### Recap

Part One of the series introduced the shortwave radiation from the sun, the balancing longwave radiation from the earth and the absorption of some of that longwave radiation by various “greenhouse” gases. The earth would be a cold place without the “greenhouse” gases.

Part Two discussed the factors that determine the relative importance of the various gases in the atmosphere.

Part Three and Four got a little more technical – an unfortunate necessity. Part Three introduced Radiative Transfer Equations including the Beer-Lambert Law of absorption. It also introduced the important missing element in many people’s understanding of the role of CO_{2} – re-emission of radiation as the atmosphere heats up.

Part Four brought in band models. These are equations which quite closely match the real absorption of CO_{2} (and the other greenhouse gases) as a function of wavelength. They aren’t strictly necessary to get to the final result, but they have an important benefit – they allow us to easily see how the absorption changes as the amount of gas increases. And they are widely used in climate models because they reduce the massive computation time that are otherwise involved in solving the Radiative Transfer Equations. The important outcome as far as CO_{2} is concerned – “saturation” can be technically described.

### Solving the Equations

The equations of absorption and radiation in the atmosphere – the Radiative Transfer Equations – have been known for more than 60 years. Solving the equations is a little more tricky.

Like many real world problems, the radiative processes in the atmosphere can be mathematically described from 1st principles but not “analytically” solved. This simply means that numerical methods have to be used to find the solution.

There’s nothing unproven or “suspicious” about this approach. Every problem from stresses in bridges and buildings to heat dissipation in an electronic product uses this method.

The problem of the effect of greenhouse gases in the atmosphere is formulated with a 1-dimensional model. This is the simplest approach (after the “billiard ball” model we saw in part one). But like any model there are certain assumptions that have to be made – the boundary conditions. And over the last 40 years different scientists have approached the problem from slightly different directions, making comparisons not always easy.

Because the role of CO_{2} in the atmosphere is causing such concern the results of these models is consequently much more important. And so a lot of effort recently has gone into standardizing the approach. We’ll look at a few results, but first, for those who would like to visualize what modern methods of “numerical analysis” are about – a little digression.. (and for those who don’t, jump ahead to the **Ramanathan**.. subheading).

### Digression on Numerical Methods

Here’s a visualization of “finite element analysis” of stresses in an impeller. See the “wire frame” look, as if the impeller has been created from lots of tiny pieces?

In this totally different application, the problem of calculating the mechanical stresses in the unit is that the “boundary conditions” – the strange shape – make solving the equations by the usual methods of re-arranging and substitution impossible. Instead what happens is the strange shape is turned into lots of little cubes. Now the equations for the stresses in each little cube are easy to calculate. So you end up with 1000’s of “simultaneous” equations. Each cube is next to another cube and so the stress on each common boundary is the same. The computer program uses some clever maths and lots of iterations to eventually find the solution to the 1000’s of equations that satisfy the “boundary conditions”.

In the case of the radiative transfer equations (RTE) we want to know the temperature profile up through the atmosphere. The atmosphere is divided into lots of thin slices. Each “slice” has some properties attached to it:

- gases like water vapor, CO2, CH4 at various concentrations with known absorption characteristics for each wavelength
- a temperature -unknown – this is what we want to find out
- radiation flowing up and down through the “slice” at each wavelength – unknown – we also want to find this out

And we have important boundary conditions – like the OLR (outgoing longwave radiation) at the top of the atmosphere. We know this is about 239 W/m^{2 }(see The Earth’s Energy Budget – Part One). Using the boundary conditions, we solve the radiative transfer equations for each slice, and the computer program does this by creating lot of simultaneous equations (energy in each wavelength flowing between each slice is conserved).

### Ramathan and Coakley, 1978

Why bring up an old paper? Partly to demonstrate some of the major issues and one interesting approach to solving them, but also to give a sense of history. A lot of people think that the concern over greenhouse gases is something new and perhaps all to do with the IPCC or Al Gore.

Back in 1978, V. Ramanathan and J.A. Coakley’s paper Climate Modeling through Radiative-Convective Models was published in Reviews of Geophysics and Space Physics.

It wasn’t the first to tackle the subject and points to the work done by Manabe and Strickler in 1964. By the way, V. Ramanathan is a bit of a trooper, having published 169 peer-reviewed papers in the field of atmospheric physics from 1972-2009..

I’m going to call the paper R&C – so R&C cover the detailed maths of course, but then discuss how to deal with the “problem” of convection.

In the lower part of the atmosphere heat primarily moves through convection. Hot air rises – and consequently moves heat. Radiation also transfers heat but less effectively. The last section of Part Three introduced this concept with the “gray model”. Here was the image presented:

Remember that each section of the atmosphere radiates energy according to its temperature. So when we are solving the equations that link each “slice” of the atmosphere we have to have a term for temperature.

