Stationarity

Stationarity—the assumption that natural-world phenomena fluctuate with a fixed envelope of statistical uncertainty that doesn't change over time—is a widely applied scientific concept that is ready to be retired.

It had a good run. For more than a century, stationarity has been used to inform countless decisions aimed at the public good. It guides the planning and building codes for places susceptible to wildfires, floods, earthquakes, and hurricanes. It is used to determine how and where homes may be built, the structural strength of bridges, and how much premium people should pay for their homeowner's insurance policies. Crop yields are forecasted and, in the developed world, insured against catastrophic failures. And as more weather stations and river level gages are built and accumulate ever-longer data records, our abilities to make such calculations get better. This saves lives and a great deal of money.

But a growing body of research shows that stationarity is often the exception, not the norm. As new satellite technologies scan the earth, more geological records are drilled, and the instrument records lengthen, they commonly reveal patterns and structures quite inconsistent with a fixed envelope of random noise. Instead, there are transitions to different quasi-stable states, each characterized by a different set of physical conditions and associated statistical properties. In climate science, for example, we have discovered multi-decadal patterns like the Pacific Decadal Oscillation (PDO), an El Niño-like phenomenon in the north Pacific that triggers far-reaching changes in climate averages that persist for decades (for example during the 20th century the PDO experienced a "warm" phase from 1922-1946 and 1977-1998, and a "cool" phase from 1947-1976) with far-reaching impacts on water resources and fisheries. And anthropogenic climate change, induced by our steady ramping up of greenhouse gas concentrations in the atmosphere, is by its very definition the opposite of a fixed, stationary process. This imperils the basis of many societal risk calculations because as the statistical probabilities of the past break down, we enter a world that operates outside of expected and understood norms.

This recognition is not new among scientists, but has been surprisingly slow to penetrate into the practical world. For example, even as awareness and acceptance of climate change has grown, stationarity continues to serve as a central, default assumption in water-resource risk assessment and planning. Floodplain zoning continues to be designed around stationary concepts like the 100- and 500-year flood, despite known impacts of land use conversion and urbanization on water runoff and the anticipated impacts of anthropogenic climate change. The civil engineering profession and most regulatory agencies around the world have been slow to acknowledge these changes and seek new approaches to address them. But viable alternatives exist, for example using the precautionary, no-regrets "probable maximum flood" (PMF) method to design dams and bridges, and incorporation of more flexible "subjectivist Bayesian" probabilities in societal risk calculations.

We can do better. Stationarity is dead, especially for our understanding of the world's water, food security, and climate.