Cliff Asness: It’s Not The Heat, It’s The Tepidity

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Cliff Asness: It’s Not The Heat, It’s The Tepidity

Clifford Asness and Aaron Brown

There is a graph you’ve probably seen a lot of lately. Articles everywhere feature it, or the data behind it, or a closely related cousin to either, highlighting temperatures at a new high, a visually strong long-term trend, and no recent temperature “hiatus.” This historical series is usually presented as proof that warming must be quickly and vigorously fought or we will reach dangerously high temperatures in the next few decades. These data and the implications taken from them require careful statistical scrutiny. We emphasize statistical at the outset because we are not challenging climate science; we are not climate scientists. We are, however, pretty experienced at statistics and inference.

The now famous graph shows global land-ocean annual mean surface temperatures since 1880 (the chart plots deviations from the 1951 – 1980 average):

While visually impressive it’s our contention that most – we’d say “all” but we haven’t seen them all – of the recent articles forget to look at the vertical axis and to ask the simple question, “are these numbers big?”

This essay is not about the science of climate change, it’s about what the data say on their own. In particular, we think it is important to distinguish the level of worry you might have from looking at this chart, versus the level of worry you might have from complex climate models.

With a chart like this, whether about climate or anything else, a natural thing is to draw a straight line through the data (we used a linear least square regression, but you get about the same thing with other statistical techniques or just doing it by eye). This is a guess at what the long-term trend is, and could be a base case for thinking about how hot things are likely to get in the future (extrapolating a trend must be done with skepticism but it seems to be a reasonable starting point for discussion).

Cliff Asness

It shows a warming trend of 0.67° Celsius per century. That doesn’t sound too scary, and as we’ll see that if that remains the trend, according to the experts, it’s indeed not too scary. It’s surprising that in the myriad of recent articles highlighting this graph, pointing to the trend, the lack of a hiatus in warming, and the recent highs, none we’ve seen mention (we apologize to any we’ve missed!) that the actual magnitude of 0.67°C per century is quite small and itself doesn’t take us to a dangerous level until much farther in the future than climate scientists forecast.

Of course the real but rather small trend doesn’t prove that global warming is a minor issue, far from it. We’re just saying the graph taken on its own is actually pretty reassuring, at least compared to predictions, and declared danger points, of the IPCC and similar groups. If things continue along the way they have for the last 135 years, the point at which we reach dangerous temperatures is a very very long time from now. Those predicting that we face a big problem much sooner aren’t arguing this from these data, instead they have to be arguing that historical warming trends will change drastically in the near future; that they will not continue at the trend of the past hundred years or so. The historical record to date, and in particular this ubiquitous graph, can’t be the basis of an argument that we will hit dangerous levels soon. To argue that we will hit them in this, or even next century requires us to explain away this graph, to explain why the rate of warming will increase.

To see this, let’s take a step back and use larger axes. We’re going to drag the timeline (the horizontal axis) out another 50 years to 2065, and extend our trend line, and enlarge the scale (the vertical axis) to go up to the 4°C of warming that has been used as a somewhat arbitrary danger level since the 1970s (we call that the IPCC limit below – later, and in our end notes, we discuss what happens if this danger level is reduced to 2°C, a level we also show in the following graphs).

Cliff Asness

It says yes, over the last 135 years the Earth has warmed, but not nearly to the danger point (the top of the graph at 4.0 on the y-axis) and if we continue at this pace (the crux of the issue) it won’t become scary until more than 500 years from now (not by the end of the 50 years we’ve added to the x-axis). That’s quite a different message from what we’ve read in the articles accompanying the original version of this chart.

Of course, this raises the very important issue of whether or not 4°C is the right danger line. No one knows the answer to this question, but 4°C seems the most common figure used by the experts. It’s what the IPCCiii uses in its most recent report. No one denies that there are some risks and costs to any amount of warming, and on the other hand, almost no one is predicting that warming at or slightly beyond 4°C will cause extinction of the human race either. Risks go up with the amount of warming. We just don’t know how fast. Despite the uncertainties, there seems to be a scientific consensus that less than 1°C or 2°C of warming would make global warming no more serious than several other environmental issues, but warming above 4°C would likely make global warming a unique danger. Even if the danger point is 2°C this trend doesn’t reach it until over 130 years from now.

Next let’s add to the graph the IPCC 1990 “business as usual” (the IPCC’s term for what happens if no efforts are made to restrain CO2 emissions) predictions for future warming. These are shown in the next graph as the three green lines, which show the expected (middle) case along with the good (lowest) and bad (highest) cases. The black line is still the linear trend implied by history and the blue line is still the actual temperature data. We start the green lines in 1990 when the forecasts were made.

Cliff Asness

Cliff Asness

See full PDF below.

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