Historical flood assessment
Introduction
In several areas of engineering, the return period (T) is a representation commonly used to present an estimate of the probability of occurrence of a given event in a given period; For example, in hydraulic engineering it is used to show the probability that a flood with a certain flow or greater will occur in any year, while in seismic engineering it is used to indicate the probability that an earthquake with a magnitude equal to or greater than a certain value will occur for any year. Similarly, the return period of an event is the amount of time for which the probability of occurrence is uniformly distributed in the periods that make up said amount of time; Thus, a return period of 50 years corresponds to a probability of exceedance of 1/50 = 0.02 or 2% for any year (the probability of exceedance for each year will be 2%). Alternatively, the return period can be understood as the average time span that separates two events of a given magnitude; However, one should not make the mistake of misinterpreting that, in probabilistic terms, an event with a return period "T" is likely to occur once every "T" years, in fact there is a probability of approximately 63.4% that an event (such as a flood) with a return period of 100 years will occur one or more times during any 100-year period.
Also called the recurrence period, the return period is a statistical concept that attempts to provide an idea of how rare an event can be considered. It is usually calculated by adjusting probability distributions to the analyzed variables, based on series of extreme values recorded within equal and consecutive periods; For example, in hydrology, the study is carried out based on tables with the maximum precipitation recorded every 24 hours over a series of consecutive years; In maritime engineering, tables are used with the values of the highest wave height reached each year, also in a series of consecutive years. The fitting of the data and the prediction of extreme values is usually carried out using the Gumbel, Log-Pearson, square root exponential distributions (sqrt-ETmax)[1] and others.[2].
The return period is usually a requirement for the design of engineering works, since it allows establishing, with a certain level of confidence, the extreme values of certain variables (precipitation, wave height, wind speed, intensity of an earthquake, etc.) for which a given work must be designed so that it behaves appropriately in terms of safety and functionality. In this way it is possible, for example, to establish for a certain probability the minimum flow that will pass through a river in the design of the intake of an aqueduct, or the maximum wave size that a dock will have to deal with at a given location. In addition to helping to select these values, the return period is useful to avoid the use of extremely unlikely extreme values, thus avoiding excessive oversizing in the design and allowing the functionality of the works to be ensured to the extent that it is reasonably practical; However, some specialists consider that, in the practice of engineering, certain return periods are excessively conservative and should be reduced as they result in works that are too costly. It is then about achieving a balance between the reliability and the economy of the proposed solutions.