A methodology will be developed for comprehensive and quantitative mathematical simulation of warning systems for rapid-onset natural hazards. The methodology will encompass all major factors that determine the performance of a total warning system: geophysical, technological, organizational, behavioral, and economic factors. Next, mathematical models of warning systems will be developed for two types of hazards: flash floods and riverine floods. The purpose of the models will be to provide a scientific basis and analytic means for engineering design, operation, evaluation of performance, and benefit-cost analyses of warning systems. Engineering usefulness of the models will be tested through representative applications.