Stationarity is Dead! Whither Water Management?

Last summer Chris Milly wrote an article in which he proclaimed "Stationarity is dead!" I noted that we hydrologists have been reluctant to admit that because it would cast doubt on the way we manage water. I commented to a colleague that when I took the late Chester Kisiel's statistical hydrology course on the early 1970s, he discussed why hydrologic stationarity was an invalid concept. Then we proceeded to apply techniques that assumed stationarity to solve water management problems - dam design, etc.

Milly and his colleagues recently published a longer article in Science:

Download milly_et_al.pdf 

So what do we mean by "stationarity", and why should we care?

By "stationarity" we mean, that, statistically speaking, the future looks like the past - whether we are talking about precipitation, runoff, or other flows in the hydrologic cycle, depicted below. The numbers represent relative flow rates (from Hornberger et al., 1998, Elements of Physical Hydrology).

Take this frequency diagram (again, from Hornberger et al., 1998, Elements of Physical Hydrology). It shows the frequencies of annual precipitation in Seattle and Denver.

Stationarity says we can assume that the mean annnual precipitation in Seattle and Denver over the next 50 years, 1990-2039, would be "around" 941 mm and 380 mm, respectively - the same as 1940-1989. In fact, by invoking the stationarity assumption we can assume that over the next few thousand years (or longer), the rainfall distributions for Seattle and Denver will look the same as they do above.   

The same would hold for the distribution of runoff (streamflow), which can also be described by frequency or probability distrbutions.

This assumption makes planning easier. For example, if we need to know runoff so that we can design a large enough dam or big enough reservoir to provide enough water or flood protection for the next 100 years, stationarity allows us to do that with some degree of confidence, provided we have enough data to construct or develop a frequency or probability distiribution.

We know that hydrologic processes do not behave like stationary ones. Why not? Well, we humans have altered the hydrologic cycle. Example: imagine your watershed and what it looked like 200 years ago, or even 20 years ago. It has probably seen much development, which has changed the rainfall-runoff relationship. So if a dam in your watershed was built 50 years ago, the runoff frequency distribution upon which it was based probably is invalid. 

Milly et al. argue that climate change is rendering hydrologic stationarity a quaint concept, and we are grasping for ways to translate observations into predictions. So we are now likely dealing with a nonstationary process - the mean precipitation (or runoff, etc.) in the future won't be the same as it was in the past. So how do we plan?

Global warming will alter runoff patterns. The figure below, from Milly et al.), shows the "winners" and "losers" (median values from 12 climate models) in the volume of runoff from ice-free areas in the mid-21st century, relative to the 1900-1970 period. What you see is nonstationarity: the future is not like the past.

The reds and yellows indicate the greatest percentage decrease.

Look at Mexico, the Southwest USA, parts of Europe, northern and southern Africa, and the Middle East. Could be ugly.

Milly et al. indicate the critical need to develop new probabilistic models for rainfall, streamflow, etc. that are nonstationary.

The hydroclimatologic future is upon us, and we are unprepared.

"Statistics always remind me of the fellow who drowned in a river whose average depth was only three feet." -- Woody Hayes, ex-Ohio State football coach

Comments

[Daniel Collins]

Milly and company suggest "we need to find ways to identify nonstationary probabilistic models of relevant environmental variables and to use those models to optimize water systems."

I'm not so sure. The fuzzier our crystal ball gets, the more adaptable and resilient to eventual surprises we must become.

I favour bolstering our resilience (a la Hashimoto as well as Holling): diversify our portfolio of water sources; reduce our demand relative to hydro uncertainties and trends.

There are a lot of non-optimal solutions that are good enough.