Another “reconstruction” of underlying temperatures from 1979-2012

Or, “could the multiple regression approach detect a recent pause in warming, part 4”.  For those following the series, you know what I mean by “underlying temperatures” is the temperature evolution if we attempted to remove the influence of solar, volcanic, and ENSO variations.  

It has been a while since I posted the first three parts of a series on whether using multiple linear regressions to remove the solar, volcanic, and ENSO effects from temperature was an accurate way to "reconstruct" the underlying trend. Generally, these did not perform too well, and tended to overestimate the solar influence and underestimate the volcanic influence, particularly if there was indeed a "slowdown" in the underlying temperature data.  One of the problems with that method is that it includes an assumption about the form of the underlying trend when doing the regressions.  

So, I’d thought I’d put a temperature series (actually, a couple of options) out there that have been adjusted for these factors, using a method that is not particularly sensitive to the form of the underlying trend.  Essentially, I take the multi-model mean of the models I used in the last post in this series to adjust for the volcanic and solar components, and then remove ENSO based on a regression against that adjusted series.  Fortunately, the ENSO variations are high enough frequency that the regression is not particularly sensitive to form of the the underlying trend (whether it be linear or quadratic) as we have limited the number of variables.

It should be noted that this method might *over-adjust* for volcanic and solar if the CMIP5 models are too sensitive, which my recent paper (Masters 2013, Climate Dynamics) seems to indicate.  I have therefore included an adjusted series that adjusts by only 50% of the MMM as well.  Since the difference between the sensitivies in the transient state are likely to be less than after equilibration, let’s say the "true" adjustment should lie somewhere in-between those two adjustments.

Anyhow, here is the reconstructed series of NCDC (NOAA) temperatures.  (On a side note, I have become a little annoyed with trying to grab data from HadCRUT4 and GISS.  The former seems to return a "Not Found" error quite frequently, and the latter doesn’t let the R default user-agent grab data at all.  Hence the usage of NOAA temperatures). 

If I were to go strictly by the eyeball test, the blue line (adjusted by 50% of MMM) seems to get it “most right” in terms of compensating for the volcanic eruptions without over-adjusting.  Below are the trends for the various start years ending in 2012 in these series:

Here you’ll note that the “adjusted” series actually results in a lower trend for all start years up until about 2001, when the influence of ENSO seems to really take over.  The blue line never dips below 0 for these adjusted trends of 10 years or longer, so one could argue that the underlying warming (if the blue line indeed captures this correctly) never really “stopped”.  On the other hand, the trends are substantially lower towards the end than they are at the beginning (and indeed smaller than in most model runs), so saying that the recent “slowdown” is simply the result of known natural factors rings a bit hollow to me.  It would be interesting to run a similar experiment on the CMIP5 model runs and see how much “natural” variation remains in those runs, of if this is something unique to the real world. 

Code and data for this post available here.

Our comment on Humlum et al. in press at Global and Planetary Change

It is available online at http://www.sciencedirect.com/science/article/pii/S0921818113000891 (actually, it has been for a while, but I haven’t had much time for blogging lately!).   For those of you who have already read this blog post, or the one at RealClimate by Rasmus, the contents should not be much of a shock.  Sadly, the article is pay-walled, but if you don’t have university access contact me and I can see about getting you a copy.  The code for the paper is available here.

Interestingly, I see that Mark Richardson of the University of Reading also has a comment on the Humlum et al. paper appearing online at Global and Planetary Change as well.

Sensitivity / CMIP5 comparison paper now in press at Climate Dynamics

It is available online and titled “Observational Estimate of Climate Sensitivity from Changes in the Rate of Ocean Heat Uptake and Comparison to CMIP5 Models”.  Apparently Nic Lewis’s paper beat mine to online release by a day, and though my estimated confidence interval for equilibrium sensitivity is significantly wider, the median sensitivity in my paper also tends to be on the lower end relative to the IPCC AR4 likely value.  It is pay-walled, but please contact me if you need a copy and do not have University access.  Anyhow, a zip that includes all my code and data is available here.  From the abstract:

Climate sensitivity is estimated based on 0-2000m ocean heat content (OHC) and surface temperature observations from the second half of the 20th century and first decade of the 21st century, using a simple energy balance model and the change in the rate of ocean heat uptake to determine the radiative restoration strength over this time period.  The relationship between this 30-50 year radiative restoration strength and longer term effective sensitivity is investigated using an ensemble of 32 model configurations from the Coupled Model Intercomparison Project phase 5 (CMIP5), suggesting a strong correlation between the two.  The mean radiative restoration strength over this period for the CMIP5 members examined is 1.16 Wm-2K-1,  compared to 2.05 Wm-2K-1 from the observations.  This suggests that temperature in these CMIP5 models may be too sensitive to perturbations in radiative forcing, although this depends on the actual magnitude of the anthropogenic aerosol forcing in the modern period.  The potential change in the radiative restoration strength over longer timescales is also considered, resulting in a likely (67%) range of 1.5 K to 2.9 K for equilibrium climate sensitivity, and a 90% confidence interval of 1.2 K to 5.1 K.

