How Likely Is The Observed Recent Warmth?

With the official numbers now in 2015 is, by a substantial margin, the new record-holder, the warmest year in recorded history for both the globe and the Northern Hemisphere. The title was sadly short-lived for previous record-holder 2014. And 2016 could be yet warmer if the current global warmth persists through the year.

One might well wonder: just how likely is it that we would be seeing these sort of streaks of record-breaking temperatures if not for human-caused warming of the planet?

Precisely that question was posed by several media organizations a year ago, in the wake of the then-record 2014 temperatures. Various press accounts reported odds anywhere from 1-in-27 million to 1-in-650 million that the observed run of global temperature records (9 of the 10 warmest years and 13 of the 15 warmest years each having had occurred since 2000) might have resulted from chance alone, i.e. without any assistance from human-caused global warming.

My colleagues and I suspected the odds quoted were way too slim. The problem is that each year was treated as though it were statistically independent of neighboring years (i.e. that each year is uncorrelated with the year before it or after it), but that’s just not true. Temperatures don’t vary erratically from one year to the next. Natural variations in temperature wax and wane over a period of several years.

For example, we’ve had a couple very warm years in a row now due in part to El Niño-ish conditions that have persisted since late 2013 and it is likely that the current El Niño event will boost 2016 temperatures as well. That is an example of a natural variation that is internally-generated. There are also natural variations in temperature that are externally-caused or ‘forced’, e.g. the multi-year cooling impact of large, explosive volcanic eruptions like the 1991 Mt. Pinatubo eruption, or the small-but-measurable changes in solar output that occur on timescales of a decade or longer. Each of these natural sources of temperature variation lead to correlations in temperature from one year to the next that would be present even in the absence of global warming. These correlations must be taken into account to get reliable answers to the questions being posed.

The particular complication at hand is referred to, in the world of statistics as “serial correlation” or “autocorrelation“. In this case, it means that the effective size of the temperature dataset is considerably smaller than one would estimate based purely on the number of years available. There are N=136 years of annual global temperature data from 1880-2015. However, when the natural correlations between neighboring years are accounted for, the effective size of the sample is a considerably smaller N’~30. That means that warm and cold periods tend to occur in stretches of roughly 4 years at a time. Runs of several cold or warm years are far more likely to happen based on chance alone than one would estimate under the incorrect assumption that natural temperature fluctuations are uncorrelated from one year to the next.

One can account for such effects by using a more sophisticated statistical model that faithfully reproduces the characteristics of actual natural climate variability. My co-authors and I used such an approach to more rigorously assess the likelihood of recent runs of record-breaking temperatures. We have now reported our findings in an article just published in the Nature journal Scientific Reports. With the study having come out shortly after New Year, we are able to update the results from the study to include the record new 2015 temperatures.

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