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The IPCC and the Credibility of Climate Science

Posted in Climate Models, Commentary on January 26, 2010| 4 Comments »

If you’re not a veteran of the blogosphere wars about climate change but have followed recent events you are probably wondering what to believe.

First, what recent events (Jan 2010)?

The issues arising from the story in the UK Mail that the IPCC used “sexed-up” climate forecasts to put political pressure on world leaders:

Dr Murari Lal also said he was well aware the statement (about Himalayan glaciers melting by 2035), in the 2007 report by the Intergovernmental Panel on Climate Change (IPCC), did not rest on peer-reviewed scientific research.

In an interview with The Mail on Sunday, Dr Lal, the co-ordinating lead author of the report’s chapter on Asia, said: ‘It related to several countries in this region and their water sources. We thought that if we can highlight it, it will impact policy-makers and politicians and encourage them to take some concrete action.

Then there are a number of stories on a similar theme where the predictions of climate change catastrophe weren’t based on “peer-reviewed” literature but on reports from activist organizations, like the WWF. And the reports were written not by specialists in the field, but activists..

And these follow the “climategate” leak of November 2009 where emails from the CRU from prominent IPCC scientists like Phil Jones, Michael Mann, Keith Briffa and others show them in a poor light.

This blog is focused on the science but once you read stories like this you wonder how much of anything to believe.

  • For some, the science is settled, these are distractions by the right/big oil/energy companies and what is there to discuss?
  • For others, we knew all along that the IPCC is a green/marxist plot to take over world government, what is there to discuss?

If you are in one of those mindsets, this blog is probably the wrong place to come.

Be Skeptical

Being skeptical doesn’t mean not believing anything you hear. Being skeptical means asking for some evidence.

I see many individuals watching the recent events unfolding and saying:

See! CO2 can’t cause climate change. It’s all a scam.

Actually the two aren’t related. CO2 and the IPCC are not an indivisible unit!

It’s a challenge to keep a level head. To be a good skeptic means to realize that an organization can be flawed, corrupt even, but it doesn’t mean that all the people whose work it has drawn on have produced junk science.

When a government tries to convince its electorate that it has produced amazing economic results by stretching or inventing a few statistics, does this mean the statisticians working for that government are all corrupt, or even that the very science of statistics is clearly in error?

Most people wouldn’t come to that conclusion.

Politics and Science

But in climate science it’s that much harder because to understand the science itself takes some effort. The IPCC is a political body formed to get political momentum behind action to “prevent climate change”. Whereas climate science is mostly about physics and chemistry.

They are a long way apart.

For myself, I believe that the IPCC has been bringing the science of climate into disrepute for a long time, despite producing some excellent work.  It has claimed too much certainty about what the science can predict. Tenuous findings that might possibly show that a warmer world will lead to more problems are pressed into service. Findings against are ignored.

This causes a problem for anyone trying to find out the truth.

It’s tempting to dismiss anything that is in an IPCC report because of these obvious flaws – and they have been obvious for a long time. But even that would be a mistake. Much of what the IPCC produces is of a very high quality. They have a bias, so don’t take it all on faith..

The Easy Answer

Find a group of people you like and just believe them.

The Road Less Travelled

My own suggestion, for what it’s worth, is to put time into trying to get a better understanding of climate science. Then it is that much easier to separate fact from fiction. One idea – if you live near a university, you can visit their library and probably find a decent entry-level book or two about climate science basics.

Another idea – for around $40 you can purchase Elementary Climate Physics by Prof. F.W. Taylor – from http://www.bookdepository.co.uk/ – free shipping around the world. Amazing. And I don’t get paid for this advert either, not until I work out how to get adverts down the side of the blog. It’s an excellent book with some maths, but skip the maths and you will still learn 10x more than reading any blog including mine.

And, of course, visit blogs which focus on the science and ask a few questions.

Be prepared to change your mind.

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CO2 – An Insignificant Trace Gas? Part Two

Posted in Climate Models on January 20, 2010| 84 Comments »

Recap

Part One of the series started with this statement:

If there’s one area that often seems to catch the imagination of many who call themselves “climate skeptics”, it’s the idea that CO2 at its low levels of concentration in the atmosphere can’t possibly cause the changes in temperature that have already occurred – and that are projected to occur in the future. Instead, the sun, that big bright hot thing in the sky (unless you live in England), is identified as the most likely cause of temperature changes.

Part One looked mainly at the radiation balance – what the sun provides (lots of energy at shortwave) and what the earth radiates out (longwave). Then it showed how “greenhouses gases” – water vapor, CO2 and methane (plus some others)  – absorb longwave radiation and re-emit radiation both up out of the atmosphere and back down to the earth’s surface. And without this absorption of longwave radiation the earth would be 35°C cooler at its surface. The post concluded with:

CO2 and water vapor are very significant in the earth’s climate, otherwise it would be a very cold place.

What else can we conclude? Nothing really, this is just the starting point. It’s not a sophisticated model of the earth’s climate, it’s a “zero dimensional model”.. the model takes a very basic viewpoint and tries to establish the effect of the sun and the atmosphere on surface temperature. It doesn’t look at feedback and it’s very simplistic.

Two images to remember..