To explain further on what I consider to be three of the more important conclusions of the paper:

First, there seems to be a relationship between the estimates of effective sensitivity from the last 30-50 years and the longer-term multi-century effective sensitivity (which is arguably more important than equilibrium sensitivity) as they are calculated in models.  To me, this gives hope that as the length of satellite record increases, we might start to narrow down a more accurate value for sensitivity that is relevant to the timescales of greatest interest.

Second, most of the CMIP5 models seem (albeit not without caveats) to show too high of sensitivity over this period.  From figure 3 of the paper:

This is showing the radiative restoration strength in the CMIP5 models examined (each X is a different run from that model), which is generally inversely related to sensitivity.  The solid gray line represents the likely value from observations, and the dashed lines represent +/- one standard deviation.  As can be seen, the vast majority of these runs fall below the observational likely value for radiative restoration strength, suggesting these CMIP5 models likely have too high a sensitivity relative to the observations.  Interestingly, inmcm4 and MRI-CGCM3 are both well above the line, and while they are among the CMIP5 models with the lowest sensitivity, they are not nearly as insensitive as the 50-yr radiative restoration strength would make them appear (which would be ~ 1.2 K for ECS if we performed a naïve calculation).  Obviously, the relationship between this radiative restoration strength and ECS can be complicated, as discussed previously at this blog and within the paper.

Finally, there is the estimate of ECS, for which I have tried to consider some effect of the potential change in Effective Sensitivity to ECS based on the CMIP3 relationships, although again I would argue that effective sensitivity is generally of more interest (but it is not the standard benchmark at this point).  Nonetheless, from figure 5 of the paper:

The gray indicates the pdf of “ECS” if we keep the radiative restoration strength fixed after the 50-year observational period, whereas the black line indicates the pdf for ECS if we take the uncertainty in the T_eff/T_eq into account based on this relationship in CMIP3 models.  The latter is reported in the upper right box and in the abstract.  The orange and purple lines represent the “likely” values for sensitivity when switching in the JAMSTEC or CSIRO OHC data rather using that from NOAA.

Clearly, the median estimate for ECS of 1.98K seems to match some other observationally-based estimates with a lower sensitivity, and the “likely” (67%) range of 1.5K to 2.9K is on the lower end as well.  Unfortunately, due to the large uncertainties in 0-2000m OHC data earlier in the record, this method continues to yield large uncertainties at the extremes, which due to the inverse relationship between sensitivity and the radiative restoration tends to increase the higher end of the range much more than the lower end.  Hence the 90% interval of 1.2K to 5.1K is not a particularly strong constraint.

Could the multiple regression approach detect a recent pause in global warming? Part 3.

Part 1

Part 2

In the first two parts of this series, I demonstrated how multiple regression methods that assume an underlying linear "signal" are unable to properly reconstruct a pause in surface temperature warming when attempting to remove the volcanic, solar, and ENSO components from my simple energy balance model.  That is, for an approach similar to Foster and Rahmstorf (2011), the method will tend to underestimate the warming influence of volcanic recovery and overestimate the cooling influence of solar activity over recent decades to compensate for the pause.  With the improvement Kevin C mentioned, there is some ability to detect a longer tail for the volcanic recovery (indeed, it does so nearly perfectly if the underlying signal is actually linear), and the solar influence is no longer over-estimated.  Unfortunately, it still underestimates the recent warming influence from volcanic recovery in my energy balance model in the "flattening" scenario 2.

I had thus wondered whether this long-tailed volcanic recovery was merely an artifact of my simple model, or indeed may have contributed substantial warming from 1996 (when the Pinatubo stratospheric aerosols were virtually gone) onward.  There are not that many models that have contributed volcanic-only experiments to CMIP5 (I showed 1 in my part 1, and Gavin showed an ensemble for GISS-EH at RealClimate in response to this discussion).  However, there is plenty of data from the natural-forcing only historical experiment, which, by averaging several of the runs for a particular model, can give us a good idea of the forced volcanic + solar influence in those GCMS.

