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Working out climate sensitivity from satellite measurements

What the science says...

Lindzen's analysis has several flaws, such as only looking at data in the tropics. A number of independent studies using near-global satellite data find positive feedback and high climate sensitivity.

Climate Myth...

Lindzen and Choi find low climate sensitivity

Climate feedbacks are estimated from fluctuations in the outgoing radiation budget from the latest version of Earth Radiation Budget Experiment (ERBE) nonscanner data. It appears, for the entire tropics, the observed outgoing radiation fluxes increase with the increase in sea surface temperatures (SSTs). The observed behavior of radiation fluxes implies negative feedback processes associated with relatively low climate sensitivity. This is the opposite of the behavior of 11 atmospheric models forced by the same SSTs. (Lindzen & Choi 2009)

Climate sensitivity is a measure of how much our climate responds to an energy imbalance. The most common definition is the change in global temperature if the amount of atmospheric CO2 was doubled. If there were no feedbacks, climate sensitivity would be around 1°C. But we know there are a number of feedbacks, both positive and negative. So how do we determine the net feedback? An empirical solution is to observe how our climate responds to temperature change. We have satellite measurements of the radiation budget and surface measurements of temperature. Putting the two together should give us an indication of net feedback.

One paper that attempts to do this is On the determination of climate feedbacks from ERBE data (Lindzen & Choi 2009). It looks at sea surface temperature in the tropics (20° South to 20° North) from 1986 to 2000. Specifically, it looked at periods where the change in temperature was greater than 0.2°C, marked by red and blue colors (Figure 1).

Figure 1: Monthly sea surface temperature for 20° South to 20° North. Periods of temperature change greater than 0.2°C marked by red and blue (Lindzen & Choi 2009).

Lindzen et al also analysed satellite measurements of outgoing radiation over these periods. As short-term tropical sea surface temperatures are largely driven by the El Nino Southern Oscillation, the change in outward radiation offers an insight into how climate responds to changing temperature. Their analysis found that when it gets warmer, there was more outgoing radiation escaping to space. They concluded that net feedback is negative and our planet has a low climate sensitivity of about 0.5°C.

Debunked by Trenberth

However, a response to this paper, Relationships between tropical sea surface temperature and top-of-atmosphere radiation (Trenberth et al 2010) revealed a number of flaws in Lindzen's analysis. It turns out the low climate sensitivity result is heavily dependent on the choice of start and end points in the periods they analyse. Small changes in their choice of dates entirely change the result. Essentially, one could tweak the start and end points to obtain any feedback one wishes.

Figure 2: Warming (red) and cooling (blue) intervals of tropical SST (20°N – 20°S) used by Lindzen & Choi (2009) (solid circles) and an alternative selection proposed derived from an objective approach (open circles) (Trenberth et al 2010).

Debunked by Murphy

Another major flaw in Lindzen's analysis is that they attempt to calculate global climate sensitivity from tropical data. The tropics are not a closed system - a great deal of energy is exchanged between the tropics and subtropics. To properly calculate global climate sensitivity, global observations are required.

This is confirmed by another paper published in early May (Murphy 2010). This paper finds that small changes in the heat transport between the tropics and subtropics can swamp the tropical signal. They conclude that climate sensitivity must be calculated from global data.

Debunked by Chung

In addition, another paper reproduced the analysis from Lindzen & Choi (2009) and compared it to results using near-global data (Chung et al 2010). The near-global data find net positive feedback and the authors conclude that the tropical ocean is not an adequate region for determining global climate sensitivity.

Debunked by Dessler

Dessler (2011) found a number of errors in Lindzen and Choi (2009) (slightly revised as Lindzen & Choi (2011)).  First, Lindzen and Choi's mathematical formula  to calculate the Earth's energy budget may violate the laws of thermodynamics - allowing for the impossible situation where ocean warming is able to cause ocean warming.  Secondly, Dessler finds that the heating of the climate system through ocean heat transport is approximately 20 times larger than the change in top of the atmosphere (TOA) energy flux due to cloud cover changes.  Lindzen and Choi assumed the ratio was close to 2 - an order of magnitude too small.

Thirdly, Lindzen and Choi plot a time regression of change in TOA energy flux due to cloud cover changes vs. sea surface temperature changes.  They find larger negative slopes in their regression when cloud changes happen before surface temperature changes, vs. positive slopes when temperature changes happen first, and thus conclude that clouds must be causing global warming.