But how do we include convection? If we don’t include it our analysis will be wrong but solving for convection is a very different kind of problem, related to fluid dynamics..

What R&C did was to approach the numerical solution by saying that if the energy transfer from radiation at any point in their vertical profile resulted in a temperature gradient less than that from convection then **use the known temperature profile** at that point. And if it was greater than the temperature gradient from convection then we don’t have to think about convection in this “slice” of the atmosphere.

By the way, the terminology around how temperature falls with height through the atmosphere is called “the lapse rate” and it is about 6.5K/km.

These assumptions in the two cases didn’t mean that absorption and re-radiation were ignored in the lower part of the atmosphere – not at all. But the equations can’t be solved without including temperature. The question is, do we solve the equations by calculating temperature – or do we use an “externally imposed” temperature profile?

There is lots to digest in the paper as it is a comprehensive review. The few of interest for this post:

Doubling CO2 from 300ppm to 600ppm

- Longwave radiative forcing at the top of the troposphere – 3.9W/m2
**Surface temperature increase 1.2°C**- Result of change in radiative forcing when relative humidity stays constant (rather than absolute humidity staying constant) – surface temperature increase is doubled

(Note: this is not quite the “standardized” version of doubling considered today of 287ppm – 576ppm)

Relative Effect of CO2 and water vapor

This is under 1978 conditions of 330ppmv for CO2 and in a cloudy sky. Here they run the calculation with and without different gases and look at how much more outgoing longwave radiation there is, i.e. how much longwave radiation is absorbed by each gas. The problem is complicated by the fact that there is an overlap in various bands so there are combined effects.

**Removing CO2 (and keeping water vapor) – 9% increase in outgoing flux****Removing water vapor (and keeping CO2) – 25% increase in outgoing flux**

Everyone (= lots of people in lots of websites who probably know a lot more than me) says that this paper calculates the role of CO2 between 9% and 25% but that’s not how I read it. Perhaps I missed something.

What it says to me is that overlap must be significant because if we take out water vapor it is only a 25% effect. And if we take out CO2 it is a 9% effect. (*I have emailed the great V. Ramanathan to ask this question, but have not had a response so far.*)

Therefore, guessing at the overlap effect, or more accurately, assigning the overlap equally between the two,** water vapor has about 2.5 times the effect of CO2.** As you will see in the next paper, this is about what our later results show.

So, more than 30 years ago, atmospheric physicists calculated some useful results which have been confirmed and refined by later scientists in the field.

### Kiehl and Trenberth 1997

*Earth’s Annual Global Mean Energy Budget* by J.T.Kiehl and Kevin Trenberth was published in *Bulletin of the American Meteorological Society* in 1997. (The paper is currently available from this link)

The paper is very much worth a read in its own right as it reviews and updates the data at the time on the absorption and reflection of solar radiation and the emission and re-absorption of longwave radiation. (There is an updated paper – that free link currently works – in 2008 but it assumes the knowledge of the 1997 paper so the 1997 paper is the one to read).

This paper doesn’t assess the increase in radiative forcing or the consequent temperature change that might imply from the current levels of CO_{2}, CH_{4} etc. Instead this paper is focused on separating out the different contributions to shortwave and longwave absorbed and reflected and so on.

*What is interesting about this paper* for our purposes in that they quantify the relative role of CO_{2} and water vapor in clear sky and cloudy sky conditions.

To do the calculation of absorption and re-emission of longwave radiation they used the *US Standard Atmosphere 1976* for vertical profiles of temperature, water vapor and ozone. They assumed 353ppmv of CO_{2}, 1.72ppmv of CH_{4} and 0.31 of N_{2}O, all well mixed. Note that, like R&C, they assumed a temperature profile to carry out the calculations because convection dominates heat movement in the lower part of the atmosphere.

Two situations are considered in their calculations – clear sky and cloudy sky.

Let’s look at the clear sky results:

The radiation value from the earth’s surface matches the temperature of 288K (15°C) – you can see how temperature and radiation emitted are linked in the maths section at the end of CO2 – An Insignificant Trace Gas? Part One.

The value calculated initially at the top of atmosphere was 262 W/m^{2}, the value was brought into line with the ERBE measured value of 265 W/m^{2} by a slight change to the water vapor profile, see Note 1 at the end.

Of course, the difference between the surface and top of atmosphere values is accounted for by absorption of long wave radiation by water vapor, CO_{2}, etc. No surprise to those who have followed the series to this point.

By comparison the cloudy sky numbers were:

- Surface – 390W/m
^{2}(no surprise, the same 288K surface) - TOA – 235W/m
^{2}. More radiation is absorbed when clouds are present. See Note 2 at end.

**Now onto the important question: of the 125W/m**^{2}** “clear sky greenhouse effect”, what is the relative contribution of each atmospheric absorber?**

The only way to calculate this is to remove each gas in turn from the model and recalculate.

