The Science of Doom

The title should really be:

The Real Measure of Global Warming – Part Two – How Big Should Error Bars be, and the Sad Case of the Expendable Bathythermographs

But that was slightly too long.

This post picks up from The Real Measure of Global Warming which in turn followed Why Global Mean Surface Temperature Should be Relegated, Or Mostly Ignored

The discussion was about ocean heat content being a better measure of global warming than air temperature. However, ocean heat down into the deep has been less measured than air temperature, so is subject to more uncertainty the further back in time we travel.

We had finished up with a measure of changes in OHC (ocean heat content) over 50 years from Levitus (2005):

Ocean heat change, Levitus (2005)

Some of the earlier graphs were a little small but you could probably see that the error bars further back in time are substantial. Unfortunately, it’s often the case that the error bars themselves are placed with too much confidence, and so it transpired here.

In 2006, GRL (Geophysical Research Letters) published the paper How much is the ocean really warming? by Gouretski and Koltermann.

They pointed out a significant error source in XBTs (expendable bathythermographs ). The XBT’s estimate temperature against depth by estimating depth from fall rate, a value which was found to be inaccurate.

The largest discrepancies are found between the expendable bathythermographs (XBT) and bottle and CTD data, with XBT temperatures being positively biased by 0.2–0.4
C on average. Since the XBT data are the largest proportion of the dataset, this bias results in a significant World Ocean warming artefact when time periods before and after introduction of XBT are compared.

And conclude:

Comparison with LAB2005 [Levitus 2005] results shows that the estimates of global warming are rather sensitive to the data base and analysis method chosen, especially for the deep ocean layers with inadequate sampling. Clearly instrumental biases are an important issue and further studies to refine estimates of these biases and their impact on ocean heat content are required. Finally, our best estimate of the increase of the global ocean heat content between 1957–66 and 1987–96 is 12.8 ± 8.0 x 10²² J with the XBT offsets corrected. However, using only the CTD and bottle data reduces this estimate to 4.3 ± 8.0 x 10²² J.

If we refer back to Levitus, they had calculated a value over the same time period of 15×10²² J.

Gouretski and Koltermann are saying, in layman’s terms, if I might paraphrase:

Might be around what Levitus said, might be a lot less, might even be zero.. we don’t know.

Some readers might be asking, does this heretical stuff really get published?

Well, moving back to ocean heat content, we don’t want to drown in statistical analysis because anything more than a standard deviation and I am out of my depth, so to speak.. Better just to see what the various experts have concluded as our measure of uncertainty.

Ocean Heat Content is one of the hot topics, so no surprise to see others weighing in..

Domingues et al

In 2008, Nature then published Improved estimates of upper-ocean warming and multi-decadal sea-level rise by Domingues et al.

Remembering that the major problem of ocean heat content is first a lack of data, and now revealed, problematic data in the major data source.. Domingues says in the abstract:

..using statistical techniques that allow for sparse data coverage..

My brief excursion into statistics was quickly abandoned when the first paper cited (Reduced space optimal interpolation of historical marine sea level pressure: 1854-1992, Kaplan 2000) states:

..A novel procedure of covariance adjustment brought the results of the analysis to the consistency with the a priori assumptions on the signal covariance structure..

Let’s avoid the need for strong headache medication and just see their main points, interesting asides and conclusions. Which are interesting.

OHC 1951-2004, Domingues (2008)

The black line is their story. Note their “error bars” in the top graph, the grey shading around the black line is one standard deviation. This helps us see “a measure” of uncertainty as we go back in time. The red line is the paper we have just considered, Levitus 2005.

Domingues calculates the 1961-2003 increase in OHC as 16 x10²² J, with their error bars as ±3 x10²² J. They calculate a number very close to Levitus (2005).

Interesting aside:

Climate models, however, do not reproduce the large decadal variability in globally averaged ocean heat content inferred from the sparse observational database.

From one of the papers they cite (Simulated and observed variability in ocean temperature and heat content, AchutaRao 2007) :

Several studies have reported that models may significantly underestimate the observed OHC variability, raising concerns about the reliability of detection and attribution findings.

