The objective of this work is to enhance the understanding of the risks and catastrophic natural and manmade events. The project will develop the mathematical bases where three concepts/issues will be integrated: a) the return period of the maximum probable flood (PMF); b) the statistics of the extreme and the choice of probability distribution function; and c) the conditional expected damage as derived from the partitioned multiobjective risk method (PMRM) that corresponds to low frequency/high impact events. This work will increase and improve our understanding of the stochastic processes associated with extreme natural events. Five tasks will be carried out, and they are: 1) develop a cogent and definite mathematical relationship between the a-priori assumptions on the return period of the PMF and their effects on dam safety problems; 2) expand findings to the dynamics of the return period of PMF in general; 3) broaden the relationship between PMRM and the statistics of extremes from certain densities to a larger class of distributions; 4) link the concept of conditional expectation of extreme events to the concept of return period; and 5) integrate tasks 3 and 4, so as to create the envisioned mathematical model. An Expedited Award for Novel research is here recommended.
