Time dependent feedbacks

There’s a very interesting new paper by Gregory and Andrews called Variation in climate sensitivity and feedback parameters during the historical period. The motivation seems to be to try and reconcile why estimates of the effective climate sensitivity using recent observations seems to suggest climate sensitivities that are somewhat lower than climate model estimates of the Equilibrium Climate Sensitivity (ECS). For simplicity, I’ll use ECS for both effective climate sensitivity and Equilibrium Climate Sensitivity, but – technically – they aren’t quite the same thing.

A standard way to assess ECS using observations is to use a simple energy balance model in which

F = N + \alpha T,

where F is the change in forcing over the time interval considered, N is the change in system heat uptake rate, T is the change in temperature, and \alpha is the feedback parameter. The assumption here is that \alpha is constant and – if one wants to equate effective and equilibrium climate sensitivity – that it will remain constant. The ECS is then simply 3.7/\alpha.

What this paper did was to use Atmospheric General Circulation Models (AGCM) and prescribe[d] time-varying observationally derived fields of [sea surface temperature] SST and sea-ice concentration, but fixed atmospheric concentrations at pre-industrial levels. In such a model, the change in forcing F is 0, but the change in temperature, T, will not only be a reasonable representation of the actual change (not quite, because the land is not warming as fast, but close – 85% to 95%), but the spatial distribution of the warming will also be similar to what actually happened. To determine the climate feedback parameter, \alpha, you then use

N = - \alpha T.

Credit : Gregory & Andrews (2016)

Credit : Gregory & Andrews (2016)


To estimate \alpha, you simply regress N against T. As shown in the top left panel of the above figure, the result for the whole period is 1.72 Wm-2K-1 (ECS = 2.2K), where N and T are relative to 1979-2008. The bottom left panel, however, shows what happens if you consider shorter time intervals, and indicates that it can vary quite substantially, depending on the time interval considered. The right-hand panels show \alpha determined by regression in 30-year sliding windows. They also show \alpha during the first 20 and first 100 years of abrupt 4xCO2 simulations and show that it is smaller (and the ECS larger) than is the case when the spatial distribution of the surface warming is chosen to represent what we probably experienced over the last 100 years or so.

As the paper itself says

Our results suggest that the differential climate feedback parameter \alpha varied on multi-decade timescales during the historical period and that it was generally larger than abrupt4xCO2, in particular during the last three decades.

The reason being that essentially

[d]ifferent geographical pattern of SST that produce the same global-mean T can give different N.

There seem to be a number of conclusions that one can draw from this study.

  • Climate models that have a reasonable representation of the pattern of surface warming do a reasonable job of estimating the resulting feedback response.
  • The reason why observationally-based estimates for ECS tend to suggest lower values than other estimates (such as climate models) may well be simply because of the spatial distribution of surface warming that we have actually experienced, rather than because our climate is actually less sensitive than these other estimates suggest.
  • Projections for future warming will likely be reasonable as long as the pattern of surface warming in climate models is a reasonable representation of what we will likely experience under increasing anthropogenic forcings.
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49 Responses to Time dependent feedbacks

  1. Roger Jones says:

    Historical hindcasts in the models cannot be used to estimate ECS if the whole ensemble is used. A confounding effect is that the representation of volcanic aerosols deliver a negative sensitivity – warming to 2005 does not correlate with ECS. I’m not surprised they got these stratified results with the more recent changes bearing fruit. Linearity is the wrong assumption.

    Caveat – I’m not sure there is an anthropogenic signal before 1960. All the available energy could have been absorbed into the system. The ocean warming in the 1930s is not well captured by the models – until this is understood, the early response will be a mystery.

  2. Roger Jones says:

    Sorry about the shorthand – am writing this all up at the moment for the third submission after two rejections. ECS cannot be backed out of either observations or models. But 1965-2015 has a signal in it – just not a great one.

  3. Roger,
    I guess, ECS is really just a model metric that gives us some idea of how sensitive our climate is to a change in external forcing. It’s probably being over-used and over-interpreted. What we’re really interested in is how much we will actually warm, not some number that simply represents some idealised scenario.

