The Pliocene and the Pleistocene

Since it’s the school holidays and I’m spending some time at home, I thought I might write a short post about a recent paper by Martinez-Boti et al. (2015), that tries to compare the climate sensitivity during the Pliocene and during the Pleistocene. The Pliocene is the period from about 5.3 to 2.6 million years ago and is an interesting period since the conditions are thought to have been very similar to what we have today. The Pleistocene is the period after the Pliocene, ending at the start of the Holocene; about 11,700 years ago. During the Pleistocene, there were extended periods of glaciation.

This is not my area of expertise, so I may get some of this wrong, but from reading the paper, it seems that there has been a suggestion that climate sensitivity is higher in warmer climates than in cooler. This paper suggests that this is not the case. As I understand it, they determine the response to a change in CO2 only, which means that everything else is a feedback and this then gives the Earth System Sensitivity (ESS). They then use estimates for sea-level rise, to determine the contribution due to ice-albedo feedback which – if they remove – then gives the Equilibrium Climate Sensitivity (ECS).

Figure 5 from Martinez-Boti et al. (2015)

Figure 5 from Martinez-Boti et al. (2015)

The basic result is shown in the figure on the right. The term \Delta MAT represents the global mean annual air surface temperature change, and the x-axis is climate sensitivity in K/Wm-2. The red graphs are for the Pleistocene, while the blue re for the Pliocene. What seems clear is that the correction for ice-albedo feedback, brings the ECS for both periods into the same range (bottom two panels).

The paper concludes with

Our findings suggest that, if the Earth system behaves in a similar fashion to how it did during the Pliocene as it continues to warm in the coming years, an ECS of 1.5–4.5 K per CO2 doubling probably provides a reliable description of the Earth’s equilibrium temperature response to climate forcing, at least for global temperature rise up to 3 K above the pre-industrial level.

and

once all feedbacks have played out for future CO doubling, ESS will very probably (95% confidence) be < 5.2 K and will probably (68% confidence) fall within a range of 3.0–4.4 K.

So, it seems that this paper is suggesting that there isn’t any evidence for a different ECS in warmer and cooler climates, but that the estimates for the ECS during both the Pliocene and Pleistocene are consistent with the recent IPCC range. It also suggests that slower feedbacks could produce an ESS as high as 5K, with a likely range of 3K – 4.4K. So, no great surprises, but interesting nonetheless.

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116 Responses to The Pliocene and the Pleistocene

  1. Spellchecker says:

    2nd para – “is a feeback” .. is a feedback?
    last para – “it seems that this paper is suggesting that there is any evidence” .. no evidence?
    feel free to delete this comment

  2. Thanks. You’ve discovered my technique for not wasting too much time writing blog posts: don’t proofread 🙂

  3. So, it seems that this paper is suggesting that there isn’t any evidence for a different ECS in warmer and cooler climates, but that the estimates for the ECS during both the Pliocene and Pleistocene are consistent with the recent IPCC range.

    Without having read the paper, but doesn’t it actually say that the climate sensitivity is larger in cold periods because of the ice-albedo feedback. While they remove it to make a comparison for the other feedbacks, the ice-albedo feedback is a real feedback. Or did I misunderstand the above post. (And a previous post in Dutch.)

  4. Victor,

    Without having read the paper, but doesn’t it actually say that the climate sensitivity is larger in cold periods because of the ice-albedo feedback. While they remove it to make a comparison for the other feedbacks, the ice-albedo feedback is a real feedback.

    Yes, that is correct. The subtlety is – I think – that the ECS is defined as being the equilibrium sensitivity with fast feedbacks only. So, by removing the ice-albedo feedback, they show that the fast response is the same in both climates, but – as you point out – the ESS (which includes fast and slow feedbacks) will be higher in a colder climate than in a warmer, because the ice-albedo feedback can be larger. Interesting, though, that even in a warmer climate the ESS can be still be substantially larger than the ECS.

  5. Andrew Dodds says:

    Even with no ice, there should be a long-ish term feedback of ocean thermal expansion, leading to a higher ocean/land ratio and so, presumably, a lower albedo.

  6. Andrew,
    Interesting, I hadn’t thought of that. Certainly the oceans have a low albedo (0.07 – 0.1) which may well be lower than the land it replaces.

  7. BBD says:

    Boreal forest replaces tundra, which also lowers albedo, although I’m not sure how large the effect on ESS is supposed to be.

  8. Robert Way says:

    I think you would see a greater difference in TCR from cold and warm climates

  9. Robert,
    I did wonder about that, because these studies can only really tell you something of the equilibrium response, not the transient response. However, I’m not sure that I see why you’d see a difference. Do you mean even after correcting for ice-albedo feedback, or not?

  10. ATTP,

    “Interesting, though, that even in a warmer climate the ESS can be still be substantially larger than the ECS.”
    Martínez-Botí only removed the influence of the large ice sheets. There are other slow feedbacks like the change in albedo due to vegetation changes or ‘the entire oceans’ (according to figure 1 in de Palaeosense 2012 paper). I have no idea how large these other slow feedbacks can be, but Lunt et al 2010 estimates the ESS to be 30-50% larger than the ECS for the Pliocene.
    Using this 30-50% range of Lunt the ESS of 3.0 – 4.4 °C translates roughly to 2 – 3.4 °C for the ECS, which indeed seems to support the IPCC range.
    I also found figure 2b in the Martínez-Botí paper interesting, it shows the non-linear behavior of the δ18O value against CO2 forcing:https://klimaatverandering.files.wordpress.com/2015/02/delta_18o_vs_lnco2_mb_fig2b.png

  11. Christian says:

    Robert & ATTP,

    It seems to me, that we have to seperate ice-albedo-Feedback, because we have a slow response from the ice-sheet and a much faster response from NH-Snowpack, in that Way, Robert is correct, in a world with and another without Snowpack, there should be a more different TCR then ECS or ESS.

  12. -1=e^ipi says:

    Cool. More evidence that the ECS is ~3 C.

    @ Jos – that 3.0-4.4 C range is the 68% confidence interval, so is less accurate than the 30-50% range of Lunt et al. Lunt et al also suggested an ECS of ~3.0 C. So this means that ESS of ~4.2 C might be the best estimate.

  13. @-1=e^ipi

    Yes, the 3.0 – 4.4 °C is the 68% range for the Pliocene era. Martínez-Botí doesn’t give a best estimate for the ESS for either the Pleistocene or the Pliocene, but if you use the median values from their figures 5a and 5b, 2.01 °C/(W/m²) and 1.05 °C/(W/m²), you get respectively ~7.4 °C or ~3.9 °C for the ESS.
    The ECS could increase though when temperatures increase, mainly due to a strengthening of the water vapor feedback, see:
    http://onlinelibrary.wiley.com/doi/10.1002/2013GL058118/abstract

  14. BBD says:

    I also wonder about a carbon cycle feedback from permafrost melt in a shift from Holocene to Pliocene-like conditions. This would be absent from Pliocene-derived sensitivity estimates as the climate system was already relatively warm, especially at higher latitudes.

  15. Everett F Sargent says:

    So, with ECS at a virtual standstill (going on like the 3rd decade now at 1.5-4.5C, or a factor of 2 (using 3C mean)), Pliocene RSL at 12-32m (~factor of 2) and pCO2 somewhere’s in the 250-500 range (Figure 1d), I’d say something, but I think those ‘numbers’ speak for themselves. 😦

    http://www.open.ac.uk/research/main/sites/www.open.ac.uk.research.main/files/files/ecms/web-content/Martinez-Boti-Plio-Pleistocene-Article.pdf
    http://scholar.princeton.edu/sites/default/files/Rohling_etal_2014_Nat_SeaLevelMedSea_0.pdf
    http://www.highstand.org/erohling/Rohling-papers/2014-Grant-et-al-ncomms6076.pdf

    See Rohling (2014) (2nd link above) Figure 1a, sea level over the past ~7ky is like +/-25m (or +/-50m if you use their orange, 95% confidence intervals), I’d say something, but I think those ‘numbers’ speak for themselves. 😦

    So, if it smells-looks-tastes-feels-sounds like the present (in a snapshot like fashion), we infer that it must be the present, because, see our numbers above.

    I do like their last paragraph (1st sentence):

    “In May 2013, atmospheric CO2 levels crossed the 400 parts per million threshold to values last seen during the Pliocene (Fig. 1c). Given current CO2 emission rates, global temperatures may reach those typical of the warm periods of the Pliocene by 2050.”