And on to Levitus et al 2009

From GRL, Global ocean heat content 1955–2008 in light of recently revealed instrumentation problems

Or, having almost the last word with his updated paper:

Ocean heat change 1955- 2009 - Levitus (2009)

The red line being the updated version, the black dotted line the old version.

Willis Back, 2006 and Forwards, 2009

In the meantime, Josh Willis, using the brand new Argo floats, (see part one for the Argo floats) published a paper (GRL 2006) showing such a sharp reduction in ocean heat from 2003 – 2005 that there was no explanation for.

And then a revised paper in 2009 in Journal of Atmospheric and Oceanic Technology showing that the previous correction was a mistake, instrument problems again.. now it’s all flat for a few years:

no significant warming or cooling is observed in upper-ocean heat content between 2003 and 2006

Probably more papers we could investigate, including one which I planned to cover before realizing I can’t find it and this post has gone on way too long already.

Conclusion

We are looking at a very important measurement, ocean heat content. We aren’t as sure as we would like to be about the history of OHC and not much can be done about that, although novel statistical methods of covariance adjustment may have their place.

Some could say, based on one of the papers presented here, “No ocean warming for 50 years”. It’s a possibility, but probably a distant one. One day when we get to the sea level “budget”, more usefully called “sea level rise”, we will probably think that the rise of sea level is usefully explained by the ocean heat content going up.

We do have excellent measurements in place now, and since around 2000, although even that exciting project has been confused by instrument uncertainty, or uncertainty about instrument uncertainty.

We have seen a great example that error bars aren’t really error bars. They are “statistics”, not real life.

And perhaps, most useful of all, we might have seen that papers which show “a lot less warming” and “unexplained cooling”, still make it into print with peer-reviewed science journals like GRL. This last factor may give us more confidence than anything that we are seeing real science in progress. And save us from having to analyze 310,000 temperature profiles with and without covariance adjustments. Instead, we can wait for the next few papers to see what the final consensus is.

Or spend a lifetime in study of statistics.

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In an earlier post – Why Global Mean Surface Temperature Should be Relegated, Or Mostly Ignored – I commented:

There’s a huge amount of attention paid to the air temperature 6ft off the ground all around the continents of the world. And there’s an army of bloggers busy re-analyzing the data.

It seems like one big accident of history. We had them, so we used them, then analyzed them, homogenized them, area-weighted them, re-analyzed them, wrote papers about them and in so doing gave them much more significance than they deserve. Consequently, many people are legitimately confused about whether the earth is warming up.

Then we looked at some of the problems of measuring the surface temperature of the earth via the temperature of a light ephemeral substance approximately 6ft off the ground.

In Warming of the World Ocean 1955-2003, Levitus (2005) shows an interesting comparison of estimates of absorbed heat over almost half a century:

Heat absorbed in different elements of the climate, Levitus (2005)

Once you find out that the oceans have around 1000x the heat capacity of the atmosphere, the above chart won’t be surprising.

For those who haven’t considered this relative difference in heat capacity before:

• if the oceans cooled down by a tiny 0.1°, transferring their heat to the atmosphere, the atmosphere would heat up by 100°C (it wouldn’t happen like this but it gives an idea of the relative energy in both)
• if the atmosphere transferred so much heat to the oceans that the air temperature went from an average of 15°C to a freezing -15°C, the oceans would heat up by a tiny, almost unnoticeable 0.03°C

So if we want to understand the energy in the climate system, if we want to understand whether the earth is warming up, we need to measure the energy in the oceans.

An Accident of History

Measuring the temperature of the earth’s surface by measuring the highly mobile atmosphere 6ft off the ground is a problem. By contrast, measuring ocean heat is simple..

Except we didn’t start until much later. Sea surface temperatures date back to the 19th century, but that doesn’t tell us much. We want to know the temperature down into the deep all around the world.

