The Underappreciated Importance of Climate Variability

A graph that changed how I think about extreme weather and climate

Adam van Breen, 1611. Skating on the Frozen Amstel River.

One of the most pervasive misunderstandings of climate — even among some who publish on climate — is the belief that any long-term trend in a measured climate variable indicates a change in climate, as defined by the IPCC. In practice, “long-term” is often defined to be only a few decades worth of observations.

Some trends in observational data are not an indication of a change in climate, and others are — telling the difference is not easy when it comes to extreme weather events. This post explains why.

The IPCC AR6 explains that the detection of a change in climate requires some certainty that the trend is not simply due to climate variability:

An identified change is detected in observations if its likelihood of occurrence by chance due to internal variability alone is determined to be small, for example, <10%.

Quantifying internal variability with respect to any climate metric is challenging, typically with multiple valid interpretations possible. Superimposed upon the challenge is the fact that internal variability itself has been influenced by human factors, notably the emission of greenhouse gases.

A common simplifying assumption underlying the belief that a particular trend indicates change is that of stationarity in the statistics of variable of interest — meaning an expectation that the various statistical characteristics of a time series (such as the mean, standard deviation, skew, etc.) would not change over time, but for a human influence.

Such an assumption obviously makes the tasks of detection and attribution of change much easier. In addition, under an assumption of underlying stationarity, a longer observational time series for a climate metric might be useful, but would not be necessary for the detection of change. For instance, if an observational record of tropical cyclones is 50 years, then an assumption of stationarity in the underlying statistics would lead to an expectation that the statistics of tropical cyclones in the 50 years before that would be the same. Similarly, any trends found in tropical cyclone metrics over the most recent 50 years would indicate a detected change.

Of course, we know that 50 years of observations is not sufficient to fully characterize internal variability associated with tropical cyclones. However, studies are routinely published suggesting the detection of trends indicating a change in climate using 50 years of data, and often much less.

The stationarity assumption is implicit in the figure below, from the U.S. Environmental Protection Agency. The figure is often used by professional climate communicators to explain how climate change increases the probability of extreme events.

Source: US EPA

The figure shows a bell curve-shaped distribution of temperatures that is shifted to the right (the red curve) due to greenhouse gas emissions, with corresponding implications for the occurrence of extreme weather events. However, climate reality is much more complex than a simple fixed bell curve that moves because of human influences, as climate measures vary over time, with and without human influences.

The figure is simple and intuitive — and deeply misleading.

The phrase in the figure above — “current climate” — is in many cases poorly understood. The notion of a “current climate” reflects an understanding of the expected likelihood of different events, like a maximum daily temperature over 40C or a record-setting flood. Conventionally, the climate community has used the most recent 30-years to represent a “current climate.”

The current climate varies on timescales both greater and less than 30 years. The IPCC AR6 defines climate variability (emphases in original):

Deviations of climate variables from a given mean state (including the occurrence of extremes, etc.) at all spatial and temporal scales beyond that of individual weather events. Variability may be intrinsic, due to fluctuations of processes internal to the climate system (internal variability), or extrinsic, due to variations in natural or anthropogenic external forcing (forced variability).

Typically, the “current climate” associated with a particular variable is defined by observations of that variable. But how near or far into the past does one need to go to adequately characterize a “current climate”?

Let’s illustrate the issues here with a detailed example.

Back in 1997, when I was a post-doctoral researcher at the National Center for Atmospheric Research studying extreme weather, I was tapped by the U.S. National Weather Service to serve on its disaster assessment team following the catastrophic flooding along the Red River of the North in Minnesota and North Dakota. In many respects, that experience was career changing.

In my research that followed the disaster assessment I came across a 1984 U.S. Geological Survey Report that changed how I understood climate and changes in climate. The figure below — which I have annotated — comes from that report.

Source: USGS 1984. Note: I added the arrows and text box as described below.

The figure show return periods for flow in the Red River of the North at Grand Forks, ND. On the vertical axis is the flow level and the horizontal axis shows the expected recurrence interval in years for flow levels for four different periods of the historical record, spanning 1882 to 1979. A return period of 100 years corresponds to a “100-year flood,” one with an expected 1% annual probability of occurring.

I remember two eye-opening conclusions I took from this graph.

First, the very notion of a stationary flood return period makes little sense in the context of significant climate variability. Even taking the entire 97-year record to create a flood return period curve (imagine a line going right up the middle of the four curves in the graph) would fail to represent annual flood risk in every year of the record.

The second conclusion was that in the presence of variability, it would be very easy to confuse a trend in a variable with a change in the statistics of that variable — That is, to confuse climate variability with climate change, in the language of the IPCC.

If we look at the entire measured time series of flow of the Red River of the North at Fargo, ND, from 1897 to 2020, we see an obvious upwards trend.

Red River of the North, peak flood levels at Fargo, 1897 to 2020. Source: St. George et al. 2021.

Obviously a detected change in flooding as defined by the IPCC, right?

Well, yes and no.

The trend is real. Clearly the chances of a major flood on the Red River of the North have been much higher over the past 30 years than they were in the first three decades of the 20th century.

Hirsch (2011) suggests of this time series:

Looking at this result, it would be easy to conclude that floods are getting larger over time and this would be very consistent with a hypothesis that increased greenhouse gases are driving this increase.

Under both the IPCC’s detection and attribution framework and methodologies of extreme event attribution, the data in the figure would be characterized as a change in climate, and associated with human-caused climate change.

