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The New Climate Dice: Public Perception of Climate Change

Posted on 14 August 2012 by Daniel Bailey, John Hartz

NOTE: This is a repost of a NASA Science Brief by James Hansen, Makiko Sato, Reto Ruedy — August 2012.  The SkS analysis of this paper is available here.

The greatest barrier to public recognition of human-made climate change is probably the natural variability of local climate. How can a person discern long-term climate change, given the notorious variability of local weather and climate from day to day and year to year?

The question is important because actions to stem emissions of gases that cause global warming are unlikely until the public appreciates the significance of global warming and perceives that it will have unacceptable consequences. Thus when nature seemingly provides evidence of climate change it needs to be examined objectively by the public, as well as by scientists.

Fig 1

Figure 1. Fire fighters battle the Taylor Creek blaze, one of several fires which have burned over 75,000 acres in southeastern Montana in summer 2012. Image Therefore it was disappointing that most early media reports on the heat wave, widespread drought, and intense forest fires in the United States in 2012 did not mention or examine the potential connection between these climate events and global warming. Is this reticence justified?credit: USFWS/Gerald Vickers via

In a new paper (Hansen et al., 2012a), we conclude that such reticence is not justified. The paper attempts to illustrate the data in ways that properly account for climate variability yet are understandable to the public.

We show how the probability of unusually warm seasons is changing, emphasizing summer when the changes have large practical effects. We calculate seasonal-mean temperature anomalies relative to average temperature in the base period 1951-1980. This is an appropriate base period because global temperature was relatively stable and still within the Holocene range to which humanity and other planetary life are adapted (footnote 1).

We illustrate variability of seasonal temperature in units of standard deviation (σ), including comparison with the normal distribution ("bell curve") that the lay public may appreciate. The probability distribution (frequency of occurrence) of local summer-mean temperature anomalies was close to the normal distribution in the 1950s, 1960s and 1970s in both hemispheres (Fig. 2). However, in each subsequent decade the distribution shifted toward more positive anomalies, with the positive tail (hot outliers) of the distribution shifting the most.

An important change is the emergence of a subset of the hot category, extremely hot outliers, defined as anomalies exceeding +3σ. The frequency of these extreme anomalies is about 0.13% in the normal distribution, and thus in a typical summer in the base period only 0.1-0.2% of the globe is covered by such hot extremes. However, we show that during the past several years the global land area covered by summer temperature anomalies exceeding +3σ has averaged about 10%, an increase by more than an order of magnitude compared to the base period. Recent examples of summer temperature anomalies exceeding +3σ include the heat wave and drought in Oklahoma, Texas and Mexico in 2011 and a larger region encompassing much of the Middle East, Western Asia and Eastern Europe, including Moscow, in 2010.

The question of whether these extreme hot anomalies are a result of global warming is often answered in the negative, with an alternative interpretation based on meteorological patterns. For example, an unusual atmospheric "blocking" situation resulted in a long-lived high pressure anomaly in the Moscow region in 2010, and a strong La Niña in 2011 may have contributed to the heat and drought situation in the southern United States and Mexico. However, such meteorological patterns are not new and thus as an "explanation" fail to account for the huge increase in the area covered by extreme positive temperature anomalies. Specific meteorological patterns help explain where the high pressure regions that favor high temperature and drought conditions occur in a given summer, but the unusually great temperature extremities and the large area covered by these hot anomalies is a consequence of global warming, which is causing the bell curve to shift to the right (Fig. 2).

Fig 2

Figure 2. Temperature anomaly distribution: The frequency of occurrence (vertical axis) of local temperature anomalies (relative to 1951-1980 mean) in units of local standard deviation (horizontal axis). Area under each curve is unity. Image credit: NASA/GISS.

Yet the distribution of seasonal temperature anomalies (Fig. 2) also reveals that a significant portion (about 15 percent) of the anomalies are still negative, corresponding to summer-mean temperatures cooler than the average 1951-1980 climate. Thus people should not be surprised by the occasional season that is unusually cool. Cool anomalies as extreme as -2σ still occur, because the anomaly distribution has broadened as well as moved to the right. In other words, our climate now encompasses greater extremes.

Our analysis is an empirical approach that avoids use of global climate models, instead using only real world data. Theories for the cause of observed global temperature change are thus separated as an independent matter. However, it is of interest to compare the data with results from climate models that are used to simulate expected global warming due to increasing human-made greenhouse gases.

Indeed, the "climate dice" concept was suggested in conjunction with climate simulations made in the 1980s (Hansen et al., 1988) as a way to describe the stochastic variability of local temperatures, with the implication that the public should recognize the existence of global warming once the dice become sufficiently "loaded" (biased). Specifically, the 10 warmest summers (Jun-Jul-Aug in the Northern Hemisphere) in the 30-year period (1951-1980) were used to define the "hot" summer category, the 10 coolest the "cold" category, and the middle 10 the "average" summer. Thus it was imagined that two sides of a six-sided die were colored red, blue and white for these respective categories. The divisions between "hot" and "average" and between "average" and "cold" occur at +0.43σ and -0.43σ for a normal distribution.