Ocean temperature vs depth in one location, "Oceans and Climate", Bigg (2003)

Here is a typical sample. Unlike the atmosphere, the oceans are more “stratified” – see Why Global Mean Surface Temperature Should be Relegated, Or Mostly Ignored for more on the basic physics of why the ocean is warmer at the surface. However, the oceans have complex global currents so we need to take a lot of measurements.

Measurements of the temperature down into the ocean depths didn’t really start until the 1940s and progressed very slowly since then. Levitus says:

Most of the data from the deep ocean are from research expeditions. The amount of data at intermediate and deep depths decreases as we go back further in time.

Fast forward to 2000 and the Argo project began to be deployed. By early 2010, over 3300 sensors have been moved into place around the world’s oceans. The Argo sensors drop to 2km in depth every 10 days and automatically measure temperature and salinity from the surface to this 2km depth:

Argo profile, Temperature and Salinity vs Depth

Why salinity? Salinity is the other major factor apart from temperature which affects ocean density and therefore controls the ocean currents. See Predictability? With a Pinch of Salt please.. for more..

As we go back from 2010 there is progressively less data available. Even during the last 10 years measurement issues have created waves. But more on that later..

The Leviathan

It’s often best to step back a little to understand a subject better.

In 2000, Science published the paper Warming of the World Ocean by Sydney Levitus and a few co-workers. The paper has a thorough analysis of the previous 50 years of ocean history.

Ocean heat change, upper 3000m, 1955-1996, from Levitus (2000)

Now and again the large number of joules (unit of energy) are turned into a comparison W/m² absorbed for the time period in question. 1W/m² for a year (averaged over the entire surface of the earth) translates into 1.6×10²²J.

But it’s better to get used to the idea that change in energy in the oceans is usually expressed as 10²²J.

The graphs above show a lot of variability between oceans but still they all demonstrate the similar warming pattern.

Comparison of OHC in top 3000m, top 800m, top 300m, Levitus (2000)

Here is the data shown (from left to right) as the energy change in the deeper 3000m, 800m and 300m.

We are used to seeing temperature graphs, even sea surface temperature graphs that go up and down from year to year. Of course we want to understand exactly why, for example see Is climate more than weather? Is weather just noise? It’s easy to think of reasons why that might happen, even in a warming world (or a cooling world) – with one of the main reasons being that heat has moved around in the oceans.

For example, due to ocean currents colder water has been brought to the surface. The measured sea surface temperature would be significantly lower but the total heat hasn’t necessarily changed – because we are only measuring the temperature at one vertical location (the top).

So we wouldn’t expect to see a big yearly decline in total energy.. not if the planet was “warming up”.

So this is quite surprising! See the change downward in the 1980’s:

Ocean heat change - global summary, Levitus (2000). Numbers in 10^22 J

What caused this drop?

Here’s a another fascinating look into the depths that we don’t usually get to see:

Temperature comparison 1750m down. 1970-74 cf 55-59 & 1988-92 cf 70-74

Here we see changes in the deeper North Atlantic in two comparison periods about 15 years apart. (As a minor note the reason for the comparisons of averaged 5-year periods is the sparsity of data below the surface of the oceans).

See how the 1990 period has cooled from 15 years earlier.

Levitus, Antonov and Boyer updated their paper in 2005 (reference below).

They comment:

Here we present new yearly estimates for the 1955– 2003 period for the upper 300 m and 700 m layers and pentadal (5-year) estimates for the 1955–1959 through 1994–1998 period for the upper 3000 m of the world ocean.

The heat content estimates we present are based on an additional 1.7 million temperature profiles that have become available as part of the World Ocean Database 2001.

Also, we have processed approximately 310,000 additional temperature profiles since the release of WOD01 and include these in our analyses.

(My emphasis added). Think re-doing GISS and CRU is challenging? And for those who like to know where the data lives, check out the World Ocean Database and World Ocean Atlas Series

Ocean heat change, Levitus (2005)

Here’s a handy comparison of the changing heat when we look at progressively deeper sections of the ocean with the more up-to-date data.