Clear Sky

- Water vapor contributes 75W/m
^{2}or 60% of the total - CO2 contributes 32W/m
^{2}or 26% of the total

Cloudy Sky

- Water vapor contributes 51W/m
^{2}or 59% of the total - CO
_{2}contributes 24W/m^{2}or 28% of the total

Note that significant longwave radiation is also absorbed by liquid water in clouds.

### Conclusion

Using these three elements:

- the well known equations of radiative transfer (basic physics)
- the measured absorption profiles of each gas
- the actual vertical profiles of temperature and concentrations of the various gases in the atmosphere

The equations can be solved in a 1-d vertical column through the atmosphere and the relative effects of different gases can be separated out and understood.

Additionally, the effect in “radiative forcing” of the current level of CO_{2} and of CO_{2} doubling (compared with pre-industrial levels) can be calculated.

This radiative forcing can be applied to work out the change in surface temperature – with “all other things being equal”.

“All other things being equal” is the way science progresses – you have find a way to separate out different phenomena and isolate their effects.

**The temperature increase in the R&C paper of 1.2°C **only tells us the kind of impact from this level of radiative forcing. Not what actually happens in practice, because in practice we have so many other factors affecting our climate. That doesn’t mean it isn’t a very valuable result.

Now the value of radiative forcing will be **slightly changed** if “all other things are not equal” but if the concentration of water vapor, CO_{2}, CH_{4}, etc are similar to our model the changes will not be particularly significant. It is only really the actual temperature profile through the atmosphere that can change the results. This is affected by the real climate of 3d effects – colder or warmer air blowing in, for example. Overall, from comparing the results of 3-d models – ie the average results of lots of 1-d models, the values are not significantly changed – more on this in a later post.

**We see that CO _{2} is around 25% of the “greenhouse” effect, with water vapor at around 60%.**

Note that the calculation uses the “US Standard Atmosphere” – different water vapor concentrations will have a significant impact, but this is an “averaged” profile.

The only way to really determine the numbers is to run the RTE (radiative transfer equations) through a numerical analysis and then redo the calculations without each gas.

The two questions to ask if you see very different numbers is “*under what conditions?*” and more importantly “*how did you calculate these numbers?*” Hopefully, for everyone following the series it will be clear that you can’t just eyeball the spectral absorption and the average relative concentrations of the gases and tap it out on a calculator.

I thought it would be all over by Part Three, but CO_{2} is a gift that keeps on giving..

*Updates:*

*CO2 – An Insignificant Trace Gas? Part Six – Visualization
*

*CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers*

*CO2 – An Insignificant Trace Gas? – Part Eight – Saturation
*

*See also – Theory and Experiment – Atmospheric Radiation – demonstrating the accuracy of the radiative-convective model from experimental results*

### Notes and References

**Note 1** – As Kiehl and Trenberth explain, there are some gaps in our knowledge in a few places of exactly how much energy is absorbed or reflected from different components under different conditions. One of the first points that they make is that the measurement of incoming shortwave and outgoing longwave (OLR) are still subject to some questions as to absolute values. For example, the difference between incoming solar and the ERBE measurement of OLR is 3W/m^{2}. There are some questions over the OLR under clear sky conditions. But for the purposes of “balancing the budget” a few numbers are brought into line as the differences are still within instrument uncertainty.

**Note 2** – I didn’t want to over-complicate this post. Cloudy sky conditions are more complex. Compared with clear skies clouds reflect lots of solar (shortwave) radiation, absorb slightly more solar radiation and also absorb more longwave radiation. Overall clouds cool our climate.

**References**

*Climate Modeling through Radiative-Convective Models* , V. Ramanathan and J.A. Coakley, *Reviews of Geophysics and Space Physics *(1978)

*Earth’s Annual Global Mean Energy Budget* , J.T.Kiehl and Kevin Trenberth, *Bulletin of the American Meteorological Society* (1997)

on February 10, 2010 at 3:58 am |CO2 – An Insignificant Trace Gas? Part Four « The Science of Doom[…] – Part Five now […]

on February 11, 2010 at 8:46 pm |CO2 – An Insignificant Trace Gas? Part Six – Visualization « The Science of Doom[…] at the earth’s surface and the comparison 1-d simulations for that particular profile. (See Part Five for a little more about 1-d simulations of the “radiative transfer equations”). The […]

on February 19, 2010 at 10:50 pm |CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers « The Science of Doom[…] Part Five we finally got around to seeing our first calculations by looking at two important papers which […]

on February 21, 2010 at 10:18 am |kaiThe idea to separate atmosphere in a convection part and a radiative part makes a lot of sense, cause it is clear that the convection is the main factor at ground level, and radiation is clearly domninant higer up where the there is stratification and virtualy no up/down air motion…..