  4. opluso says:

    This new paper sounds interesting but *sigh* is paywalled.

  5. Steven Mosher says:

    paywalled?
    sci-hub.io is your friend

    submit the DOI.. then wait.. it will show up

  6. Steven Mosher says:

    “Projections for future warming will likely be reasonable as long as the pattern of surface warming in climate models is a reasonable representation of what we will likely experience under increasing anthropogenic forcings.”

    I assume they mean patterns in trend.

    http://berkeleyearth.org/graphics/model-performance-against-berkeley-earth-data-set/#section-2-1

  7. Problems with theorizing that ECS is significantly higher than what we already observe:

    1. The largest feedback, WV, responds very quickly ( monthly ) to seasonal change – it should already be present.
    2. The much smaller albedo feedback also responds to seasonal change, and indeed since sea ice age and ice conectration have changed, albedo has fedback.
    3. The largest negative feedback, the Hot Spot, has not occured since ’79, ( though perhaps somewhat since ’58 ). Should it occur, forcing would perhaps decrease.
    4. When is Equilibrium? It only occurs fleetingly if at all on a seasonal basis. It is a nebulous concept of some unknown time.
    5. If ECS is significantly greater than TCR, should not observed warming rates be increasing? Thirty year temperature trends have been relatively stable for the past two decades, down slightly since the peak around 2003.

  8. Steven Mosher says:

    Maybe later I can plot RMS versus TCR. for all the models.
    Picking the best 3 RMS ( calculated on a gridded basis)

    http://static.berkeleyearth.org/graphics/figure32.pdf TCR 1.3

    http://static.berkeleyearth.org/graphics/figure28.pdf TCR 1.4

    http://static.berkeleyearth.org/graphics/figure38.pdf TCR 1.3

    Average TCR is 1.8.

    FWIW

  9. Steven Mosher says:

    The future response has some odd properties

    http://static.berkeleyearth.org/graphics/gcm-acceleration.pdf

  10. Hyperactive Hydrologist says:

    Steven,

    Is the future response for RCP 8.5?

  11. Hyperactive Hydrologist says:

    My questing is shouldn’t we expect an increase in radiative forcing give that we are adding more GHG to the atmosphere? The RCP scenarios are effectively a radiative forcing pathway.

    http://sedac.ipcc-data.org/ddc/ar5_scenario_process/RCPs.html

  12. Steven Mosher says:

    “Steven,

    Is the future response for RCP 8.5?
    #############

    I will have to check, but it doesnt matter.
    What the chart says is that X watts of forcing in the past produced Y change in temp
    BUT
    that same X Forcing in the future causes more warming. This has yet to be explored or explained.. got side tracked, but perhaps given some time I can go back and redo it with global data ( land and ocean ) and see what happens

  13. JCH says:

    …may well be simply because of the spatial distribution of surface warming that we have actually experienced, rather than because our climate is actually less sensitive than these other estimates suggest. …

    This confuses me (not hard). If by spatial distribution of surface warming you mean the distribution in that part of the earth system that is roughly 2 meters above the land plus the SST, then I don’t think it makes any sense as I don’t see how a difference in distribution there would make any difference wrt sensitivity. Can it? But if you mean spatial distribution throughout the earth system, then I think it does makes sense as a difference there, it would seem, could mask or exaggerate sensitivity.

  14. Hyperactive Hydrologist says:

    Thanks. I’d miss understood the graph explanation.

    Could the increase be due to feedback responses that only start to take effect at higher temperatures? Or acceleration of warming over land area?

  15. Hyperactive Hydrologist says:

    If the climate warms faster in higher latitudes does this leads to a larger energy imbalance?

  16. Hyperactive Hydrologist says:

    If I understand this paper correctly the answer to my question would be yes.

    http://www.nature.com/ngeo/journal/v7/n3/abs/ngeo2071.html

    “We find that in the simulations, the largest contribution to Arctic amplification comes from a temperature feedbacks: as the surface warms, more energy is radiated back to space in low latitudes, compared with the Arctic.”

    So models that underestimate Arctic warming would have lower sensitivity.

