melting (as is the case in north-central U.S.), 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

Flood insurance rate map - Misplaced Pages Continue

1376-409: 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. Return period A return period , also known as

1419-488: The height of the surge, and similarly for other events. This is Weibull's Formula. The theoretical return period between occurrences is the inverse of the average frequency of occurrence. 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. This does not mean that a 100-year flood will happen regularly every 100 years, or only once in 100 years. Despite

1462-439: The insurance industry, and by individuals who want to avoid moving into a home at risk of flooding or to know how to protect their property. FIRMs are used to set rates of insurance against risk of flood and whether buildings are insurable at all against flood. It is similar to a topographic map, but is designed to show floodplains. Towns and municipalities use FIRMs to plan zoning areas. Most places will not allow construction in

1505-425: 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 (rainfall or river flow rate measurement) that occurs in any one year. The fourth assumption is that the probability distribution function

1548-446: The period. 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 (P e =0.10); 500-year have a 0.2% chance of occurring in any given year (P e =0.002); etc. The percent chance of an X-year flood occurring in

1591-401: The probability of exceedance within an interval equal to the return period (i.e. t = T {\displaystyle t=T} ) is independent from the return period and it is equal to 1 − exp ⁡ ( − 1 ) ≈ 63.2 % {\displaystyle 1-\exp(-1)\approx 63.2\%} . This means, for example, that there is

1634-437: The return period of an event is 100 years, So the probability that such an event occurs exactly once in 10 successive years is: Return period is useful for risk analysis (such as natural, inherent, or hydrologic risk of failure). When dealing with structure design expectations, the return period is useful in calculating the riskiness of the structure. The probability of at least one event that exceeds design limits during

1677-404: The same event commonly represents a different recurrence interval at each location. If an extreme storm drops enough rain on one branch of a river to cause a 100-year flood, but no rain falls over another branch, the flood wave downstream from their junction might have a recurrence interval of only 10 years. Conversely, a storm that produces a 25-year flood simultaneously in each branch might form

1720-402: The uncertainties in any analysis can be large, so 100-year flood estimates have large individual uncertainties for most stream reaches. For the largest recorded flood at any specific location, or any potentially larger event, the recurrence interval always is poorly known. Spatial variability adds more uncertainty, because a flood peak observed at different locations on the same stream during

1763-403: The use of such a model is likely to provide useful information to help estimate the future return interval. One would like to be able to interpret the return period in probabilistic models. 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. An alternative interpretation

Flood insurance rate map - Misplaced Pages Continue

1806-503: 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 well sufficient for the purposes of the National Flood Insurance Program (NFIP) and offer reasonable estimates of future flood risk, if

1849-417: The width of drainage canals, water flow levels, drainage improvements, pumping stations and computer models when deciding the final flood insurance rate maps. 100-year flood A 100-year flood is a flood event that has on average a 1 in 100 chance (1% probability) of being equaled or exceeded in any given year. A 100-year flood is also referred to as a 1% flood . For coastal or lake flooding,

#572427