A Demonstration of Negative Climate Sensitivity

Guest Post by Willis Eschenbach

Well, after my brief digression to some other topics, I’ve finally been able to get back to the reason that I got the CERES albedo and radiation data in the first place. This was to look at the relationship between the top of atmosphere (TOA) radiation imbalance and the surface temperature. Recall that the IPCC says that a change in the TOA radiation of 3.7 W/m2 from a doubling of CO2 will lead to a 3°C ± 1.5°C temperature increase. This 3°C per doubling is called the “climate sensitivity”, and its value is an open question.

Figure 1, on the other hand, shows my results regarding the same question of the climate sensitivity. These reveal nothing like a 3°C temperature rise from a doubling of CO2:

Figure 1. Gridcell-by-gridcell linear trends of the change in surface temperature (∆T) given the change in TOA radiation (∆F). Note that the surface temperature data is gridded on a 5°x5° gridcell, while the CERES TOA radiation data is on a 1°x1° gridcell basis. Graph includes a two-month lag between change in forcing and the change in temperature.

There are a variety of interesting aspects to this particular graph. Let me start by describing how I constructed it.

I began by taking the gridded HadCRUT3 temperature data for the period of the CERES study, Jan 2001 to Oct 2005. The HadCRUT data is on a 5°x5° gridcell, so I first expanded that to 1°x1° gridcells. Then I took the first differences (∆T) by subtracting each month from the succeeding month, to get the monthly change in temperature (∆T) in each gridcell.

Then I compared that ∆T dataset to the change in TOA radiation (∆F), which was constructed from the CERES TOA data. For each gridcell, I took the linear trend of the temperature changes ∆T with respect to ∆F.

Of course, the climate sensitivity results from this procedure are in units of temperature change per forcing change, which is °C per watt/square metre. To convert it to change in temperature per doubling of CO2, I multiplied the results by 3.7 W/m2 per doubling of CO2.

Finally, I needed to adjust for the lag in the system. I did this in two ways. First, I selected the lag which gave the largest temperature change, which was a two month lag. These are the results shown in Figure 1. However, this is a cyclical record of the annual fluctuations, so the equilibrium sensitivity will be underestimated. Per the insights gained from my last analysis, “Time Lags in the Climate System“, the time lag is related to the size of the reduction in temperature swing. A 1-2 month lag in the system indicates a reduction in fluctuation of about 50%. So for my final adjustment, I doubled the indicated climate sensitivity. The results of this are the values shown in Figure 1.

Now, I have long argued, solely from first principles, that climate sensitivity is a non-linear function of temperature. I have said that the sensitivity was greater when it is colder, and that it is smaller when it is warmer. I have held that this relationship was non-linear, with a kink at the temperature range for tropical thunderstorm formation. Finally, I have also argued that in some places in the tropics the climate sensitivity is actually negative, due to the action of tropical clouds and thunderstorms.

To test these claims, I plotted the sensitivity for each gridcell shown in Figure 1 against the annual average temperature for that same gridcell. The results are shown in Figure 2. As far as I know, this is the first observational evidence that shows the actual relationship between climate sensitivity and temperature, and it supports all of my contentions about that relationship.

Figure 2. Scatterplot of gridcell climate sensitivity versus gridcell temperature. Colors indicate the latitude, with red at the tropics, yellow in the temperate zones, and blue at the poles. Gray dashed line shows the linear trend, indicating that the climate sensitivity varies generally as -0.009 * temperature + 0.32 (p-value < 1e-16).

There are some important things about this plot. First, it strongly supports my claim that the climate sensitivity varies inversely with the temperature. Next, it shows that a number of areas of the tropics actually do have negative climate sensitivity. Finally, it shows that the relationship is non-linear with a kink at around the temperature for the formation of tropical thunderstorms. This is important corroborative evidence for my hypothesis that the tropical clouds and thunderstorms act as governors of the tropical temperature and are the source of the negative climate sensitivity.

Let me close by railing a bit against the pernicious nature of averages. Consider Figure 2. Normally, far too many climate scientists would take an average of that data, and come up with some number as the average climate sensitivity. But that number is meaningless, and worse, it gives the impression that the sensitivity is a fixed number. It is nothing of the sort. Not only is it not fixed, it is far, far from linear, and it goes negative at times. It is a dynamic response to changing conditions, not some fixed value.

As a result, when we average it, we come away with entirely the wrong impression of what is happening in that most complex of phenomena, the climate system. While averaging is often useful, it conceals as much as it reveals, and it can lead one to badly erroneous conclusions. That is why so many of my graphs and charts show thousands of individual points, as in Figure 2. Only by seeing the whole picture can we hope to understand the system.

My best to all,

w.

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113 thoughts on “A Demonstration of Negative Climate Sensitivity

  1. RE: the equatorial cooling. There we have it, nature’s “tower heatsinks” – CuNim – shooting all the heat out into space. Probably also an element of electromagnetic energy flux via all the sprites, etc. In any case a negative energy balance in such locales.

  2. Another thought, has anyone ever tried to demonstrate an increase in Hadley Cell velocity? That would also be supportive of this result, with the increased equatorial divergence, and increased subsidence in the mid latitudes (creating the slightly positive numbers up there).

  3. I wonder if we’ll ever see Mr. Eschenbach embrace the idea that 390PPM of CO2 does nothing measurable to the Earth’s surface temperature. Surely that is a conclusion that can be drawn from the data. Sun heats Earth and water. Water and Earth heat air. Radiation is a dissipative process that always acts in the same direction as conduction and convection–it is not a mechanism for conveying work-energy from load to source. It always conveys work-energy from source to load.

    It is said that GHEs delay energy’s escape to space. Is it perpetually mobile? If not, what is the median value and distribution of this delay? How long must this delay be in order to contribute positive diurnal feedback?

  4. Well done Willis. :-)
    It is always refreshing to see an ‘outsider’ enter a field and provide insights through simple analysis rather than paper after paper based on more and more complex formalisms.

    While this will be peer-reviewed here, it deserves to be published in a journal, but I foresee a battle as the entrenched experts fail to come to grips with its simple concepts.

  5. Willis, you keep rattling the cage with that hammer of yours.

    This is going to be an interesting thread.

  6. Figure 2 scatterplot appears to me to be an inverted “U”, of say 2nd or 3rd order. Peak sensitivity is <0.5°C/3.7W/M^2 which is still, at worst, miniscule.

    Yet another of a myriad of nails in the cAGW coffin.

    Keep 'em coming Willis!!

  7. J Storrs Hall says:
    June 19, 2012 at 10:35 am

    I would be keenly interested to see the results broken down by land vs. ocean.

    So would I, J, so would I … but all these things take time. In the meantime, you can see the difference when you look at Figure 1.

    w.

  8. bacullen says:
    June 19, 2012 at 10:47 am

    Figure 2 scatterplot appears to me to be an inverted “U”, of say 2nd or 3rd order. Peak sensitivity is <0.5°C/3.7W/M^2 which is still, at worst, miniscule.

    Yet another of a myriad of nails in the cAGW coffin.

    Keep 'em coming Willis!!

    Possible, bacullen, but the problem is that we lack data near the poles. I have only calculated the trend in gridcells with a minimum of 36 data points (out of a possible 58 months of data), so a number of the cells near both poles haven’t been calculated.

    w.

  9. @ Willis “In the meantime, you can see the difference when you look at Figure 1.”

    First of all, thank you! Not only for this particular post, but for all the other thought provoking ideas you have posted. Regarding the differences between land and sea, yes, the first and obvious difference is that the wettest areas, really do show how well water vapor works to transport any extra energy input into the system. As Chiefio says, the atmosphere is a sort of spherical heat pipe using water vapor as the working fluid. And that leads to a little puzzle for me; here we have a nice demonstration of heat transport via water vapor, and then I notice the little green patches down in Antarctica. Who ordered that? One of the dryest places in the world, and we have a negative sensitivity there? Makes me wonder whether the data on radiation is a little wonky, or perhaps the temperature records have been fiddled.

  10. Wow!

    That all makes perfect sense, so clearly it will never be considered for inclusion in the IPCC’s next report. Undoubtedly, it will be trashed by ‘climate scientists’ for using raw data, not fitting their models, not being pal reviewed and/or representing a dire threat to their comfortable grant income.

    Willis, I think you need to use a change in TOA radiation of around 15W/m2, not 3.7, to get the IPCC answer. I cannot think of any reason why you should do that, but perhaps some nice ‘clmiate scientist’ could help find one.

  11. It looks to me that a non-linear interpertation could be a better fix. Maybe positive 0.4 at 0 degree C, zero at +-25 degree C, and negative below -25 or above +25. More data at the extrems would be very interesting

  12. Question: If the TOA radiates more energy out to space for any reason, say the effect of CO2 doubling, then wouldn’t that cool the atmosphere more, all the way down to the surface, until the TOA radiation balanced the TOA insolation?

  13. Publish it! Until you do that, it can’t get it into the IPCC assessment to balance everything else. While it stays in a blog its only use is to reinforce those already convinced.

  14. Excellent work, Willis, congratulations. Still, there could be some extra justifications and comments added for the research to become fairly publishable. But I would bet it may be correct.

  15. Not sure if you accounted for this, but a 1°x1° cell on the surface of the Earth is not the same square meters as the same cell at TOA. The radiating surface for TOA and Earth’s Surface are not the same. In addition, the Earth’s surface is blocked in most areas by clouds, etc.

  16. Not sure my comment made it in. Did you account for the fact the surface area of a 1×1 grid on the Earth’s surface is not the same as at TOA?

