The question of whether 2014 was or wasn’t the warmest year has recently exercised the minds of many. The answer, of course, is…

No.

At some point in the past, the Earth was a glob of molten rock pummelled by other rocks travelling at the kind of speeds that made Einstein famous, dinosaurs late and a very, very, very loud bang. There have also been periods, more hospitable to life (of various kinds), where global temperatures were in excess of what they are today.

However, if we narrow the scope of our question to the more conventional and cosmically brief period covered by our instrumental temperature record – roughly 1850 to now – the short answer is…

Maybe.

This has been an answer to a Frequently Asked Questions on the Met Office website (http://www.metoffice.gov.uk/hadobs/hadcrut4/faq.html) and has been the source of occasional ridicule.

That’s fine.

Obviously, one year was the warmest1. In other words, according to some particular definition, the global average of the temperature of the air near the surface of the Earth in 2014 or some other calendar year was higher than in any other. Unfortunately, we don’t know what that number is for any particular year. We have to estimate it1.5 from, sparse and, occasionally unreliable measurements. Some of them made with the help of a bucket.

That gap, the gap between the estimated value and the unmeasurable, might-as-well-be-mythical, actual global temperature is the reason for the “Maybe”. This is a common problem familiar to anyone who has attempted to measure anything2. If you are unfamiliar with it, ask a room full of people what time it is. You’ll get a range of answers3. These answers will be clustered close to the actual time, but not exactly on it. Most people are used to living in this chronological fog of doubt. They allow for the fact that watches and reality never line up precisely.

For global temperature (or any other measurement for that matter) we don’t know exactly how large that gap is, but we can by diverse methods get a reasonable handle on what kind of range it might fall within. Most people’s watches are within five minutes either side of the “right time”. Or, to put it another way, the right time is usually within five minutes either side of what most people’s watches say. That range is the uncertainty.

The good news is that, armed with this uncertainty information for global average temperatures, there are some years, for which the answer to the question “Well, what about this year, could this year be the warmest?” is, resoundingly, undoubtedly, 100%: No.

Non. Nein. Niet. Nopety, nopety, noooooo.

The number of years in the global temperature record which definitely aren’t the warmest is quite large. I would go so far as to say, it’s most of them. Here, for your enjoyment, is a list of definitely-not-the-warmest years.

1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1999 and 2000.

Out of a record, which currently runs to 165 years, 149 years definitely aren’t the warmest. To this we can add a few additional years that are distinctly unlikely to be the warmest.

1997, 2001, 2004, 2008, 2011 and 2012.

And, while we’re at it…

1998, 2002, 2003, 2005, 2006, 2007, 2009, 2010, 2013 and 2014.

Pick any one of those years and, more likely than not, it won’t be the warmest year either. Careful readers will have noticed that there is not a single year in all of those 165 years that is unaccounted for; the vast majority of years definitely aren’t the warmest, but even in the small remainder there is no year that is more likely to be the warmest year than not.

We really should have stuck with “maybe” because this is going to take a while to unpick.

Seriously, folks, consider maybe.

No? OK. This is on you.

According to a very good global temperature data set, 2014 was estimated to be 0.56° above the long term average. The uncertainty on that estimate is about 0.10°. In other words, according to that data set there’s about a 95% chance that the true global temperature will be between 0.46° and 0.66°. Likewise, we can consider 2010, with an estimated global temperature of 0.53°C and an uncertainty, again, of about 0.10°C. If these were the only two years and this was all we knew, we could calculate the probability that 2014 was warmer than 2010. It’s about 69%. We can also compare 2014 to 2005 (0.56 vs 0.52). In this case 2014 is about 75% likely to be warmer than 2005.

However, to work out the probability that 2014 is the warmest year on record, we have to compare it to all the other years at the same time. This is a slightly more involved calculation, so we’ll build up to it. First by asking what’s the probability that 2014 is warmer than both 2010 and 2005.

We’re going to do this using a Monte Carlo method. We’ll take the best estimates for 2014, 2010 and 2005 and use the uncertainties to generate possible “guesses” of what the real world might have done4. We’re going to do that thousands of times and count how often 2014 comes out on top.

