Despite remarkable new developments in stochastic hydrology and adaptations of advanced methods from operations research, stochastic control, and artificial intelligence, solutions of complex real-world problems in hydrogeology have been quite limited. The main reason is the ultimate reliance on first-principle models that lead to complex, distributed-parameter partial differential equations (PDE) on a given scale. While the addition of uncertainty, and hence, stochasticity or randomness has increased insight and highlighted important relationships between uncertainty, reliability, risk, and their effect on the cost function, it has also (a) introduced additional complexity that results in prohibitive computer power even for just a single uncertain/random parameter; and (b) led to the recognition in our inability to assess the full uncertainty even when including all uncertain parameters.
One of the challenges facing environmental attorneys and their clients is the development of an equitable allocation of responsibility for cleanup costs associated with groundwater contamination from several potentially responsible parties. This article provides a survey of several scientific approaches for the allocation of such responsibility