The actual numbers (change in energy) from 1955-1998 were calculated to be:

• 0-300m:   7×10²²J
• 0-700m:   11×10²²J
• 0-3000m:   15×10²²J
• 1000-3000m:   1.3×10²²J

So the oceans below 1000m only accounted for 9% of the change. This gives an idea of the relative importance of measuring the temperatures as we go deeper.

In their 2005 paper they comment on the question of the early 80’s cooling:

One dominant feature .. is the large decrease in ocean heat content beginning around 1980. The 0–700 m layer exhibits a decrease of approximately 6 x 10²² J between 1980 and 1983. This corresponds to a cooling rate of 1.2 Wm² (per unit area of Earth’s total surface).

Most of this decrease occurs in the Pacific Ocean.. Most of the net decrease occurred at 5°S, 20°N, and 40°N. Gregory et al. [2004] have cast doubt on the reality of this decrease but we disagree. Inspection of pentadal data distributions at 400 m depth (not shown here) indicates excellent data coverage for these two pentads.

And they also comment:

However, the large decrease in ocean heat content starting around 1980 suggests that internal variability of the Earth system significantly affects Earth’s heat balance on decadal time-scales.

So far so interesting, but as the article is already long enough we will come back to the subject in a later post with the follow up:

How Big Should Error Bars be and the Sad Case of the Expendable Bathythermographs.

And for one reader, in anticipation:

XBT

Update – follow up post – The Real Measure of Global Warming – Part Two – How Big Should Error Bars be, and the Sad Case of the Expendable Bathythermographs

References

Warming of the World Ocean, Levitus et al, Science (2000)

Warming of the World Ocean 1955-2003, Levitus et al, GRL (2005)

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For newcomers to the climate debate it is often difficult to understand if global warming even exists. Controversy rages about temperature records, “adjustments” to individual stations, methods of creating the global databases like CRU and GISS and especially the problem of UHI.

UHI, or the urban heat island, refers to the problem that temperatures in cities are warmer than temperatures in nearby rural areas, not due to a real climatic effect, but due to concrete, asphalt, buildings and cars. There are also issues raised as to the actual location of many temperature stations, as Anthony Watts and his volunteer work demonstrated in the US.

First of all, everyone agrees that the UHI exists. The controversy rages about how large it is. The IPCC (2007) believes it is very low – 0.006°C per decade globally. This would mean that out of the 0.7°C temperature rise in the 20th century, the UHI was only 0.06°C or less than 10% – not particularly worth worrying about.

For those few not familiar with the mainstream temperature reconstruction of the last 150 years, here is the IPCC from 2007 (global reconstructions):

IPCC 2007, Working Group 1, Historical Overview of Climate Change

New Research from Japan

Detection of urban warming in recent temperature trends in Japan by Fumiaki Fujibe was published in the International Journal of Climatology (2009). It is a very interesting paper which I’ll comment on in this post.

The abstract reads:

The contribution of urban effects on recent temperature trends in Japan was analysed using data at 561 stations for 27 years (March 1979–February 2006). Stations were categorized according to the population density of surrounding few kilometres. There is a warming trend of 0.3–0.4 °C/decade even for stations with low population density (<100 people per square kilometre), indicating that the recent temperature increase is largely contributed by background climatic change. On the other hand, anomalous warming trend is detected for stations with larger population density. Even for only weakly populated sites with population density of 100–300/km², there is an anomalous trend of 0.03–0.05 °C/decade. This fact suggests that urban warming is detectable not only at large cities but also at slightly urbanized sites in Japan. Copyright, 2008 Royal Meteorological Society.

Why the last 27 years?

The author first compares the temperature over 100 years as measured in Tokyo in the central business district with that in Hachijo Island, 300km south.

Tokyo –               3.1°C rise over 100 years (1906-2006)
Hachijo Island –  0.6°C over the same period

This certainly indicates a problem, but to do a thorough study over the last 100 years is impossible because most temperature stations with a long history are in urban areas.

