Why doesn't it get hotter every year?

One of the most common questions encountered in discussions on climate change especially by those who don't accept the science is, "Why doesn't it get hotter every year?" or other variants, such as, "Why hasn't it warmed since 1998?" (pick your favorite year). The real question underlying all this is: "If there is a warming trend of so many degrees per century, why can't we see that exact trend if we compare any two years, or any sequence of e.g. ten years?"

The answer is pretty simple. The climate change trend is a long-term effect. If it warms by 3°C per century, that means an average of 0.03°C per year. That amount is well within the limits of accuracy of measurement techniques. What's more, without a significant global warming effect, much higher variation than this occurs. The critical difference is that ordinarily, that sort of variation is short term and the highs and lows pretty much cancel out. It's only if there's a major change in the atmosphere (greenhouse gases causing warming, volcanic output causing cooling) or solar input to the system (change in the earth's orbit, change in solar activity) that you get a break out of this sort of random fluctuation -- and only a really big external change causes a real climate shift (like into or out of an ice age).

One can of course (and should, if doing serious scientific studies) apply sophisticated data analysis techniques to the problem, but what I aim to do here is to provide a feel for how to understand the difference between short-term and long-term effects with simple approaches you can apply yourself if you know how to drive a spreadsheet. All you need is the ability to plot points, and to get a trend line. The other critical thing is to ask the spreadsheet (or graphing or stats package) to give you the r² value for the trend line, which is a measure of how much you can read into it.

I took a look at the first 50 years of the HadCRUT3 dataset, from 1850 to 1899, before significant CO₂ emissions could have caused a greenhouse effect, and plotted the annual averages (HadCRUT3 uses anomalies relative to a base period of 1961-1990) to see if I could discern a trend. Over this time, data from Oak Ridge National Labs showed that annual emissions of CO₂ increased from 54 to 507 (measured as million tonnes of carbon); the latest figure is less than 10% of current levels. The effect of this increase in emissions was that atmospheric CO₂ increased less than 4%, not enough to have any measurable effect on temperature. So let's take this period as indicative of "natural variability". Solar activity over that period was on the way down, probably not enough to have a significant effect on climate.

What can we see from this picture? Aside from that there are many short-term bumps, the trend isn't too clear. The fitted trend line shows a small upwards drift (an annual trend of 0.0008°C, or 0.08° per century), but the crucial thing is to note the r² value, which shows that the trend isn't very strong. Statisticians interpret r² as an indication of how much of the variance in the data can be explained by the trend line; in this case, a bit over 1%, so the trend is not significant; you would expect an r² value in this ballpark for random numbers.

What has the trend been over the last 50 years (1958-2007)? Let's plot the graph as well and see how it looks. Note that in all graphs, I keep the vertical scale the same (-0.6 to 0.6) so the graphs are comparable. It is important to get this right: I've seen many attempts at comparing values using inconsistent scales. I do however adjust the horizontal scale when dealing with shorter sequences of years: be careful not to compare these with the longer sequences.



How does the recent data compare with the picture of 1850-1899? The trend is now much clearer. The r² value is 0.7347, meaning that the trend line is a very good fit to the data. The annual trend is an increase of 0.0129°. I haven't taken into account here that the trend may be accelerating, which is missed by a simple linear regression over the entire period, so do not get too excited that the trend is on the low side of IPCC projections.

It is a simple matter to add an annual trend of an increase of 0.0121 to each temperature record from 1850 to 1899, to see what the resulting picture looks like relative to today's. Why is this interesting? Because if I do this, I know there is a trend of 1.21° per century over and above natural variability -- and this figure will make the trend match that of the last 50 years. This allows us to explore the argument that artificial warming is behaving like a slow, long-term adjustment to natural variability which would otherwise be pretty much random. We will also be able to see whether it's possible to discern this trend at all scales, answering the question posed at the start. So let's see how the adjusted nineteenth century data looks.




