Stationarity

When the ancient capital of the Nabataeans, Petra, was "re-discovered" by Johann Burckhardt in the early 1800's, it might have seemed unthinkable that anybody could have lived in such an arid place. Yet, at its peak in the first century BCE, Petra was the center of a powerful trading empire and home to more than 30,000 people.

Petra's very existence was a testament to how water management could support the development of civilization in the most extreme circumstances. This part of the world—today in the Hashemite Kingdom of Jordan—survives on less than 70 mm of rain a year, much of it concentrated in a few events in the rainy season. The climatology two thousand years ago was similar, yet Petra thrived thanks to a system of rock-cut underground cisterns, terraced slopes, dams, aqueducts, which stored and delivered water from springs and run-off flows. Petra could grow food, provide drinking water, and support a bustling city because of that infrastructure.

This story is not dissimilar to many other places across the world today, from the Western United States to Northern China, from South Africa to the Punjab—all have thrived and grown thanks to human ingenuity and water engineering, allowing people to overcome the adversity of a difficult—at times, impossible—hydrology.

Whether the Nabataean engineers knew it or not, to deliver reliable water infrastructure, they relied—like all water engineers since—on two commonly assumed properties of hydrological events: stationarity and, rather more esoterically, ergodicity. Both concepts have well defined mathematical meaning. Simply put though, stationarity implies that the probability distribution of a random event is independent of time, while a stationary process is ergodic if, given a sufficiently long time, it will realize most of the universe of options available to it.

Practically, this allows one to assume that if an event has been observed for long enough, then one will have also in all likelihood witnessed enough of its behavior to represent the underlying distribution function at any given point in time. In the case of hydrology, it is what allows us to define events by using time statistics, like the "one in a hundred years flood".

The assumption that hydrology can be represented by such stationary processes makes it possible to design infrastructure whose behavior can be expected to be known well into the future. After all, water infrastructure like dams, levees and so on last for decades, even centuries, so it is important that they are dimensioned to withstand most predictable events. This is what has allowed Nabataean, Chinese, America, South African and Indian water engineers to design water systems they could legitimately rely on. And they have been wildly successful, so far.

Stationarity provides a convenient simplifying gambit: that plans for future water management can be based on an appropriately long historical time series of hydrology past, because the past is simply a representative sequence of realizations of a (roughly) fixed probability distribution.

Simple. But of course in the real world—where there is no counterfactual and where a single experiment is running all the time—such assumptions are only true until proven wrong. We are now realizing that those assumptions are, in fact, wrong. Not just theoretically wrong, but practically flawed.

In the last few years, a growing number of observations have been substantiating the idea that probability distributions we assumed fixed are not. They are changing, and changing fast: many of what used to be one in a hundred year events are more likely to be one in twenty years; droughts that used to be considered extreme and very unlikely are now much more common. Accelerating changes in climate, coupled with a much more sensitive global economy in which many more people and much more value is at stake, are revealing that we actually do not live in a world as stationary as we thought. And infrastructure that had been designed for that world, intended to last for decades into the future is proving increasingly inadequate.

The implications are rather monumental for our relationship with the planet and its water resources. A broadly stationary environment can be "engineered away". Someone will take care of it, as long as we can define what we need and have enough resources to pay for it. In a non-stationary world, it is different. The problem of water management is no longer decoupled from the dynamics of climate, as the climatology is no longer constant on practical timescales. We face unforeseen variability, the past is no longer necessarily a guide to the future, and we cannot simply rely on "someone taking care of it". "It" is no longer just an engineering problem. Climatology, hydrology, ecology, and engineering all become relevant instruments in the management of a dynamic problem, whose nature requires adaptability and resilience, one in which our own economy should be prepared to adapt, because no long term piece of infrastructure can be expected to manage what it was not designed for.

By the first century CE, the Nabateans were incorporated in the Roman Empire and over the course of the subsequent centuries their civilization slowly withered away, the victim of changing trade routes and shifting geopolitics (and proof that while water can support the development of civilizations, it is far from sufficient to see them thrive!) Today we have hundreds of cities around the world that, just like Petra, rely on engineered water infrastructure to support their growth. From Los Angeles to Beijing, from Phoenix to Istanbul, great cities of the world depend on a reliable source of water in the face of unreliable hydrology.

If stationarity is indeed a thing of the past, water management is no longer a "white coats" business, something that can be taken care of in the background. We must consider choices, have contingency plans for events that we might not have experienced, and accept that we might get it wrong. In other words, we must go from managing water to managing risk.