However, Dessler also plots climate model results and finds that they also simulate negative time regression slopes when cloud changes lead temperature changes.  Crucially, sea surface temperatures are specified by the models.  This means that in these models, clouds respond to sea surface temperature changes, but not vice-versa.  This suggests that the lagged result first found by Lindzen and Choi is actually a result of variations in atmospheric circulation driven by changes in sea surface temperature, and contrary to Lindzen's claims, is not evidence that clouds are causing climate change, because in the models which successfully replicate the cloud-temperature lag, temperatures cannot be driven by cloud changes.

2011 Repeat

Lindzen and Choi tried to address some of the criticisms of their 2009 paper in a new version which they submitted in 2011 (LC11), after Lindzen himself went as far as to admit that their 2009 paper contained "some stupid mistakes...It was just embarrassing."  However, LC11 did not address most of the main comments and contradictory results from their 2009 paper.

Lindzen and Choi first submitted LC11 to the Proceedings of the National Academy of Sciences (PNAS) after adding some data from the Clouds and the Earth’s Radiant Energy System (CERES).

PNAS editors sent LC11 out to four reviewers, who provided comments available here.  Two of the reviewers were selected by Lindzen, and two others by the PNAS Board.  All four reviewers were unanimous that while the subject matter of the paper was of sufficient general interest to warrant publication in PNAS, the paper was not of suitable quality, and its conclusions were not justified.  Only one of the four reviewers felt that the procedures in the paper were adequately described. 

As PNAS Reviewer 1 commented,

"The paper is based on...basic untested and fundamentally flawed assumptions about global climate sensitivity"

These remaining flaws in LC11 included:

  • Assuming that that correlations observed in the tropics reflect global climate feedbacks.
  • Focusing on short-term local tropical changes which might not be representative of equilibrium climate sensitivity, because for example the albedo feedback from melting ice at the poles is obviously not reflected in the tropics.
  • Inadequately explaining methodology in the paper in sufficient detail to reproduce their analysis and results.
  • Failing to explain the many contradictory results using the same or similar data (Trenberth, Chung, Murphy, and Dessler).
  • Treating clouds as an internal initiator of climate change, as opposed to treating cloud changes solely as a climate feedback (as most climate scientists do) without any real justification for doing so. 

As a result of these fundamental problems, PNAS rejected the paper, which Lindzen and Choi subsequently got published in a rather obscure Korean journal, the Asia-Pacific Journal of Atmospheric Science. 

Wholly Debunked

A full understanding of climate requires we take into account the full body of evidence. In the case of climate sensitivity and satellite data, it requires a global dataset, not just the tropics. Stepping back to take a broader view, a single paper must also be seen in the context of the full body of peer-reviewed research. A multitude of papers looking at different periods in Earth's history independently and empirically converge on a consistent answer - climate sensitivity is around 3°C implying net positive feedback.

Last updated on 6 July 2012 by dana1981. View Archives

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Further viewing

Andrew Dessler explains in relatively simple and short terms the results from his 2011 paper:


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Comments 401 to 425 out of 447:

  1. Moderator - Typo in my previous post, "appears to be list" should be "appears to be a list". Sorry for the bad grammar.
  2. Eric, I'm not backtracking - I'm clarifying. The 396 W/m^2 power flux at the surface already has factored into it the thermals and latent heat transfer. Without these two processes moving heat away from the surface into the atmosphere, the surface power would be about 493 W/m^2 for a temperature of about 305K. This is what the diagram is depicting.
  3. KR, re 393 I suggest that you do some 3-d atmospheric simulations yourself. Start with nominal H20/O3/CH4 and simulate at 280 ppm and 560 ppm of CO2 and see the difference. The incremental absorption is about 3.7 W/m^2 and not 7.4 W/m^2. In a very limited sense the 3.7 W/m^2 represents a reduction in power leaving the top of the troposphere, but it fails to account for the delayed release of the incrementally absorbed power back into space. As I pointed out before, even if the atmosphere absorbed 100%, 50% would still leave the planet. I challenge to you to come up with a terrestrial counter example of this. I already explained why Venus is different. re 396 Do you agree that a thermal is half of a vertical circulation current whose purpose is to redistribute energy within the atmosphere? Do you agree that evaporation/weather is another circulation current operating across both vertical and horizontal directions? If these are important to the radiative balance, then why are oceanic and atmospheric circulation currents not included as well. These serve the same purpose as moving energy around the thermal mass. The fact is that the only effect non radiative energy transfer has on the energy balance is establishing the conditions for clouds to block as much as 1/2 of the surface radiation from leaving the planet. The proportion of clouds then sets the ratio of warm surface emissions and cold cloud emissions such that the radiative balance is maintained. The physical feedback system is controlling the planets energy balance. The hypothetical feedback system proposed by the IPCC controls the surface temperature. This is the source of the disconnect because the boundary conditions and output of the hypothetical feedback system are predetermined by the physical feedback system. The hypothetical system can be forced to look correct at a specific operating point, but is useless for how the system responds to change.
  4. Mr White (co2isnotevil), in your div2 paper you state: "A further constraint of Conservation Of Energy is that the global net non radiative flux between the atmosphere and the surface must be zero in the steady state if the radiative flux is also zero. While radiative flux to and from the surface can be traded off against non radiative flux, it makes no difference to the overall radiative balance." Your prior diagram shows a radiative energy balance that excludes the latent heat and conductive (thermal driven) transfers from the surface to the atmosphere. (it is also missing the solar short wave absorption by the atmosphere). In your statement above you are declaring that the non radiative flux is zero. Can you quantify an atmosphere to surface transfer that is non radiative that balances the latent heat and conductive transfers? Can you also explain how you arrive at A=292 as a fraction of the 385 radiative flux from the surface? Thank you.
  5. Eric, The A does not include thermals and latent heat, again, thermals and latent heat only serve to move power around the Earth's thermal mass and do not participate directly in the radiative balance. To the extent that the thermal power emitted by clouds comes from evaporated water, there is a second order connection, but relative to the radiative balance, only radiation matters. In the big picture of the thermodynamic balance of the planet, clouds selectively block surface power such that the power leaving the planet is equal to the power arriving. Relative to the Trentbert picture, thermals and latent heat are returned in his mythical 'back radiation'. This is very misleading as most of the power returned to the surface is kinetic and not radiative. Only photons matter at the boundary between the Earth and space. Why is this so hard to understand?
    Response: [muoncounter] This thread is about climate sensitivity as derived in the Lindzen and Choi paper. Further discussion of the specifics of a third party website do not belong here. Please take your continuing conversation regarding how this or that particular are derived elsewhere.
  6. To stay on topic, lets address the first paragraph of my first post at #297. Read that and then answer the following questions. Why don't you complain about homogenization techniques applied to a small data set with high uncertainty which predicts a high sensitivity, yet do complain when more deterministic homogenization techniques are applied to a much larger data set with less uncertainty and which predicts a low sensitivity? Are you objecting to the uncertainty in the analysis or are you objecting to the conclusion?
  7. co2isnotevil - I believe that your objections are met in the topic itself. Lindzen and Choi's sensitivity result has a high dependence on their (arbitrary looking) start/end dates. The tropical region is not (as they seem to have treated it) a closed system, see comments in the header regarding Murphy 2010, where even small changes in tropical/polar heat exchange swamp L&C's results, that global data gives quite different results (Chung 2010), plus the multiple studies from both models and empirical data that contradict L&C's low sensitivity. That "more deterministic homogenization" won't help matters if it's incompleteness introduces errors, which it appears to do.