  17. paulski0 says:

    Steven Mosher,

    Would I be right in thinking the plot of past against future sensitivity was produced using a shared forcing history? That is, it doesn’t take into account differences between models in historical or future forcing? Just confused about the lack of correlation.

    On the trend maps, one problem is that linear trends over 1900-1999 in many regions are not robust at all, particularly high latitude NH. As an example, on your map inmcm4 shows substantially more warming than observed in Northern Siberia, Alaska and Greenland using 1900-1999 linear regression. I get that as well, but if you were to find trends over 1850-2015 instead the colours in those areas would be completely reversed.

  18. Anders,

    The reason why observationally-based estimates for ECS tend to suggest lower values than other estimates (such as climate models) may well be simply because of the spatial distribution of surface warming that we have actually experienced, rather than because our climate is actually less sensitive than these other estimates suggest.

    Since there’s no ‘O’ in ‘AGCM’, how might we rule out OHC uptake? By that, I mainly mean do you know of a paper which attempts it?

  19. Steven Mosher,

    The future response has some odd properties

    I think I used RPC8.5 CO2EQ for that, but I’d have to check. (I should put such details in the #$%ing plot to begin with …) You’ve given me some ideas for other “experiments”, thanks.

  20. Steven Mosher says:

    “Could the increase be due to feedback responses that only start to take effect at higher temperatures? Or acceleration of warming over land area?”

    I dunno. We started to look at this. Then other priorities took hold.
    Your suggestion (question) is a good one.

  21. Steven,

    I assume they mean patterns in trend.

    I think that was me, not them, but did you mean trends in patterns? If so, yes, this seems reasonable. However, I was thinking that if the ensemble produces a range of potential patterns that is a fair reflection of what we will experience, then we might expect the actual warming to fall within the ensemble range.

  22. JCH,

    If by spatial distribution of surface warming you mean the distribution in that part of the earth system that is roughly 2 meters above the land plus the SST, then I don’t think it makes any sense as I don’t see how a difference in distribution there would make any difference wrt sensitivity.

    I don’t see why. If we two situations in which the change in global mean T is the same, but in one most of the warming happens in the tropics, and in the other at the poles, we might expect the feedack response to be different.

  23. TE,
    1. Why is this relevant? In a sense this paper is showing that variability in the spatial distribution of the surface warming can influence the resulting feedbacks. Some of that variability could be internal, and could affect our estimate of ECS using observations.

    2. Albedo feedback is – I think – slow and isn’t formally part of the ECS.

    3. You should read Steven Sherwood’s post here, in particular Figure 1.

    4. This is silly. We don’t some kind of equilibrium where nothing at all changes. It simply means a state to which we will tend in which the planetary energy imbalance averages to 0 over time.

    5. Again, not necessarily. Thirty years is not that long and other factors could mask forced warming.

  24. HH,

    My questing is shouldn’t we expect an increase in radiative forcing give that we are adding more GHG to the atmosphere?

    I don’t fully understand your question. The didn’t include a change in forcing because you don’t need to if you’re specifying the surface temperature evolution.

  25. Brandon,

    Since there’s no ‘O’ in ‘AGCM’, how might we rule out OHC uptake? By that, I mainly mean do you know of a paper which attempts it?

    I don’t quite know what you’re getting at. With no O, they are indeed assuming that the oceans are an infinite source of energy (the surface temperature evolution is prescribed, so increases even if the system if losing energy). However, they’re really only trying to determine the feedback response, so not sure how adding an O would help. I also think that would make it impossible to prescribe the surface temperature evolution.

  26. Roger Jones says:

    ATTP, the 21st century warming in CMIP5 simulations is correlated with ECS to a useful degree but not the 20th. I just calculated the correlation between warming 1965-2005 from the RCP4.5 ensemble and available ECS from those models (n=91). It’s 0.28 – significant to the p<0.01 level (just) but not a great predictor (2005 is the last year of the hindcast). The [1861-2005] warming correlation with ECS is -0.01 for these hindcasts – if the earth is responding to historical forcing in a similar way this could be why the estimates of sensitivity are coming out low. And none of this can be realistically carried out without O. These low correlations are consistent with Gregory and Andrews' findings.