But it introduce imho a big question when dealing with sensitivity of ground temp to change in radiative profile induce by various CO2 concentration: is assuming constant thickness and constant lapse rate of the lower part when varying the temperature profile of the upper part valid? Are these assumptions (constant thickness, constant lapse rate of the convective bottom atmostphere) adressed somewhere?

Thanks,

Kai

on February 21, 2010 at 10:45 am |scienceofdoomKai:Think of it like this.

The one variable factor that affects the radiation from each “slice” of the atmosphere at each height is the

actualtemperature. (Due to radiation being emissivity x 5.67×10^-8 x T^4)So if we model the actual temperature from measurements of a “standard atmosphere” then the radiative output is correct.

The absorption is already correct because it’s based on the radiation into that “slice” and the % of each gas along with its known absorption profile.

However, many people have studied the various factors in detail. In Part Seven! there are a couple of papers referenced. One is Freckleton et al:

Greenhouse gas radiative forcing: Effects of averaging and inhomogeneities in trace gas distribution” This paper looks – as a minor issue – at how the definition of tropopause height affects the radiative forcing.Another paper of interest in Part Six – Visualization is by Evans & Puckrin.

What they do is measure the spectral details of the downwards longwave radiation at one particular place – and then run the 1D calculations for each of 14 trace gases.

The calculations are based on the

actual measuredtemperature, pressure and humidity profiles for that location. The calculation of downward longwave radiation (based on knowing the temp, pressure, humidity) and the measurements match very well.So the real issue is knowing the temperature profile – the

lapse rate– and the humidity – to calculate the real effect from CO2, water vapor and other gases.The GCMs try and work everything out from scratch, a much tougher proposition.

But the 1D calculation only needs to really know the temperature profile (lapse rate).

Hopefully that makes sense.

on February 25, 2010 at 2:14 pm |JohanIt would seem that it’s completely pointless to calculate CO2’s share of responsibility for the overlap, when that radiation would’ve been absorbed by water vapour anyway.

So I think there’s a logical error in your reasoning. If removing CO2 leads to a reduction of radiation by 9% then the contribution of CO2 for the purposes of calculating the consequence of increasing amounts of CO2 is only 9%.

Will I be charged for high crimes against humanity now?

on February 25, 2010 at 8:42 pm |scienceofdoomJohan:Depending on which country you are in, yes, so you had better hide out at a friend’s house..

It’s not an easy subject to get your head around and at first sight what you have said seems like the right way to approach it.

Except.. if you remove water vapor and it leads to a reduction of only 25% then water vapor is only 25% of the “greenhouse” effect. CO2 is obviously the dominant “greenhouse” gas.. Puzzling?

And the best way to think about it is if more CO2 makes it into the atmosphere we just redo the complete calculation and see what numbers we get. Part Seven has the answers.

Well, to jump ahead, CO2 from its pre-industrial levels to now adds a “radiative forcing” of 1.7W/m^2 (see that part for the definition) and doubling CO2 from pre-industrial levels adds 3.7W/m^2.

In that sense,

we just do the new calculation and it doesn’t really matter how much is apportioned to water vapor or CO2. It’s more intellectual curiosity – and of course, many people are doing a “back of envelope” calculation of radiative forcing by starting from the premise that “water vapor is 95% of the effect..” and therefore, getting the wrong answer for more CO2.In the end, without re-defining radiative physics (always an option for the brave) the only way to do a calculation is to solve the RTE using either the LBL codes (line by line absorption) for the various gases, or a band model (as explained in Part Four). The first way is a truly massive computation – even with todays computers. The second way is “quick” but not really achievable with a calculator. Or excel.

on March 10, 2010 at 11:04 am |American Thinker – the Difference between a Smoking Gun and a Science Paper « The Science of Doom[…] through the atmosphere. Solving those equations, as you can see in CO2 – Part Three, Four and Five – requires knowledge of the temperature profile as well as the concentration of the various […]

on March 28, 2010 at 6:48 am |CO2 in the Solar Spectrum « The Science of Doom[…] Really, it’s more complicated, as always with atmospheric physics. There’s nothing wrong with taking a look at the approximate difference between the two absorption spectra, but luckily someone’s already done some heavy lifting with the complete solution to the radiative transfer equations using line by line calculations. For more on these equations, see the CO2 – An Insignificant Trace Gas series, especially Part Three, Four and Five. […]

on May 16, 2010 at 10:25 am |CO2 – An Insignificant Trace Gas? – Part Eight – Saturation « The Science of Doom[…] Part Three opened up the radiative transfer equations, not solvable on the pocket calculator. Part Five showed two important solutions. And Part Seven showed the current best solutions along with what […]

on May 22, 2010 at 10:58 pm |FrankFigure 2.9 and the sections immediately below probably could use some serious revising:

1) Radiative equilibrium equations don’t predict the observed lapse rate in much of the troposphere because convection (and latent heat) supplement radiative transfer of energy into the upper troposphere. Your discussion doesn’t explain why convection can properly be ignored above a certain altitude – and neither can radiative transfer equations by themselves. A lapse rate 95% or <95%) of the discrepancy between warming at the surface and in the upper troposphere is a subject of controversy.

on May 23, 2010 at 1:55 am |scienceofdoomFrank:Apologies if I’m missing your point..