First, the sun’s radiated energy is mostly under 4μm in wavelength (shortwave), while the earth’s radiated energy is over 4μm (longwave), meaning that we can differentiate the two very easily:

Radiation vs Wavelength -Sun and Earth

Radiation vs Wavelength - Sun and Earth

Second, the aborption that we can easily measure in the earth’s longwave radiation from different molecules:

Radiation spectra from the earth with absorption

Radiation spectra from the earth showing absorption from atmospheric gases

Recap over.. This post was going to introduce the basic 1-d model of radiative transfer, but enough people asked questions about the absorption properties of gases that I thought it was was worth covering in more detail.. The 1-d model will have to wait until Part Three.

Why don’t the Atmospheric Gases Absorb Energy according to their Relative Volume?

Just because CO2 only consists of 0.04% of gases doesn’t mean it only contributes 0.04% of atmospheric absorption and re-emission of long wave radiation. Why is that?

Oxygen, O2, constitutes 21% of the atmophere and nitrogen, N2, constitutes 78%. Why aren’t they important “greenhouse” gases? Why are water vapor, CO2 and methane (CH4) the most important when they are present in such small amounts?

For reference, the three most important gases by volume are:

  • Water vapor – 0.4% averaged throughout the atmosphere, but actual value in any one place and time varies (See note 1 at end of article)
  • CO2               – 0.04% (380ppmv), well mixed (note: ppmv is parts per million by volume)
  • CH4               – 0.00018% (1.8ppmv), well mixed

Now there are three factors in determining the effect of longwave absorption:

  1. The amount of the gas by volume
  2. How much longwave energy is radiated from the earth at wavelengths that the gas absorbs
  3. The ability of the gas to absorb energy at a given wavelength

The first one is the simplest to understand. In fact, it’s knowing only this factor that causes so much confusion.

The second point is not immediately obvious, but should become clearer by reviewing the earth’s radiation spectrum:

Radiation vs Wavelength -Sun and Earth

Radiation vs Wavelength - Sun and Earth

Different amounts of energy are radiated at different wavelengths. For example, the amount of energy emitted between 10-11μm is eight times the amount of energy between 4-5μm (for radiation from a surface temperature of 15 °C or 288K).

CO2 has a wide absorption band centered around 15μm, which is where the long-wave radiation from the earth is at almost its highest level. By contrast, one of water vapor’s absorption lines is at 6.27μm – where the radiation is a slightly lower level (about 25% less) and more importantly, the other water vapor absorption lines are where the radiation is 5-10x lower intensity.

However, there is around 10x as much water vapor than CO2 in the atmosphere, which is why it is the most important greenhouse gas.

And Third, Why are Some Gases More Effective at Absorbing Longwave Energy?

Why aren’t O2 and N2 absorbers of longwave radiation?

Molecules with two identical atoms don’t change their symmetry when any rotation or vibration takes place. As a result they can’t move into different energy states.

But triatomic molecules like CO2, H2O and CH4 can bend as they vibrate. They can move into different energy states by changing their shape. Consequently they can absorb the energy from an incoming photon if its energy matches the new state.

And some molecules have many more energy states they can move into. This changes their absorption profile because their spectral breadth is effectively wider.

Here’s a graphic of one part of the actual CO2 absorption lines. Apologies for the poor quality scan..

CO2 spectral lines from one part of the 15um band

From "Handbook of Atmospheric Sciences", Hewitt & Jackson 2003

(Note that the x-axis is “Wavenumber, cm-1”. This is a convention for spectral people. Wavenumber is the number of wavelengths present in 1cm. I added the actual wavelength underneath.)

This shows the complexity of the subject once we look at the real detail. In practice, these individual discrete absorption lines “broaden” due to pressure broadening (collisions with other molecules) and Doppler broadening (as a result of the absorbing molecule moving in the same or opposite direction to the photon of light).

However, the important point to remember is that different molecules absorb at different frequencies and across different ranges of frequencies.

This third factor is the most important in determining the absorption properties of longwave radiation.

As an interesting comparison, molecule by molecule methane absorbs about 20x as much energy as CO2. But of course it is present in much smaller quantities.

Here are water vapor and CO2 across 5-25μm from the HITRANS database:

CO2 and water vapor absorption, by SpectraCalc from the HITRANS database

CO2 and water vapor absorption, by spectracalc.com from the HITRANS database

See Note 2 at the end of the article.

What about Oxygen?

A digression on oxygen.. It is important in the earth’s atmosphere because it absorbs UV, but when these high energy photons from the sun interact with O2 it breaks into O+O. Then a cycle takes place where O2 and O combine to form O3 (ozone), and later O3 breaks up again. By the time the sun’s energy has reached the lower part of the atmosphere (troposphere) all of the lower wavelength energy (most of the UV) has been filtered out.

O3 itself does absorb some longwave energy, at 9.6um, but because there is so little O3 in the troposphere it is not very significant.

What Happens when a Greenhouse Gas Absorbs Energy?

Once a gas molecule has absorbed radiation from the earth it has a lot more energy. But in the lower 100km of the atmosphere, the absorbed energy is transferred to kinetic energy by collisions between the absorbing molecules and others in the layer. Effectively, it heats up this layer of the atmosphere.