  17. It makes sense that the climate sensitivity be non-linear, and that it decreases as T goes up – negative feedback in other words. I don’t know why certain people continue to search for a single number.

  18. Your average comment reminds me of the economist joke where a guy has his head in the oven and his feet in the freezer. On average, the guy’s temperature is right on!

  19. fredb says:
    June 19, 2012 at 11:19 am

    Publish it! Until you do that, it can’t get it into the IPCC assessment to balance everything else. While it stays in a blog its only use is to reinforce those already convinced.

    Thanks for the vote, fredb. While I do publish in the journals, I am much more interested in affecting the ongoing scientific dialog about the climate. For that purpose, publishing here has much more effect than publishing in the journals.

    Rest assured that scientists on both sides of the climate debate read WUWT. The skeptics read it to find out the latest scientific advances and find evidence for their theories, while the AGW supporters read it to find out what the lunatics like me are up to. Reading WUWT (and Climate Audit) are requirements if you are serious about climate science and you want to stay up-to-date. So I reach many, many more scientists of all kinds here than I could ever hope to reach in any but the highest-impact journals.

    In addition, I also reach a host of people who for various reasons don’t read the scientific journals. Often these folks are policymakers or decision makers of various kinds, most are voters, and all of them are part of the larger scientific community. Since the climate question is not only scientific but involves policy at all levels, I see this greater outreach as being as important as reaching the scientists.

    This is not to diss the value of publishing in the journals, and I do so when I can. Unfortunately, every hour that I spend dealing with the journals, or translating a post like the one above into that most dense and opaque language called “scientese”, is an hour when I can’t be doing the research and investigations that are the raw meat that feeds my scientific hunger …

    Next is the question of timing. It often takes months to get a piece published. As I said above, I’m interested in affecting the ongoing discussion of the issues of climate science, not rehashing yesterday’s news. To do that, I need to be timely and topical. I need to be able to discuss the issues while they are still fresh.

    Next, publishing here means that I get invaluable assistance in understanding the results that I present. I’m a lone wolf, I work as a carpenter, I don’t have a bunch of colleagues with whom to toss these ideas around. As a result, the realtime feedback and the pointing out of my errors and successes here on the web is of utmost importance to me.

    Finally, a) we’re either too near to or past the deadline for inclusion in the fifth IPCC report, and b) the odds that the IPCC would include such heretical thoughts as mine are minuscule …

    However, all is not lost. I’m considering putting out a call for co-authors to take some of my ideas and rewrite them and get them published … but as always, time is the issue.

    w.

  20. Impressive work of a citizen scientist.
    Willis, can’t we have these contributions put together and delivered as ebook?
    Amazon makes that easy. It would be easier to read, reach many more people and even pay for all your effort.

  21. Here is the WUnderground tropical storm summary graphic. Notice the area bounded by the dotted line. It it the boundary of the area that spawns hurricanes. Lower surface temperatures are too cold. On the bar below the graphic we can see that that boundary temperature is about 25.8 deg C, just the temperature at which your scatterplot heads decisively below zero.
    One other thing. The fact that your plot shows that the temperature rise for a doubling is about 0.3 C does not mean that the feedback from convection is positive. You should make this clear.
    Once again, a fine piece of work.

    http://www.wunderground.com/tropical/

  22. ajstrata says:
    June 19, 2012 at 11:22 am

    Not sure if you accounted for this, but a 1°x1° cell on the surface of the Earth is not the same square meters as the same cell at TOA. The radiating surface for TOA and Earth’s Surface are not the same.

    Thanks, ajstrata. While you are correct, the difference is miniscule. The earth’s radius is about 6,378 km. The TOA is at say 15 km. The difference in the surface area of those two spheres (surface and TOA) is about half a percent. Since few of our measurements are that accurate, the difference in area is generally ignored.

    In addition, the Earth’s surface is blocked in most areas by clouds, etc.

    Also true … but I’m not clear what that has to do with net TOA radiation.

    w.

  23. These are really great analyses Willis. Looks like climate sensitivity is kinda like ocean oscillations, dynamical, non-linear, and inherently oscillatory. The T-dependence sounds very logical. I’ve watched thunderstorms explode just off shore in the Gulf of Mexico and the magic water temperature is 29 C or 84 F. It’s truly amazing. Bravo Zulu.

    -Frank

  24. Willis,

    Thanks for a neat bit of evidence which is good for supporting the contentions of both of us.

    Now, I just need to persuade you:

    i) to extend your thermostat hypothesis beyond the tropics so as to include latitudinal shifting of all the climate zones,

    ii) acknowledge that there can be a top down solar effect on the AO and AAO to offer resistance to the latitudinal shifting that occurs in response to your tropical thermostat and

    iii) hopefully one day acknowledge that average global atmospheric surface pressure has a bearing on the maximum sea surface temperatures that can be achieved before the convective response eliminates any further energy gains at the surface.

    Best wishes.

  25. eyesonu says:
    June 19, 2012 at 10:44 am
    Willis, you keep rattling the cage with that hammer of yours.
    —————————————————————————————————————————
    Here Here ! Willis Eschenbach the 21st Century Michael Faraday of Climate Science.

  26. Totally at your best with this one, it’s beginning to look like the major work has been done.
    ” the pernicious nature of averages” was acknowledged, too.
    please comment on the geographical component with respect to the poles and the stabilizing influence of phase change ice/water.
    (if you have seen farther than others, it’s not because you stood on the shoulders of midgets- it’s because you were a giant.)

  27. Willis Eschenbach says:
    June 19, 2012 at 11:47 am

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

    You are for real!

    With all the garbage that has been published over the past several years there’s not much honor in publishing in a journal. Just look at what has happened to the Nobel Prize selection process, little honor there either.

    A co-author sounds good but we like you here. You are having an impact by proxy. I pass my knowledge along to my ‘green’ friends. Some are no longer friends but most are no longer ‘green’.

  28. Stephen Wilde says:
    June 19, 2012 at 12:20 pm

    Willis,

    Thanks for a neat bit of evidence which is good for supporting the contentions of both of us.

    Now, I just need to persuade you:

    i) to extend your thermostat hypothesis beyond the tropics so as to include latitudinal shifting of all the climate zones,

    I think that there are thermoregulatory mechanisms operating at a host of scales. Whether one of them is “latitudinal shifting of all the climate zones” is not at all clear to me. I have written here and here about the “widening of the tropics” and the difficulties in measuring it … which of course only increases the difficulties in understanding it.

    ii) acknowledge that there can be a top down solar effect on the AO and AAO to offer resistance to the latitudinal shifting that occurs in response to your tropical thermostat and

    Haven’t a clue what that means, a “top down solar effect on the AO and the AAO”. I mean I know what the AO and the AAO are, but I don’t know what a “top down solar effect” is when it’s at home.

    iii) hopefully one day acknowledge that average global atmospheric surface pressure has a bearing on the maximum sea surface temperatures that can be achieved before the convective response eliminates any further energy gains at the surface.

    Like the other two, I’m not sure either what that pressure effect is or how it might be measured or established …

    Steven, all of those are fine, noble hypotheses, and all of them could be true … or not. What you need is data. You need to do what I’ve done, which is root around and find datasets and use them to demonstrate that your ideas are borne out by observations.

    In any case, this thread is about my findings, and so solar effects on the AAO are wildly off-topic, but if you have a web site that expounds and clarifies your ideas, feel free to post a link.

    All the best to you,

    w.

  29. Thank you again Willis. Very interesting analysis.

    Another story I like about averages is about the man who drowned in a stream the average depth of which was 16 inches.

  30. I have wondered why nobody has attempted to calculate sensitivity from the daily and seasonal variations in TSI and temperature. Surely if 3.7 w/m2 leads to a 3 C rise then daily and seasonal fluctuations in temperature would be much more severe. For example for Sydney the difference in average T summer / winter is 12 C. The difference in TSI is about 300 w/m2. This leads to a sensitivity of 0.04/w/m2 or about a 0.2 C for a doubling of CO2. I realise that equilibrium is not reached and if the 300 w/m2 were held for a longer period the average T difference will increase. Even if the true difference was double , say 24 C it is still only a 0.4 C per doubling. At 3 C per 3.7 w/m2 the expected difference between summer and winter is 240C Eh?

  31. Willis said:

    “I don’t know what a “top down solar effect” is when it’s at home.”

    I don’t want to derail this thread by going into detail here but you may be interested in this:

    http://climaterealists.com/index.php?id=6645

    “How The Sun Could Control Earth’s Temperature”

    The ideas expressed have been holding up well during the current low solar activity and I think such a top down mechanism needs to be added to your oceanic thermostat hypothesis to produce a more complete climate overview.

    As regards data, there isn’t much as yet but a number of new sensors are accumulating more useful data over time and in due course will prove or rebut my suggestions well enough.

  32. another one is about the statistician who was found with his head in the oven and his feet in the freezer. he was dead, but on the average he was quite comfortable.

  33. Willis I recall that Bill Illis posted a link to a graph which showed there was no greenhouse effect at the tropics and that the GHE became greater the further away from the tropics. Is this perhaps related in some way to your analysis here? Sorry I cannot find the link but I have no doubt Bill will be along in due course.

    Keep up the good work

  34. Willis said:

    “Like the other two, I’m not sure either what that pressure effect is or how it might be measured or established …”

    You could try this because it helps your ideas but I am somewhat circumspect about mentioning pressure to you:

    http://climaterealists.com/index.php?id=7798

    The Setting And Maintaining Of Earth’s Equilibrium Temperature”

  35. Willis Eschenbach said (June 19, 2012 at 10:56 am):

    “…Possible, bacullen, but the problem is that we lack data near the poles. I have only calculated the trend in gridcells with a minimum of 36 data points (out of a possible 58 months of data), so a number of the cells near both poles haven’t been calculated…”

    Why don’t you “extrapolate” the Arctic values like Hansen does?