Convection higher up in the atmosphere isn’t needed to solve these equations. The point is that to calculate the emission from each layer in the atmosphere requires knowing the temperature.

Some accurate comparison work of line by line models vs actual will measure the temperature and humidity profile in the atmosphere via radiosonde for the calculation – as you can see in Part Six.

Ramanathan and Coakley’s model calculates the temperature profile as a result of solving the RTE, and at each layer if this is lower than the actual lapse rate from convective processes, the convective temperature profile is used instead.

The RTE is simply finding absorption and re-emission. This will establish the temperature profile in the upper troposphere near the tropopause, but not in the lower and mid-troposphere.

Feel free to clarify if you were coming at this from another direction..

on May 24, 2010 at 4:03 pm |FrankSomething is wrong with Figure 2.9 – it can’t possibly apply to the real atmosphere. In the absence of convection (which is the main pathway for removing heat from near the earth’s surface), the surface of the earth will warmer, not colder. Therefore the curve labeled “Radiative equilibrium in a grey atmosphere” should be much higher than shown and it shouldn’t intersect the x-axis at 255 degC (which is the equilibrium temperature for an earth without an atmosphere and an albedo of 0.3). Figure 10.4 from Wallace & Hobbs, Atmospheric Science, p422 (citing J Atmos Sci (1964) 21, 370) shows that the surface of the earth would actually be 330 degC (57 degC or 135 degF) if surface temperature were controlled only by radiative equilibrium. The origin of the “skin temperature of 213 degC is also confusing. 213 degC is about right for the average temperature at the tropopause; but this temperature is controlled by a variety of factors including latitude, convection and radiation and certainly can’t be calculated directly from radiative equilibrium.

on May 24, 2010 at 9:57 pm |FrankYou won’t know the temperature unless you take convection into account. Using lapse rate as a substitute for convection isn’t appropriate because 3D GCM’s predict that lapse rate will change with radiative forcing. If you don’t know temperature, you can’t predict emission.

on May 24, 2010 at 8:26 pm |FrankThe problem with the 1D-models is that they don’t tell us much about the behavior of the atmosphere near the earth’s surface. Since rising air at one location must be accompanied by sinking air at another, convection can’t be explicitly included a 1D-model. The observed lapse rate demonstrates that buoyancy-driven convection (less dense warmer air rising through colder air) – not radiation – is the principal route by which energy is transported through the lower troposphere. (Existing greenhouse gases already limit radiative cooling at susceptible wavelengths.) Convection also transports energy from low latitudes to high latitudes (increasing outgoing radiation with increasing T^4), a direction of transfer not present in 1D-models. (Given that the moon cools from about 385 degK to 120 degK in two weeks of darkness, imagine how cold the poles would be after six months of darkness and radiative cooling without this longitudinal convection.) In radiative-convective models, convection is represented only by the observed -6.5 degC/km average lapse rate. (Figure 2.9 doesn’t accurately show where temperature is predominantly controlled by radiation.) Is convection stopped at the tropopause by radiative cooling or the fact that the stratosphere is warmer than the upper troposphere? (I suspect the later is the correct explanation.) So long-wavelength radiation is the principle driver of temperature only near and above the tropopause (11-17 km; the top half of misleading Figure 2.9) and it probably doesn’t even determine where the tropopause occurs. Why should we pay any attention to such imperfect models?

Long-wavelength radiative forcing and re-equilibration therefore are phenomena that dominate temperature only far from the surface. In fact, radiative forcing is defined as the change in radiative flux at the tropopause. In Part 7, you calculate that doubling of CO2 should produce a 1.1 degK temperature rise, but this temperature rise OCCURS AT THE TROPOPAUSE, not at the earth’s surface! SURFACE EFFECTS WILL CERTAINLY BE SMALLER, but 1D-models don’t allow us to predict how much smaller (because they can’t tell us how convection will change). If 3D-GCM’s can be trusted, only about half of the warming at the tropopause will be transmitted to the surface. (In the tropics, the difference between warming near the surface and in the upper troposphere suggests that only about 40% of recent surface warming in the tropics can be attributed to increased radiative forcing from increased GHG’s. Whether this discrepancy is statistically significant at the 95% confidence level, however, is a subject of controversy.)

SUMMARY: Although 1D-models may be marginally useful at the TROPOPAUSE, they don’t provide information relevant to the SURFACE of the earth. These models simply promote the ILLUSION that we have a deep understanding of how rising GHGs will impact surface climate. In the interest of fairness, ClimateofDoom should write a post about the limitations of 1D-models. (This is a difficult job because the IPCC and the global warming establishment prefer to ignore this subject.)

on May 24, 2010 at 9:25 pm |scienceofdoomFrankHopefully I will get a chance to answer some of this more fully in the next few days.