The layer itself will act as a blackbody and re-radiate infrared radiation. But it re-radiates in all directions, including back down to the earth’s surface. (If it only radiated up away from the earth there would be no “greenhouse” effect from this absorption).

Conclusion

We are still on the “zero dimensional model” – some call it the billiard ball model – of the radiative balance in the earth’s climate system.

A few different factors affect the absorption of the earth’s longwave radiation by various gases.

O2 barely absorbs any (see note 2 below), and neither does N2 (nitrogen). Among the other gases – the main greenhouse gases being water vapor, CO2 and methane – we see that each one has different properties – none of which can be determined by our intuition!

Different molecules can absorb energy in certain frequencies simply because of their ability to change shape and move to different energy states. The primary property that creates a strong “greenhouse” effect is to have a strong and wide absorption around a wavelength that the earth radiates. This is centered about 10μm (and isn’t symmetrical) so the further away from the peak energy the absorption occurs, the less relevant that absorption line becomes in the earth’s energy balance.

In the next part in the series, we will look at the 1-dimensional model and also what happens when absorption in a wavelength is saturated.

Note 1 – Water Vapor ppmv: After consulting numerous reference works, I couldn’t find one which gave the averaged water vapor throughout the atmosphere, or the troposphere. The actual source for the 0.4% was Wikipedia.

Because all the reference works danced around without actually giving a number I suspect it is “up in the air”. Here is one example:

Water vapor concentration is highly variable, ranging from over 20,000 ppmv (2%) in the lower tropospherical atmosphere to only a few ppmv in the stratosphere..

Atmospheric Science for Environmental Scientists (2009) Hewitt & Jackson

There is a great application, Spectral Calc for looking at atmospheric concentrations and absorption lines. Specifically http://spectralcalc.com/atmosphere_browser gives plots of atmospheric concentration and the data agrees with the Wikipedia number given in the body of this article:

CO2 and water vapor by volume

CO2 and water vapor by volume, from "Spectral Calculator" database

Averaging over the whole atmosphere, the concentration of water vapor does seem to be around 10x the CO2 value.

Note 2 – Optical Thickness: The spectral plots from the HITRANS database shown in the body of the article give the capture cross-section per mole (i.e. per “unit” of that gas, not per unit volume of the general atmosphere).

One commenter asked why another plot from a different website drawing on the same HITRANS database produced this:

Optical Thickness of O2 and water vapor

Optical Thickness of O2 and water vapor from http://www.atm.ox.ac.uk

Note that I’ve adjusted the plots so that similar values on the y-axes are aligned for both graphs. And note that the vertical axis is logarithmic.

His comment was that oxygen, O2, is only maybe 1000 times lower in absorption than water vapor (100 =1 vs 103 =1000) at 6.7μm and given that O2 is 20% of the atmosphere instead of 0.4%, O2 should be comparable to water vapor as a greenhouse gas.

But in fact, this graphical plot isn’t plotting the absorption by units of molecule – instead it is plotting Optical Thickness.

This is a handy variable which we will see more of in Part Three. Optical Thickness essentially takes the value of Intensity, which is per unit of molecules,  and “integrates” that value up through the entire height of the atmosphere.

As a result it gives the picture of the complete influence of that gas at different frequencies without having to work out the relative proportions of the gas at different heights in the atmosphere.

So the example above compares the complete absorption (in a simplistic model) through the whole atmosphere, giving O2 about 3000x less effect than water vapor at 6.7μm.

Update – Part Three is now online

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Understanding the Flaw

Posted in Climate Models, Commentary on December 13, 2009| 38 Comments »

The debate about climate change is a very polarized one.

Understanding the points of view of people who disagree with you is essential to making progress. Even more importantly, you should understand the arguments that summarize the best of the opposite point of view.

Much that is written in the general media is the “polarized view”. So here is a wonderful open letter from a climate scientist that sums up a “skeptical” point of view in a humble way. Emphasis added.

I would add that the view presented is also the point of view of this blog. Standing on the shoulders of giants..

=====================

Date: Mon, 07 Dec 2009 08:28:38 -0700
From: Petr Chylek
To: Climate@lanl.gov, energy@lanl.gov, isr-all@lanl.gov, ees-all@lanl.gov

Dear Climate People:

FYI below is a letter that I sent on Saturday to about 100 top climate research experts including Jim Hansen, Steve Schneider, Phil Jones (UK) and other superstars. Till now I got 14 replies which are about 50/50 between supporting of what I said and defense of the IPCC process.

Greetings,
Petr

=====================

Open Letter to the Climate Research Community

I am sure that most of you are aware of the incident that took place recently at the University of East Anglia’s Climatic Research Unit (CRU). The identity of the whistle-blower or hacker is still not known.

The selected release of emails contains correspondence between CRU scientists and scientists at other climate research institutions. My own purely technical exchange of emails with CRU director Professor Phil Jones is, as far as I know, not included.

I published my first climate-related paper in 1974 (Chylek and Coakley, Aerosol and Climate, Science 183, 75-77). I was privileged to supervise Ph. D. theses of some exceptional scientists – people like J. Kiehl, V. Ramaswamy and J. Li among others. I have published well over 100 peer-reviewed papers, and I am a Fellow of the American Geophysical Union, the Optical Society of America, and Los Alamos National Laboratory. Within the last few years I was also honored to be included in Wikipedia’s blacklist of “climate skeptics”.