However, at the end of the 1970’s, the Automated Meteorological Data Acquisition System (AMeDAS) was deployed around Japan providing hourly temperature data at 800 stations. The temperature data from these are the basis for the paper. The 27 years coincides with the large temperature rise (see above) of around 0.3-0.4°C globally.

And the IPCC (2007) summarized the northern hemisphere land-based temperature measurements from 1979- 2005 as 0.3°C per decade.

How was Urbanization measured?

The degree of urbanization around each site was calculated from grid data of population and land use, because city populations often used as an index of urban size (Oke, 1973; Karl et al., 1988; Fujibe, 1995) might not be representative of the thermal environment of a site located outside the central area of a city.

What were the Results?

Mean temperature anomaly vs population density, Japan

The x-axis, D3, is a measure of population density. T’mean is the change in the mean temperature per decade.

Tmean is the average of all of the hourly temperature measurements, it is not the average of Tmax and Tmin.

Notice the large scatter – this shows why having a large sample is necessary. However, in spite of that, there is a clear trend which demonstrates the UHI effect.

There is large scatter among stations, indicating the dominance of local factors’ characteristic to each station. Nevertheless, there is a positive correlation of 0.455 (Tmean = 0.071 logD3 + 0.262 °C), which is significant at the 1% level, between logD3 and Tmean.

Here’s the data summarized with T’mean as well as the T’max and T’min values. Note that D3 is population per km² around the point of temperature measurement, and remember that the temperature values are changes per decade:

The effect of UHI demonstrated in various population densities

Note that, as observed by many researchers in other regions, especially Roger Pielke Sr, the Tmin values are the most problematic – demonstrating the largest UHI effect. Average temperatures for land-based stations globally are currently calculated from the average of Tmax and Tmin, and in many areas globally it is the Tmin which has shown the largest anomalies. But back to our topic under discussion..

And for those confused about how the Tmean can be lower than the Tmin value in each population category, it is because we are measuring anomalies from decade to decade.

And the graphs showing the temperature anomalies by category (population density):

Dependence of Tmean, Tmax and Tmin on population density for different regions in Japan

Quantifying the UHI value

Now the author carries out an interesting step:

As an index of net urban trend, the departure of T from its average for surrounding non-urban stations was used on the assumption that regional warming was locally uniform.

That is, he calculates the temperature deviation in each station in category 3-6 with the locally relevant category 1 and 2 (rural) stations. (There were not enough category 1 stations to do it with just category 1). The calculation takes into account how far away the “rural” stations are, so that more weight is given to closer stations.

Estimate of actual UHI by referencing the closest rural stations - again categorized by population density

And the relevant table:

Temperature delta from nearby rural areas vs population density

Conclusion

Here’s what the author has to say:

On the one hand, it indicates the presence of warming trend over 0.3 °C/decade in Japan, even at non-urban stations. This fact confirms that recent rapid warming at Japanese cities is largely attributable to background temperature rise on the large scale, rather than the development of urban heat islands.

..However, the analysis has also revealed the presence of significant urban anomaly. The anomalous trend for the category 6, with population density over 3000 km⁻² or urban surface coverage over 50%, is about 0.1 °C/decade..

..This value may be small in comparison to the background warming trend in the last few decades, but they can have substantial magnitude when compared with the centennial global trend, which is estimated to be 0.74°C/century for 1906–2005 (IPCC, 2007). It therefore requires careful analysis to avoid urban influences in evaluating long-term temperature changes.

So, in this very thorough study, in Japan at least, the temperature rise that has been measured over the last few decades is a solid result. The temperature increase from 1979 – 2006 has been around 0.3°C/decade

However, in the larger cities the actual measurement will be overstated by 25%.

And in a time of lower temperature rise, the UHI may be swamping the real signal.

The IPCC (2007) had this to say:

A number of recent studies indicate that effects of urbanisation and land use change on the land-based temperature record are negligible (0.006ºC per decade) as far as hemispheric- and continental-scale averages are concerned because the very real but local effects are avoided or accounted for in the data sets used.