Remarkably (or perhaps not) the adjusted nineteenth century picture has statistical properties very similar to the modern picture. The rate of increase is the same because I made that so. The r² value is 0.7613, showing a similar degree of fit to the data to the modern (unaltered) data.

Is that cheating? Yes and no. I forced the old data to look like the new data. But the point is that the old data looked pretty close to random. That's the nature of weather. You got hot days, you get cold days. You get a heat wave, you get snow in summer. Looked at short-term, the weather is hard to predict; look at it over a span of years, and it doesn't look much different to random, if you filter out seasons (as you do with an annual average). So adding a linear trend onto the 1850-1899 data is not too different to the predicted effect of adding global warming onto natural variability.

So what of talk we have lately of how global warming has flatlined, or temperatures have dropped over the last 10 years? Let's look for a comparable case we can find in the adjusted nineteenth century data. If we look at a period of ten years of the adjusted data when the graph looks relatively flat, 1880-1889, the trend is 0.008° per year, with r² = 0.1227: somewhat better than random, but not a convincing fit to the data.



Remember, this data has been explicitly constructed so that there was a hundred-year warming trend of 1.21° and we are testing the argument that if such a trend exists, you should be able to find it in any sequence of years.

Now move the trend period back two years to 1878-1887 and what do you get? A trend of a decrease of 0.0166° per year, or a decrease of 1.66° per century, the opposite to the trend I artificially added to this data and of bigger magnitude! What's more, r² is now at a significantly more convincing level of 0.2947 than the 1880-1899 (adjusted) trend.

Remember, this is data that was explicitly constructed to add a trend of increasing temperature on top of data which was statistically random.

If you take any period of ten years, you can see similar effects: most go up in varying degrees, some are flat, a few go down.

So what can we conclude from all this?

If we have a data series with a natural variability significantly above a new source of artificial change, even if that change is consistently applied over a long time, we cannot expect to discern that change accurately by looking at a short time sequence. That change will, however, be clear if you keep looking for long enough. In other words, anyone demanding that temperatures increase every year -- or even over a period of ten years -- is not testing the theory of anthropogenic global warming, but their own understanding of data analysis.

Finally, let's apply one more data analysis technique, familiar to economists, at least when they do market analysis, even if some forget it when they consider climate change: the moving average. The way this works is you plot the average of the past n years at each data point as a way of smoothing out short-term fluctuations. NASA's GISS temperature graphs generally show a 5-year average. Here, I'll use a 10-year average to smooth out the bumps even more.

The black line with squares on the data points is the temperature data; the red line without markers on the data points is the 10-year average.

Can you see a downhill trend over the last 10 years now? Not convinced? Look at the data points since 1998 (the big spike near the end). How far back can you go before all the temperature measures are lower than any since 1998? Click on the picture if you want a larger version. To make it easier, I've put in a dotted line marking the lowest temperature since 1998. You'll see that it's higher than any temperature before 1995.

Additional Reading

For those who find my stats treatment a bit too lowbrow, plus some other interesting points:

• Uncertainty, noise and the art of model-data comparison
  
• Recent Climate Observations Compared to (IPCC) Projections
  
• Garbage is Forever
  
• Graphic Evidence
  
• Red White & Blue (noise, that is)
  

Exercise

Repeat the experiment on the modified nineteenth century data with 20-year sequences. You will see that although the trend is more consistently up and closer to the 50-year trend, you can still find at least one patch where the trend appears to be down -- though with a low r².

The Mysterious Vanishing Ice Age

On 23 April 2008, The Australian published an article, "Sorry to ruin the fun, but an ice age cometh" by Phil Chapman, geophysicist and astronautical engineer, who was also the first Australian to be sent into space by NASA.

Possibly he's still out there, because he tells us:

All four agencies that track Earth’s temperature (the Hadley Climate Research Unit in Britain, the NASA Goddard Institute for Space Studies in New York, the Christy group at the University of Alabama, and Remote Sensing Systems Inc in California) report that it cooled by about 0.7C in 2007. This is the fastest temperature change in the instrumental record and it puts us back where we were in 1930. If the temperature does not soon recover, we will have to conclude that global warming is over.