    Has anyone done a study on backing out ECS from warming in models so far?

  27. Anders,

    I don’t quite know what you’re getting at.

    It’s entirely possible I don’t know either.

    However, they’re really only trying to determine the feedback response, so not sure how adding an O would help.

    Ah, ok, that makes sense. I guess what was throwing me is that Mosher brought TCR into the discussion, so I immediately went to:

    The TCR does not scale linearly with ECS because the transient response is strongly influenced by the speed with which the ocean transports heat into its interior, while the equilibrium sensitivity is governed by feedback strengths (discussion in Frame et al., 2005).

    … and forgot the point of this paper was to go after ECS.

  28. Roger,

    Has anyone done a study on backing out ECS from warming in models so far?

    I’m not sure this has been done explicitly, but we do have papers like this, in which it is shown that the model-obs comparison is improved if you make a like-for-like comparison. The models have higher ECS values than recent obs suggest and yet can still reproduce the historical warming.

  29. Steven Mosher says:

    “I think that was me, not them, but did you mean trends in patterns? If so, yes, this seems reasonable. However, I was thinking that if the ensemble produces a range of potential patterns that is a fair reflection of what we will experience, then we might expect the actual warming to fall within the ensemble range.”

    My bad. I assumed you meant patterns in trends.

  30. Hyperactive Hydrologist says:

    Do observational estimates of ECS take into account the spacial distribution of warming in any way or are they purely done using a global energy budget equation? Is it therefore assume that the observed warming is uniform? If so how proponents of this method reconcile that a degree of warming at the equator or a degree of warming in the Arctic will cause a different response?

  31. Steven,

    My bad. I assumed you meant patterns in trends.

    No worries. The whole consensus thread is still going, so I haven’t had a chance to look through all the comments here properly.

    HH,
    I think the typical energy balance method essentially assumes that the spatial pattern doesn’t influence the warming. This paper is suggesting that that is not the case.

  32. niclewis says:

    ATTP,
    “I think the typical energy balance method essentially assumes that the spatial pattern doesn’t influence the warming”

    That’s not quite right. Rather, the global energy balance method of ECS estimation implicitly assumes that the pattern of warming that occurred over the analysis period gives rise to the same global climate feedback as the pattern of warming that would result from a doubling of CO2 concentration.

    The paper shows that climate sensitivity in GCMs, or at least the two GCMs used, depends on the pattern of SST warming. That is not surprising. The paper incorrectly implies that this is also evident in the real world, which I don’t see that they actually show to be the case (although it would not be surprising). The observed pattern of SST warming over the historical period has been rather different from the pattern typical CMIP5 AOGCMs produce during the first few decades after an abrupt rise of CO2 level, and from patterns simulated by typical AOGCMs over the historical period, particularly in the east Pacific, with the actual pattern giving rise to a lower sensitivity in the GCMs used.

    The interesting question is why AOGCMs have simulated the wrong patterns of SST warming over the historical period, and why the observed pattern of warming differs from AOGCM-simulated warming under CO2 forcing. Gregory and Andrews offer three possibilities in their section 4:

    1) That – particularly for sensitivity estimates based on GMST changes over less than the full historical record – natural internal variability may have strongly influenced patterns of SST change and hence realised sensitivity. This is possible, but it seems unlikely over the whole period – particularly as energy balance ECS estimates are virtually unaffected by the hiatus. No evidence is put forward to support this suggestion.

    2) That there is non-linearity in the response of SST patterns to the magnitude of forcing, or of climate feedback processes to the amplitude of the forced SST pattern. This is most unlikely. The linearity of response of all or most AOGCMs to the magnitude of forcing is remarkable. The example the authors give is irrelevant, since the variation in sensitivity between 1.4x CO2 and 2x CO2 is very small in AOGCMs, at least for those for which I know it.