In the figure below, I have shown the mean of the historicalNat runs for 7 individual CMIP models that have 4 or more of these experiment runs.  As such, this should give an idea of the forced response in these models without much additional unforced variation.  I have also plotted on the same chart the volcanic + solar influence as diagnosed by the FR11 and Kevin C methods when using the HadCRUTv4 dataset. 

As can be seen, the volcanic response in all of these AOGCMs is far larger and has a longer tail than diagnosed by the multiple regression methods.  Now, certainly it is possible that these volcanic responses in AOGCMs are too large, as there is evidence to suggest that the CMIP5 runs don’t properly simulate this response.  However, the fact that the FR method shows far lower sensitivity to volcanoes while simultaneously showing a much larger sensitivity to solar influences than both GCMs and simple energy balance models would indicate would seem to suggest that it may be compensation for the recent flattening.  Indeed, it is quite difficult to conceive of a realistic, physics-based model that does not indicate a substantial volcanic-recovery-induced warming contribution after 1996, despite it being virtually non-existent in the FR11 diagnosis (the increase around 1998 in the FR line is actually solar-induced).   

The table below highlights the warming contribution of the model ensembles (in K/Century, so be careful!) from the indicated start year through 2012 (I have an * by CCSM4 because the runs end in 2005).  

 

     

For comparison, the HadCRUTv4 trends over these same periods are

1979-2012: 1.55 K/Century
1996-2012: 0.91 K/Century
2000-2012: 0.38 K/Century

If one believes that this range of GCMs represent the true forced response of solar+volcanic, it would suggest that these natural forcings were responsible for 15% to 51% of the warming trend from 1979-2012.  If I had to bet, I would probably put it on the lower end, as the AOGCMs appear to be a bit too sensitive to these radiative perturbations and suggest too much ocean heat uptake, which probably creates longer tails on the early volcanic eruptions than is warranted.  However, I do think the contribution is probably greater than 0%, which is about what the FR method puts it at.  

From 1996 to present, and 2000 to present, however, are where I think we see the larger misdiagnosis.  Whereas all models (including my simple energy balance model) indicate that the solar+volcanic influence from 1996 to present was positive, comparable in amount (median: 0.81 K/century, mean: 1.05 K/century) to the actual HadCRUT trend, both regression methods either suggest a slight negative or nor-zero influence from these components.  And from 2000 to present,  while the models are more split (with only 6 of the 7 suggesting a positive influence, and the range varying more widely), it is difficult to believe that the actual influence of solar+volcanic is as strongly negative as the FR method indicates.  This is why it looks to me like the multiple regression method underplays the influence of volcanic recovery in order to partly compensate for a recent pause.

Essentially, we are left wondering if the GCMs are too sensitive to volcanic eruptions, and/or if the multiple regression method is underestimating their influence to compensate for a recent pause.  Again, if I had to bet, it would probably be in the middle – the GCM response is generally a bit too large, but the response is not nearly as small (or short) as the FR11 method would indicate.   

Data (including all of the globally processed tas for the models shown, please give credit here if you use them in this processed form) and code are available.

Could the multiple regression approach detect a recent pause in global warming? Part 2.

Previously, I posted on the multiple regression method – in particular, the method employed in Foster and  Rahmstorf (2011) – and how, when attempting to decompose the temperature evolution of my simple energy balance model into the various components (signal, ENSO, solar, and volcanic), this method encountered two large issues:

1) It did not adequately identify the longer term effect of the volcanic recovery on temperature trends, and

2) It largely overestimated the solar influence.

If you recall, I tested two scenarios in that original post.  The first scenario was a linearly increasing underlying signal.  The second scenario was a combination of a linearly increasing signal and an underlying low-frequency oscillation, resulting in a flattening of recent temperatures (one that was not caused by the combination of ENSO, volcanic, and solar influences).  The goal was to see whether this multiple regression method could identify the flattening if it existed. 

Thanks to Kevin C, who  suggested and implemented a few improvements to this F&R method, noting them in the comments of that post: “…tie the volcanoes and solar together as forcings and fit a single exponential response term instead of a delay."  This would allow a tail for the recovery from volcanic eruptions well beyond the removal of that actual stratospheric aerosols, and would not allow an over-fitting of the solar influence.  After implementing this newer method, I would say that it is a large improvement (at least in diagnosing my simple EBM components) in the first scenario of a linearly increasing trend:

 

Unfortunately, due to the underlying assumption implicit in this method of a linear trend, it still has trouble identifying the recent pause present in scenario 2:

To see where exactly it is going wrong in scenario 2 vs. scenario 1, we can again look at the individual components:

 

As should be clear, the improvements suggested by Kevin C generally improve performance across the board.  Unfortunately, in the 2nd scenario with the flattening, the multiple regression method still tries to compensate for the flattening by decreasing the diagnosed influence of volcanic recovery, therefore leading to a misdiagnosis. 