    I’m not quite sure what “global temperatures may reach those typical of the warm periods of the Pliocene by 2050” means, so if we are at +0.8C, would they all imply 0.2C or 1.2C or 2.2C additional in the next 35 years?

  16. -1=e^ipi says:

    @ Jos-
    “The ECS could increase though when temperatures increase, mainly due to a strengthening of the water vapor feedback”

    I’ll have to read your link when I get time. But I was under the impression that the water vapour increases approximately exponentially due to the Clausius-Clapeyron relation, but the forcing of water vapour is approximately logarithmic, which means that the water vapour feedback is linear.

    One thing you do get with more water vapour is more clouds (if cloud volume is proportional to water vapour, and cloud surface area is proportional to volume to the power of 2/3, then cloud surface area should increase approximately exponentially with temperature), which has an increasing negative feedback albedo effect. Though my understanding is that there is a positive cloud feedback due to the warmer climate moving clouds upwards. Though if water vapour depends exponentially on temperature and density decreases exponentially with height, then this positive feedback effect should be roughly constant with temperature.

    Put these together and it suggests that ECS should decrease with increasing temperature. Add the gradual loss of the permafrost feedback effect with temperature and there is even more reason to believe that ECS decreases with temperature. ESS certainly decreases with temperature because eventually you run out of the glacier-albedo feedback effect.

  17. BBD says:

    So the PETM never happened.

  18. -1=e^ipi says:

    @ BBD-
    “I also wonder about a carbon cycle feedback from permafrost melt in a shift from Holocene to Pliocene-like conditions.”

    Isn’t that feedback effect ~87 ppm CO2 released for a doubling of CO2 (that is the central estimate of the IPCC’s estimates AR4 chapter 7).

    Actually, I found a pretty easy way to show that this ~87 feedback effect is roughly correct:

    Henry’s constant determines the ratio between the solubility of gas in a liquid and the partial pressure of the gas above that liquid.

    http://en.wikipedia.org/wiki/Henry%27s_law#Temperature_dependence_of_the_Henry_constant

    From the wiki, one gets that the solubility of CO2 in water is proportional to exp(C*(1/T + 1/(298K))), where T is the temperature of the water in Kelvin and C = 2400K for CO2.

    Taking the natural logarithm of this gives C*(1/T + 1/(298K)). Plotting this from 0 C to 30 C gives a line of best fit of -0.0126 +/- 7.3095 and gives a very good fit (R^2 is 0.9993). Thus the amount of CO2 in water should decrease by about 1.26% if the temperature increases by 1 Celcius.

    Now the oceans contain around 37400 billion tons of carbon. So if the temperature of the ocean were to increase uniformly by 1 Celcius, then this would release ~47.12 billion tons of carbon.

    Standard atmospheric pressure at sea level is 101325 Pa. Acceleration due to gravity is 9.81 m/s^2. This implies that there is approximately 10329 kg of air above a square meter of Earth at sea level.

    The radius of the Earth is 6371 km. This means that there is approximately 4*pi*(6371000m)^2*10329kg = 5.268 x10^18 kg of air on Earth.

    If we assume an atmosphere of 78% N2, 21% O2 and 1% Argon, then the molar mass of the atmosphere is 28.96 g/mol. Thus there are approximately 1.819 x 10^20 mols of gas in the Earth’s atmosphere. This means that 1 ppm corresponds to ~ 1.819 x 10^14 mols of gas. Since the molar mass of carbon is 12 g/mol, this means that it takes ~2.2 billion tons of carbon to increase atmospheric CO2 by 1 ppm (though I think this is an underestimate, based on some regressions I have done recently).

    Thus increasing ocean temperature uniformly by 1 C would increase atmospheric ppm by ~ 21.4 ppm.

    But there is also permafrost. There are 1400-1700 billion tons of carbon in permafrost (http://en.wikipedia.org/wiki/Permafrost); I’ll use the central estimate of 1550 billion tons. Due to lack additional a priori knowledge, I’ll assume that the permafrost has a similar behaviour as the oceans (so 1 degree celcius increase releases ~1.26% of the carbon). Also, permafrost is located primarily in polar regions, so I should take into account polar amplification. The global polar amplification factor is ~2.0 according to ice core data. Putting these factors together (plus the assumption of 2.2 billion tons of carbon corresponding to 1 ppm) suggests that warming the earth by 1 C (and therefore permafrost by ~2C) increases atmospheric CO2 by ~ 17.8 ppm.

    Thus the marginal effect is that increasing global temperature by 1 C would increase atmospheric CO2 by about 39.2 ppm.

    If we have an equilibrium climate sensitivity of 3 C, then this suggests that if you doubled atmospheric CO2, then the response feedback response would be 39.2/0.126*(-exp(-0.0126*3) + 1) ~ 115 ppm. Of course, the 2.2 billion tons of carbon for 1 ppm was an underestimate, because I ignored land masses above sea level and assumed that air above the tropopause was similar to the troposphere. Making ~87 ppm reasonable.

  19. BBD says:

    Let’s stick to the problem with your previous comment:

    Put these together and it suggests that ECS should decrease with increasing temperature.

    According to you, the PETM never happened.

    If you were the clever fellow you imagine yourself to be, you would see the very serious problem with your ‘reasoning’.

  20. -1=e^ipi says:

    @ BBD –
    Please explain how anything I have written here is in contradiction with the existence of PETM. If you could show how any claim I have made here is outside the 95% confidence interval for what happened during PETM, I would greatly appreciate it.

  21. BBD says:

    Put these together and it suggests that ECS should decrease with increasing temperature.

  22. BBD says:

    It’s called a hyperthermal for a reason, -1.

  23. -1,
    I’m not sure your argument about the ECS decreasing with increasing temperature is correct. I don’t quite follow it and haven’t had time to really think of it. If we consider the ECS to be defined in terms of fast feedbacks only, then you pretty much get around 3K for various different climate states and for the greenhouse effect itself. Of course, the evidence suggests that it is most likely between 1.5 and 4.5K, but – as I understand it – there is little evidence to support a significant dependence on initial surface temperature.

  24. aTTP,

    Did you read the comment of David Lea in the News & views section of that issue of Nature. Some excerpts from there:

    Why should climate sensitivity be stronger in a warm world? A warmer world is likely to have less snow and ice, thereby reducing their amplifying effect on climate change. But how other feedbacks, such as water vapour and clouds, respond to warming is less certain. Simulations with climate models suggest that the positive feedback due to water vapour may strengthen in warmer climates, but uncertainties about how cloud feedbacks respond to warming confuse our understanding of the overall dependence of climate sensitivity on climate state.
    [..]
    Proxy reconstructions indicate that the Arctic climate during the Pliocene was much warmer than it is today, about 8–19 °C warmer, depending on location and season. But this extreme Arctic warmth seems to have coexisted, paradoxically, with atmospheric CO2 levels that are similar to the present ones, implying an extreme amplification of positive climate feedbacks in the Pliocene.
    [..]
    Martínez-Botí and colleagues challenge this existing hypothesis [..]

    I cannot really comment on what David Lea writes.

  25. Pekka,
    Yes, I aware of that as this paper was claiming that there was no indication of a different ECS in the Pliocene and Pleistocene. I was more just trying to point out to -1, that there doesn’t seem to be much evidence to suggest that the ECS goes down in warmer climates. If anything, it might be expected to go up, but this paper would seem to suggest that there isn’t a strong temperature dependence.

  26. -1=e^ipi says:

    @ BBD –
    I noticed that you were unable to provide any evidence to back up your claims.

    In any case, I’ll try to demonstrate that PETM is not in contradiction with my claims.
    http://www.skepticalscience.com/co2-rising-ten-times-faster-than-petm-extinction.html

    If you look at the data on figure two, it suggests that the ESS during PETM is ~ 4C. Not really sure what the uncertainty on this is, but that central estimate is lower than the central estimates of the Pliocene ESS, and much lower than the ESS of the Pleistocene.

    Yes, ECS is not ESS, but I see no evidence that the ECS rises with temperature. I cannot disprove that there is no evidence of PETM contradicting me just like I cannot disprove the existence of the flying spaghetti monster. The burden of evidence is on you to demonstrate the existence of this evidence.

  27. -1,

    Yes, ECS is not ESS, but I see no evidence that the ECS rises with temperature.

    Hold on, I thought you were suggesting that it drops with temperature. The paper being discussed here suggests that there is little dependence on temperature. However, according to the paper and according to Pekka’s link, there has been a suggestion that it might rise with temperature.