For me, science is the search for truth, the never-ending path towards finding out how things are arranged in this world so that they can work as they do. That search is never finished.

It seems that the climate research community has betrayed that mighty goal in science. They have substituted the search for truth with an attempt at proving one point of view. It seems that some of the most prominent leaders of the climate research community, like prophets of Old Israel, believed that they could see the future of humankind and that the only remaining task was to convince or force all others to accept and follow. They have almost succeeded in that effort.

Yes, there have been cases of misbehavior and direct fraud committed by scientists in other fields: physics, medicine, and biology to name a few. However, it was misbehavior of individuals, not of a considerable part of the scientific community.

Climate research made significant advancements during the last few decades, thanks to your diligent work. This includes the construction of the HadCRUT and NASA GISS datasets documenting the rise of globally averaged temperature during the last century. I do not believe that this work can be affected in any way by the recent email revelations. Thus, the first of the three pillars supporting the hypothesis of manmade global warming seems to be solid.

However, the two other pillars are much more controversial. To blame the current warming on humans, there was a perceived need to “prove” that the current global average temperature is higher than it was at any other time in recent history (the last few thousand years). This task is one of the main topics of the released CRU emails. Some people were so eager to prove this point that it became more important than scientific integrity.

The next step was to show that this “unprecedented high current temperature” has to be a result of the increasing atmospheric concentration of carbon dioxide from the burning of fossil fuels. The fact that the Atmosphere Ocean General Circulation Models are not able to explain the post-1970 temperature increase by natural forcing was interpreted as proof that it was caused by humans. It is more logical to admit that the models are not yet good enough to capture natural climate variability (how much or how little do we understand aerosol and clouds, and ocean circulation?), even though we can all agree that part of the observed post-1970 warming is due to the increase of atmospheric CO2 concentration. Thus, two of the three pillars of the global warming and carbon dioxide paradigm are open to reinvestigation.

The damage has been done. The public trust in climate science has been eroded. At least a part of the IPCC 2007 report has been put in question. We cannot blame it on a few irresponsible individuals. The entire esteemed climate research community has to take responsibility. Yes, there always will be a few deniers and obstructionists.

So what comes next? Let us stop making unjustified claims and exaggerated projections about the future even if the editors of some eminent journals are just waiting to publish them. Let us admit that our understanding of the climate is less perfect than we have tried to make the public believe. Let us drastically modify or temporarily discontinue the IPCC. Let us get back to work.

Let us encourage students to think their own thoughts instead of forcing them to parrot the IPCC conclusions. Let us open the doors of universities, of NCAR, NASA and other research institutions (and funding agencies) to faculty members and researchers who might disagree with the current paradigm of carbon dioxide. Only open discussion and intense searching of all possibilities will let us regain the public’s trust and move forward.

Regards,
Petr Chylek

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Those Hazy Skeptics at the IPCC

Posted in Climate Models on December 3, 2009| 16 Comments »

Back in the day, the IPCC published its 3rd assessment report and declared a high confidence in the science of doom – humans have caused the unprecedented modern warming and the future is very bleak.

In their view the science was well enough understood that climate models could be relied upon – especially as they predicted the past so nicely.

As well as their Summary for Policymakers they also published a Complete Report. It’s a very informative document and runs to just under 800 pages in 14 chapters, not including appendices. Worth a read for the serious student.

Chapter 5 examines the role of aerosols, which they introduced in Chapter 1 (p.93):

The effect of the increasing amount of aerosols on the radiative forcing is complex and not yet well known. The direct effect is the scattering of part of the incoming solar radiation back into space. This causes a negative radiative forcing which may partly, and locally even completely, offset the enhanced greenhouse effect. However, due to their short atmospheric lifetime, the radiative forcing is very inhomogeneous in space and in time.

This complicates their effect on the highly non-linear climate system. Some aerosols, such as soot, absorb solar radiation directly, leading to local heating of the atmosphere, or absorb and emit infrared radiation, adding to the enhanced greenhouse effect.

Aerosols may also affect the number, density and size of cloud droplets. This may change the amount and optical properties of clouds, and hence their reflection and absorption. It may also have an impact on the formation of precipitation. As discussed in Chapter 5, these are potentially important indirect effects of aerosols, resulting probably in a negative radiative forcing of as yet very uncertain magnitude.

(My emphasis added). A few snippets of interest from chapter 5, which runs to 60 pages:

p. 304, Under Summary of Main Uncertainties Associated with Aerosol Sources and Properties

Perhaps the most important uncertainty in aerosol properties is the production of cloud condensation nuclei (Section 5.3.3).

Earlier they lead up to cloud condensation nuclei being the tricky part – with the other bits being easier? p291-2:

..  An analysis of the contributions of the uncertainties in the different factors needed to estimate direct forcing to the overall uncertainty in the direct forcing estimates can be made. This analysis leads to an overall uncertainty estimate for fossil fuel aerosols of 89% (or a range from –0.1 to –1.0 Wm–2) while that for biomass aerosols is 85% (or a range from –0.1 to –0.5 Wm–2 ).