    3) That the patterns of SST change and hence effective sensitivity might vary because of changes in relative importance of the various forcing agents, which have different spatiotemporal “fingerprints”. The example of volcanic forcing (which produces a low sensitivity) is irrelevant to well-designed energy budget studies: the ~1860-~1880 and 1995 to date periods both had very low volcanic activity, so ECS estimates based on changes between them are almost unaffected by the response to volcanic forcing. They also raise the possibility that sensitivity to aerosol forcing is much greater than to CO2 forcing, suggested by a few model-based studies. The latest evidence on this strongly suggests otherwise, provided that aerosol effective radiative forcing is used as the measure. And, as they say, that would result in increasing sensitivity over the last few decades, the opposite of what their simulations find.

    There is a fourth possibility, omitted in section 4 but mentioned in section 5: that ECS is overestimated by GCMs. It would appear that such overestimation would arise to a large extent because GCMs simulate wrong patterns of SST change in response to anthropogenic forcing.

  33. Nic,

    That’s not quite right. Rather, the global energy balance method of ECS estimation implicitly assumes that the pattern of warming that occurred over the analysis period gives rise to the same global climate feedback as the pattern of warming that would result from a doubling of CO2 concentration.

    Okay, yes, that is indeed the case. I was simply meaning that energy balance methods do not explicitly account for variability in the spatial distribution.

    The paper incorrectly implies that this is also evident in the real world, which I don’t see that they actually show to be the case (although it would not be surprising).

    I think that it is why it was implied.

    The interesting question is why AOGCMs have simulated the wrong patterns of SST warming over the historical period,

    How do you know this? Why do some AOGCMs reproduce the historical warming despite having ECS values large than energy balance models, based on the historical period, suggest?

    1) I don’t follow your point here. This paper appears to be showing that the spatial distribution of the surface warming over the historical period can indeed produce a climate feedback parameter that is larger than would be the case for the same model under a 4xCO2 scenario.

    Since you’re here, I’m still interested in something I’ve asked you before. The TCR-to-ECS ratio in your estimates (typically, I think) is 0.8, or greater. This is quite a bit larger than has been suggested before. In fact, it seems a little implausible given that we currently have a planetary energy imbalance of more than 0.6W/m^2. If this is entirely forced, then we have at least 0.2C of unrealised warming, and probably more, given that if all our warming is forced, feedbacks would have to be positive. So, if we have more than 0.2C of unrealised warming today, how can the TCR-to-ECS ratio be 0.8 or higher?

    Also, if this high ratio seems implausible, what could it be. Your TCR best estimate is too high? Maybe, but it can’t seem to come down much, given how much we’ve already warmed. Your ECS best estimate is too small? Possibly, and – if so – we’re heading back towards the 2C level and more consistent with other estimates.

  34. niclewis says:

    ATTP
    “How do you know this? ”
    See comparative plots of observed 1900-2012 SST pattern (per the Andrews talk at Ringberg15) and of the CMIP5 mean (one run per model) historical-RCP45 pattern of 2012 surface air temperatures (anomalies relative to 1860-1880, a volcano free period), here: https://niclewis.files.wordpress.com/2016/04/obs-andrews-ringberg15-vs-cmip5-1-run-per-model-mean-simulated-2012-sst.png .

    ” Why do some AOGCMs reproduce the historical warming despite having ECS values large than energy balance models, based on the historical period, suggest?”
    They have some combination of:
    a) higher aerosol forcing (and/or lower GHG forcing) than the AR5 best estimate;
    b) higher ocean heat uptake than per observational estimates; and/or
    c) highly time dependent effective climate sensitivity

    “I don’t follow your point here. This paper appears to be showing that the spatial distribution of the surface warming over the historical period can indeed produce a climate feedback parameter that is larger than would be the case for the same model under a 4xCO2 scenario.”
    Exactly. The suggestion in the paper is that internal variability altered the SST pattern from one like that arising under a 4xCO2 scenario (producing a low climate feedback parameter) to the actually observed SST pattern, producing a much higher climate feedback parameter). I’m not surprised you didn’t get this – it does seem rather far fetched.