I haven't tracked down all four of the data sets he mentions but two should be sufficient since he claims they are all consistent.

Let's look at Hadley: HadCRUT3 is their most commonly quoted data set. What does it show (each year is represented in two rows: the first has the year, 12 monthly values and ends with an annual value, the second gives percent coverage for each monthly measure)? The global average for 2006 was 0.422° (measured as an "anomaly" versus the average over the years 1961-90). The number for 2007 was ... wait for it ... 0.402° -- a drop of 0.02°. Only a factor of 3.5 out.

What of NASA's GISS data? Their data is slightly different. Their anomalies are relative to the average over 1951 to 1980, and their data gathering and analysis also results in slightly different numbers. But this is good: if the rival data sets are consistent, it adds confidence to the credibility of the data. The numbers we want are in the column "AnnMean J-D". For 2006: 0.54° and for 2006: 0.57° for a difference of 0.03° -- in this case an increase rather than a decrease.

Whether we look at either of these figures separately or look at them together, the overall conclusion is the same: 2007 was much the same on average as 2006. If you look at NASA's graph of temperatures, you will see that these variations are well within the error bars (green vertical lines).

So where does the 0.7°C drop come from? I have to guess since he doesn't supply his working. The GISS data has a drop of about this order between the monthly average for January 2007 (0.86°) and the monthly average for January 2008 (0.12°). HadCRUT3 shows a similar but smaller effect between the Decembers of the two years (a drop from 0.536° to 0.201°). However, short term swings are common. One on this scale is unusual, but it is not uncommon for a comparable month to differ by a lot more from its predecessor than yearlong averages.

A fair number of people posted comments on the original article pointing the error out. So what did The Australian do? They made the version with comments inconspicuous (no longer linked from the main opinion pages) but kept a version without comments in a more conspicuous location.

Then, to drive the point home, the inimitable (fortunately) Christopher Pearson, the same one who incorrectly quoted the Pope as being in the anti-global warming camp, followed up with an article on 26 April 2008 "A cool idea to warm to" repeating the error. Pearson quotes Keynes: "when the facts change, I change my mind."

How about a couple more quotes for you, Chris?

Senator Daniel Patrick Moynihan:

You are entitled to your opinion. But you are not entitled to your own facts.

Or how about Richard Feynman:

Reality must take precedence over public relations, for nature cannot be fooled.

How long will we have to wait for another mea culpa? Three weeks like last time? Or is it OK to be loose with the facts unless you offend the Catholic Church?

Follow-up: The Australian on 29 April 2008 published another article, "Warming trend has not been reversed" by David Karoly, professor in the University of Melbourne School of Earth Sciences, correcting the many errors in the original article. Not bad: only 6 days after the original. The Pope will feel slighted.

More data: Karoly refers to the World Data Centre for Solar Terrestrial Physics at the National Geophysical Data Centre in Boulder, Colorado as the main source on sunspot numbers; if you want to check his 2008 data, here it is.

Zimbabwe and China: A Toxic Legacy

A shipload of armaments for Zimbabwe was turned away from South Africa on Friday 18 April 2008, thanks to activist unions, an inquiring press and a strong human rights activist community.

The timing of this shipment leads to the obvious question: is this the reason for the delays in counting the votes in the now not so recent election? Was the government waiting for fresh stocks of ammunition before embarking on all-out war on its own people? 3-million AK47 bullets would go a long way in a country of 12-million.

This is not an isolated incident.

China is accused of complicity in genocide in other parts of Africa. For example, the Rwanda government imported sufficient machetes from China to give one to every third male member of the population. Then there's Darfur -- despite worldwide publicity of horrific crimes of violence, China remains the Sudan's biggest armaments supplier.