So, on the surface at least, this paper indicates that the IPCC’s current position may be in need of modification.

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Understanding the relationship between climate and weather is important in climate science.

Here’s NASA:

The difference between weather and climate is a measure of time. Weather is what conditions of the atmosphere are over a short period of time, and climate is how the atmosphere “behaves” over relatively long periods of time.

And again:

Climate is the average of weather over time and space.

Who could argue with that succinct statement? Easy for all of us to understand.

Now Tamino, in his long running blog, says:

Time and time again, peoplewhodontagreewithus-ists try to suggest that the last 10 years, or 9 years, or 8 years, or 7 years, or 6 years, or three and a half days of temperature data establish that the earth is cooling, in contradiction to mainstream climate science…

Of course that raises an interesting question: how long a time span do we need to establish a trend in global temperature data? It’s sometimes stated that the required time is 30 years, because that’s the time span used most often to distinguish climate from weather. Although that’s a useful guide, it’s not strictly correct. The time required to establish a trend in data depends on many things, including how big the trend is (the size of the signal) and how big, and what type, the noise is…

Well, I agree with the statistical principles involved here. But his comment does raise a very interesting point.

Is the global temperature value measured for a year just noise on top of the climate signal?

If the global temperature value measured in 2009 is less than that measured in 2008 did the world actually cool that year (relative to 2008), or is it just noise ?

Digression on Noise and Signal

For those not so familiar with the technical terms it’s worth explaining signal and noise a little. Let’s choose a non-controversial topic and suppose we want to set up a radio communications link. We have a receiver which amplifies the tiny incoming radio signal so that we can hear it – or retransmit it – whatever we want to do with this signal.

The noise is the random element that get mixed in with the signal. In amplifiers they are frequently the random movement of electrons (that increase with temperature). In reception of the signal they are the other radio waves at similar frequencies that have been reflected, diffracted and otherwise distorted their way to your receiver.

In this case, noise is stuff that is NOT the signal. It threatens to stop you measuring your signal – or at least make it less accurate. Noise can have a systematic bias or it can be random. And in the real world of engineering problems, dealing with noise is often a significant problem to be solved.

Signal and Noise in Climate

We are thinking here specifically of the average global temperature. Often known by its acronym, GMST (global mean surface temperature).

What Tamino appears to be saying is that the temperature from year to year is just the “noise” on top of the climate (temperature) signal. Well we don’t want noise to upset our measurement so in that case we do need to call on statistical processes to give us the real signal.

But is it true? Is this the right way to look at it?

Other commentators and scientists have made a similar point.  Easterling’s paper Is the climate warming or cooling? submitted to GRL (2009) says:

Numerous websites, blogs and articles in the media have claimed that the climate is no longer warming, and is now cooling. Here we show that periods of no trend or even cooling of the globally averaged surface air temperature are found in the last 34 years of the observed record, and in climate model simulations of the 20th and 21st century forced with increasing greenhouse gases. We show that the climate over the 21st century can and likely will produce periods of a decade or two where the globally averaged surface air temperature shows no trend or even slight cooling in the presence of longer-term warming.

But there’s a very interesting paper in Current Opinion in Environmental Sustainability (2009) from Kevin Trenberth on the global energy budget. It’s worth paying close attention to what he has to say, and for anyone interested in the subject of the global temperature, read the whole paper. From the introduction:

The global mean temperature in 2008 was the lowest since about 2000 (Figure 1). Given that there is continual heating of the planet, referred to as radiative forcing, by accelerating increases of carbon dioxide and other greenhouses due to human activities, why is the temperature not continuing to go up? The stock answer is that natural variability plays a key role and there was a major La Nina event early in 2008 that led to the month of January having the lowest anomaly in global temperature since 2000. While this is true, it is an incomplete explanation.

In particular, what are the physical processes? From an energy standpoint, there should be an explanation that accounts for where the radiative forcing has gone. Was it compensated for temporarily by changes in clouds or aerosols, or other changes in atmospheric circulation that allowed more radiation to escape to space?