Here I’ll just comment a little.

You are picturing something about the 1d radiative-convective model which isn’t quite right. It doesn’t have to assume that air in this 1d column of arbitrary area is all rising to achieve convective equilibrium.

Think of it a different way – the 1d model needs to know the actual temperature at each height in the atmosphere to solve the equations. This is because emission is dependent on temperature.

The results from the equations match observations very closely – for example the downward longwave measurements in Part Six – Visualization. There are many other papers with similar matches.

In that particular example the temperature (and humidity) profile input into the model were the actual measured values from radiosondes. Therefore the temperature was known – rather than assumed – and so the results were accurate.

All the radiative-convective model is doing is finding the right way to “model” the temperature profile vertically through the atmosphere.

on May 30, 2010 at 11:01 am |Clouds and Water Vapor – Part One « The Science of Doom[…] humidity and lapse rates (the temperature profile up through the atmosphere). See especially CO2 – An Insignificant Trace Gas? Part Five for a little more illumination on […]

on June 12, 2010 at 5:00 am |Venusian Mysteries « The Science of Doom[…] transfer equations, which you can see in CO2 – An Insignificant Trace Gas? Part Three and Part Five (and the whole […]

on June 20, 2010 at 2:42 pm |John O'SullivanPlease answer Frank’s points, scienceofdoom, it’s now more than a ‘few days’ that we’ve been waiting for your response to his pertinent points.

Your persistent refusal (and other warmists) to address the fact that 1-D modeling and the obsessive focus on radiative forcing of GHG is a very poor way to understand climate, shows you’re merely an advocate for a political position rather than a seeker of scientific truth.

on June 20, 2010 at 9:16 pm |scienceofdoomJohn O’Sullivan:Thank you for your kind and helpful comments. It’s commenters like you that make the efforts worthwhile.

I had forgotten about this, as Frank has made similar points which have been responded to in Clouds and Water Vapor.

In brief, the purpose of the radiative-convective model is to be able to have a mechanism for calculating the first order effects from CO2 and changes in CO2 – i.e., the effects without feedback.

Many people still believe that these cannot be calculated, or that CO2 has no effect, or its effect is in mW/m^2 – as you can see in many comments in other articles on this blog.

Calculating the first order effects is a necessary pre-requisite to do anything useful like calculating feedbacks – including changes in water vapor which change lapse rates, and change the radiative balance in the troposphere.

As you will find in CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers the results here are “prior to feedbacks”, as I comment in that article:

Lastly, the “

obsessive focus on radiative forcing of GHG” is simply aimed at explaining to the many many people who don’t understand atmospheric physics how it can be that increasing concentrations of a trace gas can have a significant effect on climate.If there was a huge controversy about the adiabatic lapse rate, or the role of angular momentum in ocean currents, no doubt the blog would be biased in that direction instead.

on June 20, 2010 at 10:53 pm |John O'SullivanThank you for your refreshing and frank admission that no conclusion can be drawn about the cause of the brief 20th century rise in temperature.

Thus, after more than $50 billion spent on attempting to prove a link between a warming trend (1975-1998) with human emissions of fossil fuels, we may just as reasonably attribute such climate change to natural cycles unconnected to human influence.

on June 21, 2010 at 2:38 am |scienceofdoomJohn O’Sullivan:The calculation of the effect of CO2 in isolation doesn’t by itself demonstrate anything about temperature rises in the last 100 years.

How could it? We just did it in isolation.

Equally, we can’t rule it out at this stage. This particular series has only isolated the effect of CO2 prior to feedbacks.

But those who like nice tidy stories and already know the answer are welcome to make of these statements what they will.

on August 14, 2010 at 7:31 am |4TimesAYearIs the radiative value measured only at night?

on August 14, 2010 at 7:52 am |scienceofdoom4TimesAYear:Which values are you asking about?

Just in case – to save a bit of time – take a look at The Sun and Max Planck Agree – Part Two.

on October 24, 2010 at 12:04 pm |NeilSoD,

Based on following your excellent web site I am led to believe that doubling C02 will lead to a temp forcing ~1.2C. Obviously I have not done the analysis myself but thought this was widely accepted. I was a little perturbing reading the article about Judith Curry in Scientic American (http://www.scientificamerican.com/article.cfm?id=climate-heretic&page=3) with the following comments:-

” . . . Curry asserts that scientists haven’t adequately dealt with the uncertainty in their calculations and don’t even know with precision what’s arguably the most basic number in the field: the climate forcing from CO2—that is, the amount of warming a doubling of CO2 alone would cause without any amplifying or mitigating effects from melting ice, increased water vapor or any of a dozen other factors . . . ”

Given Ms Curry’s knowledge of the subject I am confused? For me what would be great would be a chart of Forcing Vs C02 Concentration together with meanful confident ranges? I do find it slightly suprising that we do not have this in the academic literature given the relative importance – unless of course I have simply not come across it in me searches.

