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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

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How sensitive is our climate?

What the science says...

Select a level... Basic Intermediate Advanced

Net positive feedback is confirmed by many different lines of evidence.

Climate Myth...

Climate sensitivity is low

"His [Dr Spencer's] latest research demonstrates that – in the short term, at any rate – the temperature feedbacks that the IPCC imagines will greatly amplify any initial warming caused by CO2 are net-negative, attenuating the warming they are supposed to enhance. His best estimate is that the warming in response to a doubling of CO2 concentration, which may happen this century unless the usual suspects get away with shutting down the economies of the West, will be a harmless 1 Fahrenheit degree, not the 6 F predicted by the IPCC." (Christopher Monckton)

At-a-glance

Climate sensitivity is of the utmost importance. Why? Because it is the factor that determines how much the planet will warm up due to our greenhouse gas emissions. The first calculation of climate sensitivity was done by Swedish scientist Svante Arrhenius in 1896. He worked out that a doubling of the concentration of CO2 in air would cause a warming of 4-6oC. However, CO2 emissions at the time were miniscule compared to today's. Arrhenius could not have foreseen the 44,250,000,000 tons we emitted in 2019 alone, through energy/industry plus land use change, according to the IPCC Sixth Assessment Report (AR6) of 2022.

Our CO2 emissions build up in our atmosphere trapping more heat, but the effect is not instant. Temperatures take some time to fully respond. All natural systems always head towards physical equilibrium but that takes time. The absolute climate sensitivity value is therefore termed 'equilibrium climate sensitivity' to emphasise this.

Climate sensitivity has always been expressed as a range. The latest estimate, according to AR6, has a 'very likely' range of 2-5oC. Narrowing it down even further is difficult for a number of reasons. Let's look at some of them.

To understand the future, we need to look at what has already happened on Earth. For that, we have the observational data going back to just before Arrhenius' time and we also have the geological record, something we understand in ever more detail.

For the future, we also need to take feedbacks into account. Feedbacks are the responses of other parts of the climate system to rising temperatures. For example, as the world warms up. more water vapour enters the atmosphere due to enhanced evaporation. Since water vapour is a potent greenhouse gas, that pushes the system further in the warming direction. We know that happens, not only from basic physics but because we can see it happening. Some other feedbacks happen at a slower pace, such as CO2 and methane release as permafrost melts. We know that's happening, but we've yet to get a full handle on it.

Other factors serve to speed up or slow down the rate of warming from year to year. The El Nino-La Nina Southern Oscillation, an irregular cycle that raises or lowers global temperatures, is one well-known example. Significant volcanic activity occurs on an irregular basis but can sometimes have major impacts. A very large explosive eruption can load the atmosphere with aerosols such as tiny droplets of sulphuric acid and these have a cooling effect, albeit only for a few years.

These examples alone show why climate change is always discussed in multi-decadal terms. When you stand back from all that noise and look at the bigger picture, the trend-line is relentlessly heading upwards. Since 1880, global temperatures have already gone up by more than 1oC - almost 2oF, thus making a mockery of the 2010 Monckton quote in the orange box above.

That amount of temperature rise in just over a century suggests that the climate is highly sensitive to human CO2 emissions. So far, we have increased the atmospheric concentration of CO2 by 50%, from 280 to 420 ppm, since 1880. Furthermore, since 1981, temperature has risen by around 0.18oC per decade. So we're bearing down on the IPCC 'very likely' range of 2-5oC with a vengeance.

Please use this form to provide feedback about this new "At a glance" section. Read a more technical version below or dig deeper via the tabs above!


Further details

Climate sensitivity is the estimate of how much the earth's climate will warm in response to the increased greenhouse effect if we manage, against all the good advice, to double the amount of carbon dioxide in the atmosphere. This includes feedbacks that can either amplify or dampen the warming. If climate sensitivity is low, as some climate 'skeptics' claim (without evidence), then the planet will warm slowly and we will have more time to react and adapt. If sensitivity is high, then we could be in for a very bad time indeed. Feeling lucky? Let's explore.

Sensitivity is expressed as the range of temperature increases that we can expect to find ourselves within, once the system has come to equilibrium with that CO2 doubling: it is therefore often referred to as Equilibrium Climate Sensitivity, hereafter referred to as ECS.