    /sarc, of course.

    Also, you realise that there are those who feel that your choice of HadCRUT3 will be wrong (example, SkS stated that HadCRUT3 “…has a known cool bias and has of course been replaced by HadCRUT4…”

    They state that there is simply no reason to be using the outdated data from HadCRUT3.

    We know and understand the reason – the HadCRUT3 data doesn’t extend into the period of the CERES data.

    But they’ll use that “cool bias” of the HadCRUT3 to say you’re way off.

  36. @fredb
    The problem right now is that major journals are unlikely to publish anything outside mainstream academia. This block on work by skeptics must eventually change as evidence, like that given by Willis, grows to support lower climate sensitivity and net negative water feedbacks. Model predictions of warming have been reducing gradually since 1990 to be remain consistent with the temperature data. This trend has been missed in the media/poltical sphere which continue to quote figures of up to 6 degrees warming by 2100.

    I suspect that the key paper putting to rest CAGW will have to be from someone within the climate science community ! Frustrating I know.

  37. Gary W says:
    June 19, 2012 at 1:07 pm
    I have wondered why nobody has attempted to calculate sensitivity from the daily and seasonal variations in TSI and temperature.
    ””””””””””””””””””””””””””””””””””””””’
    Interesting thought. Sunlight, falling on the Earth when it’s about 3,000,000 miles closer to the sun in January, is about 7% more intense than in July. Yet, because the Northern Hemisphere has more land which heats easier then water, most people state that the Earth’s average temperature is about 4 degrees F higher in July than January, despite the fact that the TOA flux is 7% higher in January, when in fact they should be stating that the stating that the ATMOSPHERE is 4 degrees warmer in July. In January this extra SW energy is being pumped into the oceans where the “residence time” within the Earth’s ocean land and atmosphere is the longest. There are also other factors, such as the Northern hemispheres winter increase in albedo exceeds the southern hemisphere’s winter albedo due to the far larger northern hemisphere land mass. So at perihelion we have a permanent loss to space of ? W/2m SWR due to increased albedo and a temporary loss of SWR to the atmosphere, as at perihelion the SWR is falling on far more ocean, where it is absorbed into the oceans for far longer then if that SWR fell on land. Do these balance (unlikely) or is the earth gaining or losing energy during perihelion??? The TOA seasonal flux should tell us and climate models should accurately predict the observation. In Janauary much of this extra TOA influx may also beabsorbed in water vapor formation and cloud formation. This seasonal flux in TOA radiation far exceeds anything CO2 may affect.

    Willis, do you think there is adequet observations of TOA seasonal flux, seasonal water vapor and clouds, averaget T change, etc, to see what kind of variable sseaonal enstivity exists?

    I also note that you say you do not have observations for the polar regions. I understand this, but
    TOA energy flux can not be averaged either. In other words it takes a far larger energy influx to change 89 F to 90 F, then it does to change -10 f to -9 F.

  38. Well that’s…certainly interesting. In order for it to be true, wouldn’t it require that changes in temperature in the tropics and higher latitudes vary in opposite directions? Because they mostly don’t.

    Of course, it would have perfectly described our understanding of the Eocene…before the usual suspects “fixed” the data that showed cooler tropics and warmer poles to also show marginally wamer tropics. And now argue they that the data for the tropics during the period should be adjusted even warmer!

  39. Just in case I’m not the only one who hasn’t yet worked this through, could you explain a little further how the relationship you obtained in your last post, i.e., “the time lag is related to the size of the reduction in temperature swing,” applies here, i.e., how you arrived at multiplying the sensitivity by two?

    In that post, the lag and attenuation at issue were between surface and sub-surface temperatures; i.e., both quantities were temperature, and the system is one in which the connection between the two is heat conduction. Here the lag is between changes in top-of-atmosphere net radiation and changes in surface temperature, i.e. the quantities differ, having a derivative/integral relationship, and you’re taking differences in both.

    I recognize that, as your last post suggested, the diurnal and annual (extra-tropical) lags’ being equal fractions of the stimulus period strongly suggests that the processes are mathematically analogous, but I was wondering whether you (or someone else here) had a good idea why. And I was wondering about why here it’s the quantities’ first differences rather than the quantities themselves, which (if I understood it correctly) the surface-temperature / subsurface-temperature post dealt with.

  40. Interesting graphs, Willis. And interesting paper, Stephen. My only objection (to both) is that it could be more complex than either or both together. Stephen already made part of this point in his paper where he noted that the prior state of the oceanic heat sink can significantly modulate the responses he suggests. Prior state includes prior state of the major decadal oscillations — ENSO, for example, is clearly a major modulator and trigger for Hurst-Kolmogorov-like stochastic steps in SSTs (Bob Tisdale). The PDO has long been recognized as a major player in the organization of the jet stream and heating/cooling trends, especially in the Arctic, and the NAO almost certainly plays a similar role although one that is not as strongly correlated.

    Then there is the wild card, maverick science — e.g. Svensmark. So far as I know, his hypothesis hasn’t been disproven — it works “in vitro” as it were (in cloud chambers) and may be a neglected modulator of the albedo as well.

    The problem is that we don’t know, because even if Svensmark is right and cosmic ray modulation is a second modulating factor that Stephen should consider in his stratosphere-mesosphere model (after all, that NO_2 is a potential aerosol that can help nucleate clouds AND destroy ozone, and is produced in thunderstorms for possible positive feedback to amplify or attenuate any baseline responses) there is SST variation and the phases of the DOs to consider so that a solar magnetic state fluctuation at the wrong time might have a very small response, where the same fluctuation at another time might have a strongly magnified response.

    I’m just not seeing people “get it”. The climate is a chaotic system. As such, its time evolution is highly non-Markovian — its state tomorrow doesn’t just depend on its state today plus any changes in its primary drivers today, it depends on its state last week, last month, last year, last decade, and probably last century or more. It is at least bistable, where we are in the less stable (warm) branch, given the evidence of the last million years or more and where there is at least some evidence — the LIA being the coldest part of the entire Holocene post the Younger Dryas, for example — that the Holocene may be growing unstable not in the warm direction but in the cold direction. The CAGW folks are all concerned with annual or decadal time scales, but the climate varies on century time scales. The entire 20th century neatly disappears on any graph that illustrates temperatures over the last 500,000 or 1,000,000 years, and it is only on these latter scales that things like the glacial/interglacial oscillation reveal themselves.

    So much is I love Willis’s graphs, and agree that there is almost certainly negative feedback/sensitivity from cloud-based albedo (as suggested by Roy Spencer in his book, IIRC), and agree that he makes a strong case for this from actual data, it isn’t strong enough in and of itself to explain “the climate”, only a single, fairly local, response function contributing to it. Stephen’s paper casts a wider net, connecting solar state to climate, but still not wide enough. Bob Tisdale’s papers do a marvelous job of analyzing the connection between global temperature, SSTs, and the ENSO in particular, but neglect the direct feedback Willis portrays or the indirect jet stream mediated opening or closing of a tropical heat source for the oceans that provides direction to the changes observed by Bob. Koutsayannis analyzes long term climate trends and finds them nearly random, but of course this neglects the fact that there are clear period and correlated behaviors that modulate and provide direction to the random/sudden shifts that are observed.

    What is needed is something of a synthesis of all of this. But that synthesis is not easy, because the Earth is a chaotic system, and small fluctuations today can cause the entire planet to follow a completely different path given the same intermediate forcings five or ten years from now. Or the opposite — some fluctuations are utterly ignorable because they DO average out and have little impact on long term trends. And I don’t think we even can identify which is which, let alone put the ones that matter to good predictive use.

    rgb

  41. Just a short note that the “pale yellow flower Dryas octopetella, an arctic wildflower typical of cold, open, Arctic environments” has an english name Mountain Aven.

  42. Stephen Wilde says:
    June 19, 2012 at 12:20 pm

    iii) hopefully one day acknowledge that average global atmospheric surface pressure has a bearing on the maximum sea surface temperatures that can be achieved before the convective response eliminates any further energy gains at the surface.

    The maximum sea surface temperature is largely regulated by evaporation; a surface cooling process. Evaporation increases exponentially as water temperatures in the topics rise through the 80s and 90s (f). I have heard that the peek water temperatures in the oceans occur near Middle East and are near 100 degrees. T this point, evaporation does not allow the temperature to go higher, no matter what the air temperature and how much sunshine falls on the water.

    Undoubtedly, this rapid evaporation is also fueling the tropical thunderstorms, which, in turn, augment the surface water temperature with a reduction in insolation, cooling rains and winds that produce upwelling.

    I don’t see why average global atmospheric surface pressure would have a significant bearing on sea surface temperatures, as average surface pressure doesn’t vary all that much. I also don’t see how any of this impacts Mr. Eschenbach’s hypothesis. What goes on between the surface and the TOA is very important to understanding climate, but, if Willis is correct, not required to understand climate sensitivity to increasing CO2.

  43. rgb

    I have elsewhere set out a way of integrating Bob’ Tisdale’s oceanic observations into the overall picture but I’d better not set it out here since it takes us too far off topic.

    The synthesis is not easy but the basic premise is simple enough.

    The global climate as represented by the position, sizes and intensities of the permanent climate zones is a consequence of the netted out effect of solar and oceanic influences at any given moment.