  28. -1=e^ipi says:

    @ ATTP – I agree that ECS is roughly constant throughout a large temperature range. The ESS varies much more. However, there can still be a slight temperature dependance of the ECS.

    I explained why I would expect ECS to decrease slightly with temperature. Do you want me to try to present in in point form?

    -Water Vapour increases ~ exponentially with temperature via the Clausius-Clapeyron relation.
    – Since forcing from water vapour is a logarithmic function of water vapour, this means that the effect of water vapour should be linear with temperature, so no temperature dependence of the ECS should be expected as a result of water vapour forcing.
    – Increasing water vapour also increases cloud cover, which has a negative albedo feedback effect. If cloud volume is proportional to water vapour, and cloud surface area is proportional to cloud volume to the power of 2/3, then cloud cover should increase approximately exponentially with temperature. If cloud cover accelerates with temperature, then this should result in a decrease in the ECS with increasing temperature.
    – To my understanding, the negative cloud feedback expected from AGW is primarily due to clouds moving upwards. Since water vapour increases exponentially with temperature, and atmosphere density decreases exponentially with height, the increase in cloud height for a given temperature increase should be roughly constant with temperature. So this should result in no temperature dependence of the ECS.

    2 effects that do not change with temperature + 1 effect that decreases with temperature suggests that ECS should decrease with temperature. There is also the gradual loss of the snow-albedo feedback as temperature goes up, which suggests even more that ECS decreases with temperature.

  29. -1,
    My understanding is that the cloud is thought to be slightly positive, not negative. High level, cold, clouds reduce outgoing flux. Low-level, warm, clouds increase albedo. Together, the net effect is thought to be a relatively small, positive feedback.

  30. BBD says:

    I noticed that you were unable to provide any evidence to back up your claims.

    Nope, that would be you trying to reverse the burden of proof. I’ve got Cenozoic hyperthermals.

    Yes, ECS is not ESS, but I see no evidence that the ECS rises with temperature.

    And to top it off, you have reversed your original claim.

  31. BBD says:

    If cloud feedback turned net negative then events like the PETM wouldn’t be physically possible.

    It’s really that simple.

  32. BBD says:

    If you look at the data on figure two, it suggests that the ESS during PETM is ~ 4C. Not really sure what the uncertainty on this is, but that central estimate is lower than the central estimates of the Pliocene ESS, and much lower than the ESS of the Pleistocene.

    No ice in the Paleocene. Affects ESS (slow feedbacks) but not ECS (fast feedbacks).

  33. -1=e^ipi says:

    @ ATTP –

    “My understanding is that the cloud is thought to be slightly positive, not negative.”

    I’m not saying this isn’t correct, though there is still large uncertainty on the cloud feedback.

    But you can think of the cloud feedback effect as two separate effects: the albedo effect, which is negative, and the affect of cloud formation moving upward, which is negative. If the albedo effect accelerates with temperature, where as the clouds forming higher effect is linear with temperature, then the overall cloud feedback effect should decrease with temperature, despite the overall cloud feedback effect being positive. Thus the expectation is a decreasing ECS with temperature.

  34. -1=e^ipi says:

    @ BBD-
    “Nope, that would be you trying to reverse the burden of proof. I’ve got Cenozoic hyperthermals. ”

    Again, I can’t disprove a negative that evidence that I cannot find doesn’t exist.
    It’s not my job to support your claims. Please explain how anything I have written here is in contradiction with Cenozoic hyperthermals and is outside of their 95% confidence intervals.

    “If cloud feedback turned net negative then events like the PETM wouldn’t be physically possible.”

    I think you are confusing the feedback effect with the derivative of that feedback effect with respect to temperature.

    “And to top it off, you have reversed your original claim.”

    My position is consistent: both ECS and ESS decrease with temperature, although ECS does not change very much.

  35. BBD says:

    It’s not my job to support your claims.

    You claimed that ECS decreases with T. I suggested that this is incompatible with the very existence of hyperthermals and you now say:

    My position is consistent: both ECS and ESS decrease with temperature, although ECS does not change very much.

    So it seems as though you aren’t really saying much that I’d disagree with after all.

    I think you are confusing the feedback effect with the derivative of that feedback effect with respect to temperature.

    Are you simply saying that cloud feedbacks net *weakly* negative? Per a small reduction in ECS as T increases?

  36. BBD says:

    Side note:

    But you can think of the cloud feedback effect as two separate effects: the albedo effect, which is negative, and the affect of cloud formation moving upward, which is negative.

    Do you mean positive feedback for increased height of cloud formation?

  37. -1,

    I think you are confusing the feedback effect with the derivative of that feedback effect with respect to temperature.

    Yes, I realise, but it seems as though you’ve somewhat hand-waved a temperature dependence without really providing any evidence that it actually exists.

  38. BBD says:

    ATTP

    it seems as though you’ve somewhat hand-waved a temperature dependence without really providing any evidence that it actually exists.

    While all the time insisting that the burden of proof is reversed.

  39. -1=e^ipi says:

    @BBD –
    “I suggested that this is incompatible with the very existence of hyperthermals ”

    I don’t see how it’s incompatible. Can you explain where this incompatibility because I do not see it?

    “Are you simply saying that cloud feedbacks net *weakly* negative? Per a small reduction in ECS as T increases?”

    No, I am saying that the DERIVATIVE of the cloud feedback with respect to global temperatures is negative.

    “Do you mean positive feedback for increased height of cloud formation?”

    Yeah, sorry. That is a typo.

    @ ATTP –

    “but it seems as though you’ve somewhat hand-waved a temperature dependence without really providing any evidence that it actually exists.”

    I have provided reasoning why one should expect the ECS to decrease with temperature. My expectation could be wrong, or it could be right; I don’t know.

  40. BBD says:

    I don’t see how it’s incompatible. Can you explain where this incompatibility because I do not see it?

    You modified your argument. The incompatibility with eg. the PETM only emerges if the effect is climatologically significant, which you agree that it is not:

    My position is consistent: both ECS and ESS decrease with temperature, although ECS does not change very much.

    Since you have refined your argument to ‘nothing much’, there’s nothing much to disagree with.

  41. -1=e^ipi says:

    “The incompatibility with eg. the PETM only emerges if the effect is climatologically significant, which you agree that it is not:”

    Again, back up the claim, because I do not see how PETM excludes the possibility that the temperature dependance of the ECS is not climatologically significant.

    “Since you have refined your argument to ‘nothing much’, there’s nothing much to disagree with.”

    1. You are mixing up an ‘argument’ with a claim.
    2. Saying that X is negative but the magnitude of X is not very large is not in contradiction with saying that X is negative. Rather it is clarifying my position.

  42. BBD says:

    Since you have refined your argument to ‘nothing much’, there’s nothing much to disagree with.

    And now you are trying to point-score over nothing much, which is tedious.

  43. Some research based on models regarding the dependence of climate sensitivity on the ‘state of the climate’.

    Meraner et al 2013 (see link in my previous reaction):“While ECS is often assumed to be constant to a first order of approximation, recent studies suggested that ECS might depend on the climate state. Here it is shown that the latest generation of climate models consistently exhibits an increasing ECS in warmer climates due to a strengthening of the water-vapor feedback with increasing surface temperatures.”

    Hansen et al 2013:See their figure 7b in chapter 5b – Fast-feedback sensitivity: state dependence.http://rsta.royalsocietypublishing.org/content/371/2001/20120294

    Caballero, Huber 2013:“Finally, fast-feedback sensitivity in the present model is strongly nonuniform, increasing rapidly at high temperatures due mostly to positive short-wave cloud feedbacks.”http://www.pnas.org/content/110/35/14162.full

  44. BBD says:

    And while palaeoclimate is fun, we shouldn’t lose sight of the implications for future climate. ESS appears to be dependent on the cryosphere. ESS in the Holocene is therefore higher than ESS in previous hot climate states with a smaller cryosphere. This is the bequest to futurity that we are preparing now.

  45. -1=e^ipi says:

    @ Jos – Could you please explain the physical mechanism by which the strengthening of the water vapour feedback suggests increasing ECS with temperature despite the fact that radiative forcing from water vapour is an approximately logarithmic function of water vapour.

    @ BBD – Your claim was that Cenozoic Paleoclimate data is incompatible with the possibility of a negative dependence of the ECS with temperature that is ‘climatologically significant’. I just don’t see how the uncertainty on these Paleoclimate conclusions is small enough to be incompatible with this conclusion.