But not so fast . . .

At the same time, an even longer record of flooding in the basin, from 1790 to 2011 indicates many floods pre-1897 that exceeded the largest flood of the past century. With this record, the largest recent floods have become relatively smaller.

The 1790–2011 record of Red River peak flows at Redwood bridge, Winnipeg, including floods inferred from historical accounts ( grey bars) and those determined from measurements of stage ( black bars; all data from Manitoba Water Stewardship). Source: Brooks and St. George 2015.

When considering a longer time series for the Red River of the North, Hirsch (2011) explains that,

. . . we get a very different and more complex picture. . . Now we would say that although there has been some increase in flood magnitudes over time, the pattern is no longer very consistent with a hypothesis that this is driven by greenhouse gas increases in the atmosphere. The high values in the 19th Century are inconsistent with this hypothesis. In fact, one could put forward the argument that there are two populations of annual floods at this location. One is the population that spanned the years of about 1900 to 1941, and the other population existed before 1900 and after 1942. Without the benefit of the longer record, we could easily conclude that the data were highly supportive of a greenhouse-gas driven trend in flood magnitudes, but with it we find ourselves having to entertain other highly plausible hypotheses about an abruptly shifting population, with shifts that take place at time scales of many decades. The data do not negate the possibility that greenhouse forcing is a significant factor here, but they make it much more difficult to argue that these data provide a clear demonstration of the effect of enhanced greenhouse gas forcing on flood magnitudes.

Assumptions of statistical stationarity of climate-related variables are common in climate-related policies and in climate research.

For instance, the U.S. government’s approach to flood policy is grounded in the notion of a base flood — otherwise known as a 100-year flood, one with a 1% annual chance of occurrence. The idea behind the base flood — following from the 1968 Flood Insurance Act — was that it would allow flood risks in different locations around the country to be evaluated on an apples-to-apples basis, to support rigorous cost-benefit analyses of flood mitigation opportunities.

It is an intuitive and creative way to compare flood risks around the country. However, the base flood does not accurately reflect how the climate actually behaves.

In reality, the non-stationarity of flood statistics (on human time scales at least) mean that the base flood is a moving target. This challenge has been long recognized by flood experts, even as no alternative to the base flood has emerged. Leslie Bond explained this more than 20 years ago:

In the statistical estimation of a flood peak of a specific recurrence interval requires that all of the recorded peak flows be accurate and that the record be stable over the period of the record and the period for which the estimate is to be applied. That is, if there is a 50-year record of stream flow from 1931 through 1980, and you want a current estimate of the 1% flood to be valid for 30 years, the hydrology, the meteorology and the hydraulics must be stable from 1930 through 2034. In fact, we do not have sufficient historic rainfall data to be sure that the meteorology is stable, and few watersheds in the world are not changing as a result of urbanization, deforestation, agriculture, grazing or other causes.

A paper published last week explains in much more technical terms how a short observational record — in the context of internal variability — can lead to incorrect conclusions about trends and the causes of trends in that record:

It is important to study when the ACC [Anthropogenic Climate Change] signal emerges distinctly relative to internal variability on a case-by-case basis. The ACC signal is known to have emerged in most regions of the world for temperature extremes, while this may not be the case for variables like precipitation that have much higher variability. Time of emergence is a factor that should always be considered when discussing the results of an attribution study. Our results do not provide evidence against a relationship between GMST [Global Mean Surface Temperature] and local extremes but, rather, that internal variability needs to be taken into account when fitting a distribution function to the record.

In previous posts I have explained the importance of time of emergence for the detection of trends in climate variables and the perils of ignoring climate variability when claiming the detection of a trend indicating a change in climate.

Hirsch (2011) warned of seeing trends in data when instead we are only seeing a part of a much more complex system:

Long-term persistence and human-induced trend are very easily confused. Hurst (1951) taught us about persistence many years ago. It is the natural pattern for wet years to tend to follow wet years and for dry years to tend to follow dry years. Mandelbrot and Wallis (1969) introduced the concept of “fractional noise,” which is an example of a stochastic process that exhibits long-term persistence. Mandelbrot and Wallis (1969, pp. 230-231) observed that “[a] perceptually striking characteristic of fractional noises is that their sample functions [time series data] exhibit an astonishing wealth of ‘features’ of every kind, including trends and cyclic swings of various frequencies.” Matalas (1990) commented on the problem of distinguishing trend from persistence by saying that “…a trend in the short run may be part of an oscillation in the long run.” In recent years, we have learned much more about quasi-periodic variations like El Niño, Pacific Decadal Oscillation, and Atlantic Multi-decadal Oscillation, and even the ice ages. We have learned that these ocean-atmosphere related oscillations can have significant impacts on hydrology. We also know that these phenomena are still beyond the limits of our ability to predict. Given what we have learned about these sources of long-term persistence, we need to be very careful to avoid falling into the trap of seeing a pattern that plays out over several decades and calling it a trend.

A main reason why the IPCC has not achieved detection of trends in most measures of extreme weather events, and does not expect to this century, is the magnitude of expected trends — based on model projections — in the context of documented variability.

This does not mean that humans are not influencing the climate system or extreme events, or that such influences are not important. It certainly does not mean that we should forget about mitigation and adaptation policies.

What it does mean is that the climate is more variable than many appreciate. A quest to identify trends and ascribe causality to them should not obscure the fact that whatever role humans play in altering the climate, society needs to be robust to a much wider range of possibilities than we’ve observed.

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