Dikran Marsupial noted in the comments of that last post that “there are no free lunches.”  Perhaps this helps drive the point home that assuming an underlying linear trend will lead to this misdiagnosis if the increase is not linear.  I hope to investigate further the actual influence of solar + volcanic activity on recent temperatures using some GCM runs.     

Our paper on UHI in USHCN is now published

As you know, my first interest and the bulk of the early articles for this blog dealt with the question of the urban heat island (UHI) influence on U.S. historical temperatures.  Our paper is now available (pre-print version) on this topic, and Zeke (the lead author of the paper and the one who wrangled everyone together!) and Matthew Menne put together a good post on it over at realclimate.  

Apart from the use of several different proxies for urbanization, and the thorough treatment of many UHI-related topics, I personally think an interesting aspect of this paper is how it  delves into the potential issue of “urban bleeding” during homogenization.  For those that have followed various discussions on the topic over the past few years, or have read this paper already, it is clear that the UHI signal appears much more strongly in the TOB data than in the F52 homogenized data.  A while back I also had a post, using synthetic data, that showed how the F52 algorithm could potentially alias some of the heat from urban stations into rural stations, thereby removing the appearance of UHI without removing the UHI itself.

On the one hand, if you look at figure 9 in the paper, I think it confirms the concern that the homogenization process could potentially spread urban warming to rural stations, as seen in the urban only adjustments.  On the other hand, I also think it shows that in the case of USHCN v2, this effect is pretty minor based on using only ISA < 10% for adjustments.  Now, one might wonder about UHI spreading from stations with ISA < 10% (that is, whether these “rural” stations are not strictly “rural”, and are themselves are contaminated by the UHI).  Thus, I thought it might be interesting to show another couple of figures here, which shows the difference in the “urban” vs. “rural” trends based on what cut-off in the ISA classification is used to define “rural”:

As you can see, the bulk of the UHI signal in TOB comes from those stations with ISA > 10%, such that the use of 10% seems a pretty solid cut-off for “rural”.   

Nevertheless, for an additional demonstration, we can use only the most rural stations (< 1% ISA) from a dataset that has only been adjusted by other most rural stations (< 1% ISA).  Here is that final result when compared against the gridded F52 all-adjusted, as well as GISS:

 

From a visual perspective, it seems fairly clear to me that there is not much difference, and the numerical results below seem to bear this out for the most part.  The exception is one we discussed in the paper, where the USHCN v2 all may have some residual UHI in the early part of the record and require an additional adjustment (as the one used in GISS).

1960-2010 Trends

F52 all: 0.224 K/Decade

F52-ISA01-ruralAdj: 0.219 K/Decade

GISTemp: 0.208 K/Decade

1885-2012 Trends

F52 all: 0.072 K/Decade

F52-ISA01-ruralAdj: 0.054 K/Decade

GISTemp: 0.058 K / Decade

It is thus my opinion that the impact of UHI in the homogenized USHCNv2 is minor.  This paper does not specifically speak about the UHI influence on a global scale, nor does it specifically consider micro-siting issues.  However, my initial impressions regarding the homogenization lead me to believe that there is unlikely to be any strong micro-siting bias permeating throughout the USHCN dataset.

For those interested, Zeke has already linked to the code used for the paper here.   The specific tests I ran for this post make use of that Java code and data, and the R script for graphing and batch files (which can easily be converted to shell scripts) are available from me here.

Could the multiple regression approach detect a recent pause in global warming?

Note that by “pause in global warming” I am specifically referring to a near-halt in the underlying low-frequency signal of surface temperatures (not ocean heat content), a signal not influenced by the typical “exogenous factors” of ENSO, volcanoes, or solar activity.  This has been recently attempted in Foster and Rahmstorf (2011), from which they conclude that from the “removal” of these three factors via multiple regression they have “isolat[ed] the global warming signal” and that “there is no indication of any slowdown or acceleration of global warming, beyond the variability induced by these known natural factors.”  Rahmstorf et al. (2012) proceeds to compare this adjusted temperature evolution to model projections, which I think is particularly dangerous if what you get after this multiple regression approach is not the underlying signal.