  46. -1=e^ipi says:

    last post should read: incompatible with this possibility, not incompatible with this conclusion.

  47. BBD says:

    Perhaps we need to refine the definition of ‘climatologically significant’ until it means what it says.

    If the effect was climatologically significant, then no hyperthermals.

  48. Arthur Smith says:

    For somebody with a mathematical formula for a name, I thought ‘-1’ would be a little less sloppy on the water vapor question. The Clausius-Clapeyron relation is exponential in the INVERSE of temperature – saturated water vapor pressure varies as exp(-A/T) for T on an absolute scale. The logarithm of that function is not linear in temperature. There’s a lot of sloppiness of that sort going around of course – especially regarding CO2’s rise (anthropogenic CO2 has been roughly exponential in time, yes, but on top of pre-industrial, and the logarithm of a constant + an exponential is also not linear).

  49. Arthur Smith says:

    The discussion here may also be apropos: http://climatephys.org/2012/07/31/the-water-vapor-feedback-and-runaway-greenhouse/

    Assuming a simple logarithmic relation for water vapor radiative effects is also not right in part because the distribution of water vapor throughout the atmosphere is so variable. What matters most is the radiative effects in the upper atmosphere where there isn’t much. Runaway is definitely possible. But also very unlikely for our planet.

  50. -1=e^ipi says:

    @ Arthur Smith –

    “The Clausius-Clapeyron relation is exponential in the INVERSE of temperature”

    Yes, but it being an exponential function of temperature is a very good approximation.

    Look, I’ll demonstrate how good of an approximation it is. If I take the logarithm of the August-Roche-Magnus formula (http://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation), plot it from 0 C to 30 C and perform a line of best fit, I get a slope of 0.0645 with an R^2 of over 0.999.

    If I do the exact same thing with the formula provided in the link you just gave (http://climatephys.org/2012/07/31/the-water-vapor-feedback-and-runaway-greenhouse/). I get the EXACT same thing (slope of 0.0645 and an R^2 of over 0.999).

    Actually, if you plot this, it is clear that the logarithm of water vapour is a decelerating function of temperature. A quadratic fit to both of these gives an R^2 of practically 1 with quadratic terms – 0.00025 and -0.00023 respectively.

    So that means that the water vapour feedback should be decreasing with temperature. Even more evidence to support the hypothesis that ECS decreases with temperature. Thanks for pointing this out Mr. Smith. 🙂

    “There’s a lot of sloppiness of that sort going around of course – especially regarding CO2’s rise (anthropogenic CO2 has been roughly exponential in time, yes, but on top of pre-industrial, and the logarithm of a constant + an exponential is also not linear).”

    Yes, I’m the one that pointed this out in the comments of the post about the Craig Loehle paper. I showed that Craig Loehle underestimates climate sensitivity by ~50%. You even commented saying that you thought my calculations were correct. Do you not remember this?

    “Assuming a simple logarithmic relation for water vapor radiative effects is also not right in part because the distribution of water vapor throughout the atmosphere is so variable.”

    Since the effect of water vapour is basically linear with respect to temperature (actually decreasing, as you just pointed out), the above effect you describe is only relevant with respect to polar amplification. So the water vapour feedback will ‘increase’ polar amplification.

    However the polar amplification factor decreases with temperature (which it has to since otherwise the polar temperatures would exceed equatorial temperatures at some point). This means that this uneven water vapour distribution effect will cause a decrease of the ECS with temperature (as water vapour distribution will become more even with temperature).

    Even more reason to believe that ECS decreases with temperature!

    “Runaway is definitely possible.”

    I see no reason to believe this is the case. Unless you want to extend the meaning of ‘definitely possible’ to include flying spaghetti monsters.

  51. -1=e^ipi says:

    @ Arthur Smith –

    Actually, now that you’ve brought it up, it’s fairly easy to give an approximation for how the ECS should change with temperature from the water feedback effect alone.

    The no feedback climate sensitivity is ~ 1.15 C. The effect of water vapour increases this by ~ 0.59 C. http://www.globalwarmingequation.info/global%20warming%20eqn.pdf
    Of course there are other feedback effects (which in turn cause more water vapour). And if ECS is ~ 3 C and the ratio of the water vapour feedback as a function of the total feedback is 0.59/(1.15 + 0.59), then that water vapour feedback is contributing ~1.02 C to the total 3C of climate sensitivity.

    If the natural logarithm of the clausius clapeyron relation has a slope of ~0.0645 and an acceleration of ~-0.00024*2 = -0.00048, then this suggests that the strength of the water vapour feedback effect should decrease by about 0.744% per degree celcius.

    Multiply this by the ~1.02 C and it suggests that the effect of the non-linearity of the water vapour feedback should decrease the ECS by ~0.0076 C per degree celcius.

  52. -1,
    Your numbers seem a little too certain to me 🙂

  53. BBD says:

    It’s a word placement game with -1. He gets to crap on about reduced ECS with T (speciously, IMO) and we get to hear the words ‘ECS’ and ‘reduced’ and ‘temperature’ over and over and over again.

    But palaeoclimate behaviour shows beyond any doubt that even if there is a decrease of ECS with T it is not climatologically significant or it would prevent GHG-forced hyperthermals from occurring.

  54. BBD,
    You make very confident statements.

    Having little own knowledge of the issue my natural reaction is to check IPCC AR5. What I find in Chapter 5.3.1 is (These are the only places where the acronym PETM occurs in the text of WG1.)

    The PETM was marked by a massive carbon release and corresponding global ocean acidification (Zachos et al., 2005; Ridgwell and Schmidt, 2010) and, with low confidence, global warming of 4°C to 7°C relative to pre-PETM mean climate (Sluijs et al., 2007; McInerney and Wing, 2011). The carbon release of 4500 to 6800 PgC over 5 to 20 kyr translates into a rate of emissions of ~0.5 to 1.0 PgC yr–1 (Panchuk et al., 2008; Zeebe et al., 2009). GHG emissions from marine methane hydrate and terrestrial permafrost may have acted as positive feedbacks
    (DeConto et al., 2012).

    and

    Uncertainties on both global temperature and CO2 reconstructions preclude deriving robust quantitative estimates from the available PETM data.

    IPCC authors seem to be far less confident.

  55. BBD says:

    Pekka

    If you want to argue that the Cenozoic hyperthermals are evidence of a negative feedback then you go ahead.

  56. If cloud feedback turned net negative then events like the PETM wouldn’t be physically possible.

    It’s really that simple.

    The above is perhaps the clearest example of what I had in mind.

  57. BBD says:

    If you want to argue that the Cenozoic hyperthermals are evidence of a negative feedback then you go ahead.

  58. BBD says:

    Pekka

    Perhaps I just haven’t explained my thinking in enough detail.

    The Paleocene climate was *much* hotter than the Holocene, so this hypothetical reduction in ECS with increased T is already strongly engaged before the PETM and the ETM-2. And yet you still got huge, geologically very rapid hot spikes (hyperthermals) without unfeasibly vast releases of carbon. On this basis I maintain that the hypothesised effect – if it actually exists at all – is insignificant.

  59. BBD says:

    I suppose I should also say that the ESS appears to come much closer to ECS when the cryosphere is diminished or absent, as in the Paleocene. So the temperature response of the PETM is probably more a reflection of fast-feedback sensitivity than it would be if such an event occurred in the Holocene. This being so, the magnitude of the PETM would seem to indicate that ECS does not fall significantly as T increases.

  60. BBD,

    I didn’t mean that your arguments are unjustified. Neither do I have any reason to think that the data gives any evidence for the opposite claims. I’m just interested in the power of paleoclimatic evidence, and PETM as a specific part of that.

    I understand that paleoclimatic evidence has definite strengths, mainly through the fact that climate history is history of the real Earth, not of a model, and the wide range of the climatic states the Earth has gone trough.

    The other side of the coin is more problematic. Data is indirect, and it covers only some parts of the Earth. Some periods are covered better, some worse. Interpreting the data, and in particular filling the gaps in data requires narratives and assumptions that are difficult to test. The subjective input of scientists is unavoidably significant.

    Some of the scientists seem to trust the conclusions more, other less. IPCC reports reflect the spectrum of such views. Having a personal justified view on the reliability of conclusions in a field with the above characteristics requires really extensive knowledge about very many issues. Even based on the best knowledge scientists continue to have quite different views.

    You do surely understand, why I do not easily accept very confident claims on specific conclusions from paleoclimatic research.