Temperatures simulated in a global climate model (Hansen et al., 1988) reached a level such that four of the six sides of the climate dice were red in the first decade of the 21st century for greenhouse gas scenario B, which is an accurate approximation of actual greenhouse gas growth (Hansen and Sato 2004; updates are provided by a Columbia Univ. webpage). Observed summer temperature anomalies over global land during the past decade averaged about 75% in the "hot category", thus midway between four and five sides of the die were red, which is reasonably consistent with expectations.

Fig 3

Figure 3. Frequency of occurrence (vertical axis) of local June-July-August temperature anomalies (relative to 1951-1980 mean) for Northern Hemisphere land in units of local standard deviation (horizontal axis). Temperature anomalies in the period 1951-1980 match closely the normal distribution ("bell curve", shown in green), which is used to define cold (blue), typical (white) and hot (red) seasons, each with probability 33.3%. The distribution of anomalies has shifted to the right as a consequence of the global warming of the past three decades such that cool summers now cover only half of one side of a six-sided die, white covers one side, red covers four sides, and an extremely hot (red-brown) anomaly covers half of one side. Image credit: NASA/GISS.

The relation between the bell curve and climate dice is illustrated in Fig. 3. Extremely hot outliers already occur more frequently than unusually cold seasons. If the march of the bell curve to the right continues unabated, within a few decades even the seasons that were once considered average will cease to occur.

We have shown that the increased frequency of "hot" seasons is a result of global warming. The cause of global warming is a separate matter, but observed global warming is now attributed with high confidence to increasing greenhouse gases (IPCC 2007a).

Both attributions are important. Together they allow us to infer that the area covered by extreme hot anomalies will continue to increase in coming decades and that even more extreme outliers will occur. Indeed, we conclude that the decade-by-decade shift to the right of the temperature anomaly distribution (Fig. 2) will continue, because Earth is now out of energy balance, with more solar energy absorbed than heat radiation emitted to space (Hansen et al., 2011); it is this imbalance that drives the planet to higher temperatures. Even an exceedingly optimistic scenario for fossil fuel emissions reduction, 6%/year beginning in 2013, results in global temperature rising to almost 1.2°C relative to 1880-1920, which compares to a current level ~0.8°C (Hansen et al., 2012b).

Practical effects of increasingly loaded climate dice occur mainly via amplified extremes of Earth's water cycle. The broadening of the "bell curve" of temperature anomalies is related to interactions of warming with the water cycle. Hot summer anomalies occur when and where weather patterns yield an extended period of high atmospheric pressure. This condition is amplified by global warming and the ubiquitous surface heating due to elevated greenhouse gas levels, thus increasing the chances of an extreme anomaly. Yet global warming also increases atmospheric water vapor overall, causing, at other times or places, more extreme rainfall and floods, consistent with documented changes over Northern Hemisphere land and the tropics (IPCC 2007b).

Fig 4

Figure 4. Wildfire frequency and spring-summer temperature in the western United States. Image credit: Westerling et al. (2006).

The (Northern Hemisphere) summer of 2012 is still unfolding. A global map of the anomaly distribution will be provided on a Columbia Univ. webpage) once the data are complete; the data so far suggest that parts of the United States and Asia likely will be in the extreme (+3σ) category. One of the consequences of extreme summer heat anomalies is increased area and intensity of wildfires, as shown in Fig. 4. Updates of these data and other climate impacts after the 2012 data are complete will be useful for assessing impacts of continued global warming.

Related Articles

NASA News: How Warm was Summer 2010?

NASA Earth Observatory: Image of the Day, Aug. 9, 2010: Heatwave in Russia

NASA Earth Observatory: Image of the Day, June 29, 2012: Heat Wave Fuels Wildfires in the Rockies

NASA Earth Observatory: Image of the Day, July 17, 2012: Drought Grips the United States


1 In contrast, we infer that current global temperature is above the Holocene range, as evidenced by the fact that the ice sheets in both hemispheres are now rapidly shedding mass (Rignot et al., 2011) and sea level is rising (Nerem et al., 2006) at a rate (more than 3 mm/year or 3 m/millennium) that is much higher than the rate of sea level change during the past several millennia.

James Hansen: Extreme Heat Events Connected to Climate Change

An interview by Hari Sreenivasan of PBS Newshour.

Full article here.