    “So, if we have more than 0.2C of unrealised warming today, how can the TCR-to-ECS ratio be 0.8 or higher? ”
    Forcing over the last decade, 2006-15, is about 2.25 W/m2 relative to an 1860-80 base period, and between those periods GMST rose 0.80 K, per HadCRUT4v4. This gives an energy budget TCR estimate of 1.32 K (using F2xCO2 of 3.71 W/m2). Dividing that by 0.8 implies an ECS estimate of 1.65 K, and unrealised warming of 0.80 K x 0.2/0.8 = 0.2 K – in line with your figure.

  35. Nic,
    Not quite sure how you’re concluding that from Tim Andrews’s talk.

    Dividing that by 0.8 implies an ECS estimate of 1.65 K, and unrealised warming of 0.80 K x 0.2/0.8 = 0.2 K – in line with your figure.

    That wasn’t what I actually said. 0.2C was a minimum if feedbacks are zero. Since even your work suggests that they’re positive, how can we only have 0.2C of unrealised warming if the planetary energy imbalance today is already greater than 0.6W/m^2. Consequently, how can the TCR-to-ECS ratio be only 0.8?

  36. The interesting question is why AOGCMs have simulated the wrong patterns of SST warming over the historical period,

    Just to clarify, do you mean that some kind of ensemble mean of the AOGCMs has not simulated the “correct” pattern, or that essentially no AOGCM has come close to simulating the correct pattern?

  37. MarkR says:

    ATTP,

    The TCR estimate contains feedbacks and if you assume that TCR and ECS feedbacks are the same then you can just scale, as Nic did there.

    I think it’s widely agreed that the feedbacks will probably not stay the same though, so the ECS energy budget calculation is pretty speculative.

  38. MarkR,
    Sure, but I was doing something slightly different. If you take Nic’s numbers, then the TCR-to-ECS ratio is 0.82. If we then take his current warming of around 0.8C, this would imply that if we fixed atmospheric CO2 now, that we’d warm to an equilibrium of 0.8C/0.82 = 1C (just under 0.2C). However, we currently have a planetary energy imbalance that is probably larger than 0.6W/m^2. The Planck response is around 3.2W/m^2/K, and hence a planetary energy imbalance of 0.6W/m^2 would imply a no-feedback warming of about 0.2C. Since feedbacks are almost certainly positive, our committed warming, if we fixed atmospheric CO2, is already greater than 0.2C. Hence, how can the TCR-to-ECS ratio be bigger than 0.8?

  39. Sorry, should have stressed that I’m only referring to Nic’s best estimates. Overall, Nic’s TCR and ECS ranges are reasonably consistent with other estimates.

  40. niclewis says:

    ATTP,
    Your calculations ignore the planetary heat inflow in the base period used (1859-82 or similar), estimated at ~0.25 W/m2 in Gregory et (2013) GRL; Lewis & Curry used a scaled down value of 0.15 W/m2. That needs to be deducted from today’s heat inflow. If you don’t understand why, I’m sure one of the denizens of your blog will be able to explain.

  41. Nic,

    If you don’t understand why, I’m sure one of the denizens of your blog will be able to explain.

    Wow, you don’t make it easy. I presume your intent was to be insulting which seems a bit unnecessary if you’re so convinced you’re right. Makes you feel better, I guess?

    Let me put this slightly differently. The ratio between ECS and TCR is likely to depend on the rate at which we heat the deep ocean. If the deep ocean warms slowly, then we can sustain a small planetary energy imbalance for a very long time and the TCR-to-ECS ratio will be large (they will be similar). If, on the other hand, the deep ocean warms quite fast, then we can sustain a larger energy imbalance, equilibrium will be reached more quickly, but the TCR-to-ECS ratio will be smaller (they will be more different). [Edited to get the ratios the correct way around.]

    Now, if we think that the ratio of the best estimates (as your work suggests) is 0.8 or greater, that would imply that if we warm by about 1C, that equilibrium will be at about 1.2C. The Planck response is 3.2W/m^2/K, so 0.2C of warming would produce a Planck response of about 0.6W/m^2. If feedbacks are slightly positive, then that would imply that – in this situation – the planetary energy imbalance would need to be smaller than 0.6W/m^2 if warming in the pipeline is – to reach equilibrium – only 0.2C. Hence, I still think that a planetary energy imbalance today of probably greater than 0.6W/m^2 is not really consistent with an ECS-to-TCR ratio of greater than 0.8, given that we’ve only warmed by around 1C.

