In statistics of extremes of a continuous climatic variable, the return period at a geographical point is defined as the mean value of time-intervals between successive two unusual values exceeding a critical amount of the variable.
As an extension of this conception we can define the return period on a one-dimensional domain, for instance along a quasi-straight railway line or a highway, as the mean value of time-intervals between two successive unusual values above a certain amount whose return period is T1 years at any point on the domain.
The return period on a one-dimensional domain T∞, for instance of heavy rains, is given, under certain reasonable conditions, as follows:
T∞=T1/(1+m)
Here, m is a constant determined by the nature and the length of the one-dimensional domain and the point return period T1 on the domain, and is given as the sum of probability of simultaneous occurrence of unusual values on adjacent points on the area.
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