A quote from the interview:

"In fact, [climate change] has now driven our climate outside the range that has existed the last 10,000 years..." --James Hansen

Summer Temperature Anomalies for the Northern Hemisphere, 1955-2011

Color Bar

Earth's Northern Hemisphere over the past 30 years has seen more "hot" (orange), "very hot" (red) and "extremely hot" (brown) summers, compared to a base period defined in this study from 1951 to 1980. This visualization shows how the area experiencing "extremely hot" summers grows from nearly nonexistent during the base period to cover 12 percent of land in the Northern Hemisphere by 2011. Watch for the 2010 heat waves in Texas, Oklahoma and Mexico, or the 2011 heat waves the Middle East, Western Asia and Eastern Europe. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio
+ Download hi-res visualization


Shifting Distribution of Northern Hemisphere Summer Temperature Anomalies, 1951-2011

James Hansen and colleagues use the bell curve to show the growing frequency of extreme summer temperatures in the Northern Hemisphere, compared to the 1951 to 1980 base period. The mean temperature for the base period is centered at the top of the green curve, while hotter than normal temperatures (red) are plotted to theright and colder than normal (blue) to the left. By 1981, the curve begins to shift noticeably to the right, showing how hotter summers are the new normal. The curve also widens, due to more frequent hot events. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio
+ Download hi-res visualization

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Comments 1 to 12:

  1. It's good that people are now looking at theglobal pattern of extreme events rather than at individual ones. Any signal will be detectable in the ensemble rather than in individual observations. But they really do need a statistician in on this rather than relying on their own knowledge of statistics. There are things that they have not done in this study that need to be done to make the conclusions more robust. Have they actually checked for normality or is the distribution a heavier or lighter tailed one? Have they checked for change in variance with time? Have autocorrelations in time and space been allowed for? I don't see any sign of these having been considered and as a statistician I would want them to have been looked at. This looks like a case of non statisticians doing their own statistics when they should not. I think the conclusions are probably correct but are not robust enough.
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  2. Perhaps we should wait for the analysis tomorrow on the paper itself before going too far down this road.
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  3. Tamino has a look at the paper.
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  4. Yes we need at least five sigma signal to incontrovertibly prove our premise. This will be very robust and far too late! The statistics of extreme events do not prove the case but taken with all the other indicators that are all skewed toward a warming Earth are a very compelling argument. Bert
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  5. Have they actually checked for normality or is the distribution a heavier or lighter tailed one? Have they checked for change in variance with time? Have autocorrelations in time and space been allowed for?
    I think that the statistical understanding of the researchers is rather more sophisticated than the low level that would be required to ignore such basic processing. And even though such tests are useful, there's the simple fact that many analyses are robust to departures from standard assumptions, especially where such departures are slight. Further, there's the simple fact of the consilience of different datasets with each other, and with the underlying physics. If there is a Type I error occurring, then there is a huge problem not just with some statistical analyses, but with the fundamental scientific understanding of basic physical processes. Ockham's parsimony razor is unkind to such discrepant protruberances.
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  6. Lloyd, It would be a good idea to read the paper before criticizing it. They have checked for normality and find that the distribution has shifted. Tamino does not agree with that conclusion on his blog. Hansen's work is peer reviewed. Please provide data to support your analysis. You assume that Hansen did not review the paper with a statistician. I doubt your assumption is correct. After all it was on the web for months for comments like yours.
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  7. SEAN O, I get nothing when I click on your link.
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  8. Ahh, what a lovely post. Thank you for providing such a good summary.
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  9. Sorry Try this
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  10. This article is about the public perceptions of climate change. I think we need to be very careful about the language used. I am not a mathemetician, luckily I did do first year stats at uni and although I can't remember the specifics, I do understand what a standard deviation is. However, I think most of the non-specialist audience is lost once terms like standard deviation are used. I know this is very difficult but the language really has to avoid technical terms, even simple technical terms. The dice analogy is good but deniers just come back with statements disparaging analogies! I know this is a difficult issue to explain at times and there are a lot of people out there who are willfully ignorant and wish to remain that way, but we do need to find language that works. Anyway, great site, it's going to take a lot of thought to work out how to convince people the science is correct but if we all put our minds to it we can find ways to communicate complex issues to non-specialist audiences without dumbing it down.
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  11. Skeptical Science can help Hansen with a problem he is going to have with his next paper. He used "hot" for one sigma, "very hot" for two sigma and "extremely hot" for three sigma. The data already shows four sigma events occurring. What term will he use for four, five and higher sigma?? What is a stronger term than "extremely hot"? Would these work: four sigma = "extraordinarily hot" five sigma = "unbearably hot" six sigma = "hot as Hell" seven sigma = "hotter than Hell" eight sigma = ??? Who has a suggestion?
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  12. Michael sweet@11: my suggestion for 8 sigma? KYAG. Said in other words, we're *done,* as in, stick a fork in humanity.
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