Another title for this post could be, “does the multiple regression approach actually reveal the underlying signal”?  Or, without spoiling too much, “is the Pinatubo recovery still contributing to the surface temperature trend?”  I attempt to test this using two scenarios from a simple energy balance model, with script available here.  The model is of the form ( the discrete unit of t is a month):

Which is basically the same as my previous energy balance model, except that because of the multi-decade span I have included an ocean diffusion term, which just transfers 50% of the mean TOA radiative imbalance of the year to below the mixed layer, and I’ve separated out V as the flux into the mixed layer from deeper ocean to distinguish it from a radiative forcing.  It is radiatively forced by a linear “anthropogenic component”, volcanic activity, and solar activity.  Variation is also induced via ENSO, and, in the case of scenario 2, a 60-year oscillation, represented by a heat flux from the lower ocean into the mixed layer.  Since we will force this model using the same datasets/indices that we use to remove the influence, and we don’t introduce any other noise, I consider this a best-case scenario for the multiple regression approach.

First, we have scenario 1.  This has only the three “exogenous” factors and the linear anthropogenic forcing.  The red line represents the global warming ”signal”…that is, the model run without the additional three factors.  It starts in 1955, and thus takes a bit of time to react due to the ocean terms, but as you can see from 1979 on the “signal” is pretty much a straight line. 

 

Next is scenario 2.  Here again, I have included all the factors from scenario one, but I have also include a 60-yr oscillation on top of the anthropogenic forcing for the underlying low-frequency signal, which basically increases the warming trend from 1980-1995, but counteracts much of the anthropogenic forcing from 2000 to present to produce a virtual “pause”.  I have included NCDC temperature anomalies to show that the modeled temperature result is pretty realistic, although with the amount of tunable parameters here (mixed layer heat capacity, ocean diffusion, radiative restoration strength) I will not be patting myself on the back for the match.

Next, I use the output from the modeled temperature and run the multiple regressions similar to the FR11 method (I do not include a Fourier series as the model contains no annual cycle).  Ideally, if this method were perfect, I should be able to recover the red signal from the black. 

First, we have scenario 1.  For the solar and volcanic lags and “influence”, I found largely different fits when using the modeled T than FR11 found when using actual temperatures.  Perhaps this is a sign that a more realistic model would yield better results for the multiple regressions, although I ‘m not sure how using a model with more complexities introduced would make it easier to pick out the influence of the different components.

The original modeled T is in yellow, whereas the new reconstructed/adjusted temperature set, with the exogenous factors “removed”, is in black.  Here, we see a reduction in the variability from yellow to black, but the green line representing the slope from this  reconstruction has actually increased and is greater than the true “red” signal.  As such, I’m not sure the trend of black “adjusted temperatures” better represents the true signal (red) at all!

But the real test is scenario 2.  Here we have an actual pause in the underlying signal “red”, and we would hope that the multiple regression method, having removed exogenous influences, would still leave that true signal intact.

As you can see, this approach yields an extremely poor “reconstruction”.  One might even conclude that there was little slowdown in the warming since 2000 (trend of .178 K/decade in the reconstruction) if looking at this result, despite the fact that the true signal shows a near-halt over this period (trend of 0.037 K/decade)!

So, where did this multiple regression approach go wrong?  We can diagnose this by comparing the influence determined from each regression to the actual influence in my energy balance model (determined by running the model with only that component). 

First, I will note that the influence of ENSO is diagnosed extremely well.  This is no doubt due to using the same index with no noise for both the forcing and determining the influence, while also noting the high-frequency and relatively high magnitude of the influence.  A more complex model, or the real-world, would not likely lead to such results, but remember we’re looking at a near “best case” scenario here. 

Second, we see that the solar influence is largely over-estimated.  As I’ve indicated before, I think that it is hard to pick out the solar signal among the noisy data, and so given the slow-down in surface temperatures corresponding with a recent dip in solar activity, a regression model might conclude that this has a bigger impact than it actually does.

However, the biggest error here comes from an underestimate of the volcanic influence.  Whereas the regression “removal” essentially sees the influence of the exogenous factor end after the forcing ends (plus whatever lag is diagnosed), the energy balance model used here shows a continuing influence through the last decade as part of the recovery.  In fact, this in itself contributes about a 0.1K/dec trend to the most recent decade in the model! 