There are two ways of working out the value of climate sensitivity, used in combination. One involves modelling, the other calculates the figure directly from physical evidence, by looking at climate changes in the distant past, as recorded for example in ice-cores, in marine sediments and numerous other data-sources.

The first modern estimates of climate sensitivity came from climate models. In the 1979 Charney report, available here, two models from Suki Manabe and Jim Hansen estimated a sensitivity range between 1.5 to 4.5°C. Not bad, as we will see. Since then further attempts at modelling this value have arrived at broadly similar figures, although the maximum values in some cases have been high outliers compared to modern estimates. For example Knutti et al. 2006 entered different sensitivities into their models and then compared the models with observed seasonal responses to get a climate sensitivity range of 1.5 to 6.5°C - with 3 to 3.5°C most likely.

Studies that calculate climate sensitivity directly from empirical observations, independent of models, began a little more recently. Lorius et al. 1990 examined Vostok ice core data and calculated a range of 3 to 4°C. Hansen et al. 1993 looked at the last 20,000 years when the last ice age ended and empirically calculated a climate sensitivity of 3 ± 1°C. Other studies have resulted in similar values although given the amount of recent warming, some of their lower bounds are probably too low. More recent studies have generated values that are more broadly consistent with modelling and indicative of a high level of understanding of the processes involved.

More recently, and based on multiple lines of evidence, according to the IPCC Sixth Assessment Report (2021), the "best estimate of ECS is 3°C, the likely range is 2.5°C to 4°C, and the very likely range is 2°C to 5°C. It is virtually certain that ECS is larger than 1.5°C". This is unsurprising since just a 50% rise in CO2 concentrations since 1880, mostly in the past few decades, has already produced over 1°C of warming. Substantial advances have been made since the Fifth Assessment Report in quantifying ECS, "based on feedback process understanding, the instrumental record, paleoclimates and emergent constraints". Although all the lines of evidence rule out ECS values below 1.5°C, it is not yet possible to rule out ECS values above 5°C. Therefore, in the strictly-defined IPCC terminology, the 5°C upper end of the very likely range is assessed to have medium confidence and the other bounds have high confidence.

 IPCC AR6 assessments that equilibrium climate sensitivity (ECS) is likely in the range 2.5°C to 4.0°C.

Fig. 1: Left: schematic likelihood distribution consistent with the IPCC AR6 assessments that equilibrium climate sensitivity (ECS) is likely in the range 2.5°C to 4.0°C, and very likely between 2.0°C and 5.0°C. ECS values outside the assessed very likely range are designated low-likelihood outcomes in this example (light grey). Middle and right-hand columns: additional risks due to climate change for 2020 to 2090. Source: IPCC AR6 WGI Chapter 6 Figure 1-16.

It’s all a matter of degree

All the models and evidence confirm a minimum warming close to 2°C for a doubling of atmospheric CO2 with a most likely value of 3°C and the potential to warm 4°C or even more. These are not small rises: they would signal many damaging and highly disruptive changes to the environment (fig. 1). In this light, the arguments against reducing greenhouse gas emissions because of "low" climate sensitivity are a form of gambling. A minority claim the climate is less sensitive than we think, the implication being that as a consequence, we don’t need to do anything much about it. Others suggest that because we can't tell for sure, we should wait and see. Both such stances are nothing short of stupid. Inaction or complacency in the face of the evidence outlined above severely heightens risk. It is gambling with the entire future ecology of the planet and the welfare of everyone on it, on the rapidly diminishing off-chance of being right.

Last updated on 12 November 2023 by John Mason. View Archives

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Further reading

Tamino posts a useful article Uncertain Sensitivity that looks at how positive feedbacks are calculated, explaining why the probability distribution of climate sensitivity has such a long tail.