  61. BBD says:

    The conceptual approach I took above allows for uncertainty in the data, Pekka.

  62. -1=e^ipi says:

    @ BBD – You brought up the term ‘climatologically significant’ without defining it. Not me. Yet you accuse me of word games..

    “And yet you still got huge, geologically very rapid hot spikes (hyperthermals) without unfeasibly vast releases of carbon. On this basis I maintain that the hypothesised effect – if it actually exists at all – is insignificant.”

    Also, is it difficult to understand that the uncertainty of PETM is way too large to exclude the hypothesis that ECS decreases ‘significantly’ with temperature and the hypothesis that ECS increases ‘significantly’ with temperature?

    @ ATTP – Yes, I was just trying to get a rough order of estimate. Don’t read too much into that value.

  63. Maybe we can broadly draw this discussion to a close. As I understand it, we can’t rule out that the ECS depends on climate state, but the current evidence suggests that it probably doesn’t and – if it does – the dependence is probably weak. This may not be the case, but we don’t really have any strong evidence to support a strong temperature dependence for ECS. That’s how I see it, at least.

  64. BBD,

    Yes, but how to know whether the allowance is adequate?

    Quantifying the uncertainties is very difficult in many parts of climate science. When one of the main sources of uncertainty comes from not knowing, how good the narrative is, it’s really difficult to give uncertainty estimates.

    How can we ever be sure that our narrative does not miss something that affects the conclusions essentially?

    Can we say that it’s even likely that no unknown factor has such an essential influence?

    In some cases we can consider some prior expectations so well justified that we can apply Bayesian reasoning to use the new data to just make the range of uncertainty smaller. In other cases the prior presents so badly lacking knowledge that limited additional knowledge leaves the posterior uncertainty essentially unquantifiable.

  65. BBD says:

    Yes, but how to know whether the allowance is adequate?

    That should be self-evident from what I wrote above, Pekka.

    Something else that is self-evident is the meaning of climatologically significant.

  66. ATTP,

    “As I understand it, we can’t rule out that the ECS depends on climate state, but the current evidence suggests that it probably doesn’t and – if it does – the dependence is probably weak.”

    I do not get this, see the links in my previous reactions. The CMIP5 models are quite clear on the strengthening of the water vapor feedback as T increases (Meraner et al 2013). I see this strengthening as follows:
    The water vapor pressure is exponentially related with T. Using this ’chem.okstate’ table you get an increase in water vapor pressure of 0.8 mm Hg when you increase temperature from e.g. 15 °C to 16 °C. A rise of 1 °C from e.g. 20 °C to 21 °C gives a rise in the vapor pressure of 1.2 mm Hg.
    The water vapor feedback depends on the increase of the amount of water vapor in the atmosphere. You get more water vapor when you start increasing T from a higher value: the feedback is larger.
    Or am I missing something?

  67. -1=e^ipi says:

    @ Jos – You are missing the fact that the radiative forcing of water vapour is an approximately logarithmic function of the amount of water vapour.

    @ BB – “Something else that is self-evident is the meaning of climatologically significant.”

    How ‘scientific’ of you to refuse to define a term you come up. You are as bad as those young earth creationists that tell me the existence of god is self-evident. *sarcasm*

    @ ATTP – I don’t think you can conclude something as strong as ‘ECS probably doesn’t depend on temperature’. Maybe something weaker like ‘I see no evidence that a strong temperature dependence of the ECS exists’.

  68. @-1=e^ipi

    The logarithm of an increasing number also increases: http://tutorial.math.lamar.edu/Classes/CalcI/LogFcns_files/image001.gif
    But read Meraner 2013, I do not think all CMIP5 models get it wrong.

  69. Jos,

    I do not get this, see the links in my previous reactions. The CMIP5 models are quite clear on the strengthening of the water vapor feedback as T increases

    Yes, I realise that the GCMs suggest that the feedbacks may be non-linear and that there may be a climate state/temperature dependence. I was referring mainly to paleo evidence, rather than to model evidence.

    -1,
    Fine, I’d go along with that. I do think, however, that climatologically significant is reasonably self-evident.

  70. BBD says:

    ATTP

    Palaeo modelling supports an *increase* in sensitivity in hot climate states eg. Hansen et al. (2013):

    We use a global model, simplified to essential processes, to investigate state-dependence of climate sensitivity, finding a strong increase in sensitivity when global temperature reaches early Cenozoic and higher levels, as increased water vapor eliminates the tropopause.

    And:

    (b) Fast-Feedback Sensitivity: State Dependence

    Climate sensitivity must be a strong function of the climate state. Simple climate models show that when Earth becomes cold enough for ice cover to approach the tropics, the amplifying albedo feedback causes rapid ice growth to the equator, “snowball Earth” conditions (Budyko, 1969). Real world complexity, including ocean dynamics, can mute this sharp bifurcation to a temporarily stable state (Pierrehumbert et al., 2011), but snowball events have occurred several times in Earth’s history when the younger Sun was dimmer than today (Kirschvink, 1992). Earth escaped snowball conditions due to limited weathering in that state, which allowed volcanic CO2 to accumulate in the atmosphere until there was enough CO2 for the high sensitivity to cause rapid deglaciation (Hoffman and Schrag, 2002).

    Climate sensitivity at the other extreme, as Earth becomes hotter, is also driven mainly by an H2O feedback. As climate forcing and temperature increase, the amount of water vapor in the air increases and clouds may change. Increased water vapor makes the atmosphere more opaque in the infrared region that radiates Earth’s heat to space, causing the radiation to emerge from higher colder layers, thus reducing the energy emitted to space. This amplifying feedback has been known for centuries and was described remarkably well by Tyndall (1861). Ingersoll (1969) discussed water vapor’s role in the “runaway greenhouse effect” that caused the surface of Venus to become so hot that carbon was “baked” from the planet’s crust, creating a hothouse climate with almost 100 bars of CO2 in the air and surface temperature about 450°C, a stable state from which there is no escape. Arrival at this terminal state required passing through a “moist greenhouse” state in which surface water evaporates, water vapor becomes a major
    constituent of the atmosphere, and H2O is dissociated in the upper atmosphere with the hydrogen slowly escaping to space (Kasting, 1988). That Venus had a primordial ocean, with most of the water subsequently lost to space, is confirmed by present enrichment of deuterium over ordinary hydrogen by a factor of 100 (Donahue et al., 1982), the heavier deuterium being less efficient in escaping gravity to space.

  71. Arthur Smith says:

    ‘-1’ – yes, I remember it was you who’d discussed that nonlinearity, though I’d forgotten when I wrote about it last night.

    Anyway, my point was not only that C-C is not simply an exponential and its log is not a straight line (rather curved with negative second derivative, as you note). But also that it is far from clear to me that the “forcing” (i.e. change in radiative balance) associated with water vapor is logarithmic in concentration – in part because that concentration is very far from a uniform fraction of the atmosphere (unlike for CO2 which is “well mixed”) – but also in part because of some of the commentary at the link I provided.

    As that post indicated, in the limit of very high water vapor concentrations, the effect of an increase in surface temperature is to expand the atmosphere (evaporating more of the oceans) leaving the outgoing radiation almost unchanged, as the water vapor at higher altitudes completely blocks radiation from the surface and lower layers. Under those conditions the water vapor feedback is close to completely canceling the “Planck” response (which is itself a nonlinear concave-up function of temperature), so that radiative effect of water vapor is clearly an accelerating function of (surface) temperature at that point. Is the actual response concave up even at lower temperatures? I’m not sure, but it’s clearly not exactly logarithmic in w.v. concentration at very high concentrations, so I strongly believe is unlikely to be so at lower ones.

  72. -1=e^ipi says:

    @ Jos – Thank you for explaining basic grade school math to me. *sarcasm*

    How hard is it for you to understand? The logarithm of an exponential (with no additive constant) is linear. So the effect of water vapour doesn’t cause ECS to increase with temperature. Actually if you want to get even more specific with respect to the logarithm of the Clausius-Clapeyron relation, it decreases as I explained above.

    @ ATTP – “that climatologically significant is reasonably self-evident.”

    Well I don’t know what it means so could you please define it for me?

  73. -1,
    I took it to simply mean that if there is a temperature dependence that it is likely small enough that it won’t be particularly significant, especially given, for example, the range for ECS that already exists (i.e., if it’s likely between 2 and 4.5K, the a temperature dependence that means it might be between 1.99 and 4.49K is not particularly significant).