    Other influences contribute but they are far smaller and tend to cancel one another out most of the time.

    We can determine current trends by the meridionality or zonality of the mid latitude jets and / or their average latitudinal positions globally.

    On that basis if current jetsream behaviour continues we will shortly be cooling.

  44. Willis…is it possible to calculate the non-linear trend and draw a more representative curved line through the data in figure two? The ‘apparent’ non-linear trend would indicate that any additional warming to the warmist waters of the tropics would create a rapidly increasing negative feedback, making a runaway green house effect impossible. If true…there can be no tipping point in global atmospheric warming, as long as most of the planet is covered in water! The water produces an upper limit in surface temperature with the water cycle as the controlling thermostat.

    This would pretty much negate the entire climate crisis theory!

    Perhaps it explains why it has never happened, even when CO2 was 10 times the current value.

  45. Jim Clarke said:

    “I don’t see why average global atmospheric surface pressure would have a significant bearing on sea surface temperatures”

    Because it controls the energy cost of a given amount of evaporation by setting the amount of energy required to break the bonds between water molecules. Read the article I linked Willis to.

    The relevance to this thread is that it provides a mechanism whereby Willis’s thermostat hypothesis can incorporate the apparent maximum limit for sea surface temperatures.

    It is the ultimate negative system response.

  46. Someone notify Mr. Hansen that the crisis over and he can sleep well tonight…or not.

  47. Willis, you left something out if you ever going to get any grant money. It’s called an amplification number. Let me show you how it works. Everyone knows that 2 + 2 = 4,
    but we need an answer of 8. Therefore 4 must be amplify by 2 for what ever reason (just make one up). After all we have to “Balance the Books”. LOL

  48. Thanks Willis. I’ve been saying for quite awhile that GHGs have both a warming and cooling effect. In other words, they also work as thermostats. Your analysis fits right into what I have been thinking. At lower temperatures the GHE provides the warming effect. At higher temperatures, the T^4 radiation of atmospheric energy over powers the GHE.

    Keep up the good work.

  49. Stephen Wilde says:
    June 19, 2012 at 3:33 pm

    “Because it controls the energy cost of a given amount of evaporation by setting the amount of energy required to break the bonds between water molecules.”

    Yes… I understand that the air pressure plays a role in setting the amount of energy required to break the bonds between water molecules and thus impacts the rate of evaporation. If Willis was attempting to explain everything about the climate, this would be an important addition, but average surface pressure is close to being a constant through a doubling of CO2, so it is not necessary to factor it into his hypothesis for his hypothesis to be correct. Neither is evaporation in general, or tropical thunderstorms or anything else, even though they may not be nearly constant.
    All of that is included by default in his hypothesis.

    I believe your ideas are likely correct, I just don’t believe they are required to determine climate sensitivity to increasing amounts of atmospheric CO2.

    You don’t have to no how your watch works to know what time it is.

  50. I think the issue one has here is that there is cooling in the Tropics over this period.

    Now the Tropics are clearly warming much less than other places (the central and eastern Pacific are Zero since the early 1800s) but this particular time period can’t answer the general sensitivity issues since it is cooling here at least. The Tropics are generally forecast to warm 2.5C at the surface and up to 4.0C in the troposphere so I think the time period just doesn’t work.

    It does show that the Thunderstorm Hypothesis is in effect however. Maybe the Tropics are just not going to warm at all above 28C. After that level, the heat just goes into evaporation which is then transported up and dumped off in the upper troposphere (where it will get emitted back to space very rapidly, “time” is always an important element in this debate, so far ignored) before it falls back to the surface as “now cooler” rain.

    Dolphinhead says: June 19, 2012 at 1:15 pm – The greenhouse effect in the Tropics (including net atmospheric flow of heat energy to colder regions and the poles) is only 23C (122 W/m2) versus 33C (150 W/m2) for the planet as a whole and about 80C (193 W/m2) at the north pole.

  51. Bill, If Willis had the data to do this over a couple of decades, would you believe that his method had merit?

    Willis, are natural variations in global climate, like ENSO, PDO and perhaps cosmic rays, variables in your calculations? If not, would they have an impact on the CO2 sensitivity you have calculated?

  52. Stephen Wilde says:

    i) to extend your thermostat hypothesis beyond the tropics so as to include latitudinal shifting of all the climate zones,

    Willis says:
    I think that there are thermoregulatory mechanisms operating at a host of scales. Whether one of them is “latitudinal shifting of all the climate zones” is not at all clear to me. I have written here and here about the “widening of the tropics” and the difficulties in measuring it … which of course only increases the difficulties in understanding it.

    The Hadley cells are formed by the convective weather in the tropics driving the air upward. The more vigorous the convection the higher the tropopause and larger the cells. The boundary between the Hadley and Ferrel cells is demarcated by the subtropical jet stream, Data on the position and strength of the jet streams is available and this could be linked to the data that Willis has to show that the Hadley cells expand compressing the Ferrel cells when the SSTs are high and contract when SSTs are low allowing the Ferrel cells and the associated jet streams to move equatorward. This would link Stephen’s atmospheric patterns to Willis’ variable atmospheric sensitivity through convective effects.

    …formatting fixed. -w.

  53. Tom Barney says: @ June 19, 2012 at 1:02 pm

    Right on pointy about averages. The average person has one testacle and one ovary.
    ____________________________
    I was going to make a comment about averages but I do not think I could top this one.

    When you think about it most of the sneaky little lies in CAGW are perpetrated through the use of averages…

  54. Jim Clarke says:
    June 19, 2012 at 6:13 pm
    Bill, If Willis had the data to do this over a couple of decades, would you believe that his method had merit?
    ———————-

    It would answer ALL the questions.

    Maybe I should have posted about that as well, but this methodology is really getting down to THE issue and how the real climate really operates. If one could extend it over into the ERBE data as well, there would be a long enough time-frame so that the climate science community would HAVE to take notice and say “well, we got it … (wrong or right)…” It would be that powerful.

  55. Robert Brown says:
    June 19, 2012 at 2:48 pm

    … So much is I love Willis’s graphs, and agree that there is almost certainly negative feedback/sensitivity from cloud-based albedo (as suggested by Roy Spencer in his book, IIRC), and agree that he makes a strong case for this from actual data, it isn’t strong enough in and of itself to explain “the climate”, only a single, fairly local, response function contributing to it.

    As always, Robert, I greatly enjoy and appreciate your contributions.

    However, I fear you misunderstand what I am saying. First, the issue I am pointing to is not either feedback nor sensitivity. Instead, it is that the climate is ruled by the constructal law, and as such it is constantly evolving to provide easier access to the currents that flow through it. This response occurs in the form of a whole host of homeostatic mechanisms that tend to keep the global temperature between surprisingly narrow bounds (e.g. ± a third of a degree or so over the last century).

    One of these many mechanisms involves tropical clouds and thunderstorms. These are not feedbacks, they are self-organized emergent phenomena. Clouds and thunderstorms are key because, almost alone among natural phenomena, they exhibit “overshoot”—that is to say, they can cool the surface to a lower temperature than was required to initiate cloud or thunderstorm formation. This capability is crucial to the governing of any lagged system … and as we know, the climate is a lagged system. Simple linear feedback cannot govern a lagged system. You need overshoot to do that, to bring it back when it wanders off course.

    In any case, I’m under no illusion about the limitations of each of the phenomena that I study. No one of them is sufficient to explain the climate. But the constructal law is sufficient to explain what all of the phenomena are involved in, and to give us a framework, if not for understanding the climate, at least for freeing ourselves of the absurdly simplistic idea that surface temperature is equal to TOA forcing times some constant.

    That is why it is important to demonstrate negative climate sensitivity—not to verify my ideas about thunderstorms (although it does that). It is important because the undeniable fact of negative climate sensitivity makes people rethink their basic ideas, their underlying paradigms of climate.

    Some people are skeptics, and some are AGW supporters. Me, I’m a revolutionary, I want to turn the whole thing upside-down and move forwards from the absurd linear climate paradigm to a real understanding of climate, one based on the knowledge that the climate is an active, responsive, self-regulating system with nothing linear about it.

    w.

  56. I have exactly the same view about averages. It leaves out a lot of internal structure, and moving variations in such structure can overturn or markedly change the value of the average, and is really a reverse form of greedy reductionism, implying the whole doesn’t relate to moving parts.

    As Ernst Mayr put it about the genotype, on much the same principle: “there is a lot of structure in the genotype which is not able to be determined by a purely genetic approach”

  57. Just a note of appreciation for Wills. As a retired aerospace scientist I very much look forward to reading your insightful posts, and greatly admire your ability to locate and analyse such large data sets to test your inspired hypotheses. Thank you for your unique contributions to our understanding of climate.

  58. “one based on the knowledge that the climate is an active, responsive, self-regulating system with nothing linear about it.”

    BIG SMILE and THUMBS UP !!!!

  59. Gary W says:
    June 19, 2012 at 1:07 pm

    I have wondered why nobody has attempted to calculate sensitivity from the daily and seasonal variations in TSI and temperature.

    Was done years ago by the Late Great John L Daly

    http://www.john-daly.com/miniwarm.htm

    3) By comparing changes in solar insolation with the resulting changes in temperature:

    The Earth does not orbit the sun in a neat circle, but rather in an elongated ellipse, with the sun offset from its centre (see fig. 1). The resulting solar radiation received is not constant throughout the year, but varies by nearly 7% between January and July. This phenomenon is quite unrelated to the seasons. This causes solar insolation at the equator to be about 21 wm-2 greater in January than in July. The temperature changes which result from this are less than 2 degC. (eg. as recorded at Thursday Island, Queensland, on latitude 11 deg. South).
    Thus, if it takes 21 wm-2 to change temperature a mere 2 degrees, the warming to be expected from +1.5 wm-2 is only +0.14 degC.