There have been a number of critiques of Schwartz' paper:

Denial101x videos

Here is a related lecture-video from Denial101x - Making Sense of Climate Science Denial

Additional video from the MOOC

Expert interview with Steve Sherwood

Comments

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Comments 51 to 75 out of 201:

  1. Dana, over at Climate Progress you wrote:
    I should mention, the 'Climate sensitivity' is not specific to CO2′ section isn't quite correct because different forcings have different efficacies. I updated the advanced version of this rebuttal to clarify this point. Here's the link if you want to do the same: http://www.skepticalscience.com/climate-sensitivity-advanced.htm
    I was trying to respond to that, but too many links has put my post in the could-be-spam queue, so I thought I might post this here as well in the hope that some might find it helpful. Definition of Radiative Forcing:
    The definition of RF from the TAR and earlier IPCC assessment reports is retained. Ramaswamy et al. (2001) define it as 'the change in net (down minus up) irradiance (solar plus longwave; in W m^–2) at the tropopause after allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values'. 2.2 Concept of Radiative Forcing http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-2.html
    The idea here is that increased solar radiance or increases in CO2 concentration affect the balance of radiation entering/leaving the climate system -- and will result in a response at the "top of the atmosphere" or - tos - which is typically taken to be at the tropopause which separates the troposphere and the stratosphere. Feedbacks are in response to this change. Definition of Climate Sensitivity:
    The long-term change in surface air temperature following a doubling of carbon dioxide (referred to as the climate sensitivity) is generally used as a benchmark to compare models. Climate Change 1992 The Supplementary Report to the IPCC Scientific Assessment, pg. 16 http://www.ipcc.ch/ipccreports/far/IPCC_Suppl_Report_1992_wg_I/ipcc_far_wg_I_suppl_material_full_report.pdf
    The above definition of climate sensitivity is however for the Charney Climate Sensitivity that takes into account the fast feedbacks, e.g., water vapor, clouds, sea ice, etc., but omits the slow feedbacks associated with changes in vegitation, feedbacks due to the carbon cycle and ice sheets -- the latter of which are land-based. Definition of Efficacy:
    Efficacy (E) is defined as the ratio of the climate sensitivity parameter for a given forcing agent (λi) to the climate sensitivity parameter for CO2 changes, that is, Ei = λi / λCO2 (Joshi et al., 2003; Hansen and Nazarenko, 2004). Efficacy can then be used to define an effective RF (= Ei RFi) (Joshi et al., 2003; Hansen et al., 2005). For the effective RF, the climate sensitivity parameter is independent of the mechanism, so comparing this forcing is equivalent to comparing the equilibrium global mean surface temperature change. 2.8.5 Efficacy and Effective Radiative Forcing http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-8-5.html
    Why Efficacies of Different Forcings are Different:
    The efficacy primarily depends on the spatial structure of the forcings and the way they project onto the various different feedback mechanisms (Boer and Yu, 2003b). Therefore, different patterns of RF and any nonlinearities in the forcing response relationship affects the efficacy (Boer and Yu, 2003b; Joshi et al., 2003; Hansen et al., 2005; Stuber et al., 2005; Sokolov, 2006). Many of the studies presented in Figure 2.19 find that both the geographical and vertical distribution of the forcing can have the most significant effect on efficacy (in particular see Boer and Yu, 2003b; Joshi et al., 2003; Stuber et al., 2005; Sokolov, 2006)... 2.8.5.1 Generic Understanding http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-8-5-1.html
    For more on radiative forcing and related concepts please see: Chapter 2: Changes in Atmospheric Constituents and in Radiative Forcing http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2.html Note: calculations performed by climate models do not involve the concepts of forcing, climate sensitivity or efficacy. The calculations of climate models are themselves based up the physics. Analysis in terms of forcings, climate sensitivity and efficacy only come afterward -- as a means of conceptualizing the results for the ease of our understanding.
  2. Re: Timothy Chase (51) Thanks for taking the time to put together such a thorough comment. It's appreciated. The Yooper