Was it because a lot of heat went into melting Arctic sea ice or parts of Greenland and Antarctica, and other glaciers? Was it because the heat was buried in the ocean and sequestered, perhaps well below the surface? Was it because the La Nina led to a change in tropical ocean currents and rearranged the configuration of ocean heat?

Perhaps all of these things are going on?

Interesting.

Trenberth is saying that we need to understand what happens to the global energy “account” in shorter time periods than decades. In fact, it’s essential. Because if we don’t know whether the earth warms or cools in one year, there might be important aspects of the climate that we haven’t understood in sufficient detail – or we aren’t measuring in sufficient detail. And if the earth has warmed but we don’t know where the energy actually is that is a problem to be solved as well.

All of which leads to the inescapable conclusion that the average global temperature value for one year is not “noise”. It is the “signal”. (See the technical note on temperature measurement at the end of this post)

After all, if there is a radiative imbalance in the earth’s climate system such that we take more energy in than we radiate out it must be warming. But if this energy is not being stored somewhere then the earth hasn’t warmed in that year. In fact, if there is less heat in the climate system, we radiated out more than we received in. There isn’t some secret place that is storing it all up.

Roger Pielke Sr has made that point (probably many times).

What I’m not saying is that earth is on a long term cooling trend. And I’m definitely not saying that the cold weather yesterday means the earth is cooling.

But if the global temperature in one year is cooler than the global temperature in the previous year then the earth has cooled. It’s not noise.

It’s only noise if we can’t measure temperature accurately enough to be sure whether the temperature has gone up or down.

Possibly I have misunderstood Tamino. I did post a comment on this topic to his recent blog post (twice) but possibly due to a moderating snafu, or possibly because there were much more important questions to be answered, it didn’t get published.

Conclusion

As NASA says, the climate is the average of the weather.

Monthly and annual averages of specific values like temperature and total heat stored in the climate system can change in apparently random ways. But that doesn’t mean that these changes don’t reflect real changes in the system.

I can draw a trend line through a longer time series and show lots of deviations from the trend line. But that doesn’t give some kind of superior validity to the trend line. I could take 10000 years of climate data and show that 100 year periods are just noise.

What is the climate doing? It’s apparently random, but actually always changing. Over the last 40 years it has warmed. For the more recent shorter period that Trenberth covered, it cooled. Over the last 20,000 years it has warmed. Over the last 10 million years it has cooled.

If there’s less heat in the earth’s climate at the end of 2010 compared with 2009, the planet will have cooled. And if there’s more heat at the end of 2010 compared with 2009, the planet will have warmed. Not noise, it really will have changed.

Why the total heat stored goes up and down, and how that heat is distributed is at the heart of the complex subject known as climate science.

Technical Note

More on this on a later post, but as many physicists will point out, taking the average temperature around the world is a little odd. That might seem strange – how else can you see whether the world is warming???

As a thought experiment, if you have 5 places to measure temperature, nicely distributed, the average temperature,

T_av = T₁ + T₂ + T₃ + T₄ + T₅.

But it’s not really meaningful. T₁ might be measured in a big lake – and water stores a lot of energy per unit volume. T₂ might be measured on a big piece of plastic and be storing almost no energy.

Adding up these different numbers and dividing by the number of measurements is not really a useful number. Sure if you keep calculating this same average it kind of gives you a clue where things are headed. But it could be misleading. The piece of plastic might go up 10°C and the lake might go down 5°C so the average has gone up. But the total heat in the system will have gone down.

Two more useful methods would be:

1. Sum up the energy actually stored -as Trenberth does in his paper – but it’s tougher
2. Average the fourth power of the temperatures – T⁴

Energy is radiated out as the fourth power of temperature, so averaging this value gives you more idea how much energy the system is radiating – as a proxy for the energy changes in the system. It’s easy to show that global average temperature can go up while total radiated energy is going down. Just have the colder places heat up more than the warmer places cool down and T_av increases while T⁴_av decreases. More on this in another post.

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