The probability that 2014 is warmer than both 2010 and 2005 is about 60%, less than the probability that 2014 is warmer than either one or the other separately. If we add 1998 into the mix, then the probability drops even further, to 56%. The more years we add the lower that probability goes. Why does that happen? Simply, each year gets a crack at being warmer than 2014. The more years there are, the higher the chance that just one of them will be warmer. And one year is all it takes.

However, this process doesn’t go on indefinitely. As we move further down the list of warm years, the probability that a year is warmer than 2014 drops rapidly. Soon we get to the point that it’s so unlikely that a year was warmer than 2014 that we can drop it from our calculation and it makes no difference. The probability that 2014 is warmer than 2010, 2005, 1998 and 2013 is 50%. If we compare 2014 to the other nine of the ten warmest years the probability that it comes out on top is about 47%. If we go further down the list than that the probability doesn’t change. 47% is therefore the probability that 2014 is the warmest year on record.

If we do the same analysis for a different, but equally excellent data set, we’ll get a slightly different set of probabilities, but the basic pattern will be the same. In this case 2014 has about 39% probability of being the warmest year on record.

We can repeat these analyses focusing on other years (is 2010 the warmest? 2005? 1998?) and in each case the probability will be lower than for 2014. That was all a bit tedious, but based on this simple analysis it turns out that no year is more likely than not (greater than 50% probability) to be the warmest year on record. On the other hand, we know that one year has to be the warmest, which is, if you are so inclined, pleasingly paradoxical as questions of probability often are.

We can rephrase the question and ask which year has the highest probability of being the warmest year? The answer based on these two data sets is 2014. As one blogger (I can’t remember who) put it, no year has a better claim.

All of the above needs the rather large caveat: “based on these two data sets” and “based on this particular method”. The probabilities I calculated depend on the data set and on the method. Change either one, change the probabilities. We could look at other data sets, such as those produced by Berkeley Earth (who declared 2014 a tie with 2010 and 2005), or the ECMWF reanalysis (which had 2014 in the top 10% of years in their reanalysis, nominally third warmest). Cowtan and Way look poised to put 2014 in second place. There’s no way to rigorously combine all this information to get a single best answer to any of the questions we might want to ask, but it does underline the fact that there is uncertainty and that it is limited.

For example, there’s no data set of global surface temperature that places 2014 outside the top four years based solely on best estimates. Based on those data sets that have uncertainty estimates, it is very unlikely that 2014 is outside the top 10. It’s quite unlikely that it’s outside the top 5.

So, 2014 was a very warm year. Was it a top 10 year? Yes. A top 5 year? More likely than not. The warmest?

Maybe.

1. Unless the thought-provokingly-fine tuning of various fundamental parameters stretches as far as global-mean temperature. On earth. In the 21st century. This has not, to the best of my knowledge been previously suggested. You saw it here first, folks.
1.5. There are lots of different estimates of global temperature and, obviously, in each of those there will be a year that is warmer than any other.
2. The textbook example is the carpenter’s maxim: measure twice, cut once.
3. Usually. The exception would be if a large fraction of them recently had cause to synchronize their watches, something that Hollywood would have me believe occurs a short, and presumably well-measured, period before it all kicks off
4. To do this we assume that the distribution of errors is Gaussian – the famous bell curve – with mean equal to the best estimate and standard deviation equal to the estimated 1-sigma uncertainty. Errors are considered to be independent from year to year. This is a lot simpler than the real world is, but it will give us an intuition for what’s going on and how uncertainty interacts with rankings. This analysis is a lot simpler than NOAA used too. Consequently, the probabilities I get will be somewhat different.

[Update: 4/2/2014 corrected 2005 global temperature anomaly for NCDC’s data set. Was quoted as 0.54 now, more correctly, 0.52]

[Update: 6/2/2015 First, the date immediately above this one is wildly wrong. Second, Lucia pointed out that the mystery blogger who said no year has a better claim was, in fact, Nick Stokes. Third, Significance has reposted this here.

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