I am not necessarily doubting what you say and I do find your site very informative, but this does puzzle me why a chart such as indicated above is not made available? For me this would be the first thing I would want to see.

Perhaps it is just me?

Many Thanks

on October 25, 2010 at 3:30 am |scienceofdoomNeil:I’d be interested to hear exactly what she has to say (rather than the second-hand quote from SciAm). For example, does she think it is known to 5% accuracy? 10% accuracy? Is the uncertainty because of other variability not related to forcing?

There are quite a few papers covering the accuracy of the radiative transfer equations, along with matching measurements. I will try and write an article about it soon.

on October 26, 2010 at 10:30 am |NeilSod

Many thanks – as she now has her own website I might try and ask her!

Regards

on October 26, 2010 at 10:35 amscienceofdoomI already asked:

on December 12, 2012 at 4:28 amBernard J.SoD.

Did Curry ever get around to writing that article?

on December 12, 2012 at 6:47 amScience of DoomBernard J,

Yes she did, and I read it with interest. Here is the link.

There was nothing surprising (to me) in her perspective.

Extract from her conclusion:

on December 16, 2010 at 6:17 pm |PaulMAlthough the discussion of radiation on this blog is very thorough and detailed, the discussion of convection is very brief and rather muddled (as pointed out by Frank). This is a very common problem among climate scientists.

One minor thing is that the less than and greater than are the wrong way round. If the radiatively calculated temperature gradient is less than that the convective one (subadiabatic) then you dont need to take into account convection. If it is greater than this (superadiabatic), you replace it with the adiabatic temperature gradient.

on December 17, 2010 at 7:38 am |scienceofdoomPaulM:This is the same claim that you made in Things Climate Science has Totally Missed? – Convection.

Why not explain

specificallywhat you believe is wrong with the 1d radiative convective model and why this means that “climate science misunderstands convection”.Or just link back to your specific claims in the other post.

Otherwise it becomes the all too common problem of spurious and unsupported claims by “skeptics”.

Note: My last statement – parody. See how easy – and pointless – it is to just claim away?on December 17, 2010 at 5:02 pm |PaulMWhat on earth are you talking about?

Did I say “climate science misunderstands convection”? No.

For the time being I am just pointing out a minor typo in your description.

on April 5, 2011 at 11:26 pm |Simple Atmospheric Models – Part One « The Science of Doom[…] CO2 – An Insignificant Trace Gas? Part Five – the radiative-convective model with a couple of solutions […]

on April 21, 2011 at 7:55 am |Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Eleven – Heating Rates « The Science of Doom[…] Radiative-convective models predict this. Once you’ve got to grips with basic radiation in the atmosphere, it is easy to see why the troposphere will warm. But why will the stratosphere cool? […]

on March 25, 2014 at 5:54 am |weltklima - Seite 314[…] […]

on July 13, 2014 at 10:50 pm |Pat HackettSoD

I have just come across your site and i have to say how really useful it is. There is so much well explained. I am puzzled by your statement

“if the energy transfer from radiation at any point in their vertical profile resulted in a temperature gradient less than that from convection then use the known temperature profile at that point. And if it was greater than the temperature gradient from convection then we don’t have to think about convection in this “slice” of the atmosphere.”

Should this not be the other way round. At higher altitudes the lapse rate is lower in the “gray model” and is it not here that we dont have to think about convection because radiation dominates? Or have I mistaken some reasoning?

on July 13, 2014 at 11:28 pm |scienceofdoomPat,

I’m usually unsure (and probably inconsistent article to article) about which words to use to compare two lapse rates due to the negative value implied. So apologies for any confusion caused.

What you have written is correct.

Just to confirm:

If the temperature profile due to radiation alone was -15K/km then convection would take over – because the atmosphere would be unstable, and if the temperature profile due to radiation alone was -3K/km then convection would not take place – because the atmosphere would be stable.

If the “adiabatic lapse rate” is a lower (absolute) value than the environmental lapse rate then the atmosphere is stable.

I’ve written at length about the lapse rate in:

Density, Stability and Motion in Fluids – some basics about instability

Potential Temperature – explaining “potential temperature” and why the “potential temperature” increases with altitude

Temperature Profile in the Atmosphere – The Lapse Rate – lots more about the temperature profile in the atmosphere

on July 14, 2014 at 7:54 am |FrankPat: It may also help to know that lapse rate is defined as -dT/dz. So lapse rates are usually positive numbers that tell us how much the temperature DROPS with altitude. When SOD talks about a “temperature profile” of -15K/km, he is also talking about a lapse rate of 15K/km.