..  An analysis of the contributions of the uncertainties in the different factors needed to estimate indirect forcing of the first kind can be made. This analysis leads to an overall uncertainty estimate for indirect forcing over Northern Hemisphere marine regions by fossil fuel aerosols of 100% (or a range from 0 to −2.8 Wm–2).

..  The indirect radiative effect of aerosols also includes effects on ice and mixed phase clouds, but the magnitude of any indirect effect associated with the ice phase is not known. It is not possible to estimate the number of anthropogenic ice nuclei at the present time. Except at very low temperatures (<−40°C), the mechanism of ice formation in clouds is not understood. Anthropogenic ice nuclei may have a large (probably positive) impact on forcing.

So clearly the science was settled back in 2001.

(By the way, I think the scientists who put chapter 5 together did a great job and have clearly been hard at work trying to understand an extremely complex subject).

Of course, science moves forward so let’s take a great Six Year Leap to 2007 and the 4th Assessment Report.

What do we find? First let’s note that the radiative equivalence of the anthropogenic increase in CO2 is around 1.7 Wm–2 (the radiative equivalence can view the CO2 increase as if it was an equivalent amount of radiation from the sun).

p29:

Direct aerosol radiative forcing is now considerably better quantified than previously and represents a major advance in understanding since the time of the TAR, when several components had a very low level of scientific understanding. A total direct aerosol radiative forcing combined across all aerosol types can now be given for the first time as –0.5 ± 0.4 Wm–2, with a medium-low level of scientific understanding.

(My italics). Note that one aspect of aerosols is somewhere between no effect and cancelling out half the anthropogenic CO2 warming.

p30:

Anthropogenic aerosols effects on water clouds cause an indirect cloud albedo effect (referred to as the first indirect effect in the TAR), which has a best estimate for the first time of –0.7 [–0.3 to –1.8] Wm–2

And the other key climate impact of aerosols is somewhere between not much and cancelling out all of the anthropogenic CO2 warming.

Thank goodness we now have a much better understanding of aerosols from 2001 when we knew for sure that humans had caused – and would continue to cause – significant warming.

Now we can quantify the aerosol effect, we know that they either do nothing or completely cancel out anthropogenic global warming. Back in 2001, we didn’t have to let that dent our confidence!

Just as a little footnote, those IPCC skeptics had to try and calculate error bars, but at such a low level of scientific understanding the error bars themselves might be in question.

And another footnote, I used the “Report accepted by Working Group I of the Intergovernmental Panel on Climate Change but not approved in detail” because I downloaded this when it was first released in 2007.

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CO2 – An Insignificant Trace Gas? Part One

Posted in Atmospheric Physics, Climate Models on November 28, 2009| 508 Comments »

[Note: This article was significantly updated August 5th, 2010. Therefore, many comments became obsolete, or at least proved their worth, by encouraging an update]

If there’s one area that often seems to catch the imagination of many who call themselves “climate skeptics”, it’s the idea that CO2 at its low levels of concentration in the atmosphere can’t possibly cause the changes in temperature that have already occurred – and that are projected to occur in the future. Instead, the sun, that big bright hot thing in the sky (unless you live in England), is identified as the most likely cause of temperature changes.

Argument from Inconceivability

I personally find it hard to believe that we are hurtling through space at 67,000 miles per hour on a big spinning rock. It doesn’t feel like it. (Actually that’s just the speed that we orbit the sun, and the sun is moving as well, so its more complicated..)

And is this table (you can’t see my table, but any table will do) really made of tiny atoms but science claims it’s mostly space between the little balls? What? Not likely.

Satire over.

For science, personal experience and imagination are not the deciding factors. They lead you astray. Instead, investigation of phenomena lead to hypotheses, experiments and eventually “theories” – as well-established science “facts” are known. Your intuition might be great for understanding people’s motivations, or whether a person can run 100m in 3 seconds, but not so great for the energy absorption characteristics of invisible molecules.

Let’s look at the science.

How do we analyze the Earth’s Climate?

It’s a tricky problem. And like most tricky science problems we start with some simplications. We analyze a simplified model and see where that gets us. Like, how does this simple model compare to reality? And how do we verify the results from the simplified model if the reality is so much more complicated?

Read on, it’s a journey.

Energy from the Sun

The sun is our source of heat. We are 150 million km from the sun, so how does that heat energy get here?

There are 3 mechanisms for heat transfer – conduction, convection and radiation. It’s a vacuum between the sun and the earth so energy from the sun can only arrive here through radiation. What does that radiation look like? A “body” emits radiation across a spread (a “spectrum”) of wavelengths, in a way that depends on that body’s temperature.

The fact that the wavelengths of the energy emitted vary with temperature is a key point, essential for understanding this aspect of climate science.

Here’s a few samples – each color represents a different temperature object. The blue line is a body at 5000K = 4727°C (8540°F).

Blackbody radiation

Energy intensity versus wavelength for different temperature objects

For those new to the subject, K (“Kelvin”) is absolute temperature. It tracks degree Centigrade/Celsius one for one, but whereas °C starts at the freezing point of water, K starts at, well, absolute zero.

So 0°C = 32°F = 273K;  and  -273°C = -459°F = 0K

There are reasons why this temperature scale exists, but let’s just leave it at that.