    Plus 5 other ways to calculate sensitivity.

  60. This goes perfectly with the idea that CO2 can act as a heat-to-IR and IR-to-heat converter. During the day, with all of that input of solar energy its IR-to-heat is effectively a wash, zero sum, as it gives away heat and collects heat evenly. However, at night water vapor and CO2 would have no energy input other than the surrounding gases and they would be fed heat and convert it to IR which is then lost to space. So, they help to cool the air after the Sun goes down. That’s why there is a chill in the air so rapidly after sunset.

  61. I still haven’t figured why you’re using that last post’s lag-vs.-attenuation relationship. When I look at the system and assume that the net radiation F_S at the surface is:
    F_S(t)=A cos(\omega t),
    the value I get for temperature T is:
    T(t,z)=\frac{A}{k}\sqrt{\frac{a}{\omega}}e^{-\sqrt{\frac{\omega}{2a}}z} \cos\left(\omega t-\frac{\pi}{4} -\sqrt{\frac{\omega}{2a}}z\right),
    where k is thermal conductivity and a is the diffusion constant of your last post. That is, the surface temperature lags surface radiation by \pi/4, i.e.,one-eighth of a cycle, and this seems not to have much to do with your last post’s lag-vs.-attenuation relationship. Now, if the net radiation the surface sees tracks the top-of-the-atmosphere net, the lags you’re seeing may be that \pi/4 value, rather than anything in that last post.

  62. Let me close by railing a bit against the pernicious nature of averages.

    I wholeheartedly endorse that statement. I have read numerous climate studies where the detail would tell us a great deal more than the average(s), but we are only shown the average(s), because the of the assumption that global GHG warming is the cause.

    A professor of mine once told me, “If you cannot explain the detail, you cannot explain the whole.”

  63. “I believe your ideas are likely correct, I just don’t believe they are required to determine climate sensitivity to increasing amounts of atmospheric CO2.”

    They are, because they reduce the thermal sensitivity to zero or threabouts the only ‘price’ being a miniscule shift in the climate zones.

    “All of that is included by default in his hypothesis.”

    At present Willis’s thermostat hypothesis is limited to the intensity of the convection along the ITCZ with perhaps a concession that the descending air would then affect the Hadley cells. The other issues are indeed implicit in his hypothesis but he hasn’t gone there yet. He doesn’t yet allocate a role to the sun either, nor to atmospheric pressure which is what sets the amount of energy that the oceans must contain before enough evaporation can occur so that the thermostat fully kicks in.

    With respect to Willis’s fine efforts so far I think his hypothesis is only a partial recognition of what goes on.

    Willis mentions being a revolutionary. May I make that claim too ?

  64. Willis has shown that climate sensitivity increases with latitude, when measured from TOA.

    I’ll suggest that a forcing plays a significant role is this effect. That forcing is low level aerosols and aerosol seeded low level clouds.

    Their effect on solar insolation (averaged over the year) is a direct function of latitude. The higher the latitude the greater the effect. And with a disproportionate effect on minimum temperatures (used in HADCRU).

    That the worldwide reductions in these aerosols coincides with the satellite era is a coincidence.

  65. Actually Philip I think that cloud amounts have a greater effect the nearer the equator the clouds are because the intensity of the reflected light is greater and that light energy is then no longer available to enter the oceans and contribute to the ENSO energy budget.

    However it is true that climate sensitivity increases with latitude (tropical temperatures vary hardly at all) but there is a disjunction on the equatorial side of the mid latitude jets because in fact the poles get colder when the rest of the globe warms and get warmer when the rest of the globe cools.

    That is a consequence of more zonal jets during a warming spell isolating the poles from inward flows of warm air.

    And I don’t think aerosol seeding is a significant factor. Instead it is the degree of air circulation meridionality or zonality that dictates total global cloudiness and albedo. That zonality or meridionality is the result of a combination of top down solar effects on the polar vortices and bottom up oceanic effects on the size of the Hadley cells which interact in a constant dance.

    Willis focuses on the tropical side of things only and I agree with him wholeheartedly so far as he goes.

    If I am wrong then no doubt Willis will say so.

  66. Willis’ simple approach is commendable. It does jibe with what some climate scientists say about the poles being more vulnerable to global warming. It also explains why there is no (predicted) tropical hot spot. All-in-all, it makes more sense than the gibberish churned out by so-called scientists – you know, the ones with the PhDs.

  67. For the benefit of laymen like me, are there any physicists out there who could hazard an exegesis of Mr. Eschenbach’s following explanation for why he multiplied his sensitivity value by two: “the time lag is related to the size of the reduction in temperature swing”?
    Please pardon the excruciating detail in which I set forth the problem that explanation gives me; I am hoping thereby to make manifest the misapprehension under which I seem to be laboring.
    The flow of heat by conduction through a homogeneous material is proportional to the temperature gradient. For example, suppose a semi-infinite homogeneous slab extends from \displaystyle z=0 to \displaystyle z=+\infty and its temperature \displaystyle T'(x, y, z, t) at time \displaystyle t is uniform in the \displaystyle x and \displaystyle y directions. Then, if \displaystyle q(z,t) is the heat per unit area the slab contains below \displaystyle z (where \displaystyle z increases in the downward direction), the heat flow can be expressed as:
    \displaystyle  \frac{\partial q}{\partial t}=-k\frac{\partial T}{\partial z},
    where \displaystyle k is the slab’s thermal conductivity, {\displaystyle \Large T=T'-T_0} , and \displaystyle T_0 is some arbitrarily chosen nominal temperature.
    Also, the temperature changes proportionally to the heat-flow gradient, i.e.,
    \displaystyle \frac{\partial T}{\partial t}=-\frac{1}{\rho C} \frac{\partial }{\partial z}\left( \frac{\partial  q}{\partial z}\right),
    where \displaystyle \rho is slab’s mass density and \displaystyle C is its heat capacity.
    Combining those two relationships gives:
    \displaystyle a \frac{\partial ^2T}{\partial z^2}=\frac{\partial T}{\partial t},
    where \displaystyle a=\frac{k}{\rho C} is the slab’s thermal diffusivity.
    Let’s consider the situation in which heat is introduced into the slab only at its \displaystyle z=0 surface. In the case of the irradiated earth, that is, we are making the simplifying (and highly questionable) assumption that radiation penetration is negligible. And we’ll assume that the (by assumption, uniform) temperature at the surface varies sinusoidally, i.e., \displaystyle T(0,t) = A\;cos(\omega t), where \displaystyle A is the amplitude of the sinusoidal temperature variation at the \displaystyle z=0 slab surface. Furthermore, we’ll assume Geiger’s relationship that with depth the amplitude decays exponentially and the phase lag increases linearly:
    {\displaystyle T=A e^{-\beta z} cos(\omega t-\alpha z) = \Re\{A \exp i(\omega t + \gamma z)\}},
    where \displaystyle \beta is the reciprocal of skin depth, \displaystyle \omega is the sinusoid’s radian frequency (i.e., \displaystyle 2\pi divided by the sinusoid’s period), \displaystyle \alpha is the rate of phase-lag increase, \displaystyle i=\sqrt{-1}, and we assume that \displaystyle \gamma=-\alpha+i\beta is the only unknown. We find \displaystyle \gamma‘s value by plugging our solution into the heat-flow equation:
    \displaystyle -a\gamma^2 [A \exp i(\omega t + \gamma z)]=i\omega[A \exp i(\omega t + \gamma z)]
    and solving for \displaystyle \gamma:
    \displaystyle \gamma =\pm (-1+i) \sqrt{\frac{\omega}{2a}}  .
    Plugging one of the thus-determined \displaystyle \gamma values into our equation for temperature \displaystyle T yields:
    \displaystyle T=Ae^{-\sqrt{\frac{\omega}{2a}}z} \cos\left(\omega t -\sqrt{\frac{\omega}{2a}}z\right)

    That was the wind-up. Here’s the pitch: The net heat transfer \displaystyle F into the slab (read “the net radiation absorbed by the earth’s surface”) is given by
    \displaystyle F=-k \frac{\partial T}{\partial z}(z=0) = kA\sqrt{\frac{\omega}{2a}}(\sin\omega t +\cos\omega t) =kA \sqrt{\frac{\omega}{a}} \cos\left(\omega t+\pi/4\right)
    That is, the net surface radiation leads the surface temperature by \displaystyle \pi/4, i.e., by one-eighth of a cycle. Note that this is independent of what the frequency- and material-dependent attenuation is. Now, this is surface radiation, not top-of-the-atmoshphere radiation. But, if the top-of-the-atmosphere net radiation is essentially in phase with the surface net radiation, would that not suggest that the eighth-cycle lag observed by Mr. Eschenbach has little to do with the Geiger relationships he cites?

  68. I do not even know where to begin to address this piece by Mr. Eschenbach.

    The Time lag for example. You talk about a time lag on a diurnal basis and on a monthly basis (seasonal) and even link us to another piece written by yourself about the lag. If there is a two month time lag in the seasonal system then surely there must be a time lag of decades in the climate system before it will start to warm up seriously.
    What do you know about the time lag in the climate system or is it instantly warm when CO2 starts to rise in a “cold” world? Let’s make it more comprehensible: Is a living room of 15°C instanly warm when you crank up the heater to 20°C or does it take a while before the room reaches that temperature and what about the time needed when the room reaches equilibrium stage?