Personally, I am not aware of any studies suggesting that recovery from the Pinatubo eruption might still be contributing a positive trend in 21st century temperatures.  The question that arises, then, is whether this effect is just an artifact of my unrealistic model?  Unfortunately, not many CMIP5 groups performed a historical, volcanic-only simulation, and the one I looked at only goes through 2005.  Furthermore, the volcanic-only forcing simulations still include internal dynamics such as ENSO, so it is not that easy to isolate.  Nevertheless, here is what I found for the GFDL-ESM2M run (script here): 

 

I would say the results here are still ambiguous.  The red represents a Lowess smooth, and that at least tentatively suggests an increasing trend from 2000 to present from the Pinatubo recovery, if we were to assume that that peak around 2000 and dip in 2002 were internal ENSO dynamics.  Sadly, there are no more volcanic-only runs in the CMIP5 archive for this model to test that idea.  There are a couple other models in the archive that have multiple runs for this, I will see if they reveal anything extra.  I would also like to test the multiple regression method with different types of noise added to see how that impacts the performance as well.

Conclusions

From what I can tell, in this case, the multiple regression approach used by Foster and Rahmstorf (2011) [and Lean and Rind (2008), although I haven’t investigated the specifics of that paper] can produce misleading results, even failing to recognize a pause in the underlying signal.  In those cases, the “reconstruction” can be a worse representation of the true signal than the original, unadjusted results, and should not be used to test projections.  Of course, in this particular case, much of it seems to stem from a lingering effect of the Pinatubo recovery into the 21st century, which I am currently skeptical exists in the real world.

Climate Sensitivity, the Wall Street Journal, and Media Matters

I wanted to comment a bit on the recent Wall Street Journal article by Matt Ridley ("The scientists at the IPCC next year have to choose whether they will admit…that the observational evidence now points toward lukewarm temperature change with no net harm.") and the response from Media Matters ("Ridley is just plain wrong to claim that future warming will be mild or even helpful.") (HT BH) . The primary reason is that it deals with climate sensitivity and the energy balance equation we’ve now seen over and over again:

ΔN = ΔF – λ (ΔT)

Where F is the top of atmosphere (TOA) radiative forcing, N is the TOA flux imbalance (which can be derived from Ocean Heat Content, as I did in my own recent estimate), T is the surface temperature, and λ is the strength of radiative restoration.  We can thus solve for λ, and (assuming it is constant) determine the Equilibrium Climate Sensitivity (ECS) using 3.7 W/m^2 / λ.  (3.7 W/m^2 being the forcing associated with a doubling of CO2).  

1. What’s to like about the WSJ article?

Essentially, the sensitivity estimate is straight-forward and should be seriously considered (I’ve used a similar approach and got similar results).  Nic Lewis goes into more detail here.  It is his rework of the Gregory et al (2002) result, using more recent OHC estimates and aerosol forcings from AR5, that Ridley relies on to note that the 1.6-1.7 K sensitivity is below the likely value in the AR5 report.  So, let’s walk through how these numbers shifted to give the lower sensitivity between AR4 and the 2nd draft of AR5, and see to what extent the Media Matters vs. WSJ pieces have merit.

These numbers are rough, as I’m reading them off the IPCC figures, but essentially for AR4-era estimates you have (in changes from 1880):

Temperature: 0.75 K
TOA Imbalance: 0.85 W/m^2 (from Hansen et al., 2005 modelling effort)
Anthropegenic Aerosol Forcing: -1.2 W/m^2
Other Forcings: 2.9 W/m^2

To solve for λ, we would have used Net forcing (2.9-1.2 W/m^2) minus TOA imbalance (0.85 W/m^2) divided by T (0.75 K) to yield a λ of 1.13 W/m^2/K.  The estimated ECS from AR4 is thus 3.7 W/m^2 / 1.13 W/m^2/K = 3.3 K…so at least this approach would have yielded an estimate in line with IPCC AR4 estimates using the older numbers (one might have pointed out at the time that the strong aerosol forcing was not supported by the NH/SH warming ratio, or that using the energy balance models on volcanic eruptions yielded lower sensitivities, or that the OHC data did not support an 0.85 W/m^2 estimate for TOA imbalance, however).

Flash forward to the AR5 2nd draft, and we have updated best estimates:

Temperature: 0.75 K (no change here)
TOA Imbalance: 0.5 W/m^2 (from Loeb et al., 2012, down 0.35 W/m^2)
Anthropogenic Aerosol Forcing: -0.7 W/m^2 (Difference of ~ 0.5 W/m^2 from before!)
Other Forcings: 3.2 W/m^2 (increase in CO2 forcing)

So, essentially, not only have we decreased our estimate for current TOA imbalance, but we have also greatly increased our net forcing, primarily as a result of a lessening of the cooling effect by aerosols.  If we only updated our TOA imbalance, the resulting estimate would be an ECS of ~ 2.3 K.  Updating both that AND the net forcing yields an ECS of around 1.4 K (the difference from Nic’s value comes because of slight differences in the adjusted forcing and because he is using a more robust method which accounts for uncertainties in the individual variables).