So if you look at the graph you can see that the higher the temperature, the higher the total energy (which everyone would expect) and the lower the wavelengths of the peak energy.

At the end of the post I’ll show some maths, but many people don’t want to see any equations. Just as a preview, total energy is proportional to the 4th power of absolute temperature. Double the temperature and the energy goes up by 16 times.

And it’s worth stating as well at this point, none of this is in question. It’s reproduceable, non-controversial thermodynamics – a branch of physics. You can reproduce it in the lab and measure it everywhere in the real world.

Energy from the Earth

Now the earth also emits radiation according to the same formula. If the earth isn’t heating up or cooling down the energy absorbed will be equal to the energy emitted. (And we’ll leave discussions about how we know whether the earth is heating up and exactly what that means for another day).

If you do the maths (see the end of the post), you find that the equations say that the earth should be about -18°C (255K) when in fact it is an average +15°C across the globe. What’s going on?

First let’s look at the energy from the earth and sun on the same graph. The sun has a surface temperature of 5780K:

What’s happened to the earth’s radiation? It can barely be seen on a linear plot, it is so small in comparison. However, this is at source – picture a spaceship parked just off the surface of the sun taking the measurements.

By the time the solar radiation has reached the earth it has reduced in intensity by a factor of around 46,000 (see the Inverse Square Law or The Sun and Max Planck Agree – Part Two):

Here is a comparison of solar radiation (the 5780K curve) at the top of the atmosphere, compared with a few terrestrial radiation curves for 260K (-13°C) though to 300K (27°C). Note that it is a logarithmic plot.

Here is a linear plot of the same for comparison:

Notice how the wavelength of the peak value of radiation shifts to the right as the source of the radiation gets colder. The typical value for the earth is 10μm, while for the sun it is 0.5μm.

 

What’s great about the graph is you can see clearly how the radiation from the sun can be easily discriminated from the radiation from the earth. There’s no complicated deductive work, if you measure radiation below 4μm, you know it came from the sun, no matter how many things it bounced off in the meantime. If you measure radiation above 4μm, you know it’s generated by the terrestrial system.

Check out The Sun and Max Planck Agree and The Sun and Max Planck Agree – Part Two for more on this subject.

What does this mean? It means that we can confident of the amount of energy:

  1. Arriving from the sun at the top of atmosphere and at the surface
  2. From the sun that is reflected back into space by the atmosphere or the earth’s surface
  3. Emitted by the earth

How do we work out 3)? We have satellites in space that look at the energy coming from the earth’s surface in the longer wavelengths that correspond to the lower temperatures of the earth’s surface.

And the climate science convention is to call the energy less than 4μm: short wave radiation and the energy greater than 4μm:  long wave radiation.

Note that “infrared” is radiation greater than 0.7μm – a different term than “longwave”.

Energy Absorbed by Gases in the Atmosphere

Let’s look at some more standard science.

Each gas in the atmosphere has different absorption characteristics, which vary according to the wavelength of the radiation. In detail it is very complex, but here is a broad overview of total absorption:

 

 

Absorption of different wavelength radiation in the earth's atmosphere

Absorption of different wavelength radiation in the earth’s atmosphere

Note that the horizontal axis is a logarithmic scale. The vertical axis shows “opacity” or what proportion of the energy is absorbed by the atmosphere. I picked this graph because you can easily see where the visible light fits in. What you should notice is how much radiation is actually absorbed by the atmosphere. This graphic is a bit too simplistic.

Here’s solar radiation at the top of atmosphere, and at the surface:

 

From Vardavas & Taylor (2007)

From Vardavas & Taylor (2007)

The lighter color is what we observe at the earth’s surface, while the darker surrounding is the observation of solar radiation by satellite. The difference is absorption by various molecules in the atmosphere and you can see from the annotation which gases absorb at which wavelength.

Here is a measurement of outgoing longwave radiation (terrestrial radiation) measured by satellite at the top of the atmosphere:

Outgoing longwave radiation at TOA, Taylor (2005)

Outgoing longwave radiation at TOA, Taylor (2005)

For those new to this kind of graph, they are usually shown in “wavenumber” rather than wavelength. It’s not important at this stage except to note that the longer wavelengths are to the left and the shorter wavelengths are to the right.

The reason for picking this measurement to show is that the emission curves for typical temperatures of the earth’s surface are shown overlaid. The highest one is 275K or 2°C. The surface of the earth emits radiation very close to the blackbody shape (see The Dull Case of Emissivity and Average Temperatures) but by the time the radiation leaves the earth’s atmosphere that isn’t what we see.

Here is another example, this time with a theoretical calculation (overlaid and displaced for comparison) which is something covered much later in this series:

Measured and theoretical spectra, from Goody & Yung (1989)

Measured and theoretical spectra, from Goody & Yung (1989)

Click for a larger view

On this spectrum, the authors have noted the reduced areas of outgoing radiation and marked CO2, H2O, O3 (ozone) and CH4 (methane).

How do they know these gases are the cause?

And what effect does it really have?

Measurements in the Lab

Scientists have been measuring the absorption characteristics of each gas in the atmosphere at different wavelengths for many decades.

