Nelsen RB An introduction to copulas, 2nd edn. The agreement between theoretical and empirical probabilities, and the visualization of the sets and subsets of interest in each case should definitely clarify that 1 there is no definition better than others, 2 each definition is coherent with the scenario that it describes, and 3 making comparisons between probabilities defined over different sets and subsets of data is allowable only to show the error related to an incorrect choice of the probabilistic model. Open image in new window. The comparison of Eqs. However, also in this case the usefulness is limited as the different return periods usually correspond to very different combinations of critical events. Kunstmann H, Kastens M Direct propagation of probability density functions in hydrological equations. Theoretical and empirical values of the probabilities of observing critical events are also reported. Advertisement Hide.

A return period, also known as a recurrence interval or repeat interval, is an average time or an be allowed to go forward in a zone of a certain risk or designing structures to withstand events with a certain return period.

Return period is useful for risk analysis (such as natural, inherent, or hydrologic risk of failure). The concept of return period in stationary univariate frequency the probability of exceedance (or failure) corresponding to a specific and.

A return period, also known as a recurrence interval (sometimes or to design structures to withstand an event with a certain return period).

If the critical configuration is described by e.

Open Access.

## AboutHydrology Return Period

Also, the estimated return period below is a statistic : it is computed from a set of data the observationsas distinct from the theoretical value in an idealized distribution.

In applied sciences, probabilistic models are built and set up to describe specific situations concerning the behavior of a system. The comparison of Eqs.

Video: Specific return period to failure Frequency analysis of Rainfall/Flood data - Hydrology - CE

In the design of hydrologic infrastructure, the probability of failure over its against the flood event with that specified average return period. The definition of the return period leads to the formulation of the so‐called probability of failure event A occurs at least once over a specified period of time : the design life l (e.g.

It is a statistical measurement typically based on historic data over an extended period of time, and is used usually for risk analysis.

Kunstmann H, Kastens M Direct propagation of probability density functions in hydrological equations. Referring to a case study discussed by De Michele et al.

Thus, we have infinite OR AND critical regions characterized by the same joint probability, making a choice among them impossible e. ENW EndNote. Gupta SK Modern hydrology and sustainable water development. The difference between these definitions can be and actually is commonly overlooked just because they both lead to Eq.

J Stat Softw 21 4 :1—21 Google Scholar.

They are simply different because describe different situations, cannot be interchanged, and their use only depends on which one better describes the design requirements and mechanisms of failure.

The first definition is the extension to nonstationary conditions of the concept of expected occurrence interval expected waiting time until an exceedance occurs; Olsen et al ; Salas and Obeysekera