  3. A common misconception that people have about Climate Sensitivity is that it is a fixed value over a wide range of climatic conditions. This leads to some quite bizarre 'analyses' in the denialosphere, attempting to show that CS couldn't be that high because that implies that CO2 contributes far too much of the 33 DegC of extra warmth attributed to the Greenhouse Effect. The fallacy they make is projecting the same CS value back through lower and lower CO2 levels and temperature regimes. Climate sensitivity is an idea used to encapsulate how the planet IN A PARTICULAR CONFIGURATION - temperature, distribution of land masses, ocean currents, air movements, ice cover, vegetation patterns etc - will respond to a change in radiative forcing from whatever source - GH Gases, Solar changes, Aerosols. So Climate sensitivity will certainly be different at different times. In fact sensitivity to a warming pressure would likely be different to the sensitivity to a cooling pressure in the same climate. So sensitivity to a warming pressure at the bottom of an ice age would be higher than at the top of the ice age; with ice down to lower latitudes, any retreat of that ice due to temp rise exposes a larger area of land and sea and thus has a bigger effect on albedo than the same distance of retreat when the ice is only at higher latitudes. However given the thickness of the ice sheets, the time lags in responding to the warming will be large as it takes time for the ice to melt away. Conversely sensitivity to a cooling pressure coming out of an inter-glacial is likely to be high since even modest cooling can quickly increase the area and duration of snow fall; 1 metre of snow has much the same albedo as ice sheets kilometers thick. The time lag responding to any such cooling is thus also likely to be quicker. In an Ice free world, CS to a warming pressure might be much lower since Ice based albedo change doesn't occur. Similarly in a world with very low CO2, a Snowball Earth, CS might also be low. If the world is literally covered in ice, modest warming may not be enough to cause any ice melt - going from -18 DegC to - 15 DegC for example may not cause any ice cover reduction. It would only be when enough warming pressure has occurred that ice cover retreat begins that change might be rapid. In effect, CS would change when the climatic conditions change enough. This is also important when considering the oft cited figure of 33 DegC of warming due to the GH effect. The calculation that arrives at this number is based on the Earths current Albedo; that around 30% of sunlight is reflected away and isn't part of the energy balance. However in a world that is -18 DegC ON AVERAGE, Ice Cover would be much greater, more even than an Ice AGe which still has a positive average temp. At minus 18 DegC, ice cover sufficient to cause 50% of sunlight to be reflected is quite conceivable. The calculation for this albedo gives 53 Deg extra warmth: -38 DegC
  4. ClimateWatcher (on another thread), you would be more credible if you gave the whole quote, thus : Progress since the TAR enables an assessment that climate sensitivity is likely to be in the range of 2 to 4.5°C with a best estimate of about 3°C, and is very unlikely to be less than 1.5°C. Values substantially higher than 4.5°C cannot be excluded, but agreement of models with observations is not as good for those values. Which is not based on "those climate scientist [who] happen to be part of the IPCC", but a vast body of work given here : Working Group I: The Physical Science Basis 8.6 Climate Sensitivity and Feedbacks Working Group I: The Physical Science Basis 9.6 Observational Constraints on Climate Sensitivity Working Group I: The Physical Science Basis 10.5 Quantifying the Range of Climate Change Projections
  5. There was a discussion of MEP (Maximum Entropy Production) principle and its possible bearings on climate sensitivity under The 2nd law of thermodynamics and the greenhouse effect. We were asked to move it to this thread. MEP theme was started here and after some lengthy exchanges there's a clarification attempt. If valid, it would mean equilibrium climate sensitivity, whenever "forcings" are small enough to warrant a linear approximation, is moderate (no positive feedbacks). There could still be large shifts in climate, either forced or unforced, but they would not fit into the standard climate sensitivity formalism and entirely different analytical techniques would be required to uncover them (e.g. topological analysis of the entropy production rate function over the phase space of climate states).
  6. Moderator - Starting from the "Advanced" version of this topic, then going to page 2 of comments, I see the "Basic" version appear as the topic header. Using the "Prev" link, I get the "Basic" version again. Is this the desired behavior? I would think that the advanced discussion should remain if starting there...
  7. Berényi - You argue that MEP would limit climate sensitivity and eliminate positive feedbacks. This is contradicted by real world measurements, model results, paleo-temperature records, etc., which are well demonstrated in Knutti and Hegerl (2008) - where any number of small linear forcings are used to estimate climate sensitivity, all ending up roughly in the 2–4.5 °C range. That means a range of non-negative positive feedback. The lower end of that range, still with a moderate amount of positive feedback, is quite solid. If MEP is a factor, it's always been a factor, and can be considered to be included in measured climate sensitivity. There is no data supporting your assertion of "no positive feedbacks", and in fact quite a lot of data showing that assertion to be incorrect. I would consider this 'low sensitivity' hypothesis clearly disproven, as contradicted by all the evidence.