    You’re free to convince me otherwise, ideally without being too insulting, but if you can’t avoid that that’s fine too. I don’t expect much these days.

  42. niclewis says:

    ATTP,
    I wasn’t trying to be insulting. I just don’t have any more spare time to spend on convincing you about this.

  43. Well you’re pretty good at it if you’re not even trying. Convincing me shouldn’t – IMO – be the goal.

  44. To get a sense of what I’m trying to get with respect to my comment to Nic, you can read Section 4 of this paper. As I understand it, the TCR-to-ECS ratio is going to depend on how rapidly one can mix energy into the deep ocean. If it is fast, the climate responds slowly (i.e., takes a long time to reach equilibrium). If it is slow, we reach equilibrium quickly as the climate responds quickly.

    I’ll post some of it below

    Global surface temperature does not respond quickly to a climate forcing, the response being slowed by the thermal inertia of the climate system. The ocean provides most of the heat storage capacity, because approximately its upper 100m is rapidly mixed by wind stress and convection (mixing is deepest in winter at high latitudes, where mixing occasionally extends into the deep ocean). Thermal inertia of the ocean mixed layer, by itself, would lead to a surface temperature response time of about a decade, but exchange of water between the mixed layer and deeper ocean increases the surface temperature response time by an amount that depends on the rate of mixing and climate sensitivity (Hansen et al., 1985).

    The lag of the climate response can be characterized by a climate response function, which is defined as the fraction of the fast-feedback equilibrium response to a climate forcing.
    …….
    The coupled modelE-R has been characterized in detail via its response to many forcings (Hansen et al., 2005b, 2007). About 40 percent of the equilibrium response is obtained within five years. This quick response is due to the small effective inertia of continents, but warming over continents is limited by exchange of continental and marine air masses. Only 60 percent of the equilibrium response is achieved in a century. Nearly full response requires a millennium.

    Below we argue that the real world response function is faster than that of modelE-R. We also suggest that most global climate models are similarly too sluggish in their response to a climate forcing and that this lethargy has important implications for predicted climate change.

    So, in some sense, James Hansen is arguing that most climate models respond too slowly and – if you look at Figure 7 – this is reflected in different planetary energy imbalances for the same change in surface temperature. This is consistent – I think – with a higher TCR-toECS ratio. However, I think his overall conclusion that an intermediate response function is more consistent with observation than the slow one in most climate models, but I don’t know what this implies with respect to the expected TCR-to-ECS ratio.

    So, my question is basically whether or not a TCR-to-ECS ratio greater than 0.8 is consistent with a planetary energy imbalance today of, probably, greater than 0.6W/m^2. I still don’t know the answer to this.

  45. paulski0 says:

    To put it another way, an ECS of 1.65K corresponds to a radiative restoring parameter of -2.24W/m-2/K. Using that, temperature change and a forcing history, we can predict an expected current imbalance.

    Using 2.25W/m-2 forcing for 2006-2015 and 0.91K temperature change for 2006-2015 vs. 1860-1880 in Berkeley Land+Ocean and Cowtan and Way, imbalance prediction = dF + (dT*RadRestore) = 0.21W/m-2. Add that to the 1860-1880 imbalance estimate of 0.15W/m-2 = 0.36W/m-2.

    Using HadCRUT4, dT is 0.81K, so current imbalance prediction = 0.43W/m-2 + 0.15 = 0.58W/m-2.

    From multiple lines of evidence (sea level rise, ARGO measurements, updating Allan et al. 2014), imbalance for 2006-2015 appears to converge around 0.7-0.8W/m-2. Taking uncertainties into account a 1.65K ECS is probably compatible if you use HadCRUT4. I suspect it would be difficult to reconcile with the interpolated datasets.

  46. Paul,
    Thanks. That’s a clear way of putting it. You’re probably right that the key issue is what datasets you choose to use.

  47. Pingback: The TCR-to-ECS ratio | …and Then There's Physics

  48. Pingback: Sea surface warming and cloud feedbacks | …and Then There's Physics

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