Throughout all this -- and protests about Tibet and human rights violations generally in China itself -- the continuing mantra has been "no interference in internal affairs". If you check out the Chinese human rights policy in detail, you will see it's very carefully fudged to allow interference where activities "endanger world peace and security", which means

colonialism, racism, foreign aggression and occupation, as well as apartheid, racial discrimination, genocide, slave trade and serious violation of human rights by international terrorist organizations.

How, I wonder, is supplying weapons in Darfur, Rwanda and now Zimbabwe justified in this light? "Genocide" is listed in the categories where interference is allowed. Some might argue that annexing Tibet and destroying its culture is "colonialism".

The saddest thing of all though about this whole debacle is the way South Africa has repositioned itself as fudging human rights in its policy to Zimbabwe. The armaments shipment was not stopped by an intervention of the government. On the contrary, there is evidence that the South African government was facilitating it, offering a government-owned logistics operation when others refused to handle the shipment. It was the ruling African National Congress which, in opposition, did the most to change the inviolability of "non-interference in internal affairs" by making human rights a limiting factor on what governments could do.

If the Chinese government can see no evil, it's sad but not surprising. If the South African government can neither see nor hear any evil, it's pathetic. You have to wonder what the whole anti-apartheid movement was actually about. It certainly has not resulted in the ANC perpetuating the legacy in international affairs that it fought for. Thanks to a vigilant press, an activist civil society and a strong union movement, South African has been saved from total disgrace. But it's hard to see how Thabo Mbeki (a leading promoter of the ANC in exile) can't leave office as a total failure. First there was the debacle of failing to deal with the HIV pandemic based on the remote possibility that the mainstream science was wrong, then there was backing incompetent ministers at all costs, now this -- the defense of a failed policy on Zimbabwe at all costs.

And China? I hope there will be a day not too far in the future when China will be a more open society, and its people will look back on its role in Africa with shame and embarrassment. But I am not holding my breath; the Belgians, for example, have battled to accept their role in the destruction of the Congo, including complicity in the murder of independence prime minister, Patrice Lumumba. And of course, for Chinese readers, there's the reluctance of the Japanese to admit their crimes in World War II.

Crimes against humanity are not crimes only against individuals, but crimes against us all: they violate the very concept of what it is to be human. Until this idea is widely accepted, we will have made no advance over the barbarity that was unleashed in Europe in 1914, when old-fashioned limits to the projection of power were overwhelmed by mechanized warfare. Until we develop limits not only on what we can do, but on what we should do, crimes will continue to be committed.

Follow Up

South Africa's main union federation, COSATU (Congress of South African Trade Unions), is playing an increasing role in regional pressure on Zimbabwe. A good source on news on that country is ZimOnline, e.g., here's a story about COSATU's role.

The arms shipment has subsequently been reported as delivered, allegedly with connivance of the South African government.

An update of this article has been published at Online Opinion on 24 June 2008. Sadly, very little had to be altered other than noting the withdrawal of the MDC from the presidential run-off, and integrating the paragraph preceding this one into the text.

Rob Robertson: A Tribute

I did not know Rob Robertson and his wife Gert well. My wife Fiona Semple introduced me to them, and they immediately felt like old friends. In a few visits, I had a sense of a big life, lived to the full, yet without selfishness.

On our last visit in December 2006, he proudly showed off mementoes of his bungee jump. He had done this at the highest jump site in the world. He had negotiated to do it for free for the publicity value of being the first 80-year-old to do so and was very disappointed that another octogenarian (a word that didn't fit his demeanour) had beaten him to it. Nonetheless, the operators let him have his jump free of charge.

That Fiona had over 50 emails from various people within days of hearing of his death – he was knocked down by a speeding car while crossing the road on the way home from a run – indicates that his life had a lot more depth to it than I experienced personally. I would like anyone who knew him to post a comment here; I feel unqualified to comment on his long life and quiet achievement, including his early attempts at breaking down the walls of apartheid.