  8. #57 KR at 01:44 AM on 28 October, 2010 If MEP is a factor, it's always been a factor, and can be considered to be included in measured climate sensitivity No, it is not that simple. Please try to understand what was said before you venture in. You would make me happy if just once you could abandon the holistic approach and concentrate on the problem at hand with an analytical mind. This kind of thinking, although requires some discipline, is surprisingly effective and is much more in line with our own cultural heritage.
    Response: BP, out of respect to KR and his reply to this I won't delete this, but please try to be less adversarial in the future. Disagree, certainly, but keep it cordial.
  9. Berényi - I did read what you wrote, ad hominem responses on your part not-withstanding. There is considerable evidence for positive feedback in climate sensitivity, and none for the "no positive feedbacks" claim you have made. In fact, the MEP is inappropriate when discussing the final destination in thermodynamics. "A system will select the path or assemblage of paths out of available paths that minimizes the potential or maximizes the entropy at the fastest rate given the constraints" (Swenson, R. 1989). This means that the MEP principle will "select the pathway or assembly of pathways that minimizes the potential or maximizes the entropy at the fastest rate given the constraints" (Swenson, R. and Turvey, M.T. 1991), emphasis added. The Second Law indicates that systems act to minimize potential/maximize entropy. It does not say by what path. MEP is an additional constraint on the 2nd law, not a replacement thereof. At most (if correct) it will affect the speed of climate convergence upon equilibrium when forcings change, not the final equilibrium. To quote Christopher Hitchens: "That which can be asserted without evidence, can be dismissed without evidence." MEP certainly qualifies in regards to climate sensitivity.
  10. To address some of what I might expect as a response to my last posting, I would like to note that if some mechanism (such as maximum entropy production, MEP) were operative in regards to thermodynamic equilibrium, it would certainly operate at all times. If it operated in the fashion described by Berényi, by increasing energy release to space and preventing temperature rises when GHG forcings would otherwise cause them to occur, it would operate at all times to maximize entropy, lowering the climate temperature as far as the system degrees of freedom allowed. TSI increases, for example, as seen in the early 20th century, would have no effect. Unfortunately for Berényi's formulation, it does. The 2nd law of thermodynamics sets the equilibrium (and yes, the steady-state) points, not an MEP effect, which is merely a constraint on how systems reach such states under the 2nd law. Climate sensitivity exhibits positive feedback. MEP cancellation of positive feedback is therefore prima facie incorrect; that emperor has no clothes.
  11. #59 KR at 04:42 AM on 28 October, 2010 At most (if correct) it will affect the speed of climate convergence upon equilibrium when forcings change, not the final equilibrium. Dear KR, what you say, does not make sense. Until you learn to differentiate between thermodynamic equilibrium (isolated system, no entropy production) and steady state with energy flowing through the system and entropy produced by it at a constant rate, unfortunately we can't move a single step further.
  12. Berényi Péter following your definition, the entropy production (EP) is determined by the temperature of the atmosphere at TOA (Ta), the temperature of the sun (Ts) and the earth albedo (α). Starting with the system in steady state, by suddenly increasing IR atmospheric absorption you're indeed lowering the EP via a reduction in Ta. Restoring steady state requires to increase Ta back to its original value and/or lowering the "incoming part" of EP through α. The latter alone would lead to a positive feedback which decreases Ta further. This is as far as we can get with this simple use of the MEP principle. We see the possibility of a negative feeback, which we already knew, and cannot rule out other positive feedbacks. Definitely more work need to be done in this field to obtain usefull insights from the use of the MEP principle in climate science. As of now, scientists are just looking at its range of validity mainly studying steady state situations, which presumably won't give new "practical" informations. Quoting Kooiti Masuda, "So MEP does not seem to me helpful as a piece of policy-relevant science of climate at present.".
  13. Maybe we discuss different things by the same term MEP (Maximum Entropy Production). I am not familiar with Swenson's theory, but as I browse abstracts shown at links by KR (#59), they seem to say too far-fetched things to be demonstrated by physical science (though they may be interesting philosophical thoughts). I do not think it helpful to discuss matters of physical science following Swenson's reasoning. What I remember by the key word "maximum entropy production" is something like the Wikipedia articles Non-equilibrium thermodynamics and Extremal principles in non-equilibrium thermodynamics mention by the key word. (Wikipedia may be rewritten. I mean the contents as of today.) I do not fully understand these theories, but I understand themes which some of these authors wanted to discuss.