  8. BTW, Does anyone have a link to the updated Lindzen and Choi 2010 paper? I believe the original was criticized for cherry picking data points, but when they re-did in 2010 using "all points" the result was the same.
  9. co2isnotevil, This post also referenced Chung et al. 2010, which used a more global dataset and found that the results were not consistent with Lindzen. In general, the validity of the temperature records is addressed here.
  10. Why is the Lindzen and Choi resulting sensitivity consistent with how each 1 W/m^2 of power from the Sun is treated at the surface, but the IPCC models that predict a 3 C sensitivity are not?
  11. The Chung et all paper is not freely available, but based on the abstract, it makes a very weak case by trying to connect the radiative dampening rate with positive feedback. The issue with the temperature measurements is homogenization (Hansen Lebedeff 1987) which incorrectly justifies the use of a very small sample set to discern trends, which tends to encourage cherry picking. My point is that none of the surface temperature reconstructions which predict large sensitivities or large warming cover more than about 1% of the planet and interpolate everything else. If you want to complain about the 30% coverage of L&C, you better start complaining about all reconstructions that do not start with 100% coverage.
  12. RW1 at 10:26 AM on 28 December, 2010 ”Why is the Lindzen and Choi resulting sensitivity consistent with how each 1 W/m^2 of power from the Sun is treated at the surface, but the IPCC models that predict a 3 C sensitivity are not?” The answer is that Lindzen and Choi chose to make an erroneous analysis that gave them a result that they wittingly, or unwittingly, were aiming for. There are virtually an infinite number of ways of obtaining a false result in science RW1. Lindzen and Choi’s analysis is simply wrong as has been well established by several groups of atmospheric physicists (and see account in the introductory description of this thread): Chung ES, Yeomans D, Soden BJ (2010) An assessment of climate feedback processes using satellite observations of clear-sky OLR Geophys. Res. Lett. 37, art # L02702 abstract Murphy DM (2010) Constraining climate sensitivity with linear fits to outgoing radiation Geophys. Res. Lett. 37, art # L09704 abstract Trenberth KE, Fasullo JT, O'Dell C, et al. (2010) Relationships between tropical sea surface temperature and top-of-atmosphere radiation Geophys. Res. Lett. 37, art # L03702 abstract Chung ES, Soden BJ, Sohn BJ (2010) Revisiting the determination of climate sensitivity from relationships between surface temperature and radiative fluxes Geophys. Res. Lett. 37, art # L10703 abstract So you're really asking the wrong questions RW1. You should be pondering: (i) Why do people chose to believe analyses that are clearly and objectively flawed? (ii) How can one seriously maintain allegiance to an analysis of Earth climate sensitivity that is woefully inconsistent with straightforward empirical evidence? Remember that Lindzen’s, and the flawed analysis of the website from which you have sourced your analysis, come up with a climate sensitivity (~0.6 oC of Earth surface warming for a radiative forcing equivalent to a doubling of atmospheric [CO2]?) that is simply at odds with a vast body of empirical analysis, as explained here, and here, and here and here. (iii) How can one possibly obtain a realistic estimate of the Earth climate sensitivity (the Earth surface temperature response at equilibrium resulting from a radiative forcing equivalent to a doubling of atmospheric [CO2]), from transient temperature responses to transient variations in forcing (seasonal variations in forcing resulting from the earth’s rapid passage around the sun)? (iv) why would one raise a false argument that "the IPCC models that predict a 3 C sensitivity are not" consistent with empirical observations, when the models (they're not "IPCC models, RW1, but the models of a large body of physicists) are clearly entirely consistent with empirical observations (e.g. 20th century warming) as indicated in the links in (i) above)?
  13. co2isnotevil at 11:12 AM on 28 December, 2010 There is an inherent illogic in your attempt to equate: (i) the very specific flaw (of Lindzen and Choi) of attempting to treat the tropics as a closed system for attempting to assess readiative flux responses to changes in surface temperature (when the flows of energy to higher latitudes dominate outgoing (space-directed) energy flows by factors of 10-fold)... and: (ii) the fact that Earth temperature measures are sampled at discrete points on the surface. A physicist should really be able to spot the logical flaw! In selecting to analyze data covering only the tropics (20o N to 20o S) Lindzen and Choi omit not only the massive bulk of the Earth's surface, but the regions of the Earth to which massive flows of solar energy insolating the tropics flow to higher latitudes in the shape of air and sea currents. Note that you are ignoring the particularly dismal flaw of Lindzen and Choi which is the cherry-picking of periods of temperature change (see top article above). As a scientist you really should be appalled at the level of false analysis. On the other hand the Earth temperature measurements sample virtually the entire world (with only the Arctic and Antarctic poorly sampled) and there is a huge body of evidence that: (i) the Earth surface temperature measurement is robust to at least 5 independent analyses (by teams in the US, UK, Japan and Europe), (ii) the Earth surface temperature is robust to large reduction of temperature stations (e.g. the US temperature data is hardly changed when selecting a small subselection of what a climate contarian group have asserted are the "good" set of stations by their own criteria). In other words the Earth surface temperature is over-determined and the reason for this is quite well established (it relates to the well-characterized observation of the spatial correlation of surface temperature anomalies over distances of several hundreds of kilometres). etc.