    “I have said that the sensitivity was greater when it is colder, and that it is smaller when it is warmer.”
    “This is important corroborative evidence for my hypothesis that the tropical clouds and thunderstorms act as governors of the tropical temperature and are the source of the negative climate sensitivity.”

    - Can you also tell us what the tropical mean surface temperature is?
    - Have you ever heard of the expanding of the tropical region to Northern and Southern lattitudes because these colder regions are more sensitive and thus warm up faster?
    - Do you know that we had such conditions in the past where it was tropical on higher lattitudes?

    Here is a piece from which you actually can learn something:

    http://phys.org/news/2011-07-hot-earth-scientists-uncovers.html

    It’s exactly what you are describing here and in complete agreement with a warming world due to increasing CO2.

    Only your sensitivity numbers don’t fit and they are wrong. I asked you several questions about the same subject before in some of your previous blogs. You never answered them. If you want to conduct science here you should be courteous enough to answer these questions. That’s what science is all about.
    You need to explain the basics of climate science first in order to reconcile the strong negative feedback by water vapor (hence tropical thunderstorms and clouds) in your hypothesis. I gave you a good explanation that your hypothesis of strong negative feedback is simply wrong.
    You also need to explain why a doubling of CO2 (causing a 1-1.2°C rise when nothing else changes – every climate scientist agrees on this) causes less warming by the extra increased water vapor by that initially increased CO2. You need to explain how much extra water vapor is evaporated by doubled CO2 and why it causes such a strong negative feedback. All of this you need to back up with what has been written in the scientific literature about it. That’s science.
    Also the Total and Observed Greenhouse Effect would not make sense anymore in your hypothesis when true. It’s basic physics.

    You are conducting an experiment in a cold world getting ready to warm up by increasing CO2 due to the climate time lag. Surprisingly you are accepting the lag diurnally and seasonally, but you are leaving out this very important climate time lag of maybe hundreds of years.
    You are nothing more than measuring the temperature in a room that is beginning to heat up before it reaches it’s destined temperature setting. And from these findings you are trying to produce some claims.
    I can agree that thunderstorms and clouds will have a somewhat stronger negative feedback in tropical regions than elsewhere, but not in the milder and colder regions of the planet. Exactly the reason why the tropics don’t warm up that much in a warming world.

  69. Joe Born: “But, if the top-of-the-atmosphere net radiation is essentially in phase with the surface net radiation, would that not suggest that the eighth-cycle lag observed by Mr. Eschenbach has little to do with the Geiger relationships he cites?”

    I put that poorly. Personally, I would actually expect the top-of-the-atmosphere net radiation to lead the net radiation absorbed by the surface rather than be in phase with it. But my discussion above seems to indicate that this absorbed radiation will in turn lead the surface temperature by a fixed, \pi/4 phase that is independent of the sensitivity. And, since a lead of approximately that size between the top-of-the-atmosphere net radiation and the surface temperature is what Mr. Eschenbach’s data exhibit, that sensitivity-independent quantity appears to dominate the observed lead/lag, so I’m still struggling with how he obtains a sensitivity adjustment out of the observed phase lead.

  70. Stephen Wilde says:
    June 20, 2012 at 3:00 am
    Actually Philip I think that cloud amounts have a greater effect the nearer the equator the clouds are because the intensity of the reflected light is greater and that light energy is then no longer available to enter the oceans and contribute to the ENSO energy budget.

    Stephen. you missed the point, which I stated rather tersely.

    The significance of low level aerosols and seeded clouds is that they affect solar insolation predominantly when solar radiation traverses the atmosphere at a low angle. That is, in winter at mid-latitudes, in summer at high latitudes, and in the early morning everywhere.

  71. Joe Born says:
    June 19, 2012 at 9:10 pm

    I still haven’t figured why you’re using that last post’s lag-vs.-attenuation relationship.

    Joe, I noted in the last post that there is a relationship between the amount of the lag, and the attenuation of the signal. The relationship was such that with a 1-2 month lag in a system, the signal is attenuated to about half its original size.

    Now, it’s obvious that any climate sensitivity that is calculated directly from annual variations in the temperature is attenuated by some amount from the actual signal. But how much will it underestimate it by? I needed to pick a number, and my best estimate for that value is the number I calculated from my previous post, that is to say, the attenuation indicated by the lag.

    If you have a better estimate, that’s fine. But that’s the one I used. It’s not hugely significant, because it doesn’t affect my conclusions about a) the variability of the climate sensitivity with temperature, or b) the existence of large areas of negative climate sensitivity.

    w.

  72. Stephen Wilde says:
    June 20, 2012 at 3:00 am

    However it is true that climate sensitivity increases with latitude (tropical temperatures vary hardly at all) but there is a disjunction on the equatorial side of the mid latitude jets because in fact the poles get colder when the rest of the globe warms and get warmer when the rest of the globe cools.

    Cite for the poles cooling when the rest of the globe is warming and vice versa? I don’t find that anywhere in the data.

    Thanks,

    w.

  73. Willis Eschenbach: “If you have a better estimate, that’s fine. But that’s the one I used. It’s not hugely significant, because it doesn’t affect my conclusions about a) the variability of the climate sensitivity with temperature, or b) the existence of large areas of negative climate sensitivity.”

    As you may have inferred, no, I don’t have a better estimate. And my (not-very considered) opinion is in line with yours: the issue I raise not hugely significant, at least as to your main points. I’m merely trying, in my plodding way, to learn something from your (fascinating) previous post, but, for the reasons I gave in my last two comments, I haven’t been able to jump from those Geiger equations (which I essentially derive above) to the use you’ve put them to here.

    I understand completely if you consider this issue a mere distraction. At the same time, I will be grateful if one of the more theory-minded physics types out there can set me straight.

  74. Willis said:

    “Cite for the poles cooling when the rest of the globe is warming and vice versa? I don’t find that anywhere in the data”

    It seems to have applied during the Eemian warm period..

    http://wattsupwiththat.com/2012/06/15/study-shows-the-arctic-was-much-colder-while-earth-was-warmer-during-eemian-warm-period/

    During the late 20th century warming spell the Antarctic got colder but I would say that the Arctic doesn’t follow the pattern so closely because of warm water entering the Arctic Ocean from the south.

    Furthermore the isolation of the polar air masses when the polar vortices are positive is well accepted and a warming world is supposed to accompany more positive AO and AAO.

    see here:

    http://en.wikipedia.org/wiki/Arctic_oscillation

    “When the AO index is positive, surface pressure is low in the polar region. This helps the middle latitude jet stream to blow strongly and consistently from west to east, thus keeping cold Arctic air locked in the polar region.”

  75. Possible explanation for why the increase in temperature is limited to the non-tropical NH. When CO2 enters the atmosphere, it does so by burning of hydrocarbons or respiration, both of which also add H2O. It’s the H2O, in the form of water vapor, that has the greater IR and warming effect. Since H2O precipitates out, over a period of days to weeks, an increase in NH H2O would have little effect on SH H2O. And in the tropics, an increase in H2O would lead to clouds and rain, increasing albedo and radiation loss to space via convection.

    So I would expect that an increase in CO2 would raise temperatures primarily where there is a persistent increase in absolute humidity, and without a large increase in albedo/convection, and would not consider this a feedback, but rather a reflection that original CO2 increases and H2O increases are due to respiration and burning of hydrocarbons. One would need humidity observations at both the surface and at various altitudes to confirm, and I don’t know if our observations include enough humidity detail to test the hypothesis.

  76. Stephen Wilde says:
    June 20, 2012 at 11:05 am

    Willis said:

    “Cite for the poles cooling when the rest of the globe is warming and vice versa? I don’t find that anywhere in the data”

    It seems to have applied during the Eemian warm period..

    Ah. My bad, Steven, I thought you were referring to the present time, which is why I asked.

    w.

  77. Robbie says:
    June 20, 2012 at 7:41 am

    I do not even know where to begin to address this piece by Mr. Eschenbach. …

    In that case, you shouldn’t have begun.

    Robbie, if you had been even mildly polite instead of snarkily condescending, I would have been glad to clarify your questions, point by point, as is my usual habit and general custom.

    In your case, however, I’ll make an exception. You get nothing except the joy of knowing that your arrogance has prevented you from achieving your stated goal. Next time, keep a civil tongue in your head, you’ll find that people here will be more than happy to discuss science with you. As it is … not so much.

    w.

  78. You are talking like a Real climate scientist now, Willis. Don’t be petulant. It doesn’t help your credibility.

  79. Robbie says: June 20, 2012 at 7:41 am
    “…Here is a piece ….:
    http://phys.org/news/2011-07-hot-earth-scientists-uncovers.html ….”

    Thanks Robbie, interesting information: So the much warmer world of the early Eocene was much warmer at the poles and much the same as now in the tropics? (and an aside: doesn’t THAT sort of warmer world sounds like it might possibly be VERY productive?)

    Seems to support Willis’ argument. The interesting thing is his observation that he is already seeing evidence of a lower sensitivity to ‘current forcings’ at lower latitudes.

    .

    “Our study shows that previous estimates of temperatures during the early Eocene were likely overestimated, especially at higher latitudes near the poles,” Keating-Bitonti says. “The study does not mean elevated atmospheric CO2 levels did not produce a greenhouse effect—the Earth was clearly hotter during the early Eocene. Our results support predictions that increasing levels of atmospheric CO2 will result in a warmer climate with less seasonality across the globe.”……
    ……”The early Eocene Epoch (50 million years ago) was about as warm as the Earth has been over the past 65 million years, since the extinction of the dinosaurs,” Ivany says. “There were crocodiles above the Arctic Circle and palm trees in Alaska. …….
    …….The SU and Yale research team found that average Eocene water temperature along the subtropical U.S. Gulf Coast hovered around 27 degrees centigrade (80 degrees Fahrenheit), slightly cooler than earlier studies predicted. Modern temperatures in the study area average 75 degrees Fahrenheit.