  14. Berényi - Further reading into non-equilibrium thermodynamics is proving interesting; in particular the internal fluctuations of such a system. You are correct, the climate is a non-equilibrium system, due to the energy flows. So: You hypothesize that maximal entropy production will prevent positive feedback to greenhouse gases, minimizing climate sensitivity. First objection to your hypothesis: I would hold that the climate has stable stationary states, where there is a local max of entropy. Given the internal fluctuations (including seasons, PDO, ice ages) over the history of the climate, I would find it difficult to believe that the climate could find nearby local entropy maxima to switch to based on small linear forcings; surely the climate would have long since hit those maxima based simply on climate variability. not impossible, but highly unlikely. There may indeed be critical points (ice age initiations, major clathrate/permafrost upheavals); those are points of concern, but certainly not involved in response to small linear forcing changes. Second objection: Climate sensitivity has been measured, and shown to have positive feedback. Your claim that the MEP effect would cause "no positive feedback" (your words) is thereby falsified. Until you recognize this (and you've spent quite some time ignoring this issue raised repeatedly both by me and also by 'e'), the conversation will go nowhere, and I will continue to consider this a lengthy thought experiment unrelated to the real world.
  15. Berényi Péter makes many interesting remarks, but I am afraid his arguments are incoherent in the sense Stephan Lewandowsky wrote here in the areticle The value of coherence in science. I admit that my own arguments are sometimes incoherent, but I then also admit that I am not confident about what I say. I read his comments on the blog article here The 2nd law of thermodynamics and the greenhouse effect. Though it may be different from his own summary, I think he effectively say that the way how to apply thermodynamics to the actual climate of the earth is not very sure on one hand, and that he can say something certain about the climate of the earth by applying the maximum entropy production (MEP) principle, that is an advanced part of thermodynamics, on the other hand. Also, in his recent comment in thread on the 2nd law, he suggested that the average temperature at the surface (the surface between air and sea or between air and land) may not be a good measure for thermodynamic discussion of the climate system. On the other hand, the concept called "climate sensitivity" conventionally by climate scientists is defined in terms of the average surface temperature. It may be coherent from his position to say that the "climate sensitivity" is not a well defined quantity and we cannot say anything certain about it. I do not think he can be sure that the value must be low.
  16. Well, I have looked into the issue a bit deeper and have found that my point 1. in #85 under The 2nd law of thermodynamics and the greenhouse effect is actually not a valid claim. It says "If IR optical depth of the atmosphere is increased by a small amount by adding to it some well mixed greenhouse gas while everything else is held constant, entropy production rate would decrease". In fact it is only true if optical depth is high enough, that is, in a high IR opacity approximation. For optically thin atmospheres the opposite is true. In other words there is a limit value of IR optical depth for which entropy production rate is at its maximum. I still think IR optical depth of the real atmosphere has to be close to this value (due to MEP), but it would need some deeper analysis and actual data to determine if it is below or above this threshold at the moment. Under these circumstances the original argument may not work without restrictions, however, the very existence of an "optimal" IR optical depth suggests a negative water vapor feedback (on overall IR opacity).
  17. #57 Albatross at 08:23 AM on 30 December, 2010 under Did global warming stop in 1998, 1995, 2002, 2007, 2010? I see that you are failing to differentiate between Charney feedbacks (transient climate response, Gregory and Forster 2005) and equilibrium climate sensitivity. Annan and Hargreaves, and others, show the PDF for EQS dropping off sharply below about 2.5 C. (On moderator's advice discussion started there is continued here) Well, let's suppose there is a first order low pass filter between "forcing" and "climate response" (lower troposphere temperature anomaly). If we apply a small step-like forcing ΔF to a climate system in equilibrium and the long term temperature anomaly response is ΔT = βΔF, than β is said to be the equilibrium sensitivity, right? The impulse response function of the filter in this case is (β/τ)e-t/τ for t > 0, zero otherwise, where t is the time variable and τ is a time constant characteristic to the relaxation time of the system. The response to a step-function is of course β(1-e-t/τ). Now, let's suppose the forcing is increasing linearly with time (instead of kicking in in a step-like fashion). With CO2 more or less this is the case, that is, ΔF = ft, where f ~ 0.006 year-1, if unit of forcing is CO2 doubling. The relation seems to hold pretty well at least during the last 70 years. The response of the low pass filter above to such a forcing is βf(t-τ). That is, the time constant τ has no effect other