Here is a good summary of the main absorption bands:

The last bottom line shows the total in the atmosphere. You might notice that N2 (nitrogen) doesn’t show up. Is climate science ignoring this important gas? No – nitrogen absorbs almost nothing, for reasons that are touched on in Part Two. We can say that nitrogen is transparent to solar and terrestrial radiation.

You will also notice that O2 and O3 (oxygen and ozone) are shown. There is a chemical cycle in the upper atmosphere called the Chapman cycle which is responsible for generating ozone. In the very short wavelengths – below 0.3μm – oxygen and ozone both absorb solar radiation. In the longer wavelengths, ozone absorbs around 9.6μm. Oxygen doesn’t absorb at all in longwave – it is also (like nitrogen) transparent to terrestrial radiation.

What you can’t tell from the chart above is how influential each of the gases is in terms of total energy absorbed. That is a much more complex challenge – covered in later articles (but it isn’t as simple as the ratio of each of the absorbing gases in the atmosphere).

Before we leave the subject of absorption, it’s worth showing some lab measurements – from the HITRANS database. This might help see the main characteristics of CO2 and water vapor as well as the complexity.

First the main characteristics on a linear graph:

From the HITRANS 2008 database, via spectralcalc.com

From the HITRANS 2008 database, via spectralcalc.com

You can see that CO2 has high absorption around 15μm and water vapor around 6.3μm.

Now on a log plot – this shows the complexity – but note that each horizontal line represents a factor of 100. O2 and N2 are included at the bottom for comparison:

From the HITRANS 2008 database from spectralcalc.com

From the HITRANS 2008 database from spectralcalc.com

Note the vertical scale for N2 and O2 – even at their peak they absorb less than a billionth the radiation of CO2 and water vapor.

What Effect Does it Have?

Outside the world of atmospheric physics there is a lot of confusion about some thermodynamics basics. There are many articles on this blog that address those specific points (checkout the Roadmap) and there is no way to cover all of the misconceptions in this article – without it being 100 pages long..

As the surface of the earth heats up from the solar radiation absorbed, it in turn emits radiation – as shown in the 3rd and 4th graphs above.

If the atmosphere didn’t absorb any of this radiation then we would measure a spectrum like one of the Planck curves (as they are known). Instead we see large “chunks” (to use a non-technical term) of energy removed by the time the radiation leaves the atmosphere – “chunks” corresponding to water vapor, CO2 and ozone (as well as a number of other gases). And the larger the “chunk”, the more energy has been absorbed by the corresponding gas from the radiation.

When the atmosphere absorbs radiation it heats up. The absorbed energy is shared thermally via collisions with all other gas molecules, so the whole atmosphere in that region heats up. And the gases like CO2 and water vapor emit radiation – more emission as they increase in temperature.

The atmosphere, once heated up, radiates equally in all directions. Some of this is downward. Here is a measured spectrum at the earth’s surface:

Wisconsin, Ellingson & Wiscombe (1996)

Wisconsin, Ellingson & Wiscombe (1996)

As you can see, the emission of radiation measured at the earth’s surface corresponds to the missing sections at the top of the atmosphere. See The Amazing Case of “Back-Radiation” and The Amazing Case of “Back Radiation” – Part Two.

Note: If a gas can absorb 15μm radiation it can also emit 15μm radiation. If a gas can’t absorb 15μm radiation it also can’t emit at that wavelength.

The energy radiated by the atmosphere which is received at the earth’s surface increases the temperature at the surface. (See The Amazing Case of “Back Radiation” – Part Three).

Although many people have become confused with imaginary second laws of thermodynamics to believe that this can’t happen, here is the easy way to understand the problem:

If we average the incoming solar radiation that is absorbed by the earth’s climate over the surface of the earth we get around 239 W/m2. (See The Earth’s Energy Budget – Part One).

If we average the outgoing longwave radiation from the top of atmosphere we get the same value: 239 W/m2.

If the atmosphere didn’t absorb any terrestrial radiation then the surface of the earth must also be emitting 239 W/m2.

The only way that the surface of the earth could emit this amount is if the temperature of the earth was around 255K or -18°C.

And yet we measure an average surface temperature of around 15°C – an emission of radiation of 396 W/m2. (See note 1).

If the atmosphere wasn’t absorbing and re-radiating longwave then the surface of the earth would be -18°C. This is the inappropriately-named “greenhouse” effect (and note that I haven’t used a greenhouse to demonstrate anything).

Conclusion

The question asked at the start was “Is CO2 an insignificant trace gas?” and the answer is no.

CO2 and water vapor are very significant in the earth’s climate, otherwise it would be a very cold place.

What else can we conclude? Nothing really, this is just the starting point. It’s not a sophisticated model of the earth’s climate, it’s a “zero dimensional model” or “billiard ball model” which takes a very basic viewpoint and tries to establish the effect of the sun and the atmosphere on surface temperature. It doesn’t look at feedback and it’s very simplistic.

Climate is a complex subject. Hopefully this explains some basics and we can start looking a little deeper in subsequent posts.