  14. chris, Would you consider a pot of water at thermal equilibrium on the stove with the burner underneath at a fixed setting as being analogous to the oceans of the Earth (the water in the pot) and the current amount of average radiative forcing acting on them (the burner underneath)?
  15. It's unfortunate that a moderator has deleted the last two comments (co2isnotevil's and mine) since these get right to the crux of the issue. It's directly relevant to the Lindzen and Choi analysis and to all attempts to establish equilibrium Earth response climate sensitivity by analysis of transient responses to forcings. I'll post the relevant bit of my deleted post. If the moderator considers this non-relevant (discussion of climate response times to forcing) then something's badly amiss!
    co2isnotevil: "The Earth responds far more quickly to changes in forcing than you think."
    Yes, it responds immediately to changes in forcing. However in establishing the climate sensitivity we are interested in the response when the system has come to equilibrium with the forcing. This is a fundamental error that your website and RW1 are simply not addressing.
    co2isnotevil: "The climate system's time constant is on the order of 2 months"
    That's horribly incorrect. Even the most generous models of Earth climate response to forcing arrive at a time constant [time for the response to achieve (1-1/e)-fold magnitude of its equilibrium response] of around 7.5 years (see discussion here here, for example). Of course there are several time constants of relevance (the atmosphere responds faster than the land surface which responds faster than the ocean surface...the response of the deep oceans is very slow indeed). It's very easy to see that this must be the case, and must be considered for determination of the climate sensitivity. The sea and mountain ice response to warming is a significant part of the climate sensitivity. As sea and land melts in a warming world the Earth albedo reduces. It's not possible to maintain the ludicrous notion that this response comes to equilibrium with a time constant of 2 months! Try 20 or 30 years (and maybe 100-1000 years for polar ice....
  16. Chris, No. L&C do not treat the tropics as a closed system. They treat it as part of a closed system whose specific behavior is linked to the behavior of the whole. Besides, the specific complaint was that the coverage was only between -20 and 20 degrees latitude and not that they were treating that region as a closed system. Have you even looked at full coverage surface temperature reconstructions? Consider the ISCCP reconstruction which is exactly as you claim. Here is the monthly global temperature plot. You might notice the spike around 10/01 which was caused when the transition from NOAA-14 to NOAA-16 didn't fit within the ability of Rossow's code to properly adapt and the baseline shifted. I pointed this out more than 3 years ago and while Rossow acknowledged the error privately, it has yet to appear in the formal errata and this is a bigger error than anything else reported. Here is the same reconstruction with 5 year averaging applied. In both plots, the red is the monthly temperature and the black dotted line is the running 12 month average of the red line. Notice how when 5 year averaging is applied a 1 month data anomaly suddenly appears as a multi year temperature trend? This shows the same data where the baseline has been corrected and this shows corrected data with 5 year averaging. Hmm. It seems that Hansen's data is showing a cooling trend? How odd ,,, I also suggest you review a little about control theory, time constants and how they operate. If the planet was as sluggish as you claim, then how do you explain the global temperature changing by over 3C during a 12 month period? A time constant of 7.5 years says that it takes 7.5 years for 37% of the equilibrium change to occur. Do you not believe that the Sun forces the climate? How can you even explain seasonal change? The ebb and flow of glacial ice works on a somewhat larger scale, but if you're seriously trying to claim that the intrinsic 0.5C or so from doubling CO2 will melt enough ice to affect a 3C global temperature rise, you better go back and run your numbers again. Even your inflated 1.1C intrinsic effect is not enough. We are pretty close to minimum ice, as we are during every interglacial epoch, and as such, there is not enough ice to melt and cause your hypothetical 3C rise. Ice related feedback is a clamped effect and you can't equate the effects of ice melting as we are leaving maximum ice with those with ice melting when we are already at minimum ice.