than introducing a delay in this case - or an additive constant, if we look at it the other way around. It has no influence on the trend whatsoever. Provided of course τ is not larger than several decades, that is, the pre-industrial flat part of the CO2 forcing curve has negligible effect beyond the start of satellite era (late 1978). Therefore my calculation is correct, the climate sensitivity is considerably less than 2°C (per CO2 doubling), for the reasons I've stated in the other thread. BTW, I think it is even lower, because satellite lower troposphere temperature anomalies are not reliable either. Back-calculation of temperature from narrow band radiances depends heavily on the atmospheric model used, especially on fine details of water vapor distribution, which is neither measured nor modeled properly. On top of that all climate variables behave like pink noise even in the unforced case, that is, they have large spontaneous fluctuations on all scales (this is characteristic of systems in a state of self-organized criticality).
  18. Berényi - "satellite lower troposphere temperature anomalies are not reliable either": Please keep in mind that this cuts both ways - if the records are not as reliable as we would like (which you have really not established, mind you), any errors could go in either direction, so claiming temperature measurements are bad (which should be discussed here, really) does not establish that warming isn't happening.
  19. Berényi - "Provided of course τ is not larger than several decades" - many of them (the feedbacks) have time constants longer than this. I listed a few (certainly not an exhaustive list) in this post. I'm not a specialist in this field - I'm certain that other feedbacks with fairly long time constants could be added.
  20. @BP: "That is, the time constant τ has no effect other than introducing a delay in this case - or an additive constant, if we look at it the other way around. It has no influence on the trend whatsoever." That's nonsense: a delay will in effect raise the temperature of the system, as the sun continues to send energy. Like RW1 and co2isnotevil in another thread, you seem to forget this is a dynamic system, and that power input is constant.
  21. #67: "Therefore my calculation is correct," Since no new information other than a transfer function was involved, what exactly did you calculate? And given that you started with "Well, let's suppose there is ... ", even that is cast in some doubt by your own presentation. A sensitivity calculation that does not match the observed changes in temperature isn't worth much. But you'll likely deny those observations as well. So the only logical result of this latest exposition is that there's some grand unknown force operating beyond our ability to influence or even measure. A fine science, that, as it is ultimately not falsifiable. But the truth is out there ... .
  22. #70 archiesteel at 14:03 PM on 30 December, 2010 That's nonsense: a delay will in effect raise the temperature of the system, as the sun continues to send energy. Listen, you either know how a linear time-invariant filter works or not. In the latter case you'd better have a look at convolution integrals. If g(t) = ft and h(t) = (β/τ)e-t/τ, then g*h(t) = βf(t-τ). It is a fact, no amount of babbling about the sun would change that. It is also equal to βft-βfτ. If climate sensitivity is positive (β > 0) and there is an increasing forcing (f > 0), the additive constant -βfτ is surely negative. Therefore the delay would not increase the temperature, but it would decrease it, while the trend itself (temporal derivative of temperature, βf) is clearly independent of said delay. So much about nonsense. (You could also work on your physics. There is a difference between temperature and heat.)
  23. Berényi Péter wrote : "So much about nonsense." At last : something you have written which all can agree with ! I just wish you would heed your own words... PS Have you read the Advanced Version of this topic ? It may help.
  24. @BP: I'm sorry, BP, but you're just throwing numbers around and hiding behind formulas. If you really understood the science, you'd be able to explain it simply. You might also try to explain why your (purposefully confusing) argument does not agree with actual observations. If you want to go and play the savant, why don't you write an actual scientific article and have it peer-reviewed. After all, since you're apparently able to disprove AGW theory is an important scientific discovery. The fact you haven't is a good indication you don't really believe your theory is exact, but are in fact only trying to further obfuscate the debate.
  25. UCAR strikes again: New study sure to stir up the sensitivity discussion: The study also indicates that the planet’s climate system, over long periods of times, may be at least twice as sensitive to carbon dioxide than currently projected by computer models, which have generally focused on shorter-term warming trends. This is largely because even sophisticated computer models have not yet been able to incorporate critical processes, such as the loss of ice sheets, that take place over centuries or millennia and amplify the initial warming effects of carbon dioxide. --emphasis added

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