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The University of Massachusetts Amherst

The End of Reliability


Casey Brown

Publication Type:
Journal Article
Year of Publication:
Secondary Title:
Journal of Water Resources Planning and Management


Recent attention has focused on the declaration of the death of stationarity and the associated implications for water management (Milly et al. 2008; Lettenmaier 2008). A recent panel convened by the EPA on the subject of water infrastructure planning in the context of climate change was notable for a lack of consensus and need for guidance expressed by water managers. Here I argue that the major implication of the end of stationarity is the end of the static design paradigm, exemplified by the concept of reliability, as the underlying design principle for water resource systems. Here reliability is defined in a general way, as "the probability of failure." To define failure it is useful to consider two archetypical water resources challenges that water engineers face. The first is planning for excess water, which normally involves a flood control system, as a result of drought. In this case failure would occur when the water supply system is unable to deliver the water that is demanded by its customers. Reliability is the probability that these failures do not occur. In wach of these cases, static assumptions about long-term probabilities, such as reliability, are a primary design consideration. The water system is designed to be reliable up to a given probability. Typically, the marginal cost of increases in reliability are low up to a point of high reliability where the marginal cost then increases rapidly for each incremental increase in reliability. The decision to build the infrastructure for a specified reliability reflects the decision makers' choice on the tradeoff between cost and reliability and is typically taken by the engineer as a fixed design variable. Flood control systems may be designed to withstand all floods up to, say, the flood, which is the flood that is estimated to have a 1% chance of being equaled or exceeded in a given year and consequently have a reliability of 99% in a given year. The traditional design of infrastructure where greater reliability is achieved through more storage volume and greater dike heights, which equal greater cost, means that there is a tradeoff between reliability and cost, including the cost of failure of the system. These decisions are dependent on our ability to accurately estimate reliability. An estimate of reliability depends on the assumption that it is possible to estimate the probability of a rare hydrologic event. As currently practiced, it relies on an assumption of stationarity. Reliability can also be calculated on a dynamic basis but is rarely done so in practice. Systems are designed to be reliable to a degree that is based on statistics of the historical record and thus the estimated reliability is dependent of unchanging statistics. The death of stationarity means that those statistics are changing and therefore our estimated reliability is not what we expect it to be. More generally, the traditional approach to water supply design depends on precise estimates of the probabilities of events that are difficult to estimate, involve linked physical and societal processes that are difficult of impossible to model and have only recently been considered worthy of research, and due to secular changes in climate, land use, etc., are becoming even more uncertain. This presents the water manager and the larger water resources research community with a dilemma.