  74. -1=e^ipi says:

    @ Arthur Smith-

    “But also that it is far from clear to me that the “forcing” (i.e. change in radiative balance) associated with water vapor is logarithmic in concentration – in part because that concentration is very far from a uniform fraction of the atmosphere (unlike for CO2 which is “well mixed”) – but also in part because of some of the commentary at the link I provided.”

    The logarithmic approximation holds for high concentrations, so is applicable to CO2 and water vapour. For gases like methane, NO2 and SO2, the concentrations are small enough that the logarithmic approximation breaks down and radiative forcing is approximation linear with concentrations.

    One simple explanation for why the radiative forcing holds is that the logarithm of the absorption spectra decreases approximately linearly with wavelength for the tails as one moves away from the absorption peak (thanks very much due to all the degrees of freedom of vibration of triatomic molecules like water and CO2).

    But if you want to get even more fancy, the tails of the logarithm of a lorentian decreases linearly as one moves away from the peak, where as the tails of the logarithm of a gaussian decreases quadratically as one moves away from the peak. This means that a Voigt profile decreases between linearly and quadratically as one moves away from the peak. So if you get really high concentrations of water vapour, then ECS should decrease with temperature due to this effect.

    Even more reason to believe that ECS decreases with temperature!

    “leaving the outgoing radiation almost unchanged”

    Of course outgoing radiation has to be unchanged if you are going from 1 equilibrium to a new equilibrium. In equilibrium, outgoing radiation from the earth has to equal incoming radiation from the sun (plus I guess other minor factors like internal energy from the Earth, heat generated by tidal friction, etc.).

    “Under those conditions the water vapor feedback is close to completely canceling the “Planck” response (which is itself a nonlinear concave-up function of temperature)”

    The water vapour feedback being close to canceling out the Plank response is not substantiated by the evidence as far as I know (please present evidence to the contrary if you disagree).

    And I can’t believe you are trying to use the non-linearity of the Planck response to suggest that the ECS doesn’t decrease with temperature.

    Outgoing radiation of a black body is proportional to the temperature to the power of 4. Thus in equilibrium one has that forcing F is proportional to T^4. This implies that dF/dT is proportional to T^3, which implies that dT = dF/T^3. Thus the change in temperature due to a change in forcing decreases with temperature. In fact, given the current global temperature of 288K, I can estimate how this non-linear plank response. dln(T^3)/dT = 3*T^2/T^3 = 3/T = 3/288 = 0.0104. So this effect should cause the ECS to decrease by about 1.04% per Celcius. For an ECS of 3 C, this suggests ECS drops by ~0.031 C per C.

    Yet another reason to believe that ECS decreases with temperature!

    All these non-linearities you keep pointing out just suggest that ECS decreases with temperature. Thank you for pointing out 2 more reasons.

  75. -1=e^ipi says:

    @ATTP –
    “I took it to simply mean that if there is a temperature dependence that it is likely small enough that it won’t be particularly significant”

    And how are you defining ‘significant’? If you mean ‘statistically significant’, then the term ‘climatologically significant’ is redundant.

    “the range for ECS that already exists (i.e., if it’s likely between 2 and 4.5K, the a temperature dependence that means it might be between 1.99 and 4.49K is not particularly significant).”

    The range is artificially large because with the very high and very low estimates are making false assumptions in their estimates that skew their results. If you look at the research that has solid methodology, the range of estimates are much smaller and many studies have a much smaller uncertainty range.

    And if you are going with this ‘definition’, then your term ‘climatologically significant’ is based entirely on one’s uncertainty. In which case, you can make pretty much anything ‘climatologically insignificant’ when looking at paleo data because the uncertainty is so large.

  76. -1,
    Let’s not play semantic games. It’s tedious and boring. Yes, the uncertainties are large, therefore arguing about some effect that will have virtually no impact on the range might be technically interesting, but not particularly significant/relevant/….. (choose whatever word you like).

  77. -1=e^ipi says:

    @ BBD –

    Oh look you have tried to reference your god Hansen again. How surprising! *sarcasm*

    “finding a strong increase in sensitivity when global temperature reaches early Cenozoic and higher levels, as increased water vapor eliminates the tropopause.”

    No he doesn’t. The uncertainty on paleo data is too large to justify this conclusion. And knowing Hansen, the statistical analysis is practically non-existent.

    “Climate sensitivity at the other extreme, as Earth becomes hotter, is also driven mainly by an H2O feedback… blah blah… Venus… escaping gravity to space.”

    BBD I think you have to understand the different between scientifically derived results that are obtained through proper methodology & reasoning and nonsense, alarmisty, speculative ramblings that scientists fit into their conclusions because they can, even though this speculation is not based on evidence.

  78. -1=e^ipi says:

    @ ATTP –

    It wasn’t my intention to play semantic games. I prefer to stick with clearly defined terms. BBD brought this term up, which is why I asked for a defintion. If you mean that for all practical purposes we can assume that ECS is constant with temperature, then I agree with you.

  79. -1,
    I think that was essentially BBD’s point or, at least, what I understood him to be saying.

  80. BBD says:

    So this effect should cause the ECS to decrease by about 1.04% per Celcius. For an ECS of 3 C, this suggests ECS drops by ~0.031 C per C.

    Can we say ‘climatologically insignificant’ now?

  81. BBD says:

    A side note:

    Being rude then attempting to excuse the offensive statement as *sarcasm* is a crude mechanism for extending the scope of word-placement games.

  82. -1=e^ipi says:

    @ BBD –

    “Can we say ‘climatologically insignificant’ now?”

    No. For one you haven’t even given a proper definition of this term. Secondly, I brought up 6 reasons why the ECS would drop with temperature, but only quantified 2 of them.

    “Being rude then attempting to excuse the offensive statement as *sarcasm*”

    BBD, I use *sarcasm* for the sake of clarity. On an anonymous internet website where communication is done primarily through text, it is very common that people can misinterpret each other. Now if only you could be more clear and define ‘climatologically significant’…

  83. BBD says:

    Now if only you could be more clear and define ‘climatologically significant’…

    = Makes a difference to palaeoclimate behaviour that supports what you say.

  84. BBD says:

    BBD, I use *sarcasm* for the sake of clarity.

    Can we say ‘climatologically insignificant’ now?

    * sarcasm *

  85. -1=e^ipi says:

    “Makes a difference to palaeoclimate behaviour that supports what you say.”

    That is a pretty useless definition as paleoclimate data has large uncertainties.

  86. BBD says:

    In which -1 finally admits that this has been a word-placement game all along.

  87. Arthur Smith says:

    -1 – clearly you misunderstood the reference I gave. The “tails of the spectrum” argument for the logarithmic dependence does NOT apply, I believe, in the case of very high water vapor concentrations because there ARE no tails, it pretty much fully absorbs across the entire IR spectrum. The effect in that case is as illustrated in he fifth diagram in the article I mentioned – emission from TOA saturates even as surface temperature increases. So the feedback necessarily varies as T^4 (concave upward) while C-C approaches a limit. Now that is a limiting case, but it implies the dependence of the feedbacks on water vapor concentration cannot be strictly logarithmic. If the dependence is even as log^2 or something like that your argument breaks down. And it is likely higher order than that, I just haven’t been able to find a good reference on the numerical dependence. I suggest if you really believe it must be logarithmic that you try to find a source in the peer-reviewed literature that demonstrates the computation of that effect.

  88. -1=e^ipi says:

    @ Arthur Smith –
    “I believe, in the case of very high water vapor concentrations because there ARE no tails, it pretty much fully absorbs across the entire IR spectrum.”

    H20 is pretty transparent around 10 μm…
    In any cause, if there are no tails and a GHG absorbs across the entire IR spectrum then if that gas has very high concentrations then its forcing as a function of concentration has to be less than logarithmic (since the atmosphere is becoming opaque at all wave lengths). A simple analogy is that if you put on 1 pair of sun glasses, it absorbs more radiation than a 2nd pair of sun glasses and so on.

    But now that I think about it, my argument for the forcing of water vapour to be a logarithmic function of concentrations fails because water condenses, which means that water vapour concentrations are much less in the upper troposphere, so concentrations are arguably not high enough to have a logarithmic or less than logarithmic dependence.