  17. I agree with Chris that deleting those comments is counter productive to the thread. The response time of the climate system is intimately related to the sensitivity. High sensitivities are claimed only when then can also claim that the affect is deferred decades into the future because we can't discern from the data what current CO2 concentrations are supposed to have done. For example, there is no monotonic trend corresponding to the CO2 trend in the temperature data.
  18. co2isnotevil at 12:37 PM on 28 December, 2010
    "I also suggest you review a little about control theory, time constants and how they operate. If the planet was as sluggish as you claim, then how do you explain the global temperature changing by over 3C during a 12 month period? A time constant of 7.5 years says that it takes 7.5 years for 37% of the equilibrium change to occur. Do you not believe that the Sun forces the climate? How can you even explain seasonal change?"
    (i) Note that the time constant is the time for ~63% (1-1/e) of the equilibrium response to be achieved (not 37%). (ii) The global temperature changes seasonally due to the large excess of N. hemisphere land compared to the S. hemisphere and the lower heat capacity of land compared to ocean. In other words one of the more rapid elements of the climate system (land warming) dominates when the N hemisphere is tilted towards the sun even although this occurs during the short period that the Earth moves to and from aphelion. Temperature changes of the vast S. hemisphere oceans occur much more slowly than N hemisphere land. (ii) The seasonal changes result from varying insolation patterns (with a lesser effect from the change in surface solar irradiance due to orbital eccentricity). (iv) this is all obvious. Clearly if the Earth were to come to a grinding stop in its orbit at aphelion and sit there rotating as normal, the N. hemisphere would warm further. However the orbital properties of the Earth aren't very relevant to persistent changes in forcings that are fundamental to determination of climate sensitivities. That's because the orbitally-paced sinusoidal insolation occurs more rapidly than the various elements of the climate system can equilibrate with the changing forcings, and thus average out on time scales relevant to establishing the Earth's equilibrium response to forcing.
    "...intrinsic 0.5C or so from doubling CO2 will melt enough ice to affect a 3C global temperature rise..."
    That's just argumentation co2isnotevil. To establish the physical response requires an effort at rigorous analysis. The intrinsic response to a forcing equivalent to a doubling of atmospheric [CO2] is of the order of 1 oC and then one needs to factor in the water vapour feedback (lots of evidence that this is positive and rather significant) and land and sea ice melt. There is a vast science on this (e.g. check to loink in post 413). One of the essential problems that you and RW1 have failed to address is the empirical evidence that the Earth's climate sensitivity is very unlikely to be below 2 oC (as explained, for example, here, and here, and here and here)
  19. co2isnotevil at 12:42 PM on 28 December, 2010
    "...For example, there is no monotonic trend corresponding to the CO2 trend in the temperature data..."
    Why should one expect such a thing co2isotevil? Attribution of warming trends requires an effort at a realistic assessment of all the contributions to temporal changes in surface temperature. This has been done in detail by scientists. Some useful examples are Lean and Rind (2008) and Hansen et al (2005).
  20. chris, "However the orbital properties of the Earth aren't very relevant to persistent changes in forcings that are fundamental to determination of climate sensitivities. That's because the orbitally-paced sinusoidal insolation occurs more rapidly than the various elements of the climate system can equilibrate with the changing forcings, and thus average out on time scales relevant to establishing the Earth's equilibrium response to forcing." Who is claiming the changing seasonal hemispheric and orbital changing forcings don't average out? They do. The point is that as the forcings change, the climate responds fairly quickly via a significant change in air and ocean water temperature. Are you going to argue that the physics of the oceans are different globally then they are hemispherically? If so, under what law of thermodynamics do smaller, slower increases in thermal forcing take longer than larger, faster increases in thermal forcing to raise the temperature of water to equilibrium?
  21. @RW1: "Are you going to argue that the physics of the oceans are different globally then they are hemispherically?" Strawman argument fallacy. That is not at all what Chris is arguing. What he's saying is that, because seasonal changes happen in a relatively rapid cycle (and are balanced between the hemispheres, one being warmer while the other one is cooler), there is not much feedback to the forcing. With CO2, however, the increase is gradual, over decades, which triggers feedbacks that are little affected by seasonal change. Even the direct effect of CO2 is delayed compared to the direct energy transfer caused by insolation. CO2-induced warming takes longer as energy travels back an forth between the GG molecules and the ground. All these comments, and neither RW1 or co2isnotevil (true, it isn't, but increasing it is warming our world) have managed to present a convincing case against a climate sensitivity of 3C.