I want to stress that Nic Lewis’s approach is nothing new here (as he acknowledges), nor is it out of the mainstream.  I think the method is conceptually sound and this estimate in this WSJ should be taken seriously.  While there are reasons why this may not be the end-all be-all estimate (I get into that below), I do think it is indeed somewhat awkward for it to fall outside the range of "likely" estimates (2-4.5 K) from the IPCC report (although this may just be a consequence of how it is put together).

Moreover, the fact that the AOGCMs generally do a poor job of simulating the magnitude of λ (which is directly tied to the sensitivity), as I go over in a slightly different period, should raise serious questions about their ability to produce accurate sensitivity estimates on longer timescales.  This is because while temperature may be greatly affected by things like the rate of ocean diffusion and ENSO variations, making the link between temperature on shorter scales and climate sensitivity less obvious, the understatement of λ typically indicates an overstatement of ECS (with caveats that I will note in the bottom section). 

2. What’s to like about the Media Matters article?

To me, not a lot.  There are reasons to be skeptical of the sensitivity estimate in Ridley article, but MM fails to focus on these, instead quoting scientists and making points that do not actually engage the issues:

First, Ridley wrongly argues that three variables factored into current climate models are overstated (and thus that climate models are "unproven"). In fact, experts agree that the impacts of each variable that Ridley cites — the cooling effect of aerosols (or particles in the air); the rate of heat absorption by the world’s oceans; and the role of water vapor in amplifying climate change — are unambiguous.

First, given the large uncertainty in the aerosol forcing, I’m not sure I would consider their impact "unambiguous".  MM quotes John Abraham, who notes that "it is very clear [aerosols] have a cooling impact", and Kaufman, who notes that "I know of no evidence that would suggest that the temperature effect of sulfur emissions are small".  However, Lewis (and Ridley) is not claiming that aerosols do not have a substantial cooling effect…in fact they are noting that recent best estimates indicate that the cooling effect is likely closer to -0.7 (-0.9 adjusted) W/m^2 rather than the -1.2 (-1.4 adjusted) W/m^2 estimate of before.  Neither Kaufman nor Abraham’s statement would seem to contradict the value used.

Second, MM notes, "As this chart from Skeptical Science shows, the rate of ocean heat absorption remains high".  Unfortunately, it again fails to quantify this.  In fact, the chart referenced is using the same Ocean Heat Content data used by Lewis!  If you take the slope of the recent decade on the chart to convert from OHC to TOA imbalance, and convert the units appropriately, you get the same TOA imbalance used by Lewis…well down from the previously modeled assumption of 0.85 W/m^2.  So again, nobody is claiming here that the ocean isn’t heating up, but rather that this rate is ~0.5 W/m^2 from observations rather than the 0.85 W/m^2 from modeling efforts.

Neither of these objections are of any value in assessing the sensitivity estimate.  The MM articles does, I think, correctly point out that Ridley makes some claims about water vapor that are contradicted by most observational evidence.  I get into that below.

3. What’s to be skeptical of in the WSJ article?

For one, I find the claim that "’We don’t even know the sign’ of water vapor’s effect" highly dubious.  Unlike cloud feedbacks, which may behave very differently in response to ENSO variations versus longer timescales, the water vapor feedback appears to be certainly positive across all timescales, as one would expect from the physics.  Even if the "water vapor effect" is extended to include cloud feedbacks, the net effect of these two is almost certainly positive.  Consider even those lower estimates of 1.2K to 1.7K.  This ranges from a net neutral feedback to a slightly net positive feedback relative to the Planck response…since the magnitude of the negative lapse rate feedback is likely greater than the magnitude of the positive albedo feedback, the combined water vapor + cloud must still be slightly positive to get to that 1.2K level.

Now, one may argue that the water vapor feedback hasn’t been as positive lately as in models, largely due to the warming distribution, as I’ve done previously on this blog.  However, such a distribution is almost completely counter-acted by a lessening of the negative lapse rate feedback with the same distribution, as I also went over, due to the close relationship between the two.  In fact, the combined water vapor + lapse rate feedback is very similar across all AOGCMs (in stark contrast to the cloud feedback).

Second, the claim that < 2 C ECS means that future warming won’t be dangerous, or the lack of discussion of paleo estimates (seemingly implying they are unimportant), both made me raise my eyebrows.  I am not particularly familiar with the literature in these areas, but I would definitely classify those more as opinions rather than well-established science.