    I tried to search for the relationship between water vapour concentrations and forcing. The best I can find is Lenton 2000 (http://www.tellusb.net/index.php/tellusb/article/viewFile/17097/19092) who suggests that the opacity of the atmosphere to H20 given by Kasting et al. 1993 can be approximated very well as being proportional to the water vapour concentrations to the power of 0.503 (for 0-40C). If I use this relation plus the clausius-clapeyron relation, the implication is that water vapour forcing is an exponential function of temperature. Although, for 0-30 C, it can be approximated very well by a quadratic. This suggests that around 15C, the derivative of the water vapour forcing with respect to temperature increases by ~2.57% per degree celcius.

    Also, earlier I misread http://www.globalwarmingequation.info/global%20warming%20eqn.pdf on the strength of the water vapour feedback. It really suggests that about 49.4% of the ECS is due to the water vapour feedback. So if we have an ECS of 3 then the ECS should increase by ~0.066 C per celcius. This exceeds the ~0.031 C per celcius effect for the plank effect that I calculated earlier.

    “The effect in that case is as illustrated in he fifth diagram in the article I mentioned – emission from TOA saturates even as surface temperature increases.”

    That doesn’t occur until like 400 K though…

  89. -1,

    In any cause, if there are no tails and a GHG absorbs across the entire IR spectrum then if that gas has very high concentrations then its forcing as a function of concentration has to be less than logarithmic (since the atmosphere is becoming opaque at all wave lengths).

    Aren’t you forgetting that as the concentration goes up, the effective emitting height increases and so, given a fixed lapse rate, the surface temperature continues to rise and (as I understand it) is essentially how a runaway process can be initiated.

  90. -1=e^ipi says:

    So I’ll try to put a rough estimate on how the albedo effect of clouds changes with temperature, and how that relates to the temperature dependence of the ECS.

    So if I take the clear-sky albedo of earth (http://www.climatedata.info/Forcing/Forcing/downloads.html) and I weight it by the cosine of the latitude (to take into account the directness of sunlight) then I get an albedo of 0.157.

    Now if I assume that average cloud cover is 0.56 (http://en.wikipedia.org/wiki/Cloud_cover) and that the Earth’s albedo is 0.35 (http://en.wikipedia.org/wiki/Albedo), then this suggests that cloud albedo is roughly 0.502, which agrees with various estimates of cloud albedo.

    Now given a solar irradiance of 341 W/m^2, this suggests that the presence of clouds cause an additional 65.88 W/m^2 of radiation to be reflected into space. Thus the albedo effect of clouds cause the earth to be approximately 65.88/4/stefan-boltzman-constant/(288 K)^3 = 12.2 K cooler.

    Now I guess it was wrong of me to suggest earlier that cloud cover is roughly proportional to cloud volume to the power of 2/3 (since obviously you cannot have cloud cover exceed 1). If I assume that new cloud volume forms independantly of old cloud volume (as water vapour increases), then this suggests that the change in cloud cover is roughly proportional to (1-c)*(change in cloud volume)^(2/3), where c is the cloud cover. This suggests that c/(1-c) is proportional to (change in cloud volume)^(2/3).

    Using the clausius-clapeyron relaion and assuming that cloud volume is proportional to water vapour suggests that c/(1-c) is proportional to exp(-2*5419/3/T). Using the fact that at T = 288K, c=0.56 one obtains a constant of proportionality of 356876. So c/(1-c) = 356876*exp(-2*5419/3/T). Isolating for c gives c = (1 + exp(2*5419/3/T)/356876)^-1.

    Taking the first derivative suggests that cloud cover should increase by approximately 0.0107 per celcius at 15 C. Note that from the stefan-boltzman relation, this corresponds to a negative feedback effect of 0.196 C per C. Taking the second derivative suggests that this rate of increase should decrease by ~4.5% per celcius. That’s interesting… I guess the effect of running out of cloudless sky area exceeds the effect of the exponential increase in cloud volume. Though maybe I should treat cloud albedo as a function of thickness as well.

    This suggests that the negative albedo cloud feedback effect declines by ~0.00882 per celcius. Given an ECS of 3C, this suggests that the temperature dependence of the cloud albedo feedback should cause the ECS to increase by approximately 0.026 C per C.

  91. -1=e^ipi says:

    @ ATTP –

    “Aren’t you forgetting that as the concentration goes up, the effective emitting height increases and so, given a fixed lapse rate”

    That’s a justification that I see used a lot to justify that radiative forcing is a logarithmic function of CO2 (since density decreases exponentially with altitude, so the change in the effective emitting height is proportional to the change in CO2 concentrations). In any case, Lenton 2000 suggests that radiative forcing is proportional to water vapour to the power of 0.503, so I will go with that.

    “the surface temperature continues to rise and (as I understand it) is essentially how a runaway process can be initiated.”

    I don’t understand how you think this. A runaway process would require that the feedback effect is greater than 1. Look at the link that Arthur provided (http://climatephys.org/2012/07/31/the-water-vapor-feedback-and-runaway-greenhouse/). Runaway global warming won’t occur until temperatures reach 647 K.

  92. -1,

    I don’t understand how you think this.

    I may have got that wrong, but I wasn’t quite sure how you were getting your argument either. If I understand the post Arthur links to, then you reach a point where the temperature profile becomes essentially a fixed function of pressure, so the emission to space is therefore fixed. If you add more water vapour it increases the pressure in the lower atmosphere, pushing the emitting surface higher, but keeping the pressure and temperature fixed and keeping the outgoing flux fixed. If the system is receiving more flux that it is losing it’s in a runaway process. Not that we’re likely to get there, but I think Arthur’s point was that the simple relationship you were suggesting breaks down well before this would happen.

  93. -1=e^ipi says:

    @ ATTP – we clearly have very different definitions of ‘runaway process’. Because what you describe above, I would call ‘out of equilibrium’. I don’t think your definition is consistent with it’s usual definition (http://en.wikipedia.org/wiki/Runaway_climate_change).

    Also, I am getting the impression that you are not reading the entirety of my posts…

  94. -1,

    Because what you describe above, I would call ‘out of equilibrium’.

    We’re out of equilibrium now. What I was describing was my understanding of the post Arthur linked to which described how you can reach a state where the water vapour ensures an essentially constant outgoing flux. In such a scenario, if the incoming flux exceeds the outgoing flux I would think runaway would be the right word, since there is no easy way to retain equilibrium since the system will warm until it reaches some kind of state where it is back in equilibrium. As the post itself says

    The planet becomes locked into a state in which it continues to absorb more solar radiation than can be emitted to space, and temperatures can runaway into excess of 1000 K.

    Also, I am getting the impression that you are not reading the entirety of my posts…

    Quite possibly.

  95. Arthur Smith says:

    Square-root like power law then rather than logarithmic? I hope we’re in agreement then that the expected nonlinearity in water vapor feedback would be to increase sensitivity. I see you’ve moved on to clouds but those effects are of course very uncertain and complicated, I doubt the crude approximations you’re playing with have much relevance.

  96. -1=e^ipi says:

    @ ATTP –
    I think you are definitely misusing ‘run-away’. For run-away warming, you would need the feedback effect to exceed 1 (at least for local temperatures). Basically, run-away = divergence, but in reality we will have convergence. The feedback effects are not remotely strong enough for this.

    “Quite possibly.”

    No, not ‘quite possibly’. Not possible. Look, I’ll even point out the relevant paragraph of the link Arthur provided:

    “Some claims have surfaced (e.g., by NASA’s Jim Hansen) that a runaway greenhouse is possible if we burned all the CO2. Unfortunately, there is no evidence in the planetary science literature to support the claim, and it can be dismissed based on the fairly trivial fact that the amount of sunlight that Earth absorbs does not even come close to the limiting OLR values typically found in the literature (usually > 300 W/m2). Thus, even if the temperature is shifted to higher values, there will always be a radiative equilibrium… a runaway wouldn’t occur at the modern boiling point of 373 K, since atmospheric pressure has increased quite a bit…one would need to wait until the critical point, 647 K”

  97. -1,
    For goodness sake, don’t complain about me not reading what you write if you don’t read what I write. I wasn’t arguing that a runaway was possible, I was simply discussing the point about water vapour that Arthur pointed out earlier. If you think we can reach a situation where the incoming flux exceeds the outgoing flux, with the outgoing flux fixed, without undergoing runaway then you’ll need to explain where the excess energy is going. Remember, the OUTGOING FLUX IS FIXED! Also reread the quote from the post

    The planet becomes locked into a state in which it continues to absorb more solar radiation than can be emitted to space, and temperatures can runaway into excess of 1000 K.

    Again, to be clear, I was simply discussing the issue of water vapour, not whether or not we will actually undergo runaway.