    Of course, the questions remain, what caused that temperature shift of the early Eocene, and was increasing carbon dioxide a cause or a result?

  80. Joe Born says:
    June 20, 2012 at 10:29 am

    Willis Eschenbach:

    “If you have a better estimate, that’s fine. But that’s the one I used. It’s not hugely significant, because it doesn’t affect my conclusions about a) the variability of the climate sensitivity with temperature, or b) the existence of large areas of negative climate sensitivity.”

    As you may have inferred, no, I don’t have a better estimate. And my (not-very considered) opinion is in line with yours: the issue I raise not hugely significant, at least as to your main points. I’m merely trying, in my plodding way, to learn something from your (fascinating) previous post, but, for the reasons I gave in my last two comments, I haven’t been able to jump from those Geiger equations (which I essentially derive above) to the use you’ve put them to here.

    I understand completely if you consider this issue a mere distraction. At the same time, I will be grateful if one of the more theory-minded physics types out there can set me straight.

    Joe, I have never seen a single one of your comments that is a “mere distraction”. And I was fascinated by your math above, I just haven’t had time to fully understand it.

    The question I would pose to you is this: I see where the surface heating is going to lag a cyclical radiation source. And although I haven’t had time to check your math, I see that the lag, {\displaystyle \frac {\pi} {4}}, is an independent constant. The part I don’t understand is this:

    The net heat transfer into the slab (read “the net radiation absorbed by the earth’s surface”) is given by
    {\displaystyle F=kA \sqrt{\frac{\omega}{a}} \cos\left(\omega t+\pi/4\right)}

    The part that is unclear is, since the earth is generally at thermal equilibrium, the net heat transfer into the slab over a full cycle ≈ zero … I don’t understand how that fits with your equation. Is that instantaneous heat transfer? If so, can it be integrated to give us the sensitivity? These questions and more …

    Many thanks, and always good to hear from you. Oh, btw, you were 100% right and I was wrong in the previous thread about the trend of x on y NOT being the reciprocal of the trend of y on x, I just happened to pick a dataset where that was the case.

    w.

  81. Don Monfort says:
    June 20, 2012 at 4:07 pm

    You are talking like a Real climate scientist now, Willis. Don’t be petulant. It doesn’t help your credibility.

    Sorry, Don, but if someone wants to come in and talk down to me and be all snarky, I feel like I owe him an explanation as to why I’m ignoring him. Or would you advise I just ignore him and say nothing?

    Because I won’t answer that kind of snide attack—I have far too many calls on my time, and people who are interesting and polite making fascinating comments, to respond to some jerkwagon who wants to insult me.

    So how should I respond?

    w.

  82. markx-The Eocene is a very interesting case of past climate variability. The earliest analyses actually found cooler tropical temperatures than the present. Naturally this was “fixed” to make models look better, and now it is claimed that the Eocene had warmer tropics…but the diminishing of the Equator to Pole temperature difference is still greater than models appear to be able to explain.

    If the tropical corrections are actually wrong…

  83. Willis Eschenbach: “The part I don’t understand is this: ‘The net heat transfer into the slab (read “the net radiation absorbed by the earth’s surface”) is given by
    F=-k \frac{\partial T}{\partial z}(z=0) = kA\sqrt{\frac{\omega}{2a}}(\sin\omega t -\cos\omega t) =kA \sqrt{\frac{\omega}{a}} \cos\left(\omega t+\pi/4\right)
    The part that is unclear is, since the earth is generally at thermal equilibrium, the net heat transfer into the slab over a full cycle ≈ zero … I don’t understand how that fits with your equation. Is that instantaneous heat transfer?”

    That expression is indeed (if I have this right) the instantaneous heat transfer, so it is consistent with the heat transfer’s being ≈ zero over a full cycle. I got it by plugging the solution
    T=A e^{-\beta z} \cos(\omega t-\alpha z) into the equation stating that heat transfer is proportional to temperature gradient, i.e., into \frac{\partial q}{\partial t}=-k\frac{\partial T}{\partial z} .

    Willis Eschenbach: “If so, can it be integrated to give us the sensitivity?”

    Well, I’ve been trying to infer sensitivity from it somehow, but I’m a little weak (okay, clueless) at differential equations (and my wife’s kept me busy shopping for patio furniture) so I’m pessimistic. But I’ll sleep on it.

    By the way, at least one of the equations above has an error. It should be:

    \displaystyle F=-k \frac{\partial T}{\partial z}(z=0) = kA\sqrt{\frac{\omega}{2a}}(\sin\omega t +\cos\omega t) =kA \sqrt{\frac{\omega}{a}} \cos\left(\omega t+\pi/4\right)

    That is, the minus sign originally in the middle expression should have been a plus sign. [Fixed. w.]

  84. “Ah. My bad, Steven, I thought you were referring to the present time, which is why I asked.”

    The rest of my post did refer to the present time.

  85. Joe, I’ve been playing with your equations. You say:

    \displaystyle F=-k \frac{\partial T}{\partial z}(z=0) = kA\sqrt{\frac{\omega}{2a}}(\sin\omega t +\cos\omega t) =kA \sqrt{\frac{\omega}{a}} \cos\left(\omega t+\pi/4\right)

    I looked at the right hand side of that, which is:

    \displaystyle kA\sqrt{\frac{\omega}{2a}}(\sin\omega t +\cos\omega t) =kA \sqrt{\frac{\omega}{a}} \cos\left(\omega t+\pi/4\right)

    Canceling out common terms and substituting \displaystyle x = \omega t gives us

    \displaystyle  \sqrt{\frac{1}{2}}(\sin x +\cos x) =  \cos\left(x+\pi/4\right)

    But when I try those two, I get different curves, viz:

    Curiously, your old equation with the “-” in place of the “+” works out perfectly … so I’m in mystery here.

    w.

    PS—After much experimentation, I’ve found that using the LaTEX tag “\displaystyle” makes the latex much more readable.

  86. Joe, I’ve found at least part of the problem, with the always invaluable aid of Mathematica:

    Note that where you have

    \displaystyle F=-k \frac{\partial T}{\partial z}(z=0) = kA\sqrt{\frac{\omega}{2a}}(\sin\omega t +\cos\omega t)

    Mathematica, on the other hand, says:

    \displaystyle F=-k \frac{\partial T}{\partial z}(z=0) = kA\sqrt{\frac{\omega}{2a}}( \cos\omega t - \sin\omega t)

    Next, the right hand side of that in turn resolves to

    \displaystyle F= kA\sqrt{\frac{\omega}{a}}( \cos\omega t - \frac {3 Pi}{4})

    or alternately to

    \displaystyle F= - kA\sqrt{\frac{\omega}{a}}( \cos\omega t + \frac {Pi}{4})

    (note the minus sign in front)

    I haven’t checked the earlier part of your derivation yet.

    w.

  87. Don Monfort says:
    June 20, 2012 at 11:19 pm

    whatever

    I gave you a reasoned reply to your objection above, and I asked you how you thought I should have responded Robbie … and that’s your answer?

    Whatever … I should learn to never wrestle with pigs, I just get dirty, and the pigs like it.

    w.

  88. Willis Eschenbach: “Joe, I’ve found at least part of the problem.”

    Sorry about the “correction.” Somehow I can never keep track of canceling minus signs. If I differentiate it again I’ll probably get yet another combination of plus and minus signs.

    So I’m unlikely to be equal to solving the one-dimensional wave equation for a semi-infinite slab with the initial condition T(z,0)=0 and the boundary condition \displaystyle -k\frac{\partial T}{\partial z}|_{z=0}=A\, u_{-1}(t)-fT(0,t), where A is some fixed level of incoming radiation at the surface, u_{-1}(t) is the unit step function, and fT is the radiation leaving the surface. I don’t suppose Mathematica could solve it? (I probably could have bought Mathematica for what I paid for patio furniture.)

  89. My personal view of the climate is of a bounded pseudo-chaotic system. Based on geologic history it is bounded. Because of the vast numbers of variables interacting it appears chaotic, but unless someone comes up with a solid proof of same, assuming it’s knowable in bounded fashion seems to promise at least some level of understanding. Somehow I can’t get my head around the idea that the cycles we’ve seen in the past are some strange attractor and that any slight perturbation could drive it off into another phase space. If that is the case, then negative feedback or not, we’re already in deep sneakers, and not because of CO2.

  90. Mr. Eschenbach:

    Robbie says: June 2, 2012 at 7:23 am in this link: http://wattsupwiththat.com/2012/05/31/a-longer-look-at-climate-sensitivity/

    In this link you asked me for evidence for my claims. I was so kind of presenting my case with backing up what’s in the literature. Basic climate science it was. But when I asked for your evidence in the cloud response (just one of your many claims) for example, because of the Pinatubo eruption, there was only silence. I clearly showed you the opposite of what you were claiming.

    I haven’t got any idea why you are avoiding to discuss basic climate science with me and your hypothesis just to see if they fit together. Because in my view they simply don’t fit and make sense. The reason why you react like this towards me can only mean that you are out of arguments or is it that you can’t withstand critique of your work?
    That’s the very essence of the scientific discussion. You have to be able to withstand critique. Any serious reviewer of your work will ask tough questions. If you start to react like this your article will be rejected again and again.
    It’s maybe exactly the reason why your hypothesis won’t be published in the peer-reviewed literature, because it stands on too much of a shaky ground.

