Return Period and Risk of Hydrologic Events. I: Mathematical Formulation

Abstract

The estimation of return periods of hydrological events and the corresponding risks of failure of hydraulic structures that are associated with such events are important aspects in many water resources studies. For simple hydrologic events such as those related to independent annual floods, both the return period and the risk of failure can be readily calculated. However, no general applicable methods are available for the estimation of return periods, risk of failure, and reliability of service in cases of more complex hydrological events such as those related to dependent annual flows and droughts. In this paper, the definitions commonly employed for return period and risk of failure are reexamined and a general procedure for their estimation are presented, which may be applicable to a wide range of hydrological events related to floods, droughts, minimum flows, aquifer levels, and reservoir levels and outflows. Part II of this paper includes numerical examples and applications.