  98. -1=e^ipi says:

    “I wasn’t arguing that a runaway was possible”

    Sorry, I apologize for misinterpreting you. Please forgive me, I currently have brain damage due to being assaulted a few months ago.

    “If you think we can reach a situation where the incoming flux exceeds the outgoing flux, with the outgoing flux fixed”

    Okay, sure I agree that would lead to run away, if the outgoing flux was fixed (unless you had some sort of very strong albedo feedback that reduced incoming flux).

    Anyway, let’s review the 5 mechanisms I mentioned in this comment section that could lead to ECS dependence on temperature:

    Changes in cloud albedo feedback: ~0.026C per celcius. The cloud albedo feedback might actually cause an increase in the ECS with temperature if the effect of running out of cloudless skies exceeds the exponential increase in cloud volume. I didn’t take cloud albedo as a function of cloud thickness into account though.

    Changes in water vapour feedback: ~0.066C per celcius.

    Plank effect: ~-0.031C per celcius.

    Snow-albedo feedback: This should decrease with temperature as you run out of snow covered areas, especially those in more direct sunlight.

    Polar amplification affect: The polar amplification factor should decrease with temperature (since otherwise you could reach a point where polar temperatures exceed equatorial temperatures).

    Anyone want to try to quantify the last two with rough estimates?

  99. -1,

    I currently have brain damage due to being assaulted a few months ago.

    I’m sorry to hear that. Hope your recovery is going well.

    Anyone want to try to quantify the last two with rough estimates?

    I guess the problem is that these are all ballpark-like estimates, which is fine, but it’s almost certainly more complicated in reality than these estimates might indicate.

  100. guthrie says:

    -1 you could try using google scholar:
    http://scholar.google.com/scholar?q=equilibrium+climate+sensitivity+runaway+greenhouse+effect

    That way we don’t have to teach you everything, you can learn it yourself. Your local library may have better paper access, or if in the UK, the national libraries do, and membership of university libraries is reasonably cheap.

  101. -1=e^ipi says:

    I thought I would mention something that I think is relevant here. I was looking at papers on impulse response functions and this one struck my attention: http://www.climate.unibe.ch/~joos/papers/hooss01cd.pdf.

    It gives a number of different impulse response functions for different things. On page 7, it gives a 2 exponential impulse response function for temperature to changes in CO2 levels. The two decay times are 12 years and 400 years. If we interpret the first decay time to be due to the equilibrium climate sensitivity and the second decay time to be due to the Earth system sensitivity, then one obtains that the earth system sensitivity is 1/0.710 = 1.408 times the equilibrium climate sensitivity.

    This is completely consistent with the Lunt et al. paper that found using paleoclimate data from the Pleistocene that the Earth system sensitivity is approximately 1.4 times the equilibrium climate sensitivity.

  102. BBD says:

    This is completely consistent with the Lunt et al. paper that found using paleoclimate data from the Pleistocene that the Earth system sensitivity is approximately 1.4 times the equilibrium climate sensitivity.

    Did you mean Pliocene?

  103. -1=e^ipi says:

    Yeah I meant Pliocene. Sorry for the typo.

  104. BBD says:

    So we can confine our conclusions about the ESS as determined from Pliocene data (Lund et al.) to the Pliocene. We cannot generalise to the Holocene as you appear to be doing above:

    This is completely consistent with the Lunt et al. paper that found using paleoclimate data from the Pleistocene that the Earth system sensitivity is approximately 1.4 times the equilibrium climate sensitivity.

  105. -1=e^ipi says:

    Did you mean Lunt instead of Lund? You make typos too. 🙂

    But we are expected to go from Holocene temperatures to Pliocene temperatures and current CO2 levels are at Pliocene levels. So I think that an ESS of 1.4 times ECS makes a lot of sense for the Earth’s current situation.

  106. BBD says:

    -1

    But we are expected to go from Holocene temperatures to Pliocene temperatures

    And then some. I have already made the point that ESS from a Holocene baseline will be higher than ESS from a Pliocene baseline because the cryosphere is much larger now than it was in the Pliocene. Especially early-mid Pliocene. This will increase the difference between ECS and ESS relative to the Pliocene.

    Did you mean Lunt instead of Lund? You make typos too.

    [Mod: a bit inflammatory]

  107. -1=e^ipi says:

    @ BBD –

    And here I thought that you were convinced that ESS increases with temperature based on your favorite Hansen claims. If this were true, then that would suggest that the ESS is even lower now than during the Pliocene.

    So does this mean you now admit that ESS falls with temperature and that ECS might do so as well (although is pretty much constant)? If so, we are in agreement.

    Today the ESS should be larger than the Pliocene ESS. However, how much larger, I don’t know. The Joos paper suggests a ratio of 1.408, which is greater than 1.4, but not by much. The remaining cryosphere is at pretty high latitudes so does not get that much direct sunlight.

  108. BBD says:

    And here I thought that you were convinced that ESS increases with temperature based on your favorite Hansen claims.

    Best go back and read the thread again, then.

    So does this mean you now admit that ESS falls with temperature

    When did I say otherwise?

    and that ECS might do so as well

    I have seen no evidence at all that indicates this to be the case. You are putting words in my mouth. Stop it.

  109. Can we maybe avoid this discussion starting all over again?

  110. BBD says:

    So does this mean you now admit that ESS falls with temperature

    On second reading, this is just another one of your tedious attempted gotchas. I’ve pointed to the role of the cryosphere and the importance of defining baseline conditions rather than making misleading statements like the one you repeat here.

    I am really tired of your shtick, -1.

  111. BBD says:

    ATTP

    We crossed.

  112. -1=e^ipi says:

    Thought I would give a rough value of this cryosphere effect.

    The average albedo of the earth is 0.31. The average albedo of Antarctica is about 0.80. So suppose that as a rough approximation that if the Antarctic and Greenland ice sheets melt, they have an albedo increase of about 0.49.

    The average direct solar irradiance directed upon a square meter of Earth at latitude φ is proportional to:
    ϑ*Integral(μ = 0 to 2π; [cos (φ) cos (sin-1 (cos (μ) sin (ψ0 ) ) ) sin (ψ) – sin (φ) cos (μ) sin ( ψ0) ψ ]dμ)
    Where ϑ = 1366 W/m^2 is the solar irradiance at 1AU from the sun, ψ0 = 23.4*π/2 is the Earth’s tilt in radians, and ψ = cos-1 (min(0,max(1,tan (φ) tan (sin-1 (cos (μ) sin ( ψ0) ))) ). I’m missing a normalization constant here, but it is trivial to normalize.

    For simplicity, let’s represent Antarctica as a circle of radius 24 degrees centered at the south pole. Then the change in forcing over Antarctica due to this albedo change divided by the surface of the Earth is roughly 2.09 W/m^2. Greenland is roughly 15.5% the size of Antarctica, so as an approximation, let’s multiply this number by 1.155 to get 2.41 W/m^2.

    Now for a black body with temperature 255 K (Earth’s effective temperature), this forcing corresponds to a global temperature change of 2.41/4/Stefan-Boltzman Constant/(255)^3 = 0.64 C.

  113. -1=e^ipi says:

    @ BBD –
    “On second reading, this is just another one of your tedious attempted gotchas.”

    You are really going to play this game?

    I’m not the one who has been claiming that PETM excludes the possibility of ESS decreasing with temperature…

  114. BBD says:

    I’m not the one who has been claiming that PETM excludes the possibility of ESS decreasing with temperature…

    I said read the thread, -1.

    You will find that I said that a decrease in ECS with temperature – not ESS – would militate against a hyperthermal.

    Did I mention being fed up with your schtick? Why yes, I did.

  115. -1=e^ipi says:

    Sorry if I misinterpreted your position. So are you claiming that the ESS decreases with temperature, but paleo data somehow excludes the ECS decreasing with temperature?

  116. BBD says:

    Once again:

    There is no evidence whatsoever that ECS decreases as temperature rises.

    There was little or no planetary ice in the Paleocene. ESS is dependent on the baseline state of the cryosphere and so did not change significantly as T increased during the PETM.

    ESS appears to be closer to ECS when the cryosphere is diminished or absent, as in the Paleocene. So the temperature response of the PETM was probably more a reflection of fast-feedback sensitivity than it would be if such an event had occurred in the Holocene. This being so, the speed and magnitude of the PETM would seem to indicate that ECS does not fall significantly as T increased.

    * * *

    Okay, enough. We’ve been through all this above, often several times. IMO you are tr0lling me and I have indicated that I don’t appreciate it.

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