    I think it’s a pitty that you reacted like the way you did and Don Monfort was right in his comments about it.

  91. Don Monfort says:June 20, 2012 at 11:19 pm

    “…whatever..”

    Don is a teenager??! Wow, I didn’t realize ….

  92. You are an immature hothead, Willis. And you would get more than dirty wrestling with me. Carry on, little man.

  93. Robbie
    “a doubling of CO2 (causing a 1-1.2°C rise when nothing else changes – every climate scientist agrees on this)”
    You believe so fervently in your oversimplified physics that you deny, with the rest of your congregation, any physical evidence to the contrary.
    Get off your knees and open your eyes.

  94. Don Monfort says:
    June 21, 2012 at 8:34 am

    You are an immature hothead, Willis. And you would get more than dirty wrestling with me. Carry on, little man.

    Whatever …

    w.

  95. Joe Born says:
    June 21, 2012 at 2:49 am (Edit)

    Willis Eschenbach:

    “Joe, I’ve found at least part of the problem.”

    Sorry about the “correction.” Somehow I can never keep track of canceling minus signs. If I differentiate it again I’ll probably get yet another combination of plus and minus signs.

    That’s my problem as well, which is why I bought Mathematica. Unfortunately, while it is invariably correct, it’s only as good as the guy driving it …

    w.

  96. Don’t know anything about warmer at the poles – but recall when Britain in deep freeze couple of years ago they said it was balmy weather for Iceland – all to do with shifting wind systems.

  97. Gosh, “Britain europe freeze iceland warm” got it first time: http://www.dailymail.co.uk/news/article-2093450/UK-weather-Britain-braced-cold-snap-year-ice-snow-transform-countryside.html

    “Temperatures are set to plunge as low as -11C this week as Arctic winds bring in a big freeze with ice and snow expected to blanket the countryside, forecasters said today.
    Parts of Britain were waking up yesterday morning to up to two inches of snow as the longest spell of cold weather so far this winter sets in.

    The chill is being caused by a high pressure system hanging over Scandinavia and western Russia which is set to push raw, easterly winds towards the UK as the week progresses. It will cause the longest spell of cold weather so far this winter, experts say.”

    “Colder than Iceland: Snow covers a track leading to a farm near Wheddon Cross. Daytime temperatures are expected to be barely above freezing in most of England Wednesday and Thursday while Iceland’s capital Reykjavic will be warmer at six degrees Celsius”

    Briiain got the tip of it:

    “A tractor with a snow plough clears snow off the road near Dulverton on Exmoor, England. The weather in the next few days is definitely looking like being the coldest weather we have seen this winter’ Meanwhile, residents all over the country were bracing themselves for the Siberian weather front heading for Britain.”

    “In Europe, the big freeze has killed at least 32 people and many areas have been under emergency measures with schools closed down, roads became impassible and power supplies were cut off.
    As temperatures dropped to around minus 20 Celsius, eastern European authorities opened emergency shelters and urged people to be careful and remain indoors.
    Ukraine’s Emergency Situations Ministry said 18 people died of hypothermia in recent days and nearly 500 people sought medical help for frostbites and hypothermia in just three days last week.
    At least 10 people froze to death in Poland over the weekend as the cold reached minus 26 Celsius”

    &

    http://www.euronews.com/2012/02/08/iceland-enjoys-unusually-warm-winter-weather/

    “As Europe shivers, Iceland is positively sweltering with temperatures of four degrees celsius in the capital on Wednesday.

    The sparsely-populated island is enjoying a spell of unusually mild winter weather after a snowy December and January. Nearly ten degrees celsius was recorded in Reykjavik on Monday!

    Mild air from the Tropics has headed up to the North Atlantic, meaning Iceland has escaped the big freeze that has got Europe in its grip.

    It is still no tropical paradise. But wind and rain seem almost appealing compared to biting sub-zero temperatures.”

    Ahh… just noticed the dates, not the big freeze I was recalling of a couple years ago – but this last winter – which for some reason missed us in Ireland. Sorry, must have been this one in winter 2011/2012 where I heard the Iceland warmer because wind change, but, there was hardly any coverage at all of these events on tv. The first big freeze was covered practically 24/7, this time, hmm. I recall wondering at the time why they weren’t showing any footage of this.

  98. Willis, do you think you would see different sensitivities in the “nino” area of the Pacific if you did the same analysis on el Nino periods vs la Nina ones?

  99. jim2 says:
    June 22, 2012 at 4:42 pm (Edit)

    Willis, do you think you would see different sensitivities in the “nino” area of the Pacific if you did the same analysis on el Nino periods vs la Nina ones?

    I would strongly suspect that they would be different. My opinion is that the Nino/Nina alteration is another of the many feedback systems controlling the temperature. As such, I’d expect it to affect the sensitivity.

    w.

  100. @WIllis:

    Don’t know how I missed this on the first posting… Very well done.

    ( I notice you also defined “forcing” as used here… Thanks ;-)

    Your observations on averaging are “Spot on”. I’ve tried making that case too, but not as well as you did.

    It’s also very nice to see confirmation of the importance of thunderstorm formation. As places like Alaska can get thunderstorms in summer, it might be interesting to make a similar plot but with “month” identified. If you find that Alaska, for example, behaves rather like the more temperate zone during summer, you get a “sensitivity” that not only changes with latitude, but with season.

    On a first read, some of the reasoning for things like doubling the indicated sensitivity seem a bit vague. Why double and not 1.5 or 3x? I’ll re-read it and read the comments and see if it become clearer. (Or perhaps add a cup of coffee and see if that helps ;-) I did an all-nighter last night and I’m a bit slow today…) If it’s just a ‘plug value’ as a guess for a reasonable adjustment, that looks, well, ‘reasonable’…

    Again, nicely done.

  101. I had sent this to Anthony Watts regarding an experiment that he showed that came from a suggested experiment that Al Gore had proposed and after carrying it out it was proven to be bogus, no surprise there; but, the question that I have is why bother?

    Actually, this whole concept of a green house like effect surrounding the earth like a pane of glass is a ludicrous attempt to present a vision in children’s heads and I well imagine many adults also believe this. The question is, when was the last time anyone was able to “capture” anything with a gas? That this ubiquitous, odorless, colorless, and benign trace gas essential for life on earth, CO2, that is one and one-half times heavier than the rest of the atmosphere (maybe there is intelligent design after all because everything that utilizes CO2 is on the surface of the earth) and be reminded that it constitutes only .037% of the total atmosphere of our planet can have basically anything to do with the earth’s climate can not and never will be shown by ANY experiment to do so.
    That H2O is what causes the green house effect should be realized by anyone that has ever noticed that the coldest nights of the winter occur when there is no cloud cover and this is why the deserts can get to 130*F during the day and freezing at night, no cloud cover.
    Carbon dioxide is one and one half times heavier than “air”. This point was sadly proven on Aug, 21, 1986 when Lake Nyor in Cameroon released about 1.6 million tons of CO2 that spilled over the lip of the lake and down into a valley and killed 1,700 people within 16 miles of the lake. “Carbon dioxide, being about 1.5 times as dense as air, caused the cloud to “hug” the ground and descend down the valleys where various villages were located. The mass was about 50 metres (164 ft) thick and it travelled downward at a rate of 20–50 kilometres (12–31 mi) per hour. For roughly 23 kilometres (14 mi) the cloud remained condensed and dangerous, suffocating many of the people sleeping in Nyos,Kam,Cha,andSubum.
    “http://en.wikipedia.org/wiki/L…
    This coincides with the above fact about CO2:
    ppm of CO2 with altitude and mass of CO2 in atmosphere to 8520 metres beyond which there is practically no CO2

    http://greenparty.ca/blogs/169/2009-01-03/ppm-co2-altitude-and-mass-co2-atmosphere-8520-metres-beyond-which-there-practic

    (It is strange that I happened on this above at the Green Party of Canada’s site)
    There are some obsessed with the supposed increase of 280 ppm to 392ppm of CO2 and I hope that this information will help them to sleep better at nights.
    This, I hope, will put this into some kind of a perspective that makes one understand just how insignificant this increase is.
    A part per million is like 1 drop of ink in a large
    kitchen sink.
    A large kitchen sink is about 13-14 gallons. There
    are 100 drops in one teaspoon, and 768 teaspoons
    per gallon.
    Some other things that are one part per million are…
    One drop in the fuel tank of a mid-sized car
    One inch in 16 miles
    About one minute in two years
    One car in a line of bumper-to-bumper traffic from
    Cleveland to San Francisco.
    One penny in $10,000.
    I know that you understand that these 112 additional ppm are spread out over this 16 miles in different one inch segments and wouldn’t it be a task to be told to sort out the 392 pennies from the number that it would take to make up $10,000.
    At 392 parts per million CO2 is a minor constituent of earth’s atmosphere– less than 4/100ths of 1% of all gases present. Compared to former geologic times, earth’s current atmosphere is CO2- impoverished.
     
    Let’s picture this in another way to really get an idea of the scale of CO2 compared to the total atmosphere. The Eiffel Tower in Paris is 324 metres high (1063ft). If the hight of the Eiffel Tower represented the total size of the atmosphere then the natural level of CO2 would be 8.75 centimetres of that hight (3.4 inches) and the amount added by humans up until today would be an extra 3.76 centimetres (1.5 inches)

    http://a-sceptical-mind.com/co2-the-basic-facts

    J Doug Swallow

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