Life gets more confusing when looking at plots of temperature (x-axis) vs altitude, which is on the y-axis by tradition (even though altitude is the independent variable). Slope on such plots has units of km/K – the reciprocal of the units for lapse rate. Regions with a gentle slope downward from left to right are those with the greatest lapse rate (or most negative temperature profile). It seems a little strange to me that flat or nearly flat regions are convectively unstable (as are regions with positive slope), while the stable regions are those with a steep negative slope.

In the gray atmosphere (Figure 2.9 above), the atmosphere unfortunately doesn’t have enough GHG to produce a regions with a lapse rate larger (or flatter) than 6.5 K/km that would be convectively unstable. In our atmosphere, the concentration of water vapor increases dramatically at lower altitudes, so the curve for pure radiative equilibrium flattens dramatically and doesn’t intersect the x-axis until well above 300 degK.

on July 14, 2014 at 2:55 pm |Pat HackettThanks SoD. That explains that clearly. I was ignoring the negative sign. So the convention you are using in this article is that -15K/km is smaller than – 3K/km and now it makes sense. Sorry Frank In this article, SoD does not mean, in this article, that -15K/km =+15K/km. That is how I first read it and that was the area of my confusion.

on July 14, 2014 at 6:08 pm |DeWitt PayneA temperature profile of -15 K/km is defined as a lapse rate of 15 K/km. So by convention a temperature profile of -15 K/km has a lapse rate

greater thana temperature profile of -3 K/km. Any lapse rate greater than the adiabatic lapse rate is unstable because a packet of air when raised to a higher altitude will be warmer and less dense than the air around it at the new altitude. That means buoyancy will keep the packet moving upwards, In other words, convection will ensue. The adiabatic lapse rate is inversely proportional to the heat capacity at constant pressure of the air, Cp. Increased humidity increases Cp and lowers the adiabatic lapse rate, i.e. makes the adiabatic temperature profile decrease less rapidly with altitude.on July 15, 2014 at 1:03 am |Pat HackettDeWitt. Thanks for that reply. Most helpful. The first point you make is about convention and I am happy either way as long as I know the convention used. Your other points (apart from the last point) are clear and seem to confirm my own thinking on this ( I am a learner here) and that as expressed in SoD. However the last point is one that I have not thought about and dont know if this is addressed elsewhere on this site yet. My interpretation/possible conclusion of this (asking if this is right) is that this would result in a negative feedback reducing the positive feedback effect of water vapour to temperature. In other words if temperature changed either way the +ve feedback from WV would dominate but this effect on the lapse rate would reduce this somewhat.

on February 6, 2015 at 7:15 am |Steve Sykes (@StoneSoupBKK)I must be missing something. I look at the image” “Longwave radiation – clear sky” and see the radiation values in which it appears that the differential in emissions between the two surfaces is 125 W/m2 – and that is the value that you start using, immediately below the image – FOR ABSORPTION.

But that is not correct. The surface area of the sphere at TOA is much larger than the surface area of the sphere formed by Earth’s surface. So – a given amount of radiation is radiating outward from a given sphere, and penetrating a larger sphere. The radiation per unit of surface area (square meter) will always go down at the surface of the larger sphere,even if there is no absorption.

The surface area of earth is roughly 4 pi (6,360 km)^2

I do not know what radius was used for the TOA surface.

But it should be easy to determine the amount of emission decrease per square meter caused by simple diffusion of radiation, subtract that from the earth’s surface value, and then determine absorption up to the TOA by subtracting the TOA emission value from the previous result.

Or – have I missed something?

on February 6, 2015 at 11:13 am |scienceofdoomSteve,

The difference in surface area is very small.

Typically, for reasons that can get quite technical (see note), the values at the tropopause are used. This is around 15km above the surface.

But if instead we used the values at the top of the stratosphere this would be only 50km.

The radius of the earth is 6370km.

So the area at the surface, using a sphere (which is a bit of an approximation) is 4.pi.6370

^{2}= 510M km^{2}.And the area at the tropopause is 4.pi.6385

^{2}= 512M km^{2}.Another way to look at it, the ratio is (6385/6370)

^{2}= 1.005 or 0.5% difference.If we considered the top of the stratosphere, the ratio is (6420/6370)

^{2}= 1.016 or 1.6% difference.The graphical representations of the atmosphere above the earth are for education, they are never (?) drawn to scale.

Technical note: this is probably best explained in Wonderland, Radiative Forcing and the Rate of Inflation.

on November 21, 2015 at 5:33 pm |BindidonMany thanks for your incredible work!

Just a detail on this page: the link to Kiehl/Tremberth inbetween has gone out of life 😦

Interested readers might find the text under

http://journals.ametsoc.org/doi/abs/10.1175/1520-0477%281997%29078%3C0197%3AEAGMEB%3E2.0.CO%3B2