More in this series

Part Two – why different gases absorb different amounts of energy, why some gases absorb almost no longwave radiation

Part Three – the Beer Lambert model of absorption and the concept of re-emission of radiation

Part Four – band models and how transmittance of CO2 changes as the amount of CO2 increases under “weak” and “strong” conditions

Part Five – two results from solving the 1-d equations – and how CO2 compares to water vapor

Part Six – Visualization -what does the downwards longwave radiation look like at the earth’s surface

Part Seven – The Boring Numbers – the values of “radiative forcing” from CO2 for current levels and doubling of CO2.

Part Eight – Saturation – explaining “saturation” in more detail

CO2 Can’t have that Effect Because.. – common “problems” or responses to the theory and evidence presented

Other later series covering similar material

Visualizing Atmospheric Radiation – a lot more detail on how radiation travels through the atmosphere, and how it is absorbed and re-emitted by various “greenhouse” gases

Atmospheric Radiation and the “Greenhouse” Effect

The Maths

The Stefan-Boltzmann Law states:

j = εσT4

Where

j = total energy radiated per unit area per unit time
ε = emissivity, ranging from 0 to 1, where 1 is a perfect black body
σ = the Stefan Boltzmann constant, 5.67 x 10-8
T = temperature in K

The effective temperature of the sun is 5780K, its emissivity is quite close to 1, and so it radiates 6.3 x 107 W/m2

As the sun is a long way from the earth, its radiation by the time it reaches the earth is reduced according to Inverse Square Law.

The radius of the sun, rsun = 696 x 106m

Distance from the sun to earth,  ao = 1.5×1011 m (150 million km)

Therefore the solar radiation is reduced by a factor of (1.5×1011/(696 x 106)2 = (215)2 = 46,225. Therefore, the solar radiation reaching the earth’s atmosphere = 6.3 x 107 / 46,225 = 1360 W/m2.

And from measurement by satellite we get 1367 W/m2.

Now we have to note two important facts:

  • Some of the solar radiation is reflected
  • The sun isn’t directly above all points on the earth at the same time

So how much energy is actually absorbed by the climate system?

The measured proportion of reflected solar radiation is 30% – we call this the albedo.

To work out the effect of the day and night and different angles of solar radiation sounds tricky but it’s actually an easy problem. The solar radiation from a long way away hits a disc of area = πr². But the surface of a sphere is 4πr² – (see The Earth’s Energy Budget – Part One for a fuller explanation). Therefore, to calculate the energy absorbed by the climate system averaged over the surface of the earth we can just divide by 4:

Esolar = 1367 x (1 – 0.3) / 4 = 239 W/m²

If the earth is not heating up or cooling down then the earth’s climate system must also be emitting radiation at the same rate.  Note that these are global annual averages.

If there was no absorption of surface radiation by the atmosphere then the surface radiation would also be – on average – 239 W/m².

What temperature of the earth’s surface does this correspond to?

Remember the equation at the start of the maths section: j = εσT4
Rearranging to solve, T = (j/εσ)1/4

The emissivity of the earth is very close to 1 (see The Dull Case of Emissivity and Average Temperatures), therefore:

T = 255K or -18°C

Given that we actually experience much higher temperatures on the surface of the earth, we need an explanation. This can be found in the inappropriately-named “greenhouse gases”, which include water vapor, CO2 and methane (CH4).

When the earth emits its longwave radiation, these gases absorb energy and then re-emit, so that the earth’s energy doesn’t just fly off into space but instead it’s absorbed and re-transmitted, some of it back down to earth.

The “greenhouse gases” heat the earth’s surface up approximately 33°C higher than it would be otherwise.

Note 1:

There is a lot of confusion about the use of average temperatures in this approach to explaining the role of CO2 and water vapor in the atmosphere.

Calculating an average temperature has a lot of issues, as explained in Why Global Mean Surface Temperature Should be Relegated, Or Mostly Ignored. However, the explanation above doesn’t rely in any way on the arbitrary construct of average temperatures.

I simply used average temperatures to help newcomers visualize the issue more clearly. If I say that the earth’s average temperature should be -18°C everyone knows that I am wrong. If I say that the emission of surface radiation should be 239 W/m² who would know?

The use of energy per m² also confuses – the poles are colder, the equator is hotter – maybe the averages have lost something important. Once again, the averages just make it easier to understand. However, for those readers convinced that there is a problem in comparing average values, we can calculate the total energy:

Total solar energy absorbed globally annually = solar “constant” x (1 – albedo) x surface area the solar radiation irradiates x number of seconds in a year

Total energy = 1367 W/m²  . (1 – 0.3) . πre² . 365.24.3600 = 3.8 x 1024 J

where re = radius of the earth = 6.37 x 106m.

How much energy does the surface of the earth radiate? Well, it can be calculated from the global temperature database and the Stefan-Boltzmann law.

This was done in Earth’s global energy budget, Trenberth and Kiehl, Bull. Amer. Meteor. Soc. (2009). They expressed the number as an global annual average – 396 W/m². We can simply multiply it back up the same way – using the surface area of the earth – to get

Total energy radiated from the surface = 396 x 4πre² . 365.24.3600 = 6.4 x 1024 J

Now there are no averages and no temperatures involved, but the same fundamental issue – the incoming and outgoing radiation balance at the top of the atmosphere, but the energy leaving from the surface of the earth is much higher than the incoming solar energy.

The absorption and re-radiation by “greenhouse” gases in the atmosphere is responsible.

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