  22. Chris, The exponential approach to equilibrium is quantified as A*exp(-t/tau), where tau is the time constant, A is the equilibrium value and t is time. Exp(-1) is about 0.37 and 5 time constants, exp(-5), is greater than 0.99. This form of approach to equilibrium arises as the solution to the first order LTI describing the thermodynamic climate system. The related response to a sinusoidal stimulus like exp(-jwt) is a delayed sinusoid whose delay is equal to the time constant for periods larger than 4 or 5 time constants. If we filter the ISCCP data to only those grids over ocean, there is still 1.5C or more yearly variability globally and more than 4C hemispheric specific temperature variability. Equatorial water temperatures are relatively constant, so there is little to no flux between the 2 hemispheres and hemispheric specific heating and cooling tells us exactly how big the planets thermal mass is on a per hemisphere basis. You state that the climate system responds slower than seasonal change. This is clearly wrong because if it was the case, seasonal change would not happen! Just like a capacitor resists a change in voltage, a thermal mass resists a change in temperature and the equations describing this response are nearly identical and the time constants have the same physical significance. Venus has the property you claim relative to the surface, but this is because it's thermal mass is energized CO2 above the surface, while the Earth's thermal mass is primarily ground state water below the surface. While the Venusian 3 degree axis (177 accounting for retrograde rotation) is less than ours, there are no seasonal differences at the surface or even differences across latitudes. There are not even differences between night and day even though the Venusian day is about as long as our year. This is what you would expect from a system with a time constant on the order of years to decades. The Earth behaves in a manner consistent with a short time constant. Regarding the amount of ice that would need to melt to cause a 3C rise, all else being equal, nearly half of the difference between the min and max seasonal snow pack would need to melt. There's just not this much additional ice to melt during the summer! This arises as the incremental reflectivity from the full winter snow pack has about an 7C effect on the surface temperature. This is why the global average temperature in January is 3C cooler, rather than 4C warmer as the increased insolation at perihelion would suggest. This all works out quite nicely when you consider the measured reflectivity variability seen in the ISCCP data.
  23. co2isnotevil - In regards to climate sensitivity, please keep in mind that there is not a single 'climate response' with a particular time constant - there are many. Climate response tau's: - Air temperature: hours - Water vapor: week(s) - Northern/Southern temperate snowfall/albedo: months - Ocean surface temperature: weeks/months - Arctic ice cap size: Year plus - Vegetation albedo: Years due to species spread - Greenland ice cap size: 10's of years - Glaciers: Years to 10's of years - Antarctic ice cap: 10's of years plus? - Deep ocean temperature: Decades? Still under investigation - CO2 ocean sequestration/release: months to 100's of years depending on depth. - CO2 rock weathering: 10,000 years plus Yes, for each of these, there will be either a direct response to a sinusoidal forcing cycle (seasons or orbital distance) or, if the forcing is shorter than the response time, a delayed sinusoid - with amplitude decreasing as the response becomes more multiples of the forcing. Note that these responses for different feedbacks will likely not be in reinforcing phase, and may cancel out/reinforce from time to time. On the other hand, a steadily changing trend (such as CO2 forcing) will not cause a sinusoidal response in feedback, but a driven change in the baseline (with weather variability making it non-monotonic). And that's what we see on all of these feedbacks for the CO2 forcing, as evidenced by the temperature record and other data. Cyclic changes don't move the baseline. Non-cyclic changes such our CO2 output do.
  24. co2isnotevil - An additional note on these various forcings and feedbacks: Statistical significance in temperature measurements requires 25-30 years of temperature records to establish a trend, based on the inherent variability of weather (PDO, AO, other influences, clouds, volcanoes, etc.). Your delayed sinusoid feedback responses to cyclic forcings of one year cyclic duration will be completely lost in the noise of the climate. Longer term changes such as CO2 increases and Milankovitch cycles will not.
  25. Rw1 - sorry for taking a long time to respond but only intermittent access to internet. "Explain to me how the surface, whose temperature is directly tied to the total power flux via Stefan-Boltzman, is going to 'know' the difference from increased power from Sun or CO2?" It doesnt, I agree, but as I said, 1W/m2 as global annual average has a very different temporal, spatial and spectral distribution for sun versus CO2. The direct radiative balance is obviously maintained but to consider a simplification, 1W/m2 could by say 2W/m2 in one hemisphere and 0 in the other. The temperature response for radiative balance is 0.6 in one hemisphere, 0 in the other still for global average of 0.3. Sensitivity it about feedbacks though. The milankovich forcing driving the ice age cycle is tiny as global average, but the large forcing at 65N over long time delivers feedbacks enough to drive the cycle. The identical forcing at 65S does not - far less scope for feedbacks in the south. You cant do the sensitivity by back-of-the-envelope stuff. You have to run the physics and see how it pans out.

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