Third, the real reason to be wary of the sensitivity estimate is the possibility that λ varies across timescales.  This is related to why I think we need to consider paleo as well, and is the typical reason one should be wary of making certain estimates for ECS while in transient states.  This is NOT to be confused with saying that the Gregory et al. (2002) method used by Lewis is calculating the transient sensitivity (it is indeed calculating ECS), or that the method does not take into account heating "in the pipeline" (it does indeed via the ocean uptake term).  Rather, it is possible that the strength of feedbacks themselves change between (for example) 100-year timescales and the hundreds to thousands of years it takes to equilibriate.

This has been discussed several times on this blog and elsewhere (I’ll just refer to here for now for some background).  However, suffice to say, it is not clear whether the "effective sensitivity" response (λ_eff) calculated from transient states departs significantly from the "equilibrium sensitivity" response (λ_eq), or even whether this effect means using transient states would lead to underestimates or overestimates of climate sensitivity.

The following table highlights the relationship between T_eff and T_eq in the CMIP3 models, calculated with numbers taken from Winton et al (2010) and Soden and Held (2006):

 

Model	T_eff/T_eq
GFDL CM2.0	1.02
GFDL CM2.1	0.75
GISS ER	0.92
IPSL	1.29
MIROC MEDRES	0.85
MRI	0.72
MPI ECHAM5	1.34
NCAR CCSM3	0.90
NCAR PCM1	1.12
UKMO HADCM3	1.03
Mean	1.00
SD	.21

As you can see, the models average out to about 1, meaning that T_eff may very well be a good estimate for T_eq.  On the other hands, you see several models where they two values diverge, so on top of all the other uncertainty in this method, we are also uncertain about this factor.  I don’t know of any source for the CMIP5 model relationships since running them to equilibrium is not part of the experiment, and in fact Andrews et al. (2012) uses the "effective sensitivity"/transient state method to diagnose ECS for the CMIP5 models (albeit using an instantaneous quadrupling of CO2).  Of course, if this T_eff is much smaller in observations than in AOGCMs, it is worth questioning whether these AOGCMs actually provide any solid insight into the T_eq/T_eff factor at all.      

Changes in feedback strength with time: a look at the 1pct2xCO2 GFDL CM2.1 experiment

In this half-baked post, I want to look a bit more at the issue of how the radiative response (λ) in our familiar equation (ΔN = ΔF + λ*ΔT) changes as we progress through the 1% CO2 increase per year to doubling experiment in GFDL CM2.1.  As we’ve discussed before, this issue makes it extremely difficult to diagnose equilibrium climate sensitivity (ECS) in models even if we have 100 years of the exact global energy balance observations. The "effective sensitivity" (λ after 100 years in the A1B scenario, per the label in Soden and Held (2006)) when used in the equation F_2xCO2 / λ , may yield an ECS that is greater or lower than the actual ECS of the model.  Examples of the two extremes in CMIP3 (per Winton et al. 2010): 

1. For MPI-ECHAM5, "effective sensitivity" λ = -0.88 W/m^2/K, F_2xC02 = 4.01 W/m^2, yielding ECS (assuming constant λ) of 4.01/0.88 = 4.6 K, compared to the actual ECS 3.4 K.
2. For GFDL CM2.1, "effective sensitivity" λ = -1.37 W/m^2/K, F_2xCO2 = 3.5 W/m^2, yielding ECS (assuming constant λ) of 3.5/1.37 = 2.6 K compared to the actual ECS of also 3.4 K.

But really, the issue is more than just about whether λ after 100 years matches the "final" value for λ from a CO2 doubling.  In the real world, we have far less data relevant to the Earth’s energy balance (a little over a decade of continuous satellite measurements, with OHC extending back further, as I used previously), so knowing how the radiative response (λ) changes with time and temperature would be crucial for diagnosing longer-term sensitivity.  Again, I will recommend the Paul_K post on the Blackboard and Isaac Held’s post or more in-depth background. 

Unfortunately, from the CMIP3 archive, only 220 years of the 1% increase to CO2 doubling is available, which is far from the time it takes to achieve equilibrium.  Nevertheless, by plotting the CO2 doubling forcing (3.5 W/m^2 in CM2.1) minus the radiative response to T (very similar to Dr. Held’s graph in that post), we can still see that λ (the relationship between the radiative response and T) is not a constant, as the values plotted drop below the "constant λ" (3.5/3.4 = 1.03 W/m^2/K) line. 

I wanted to explore a case for the apparent non-linearity in the global radiative response strength being the result of differing spatial patterns in the surface temperature changes in different time frames.  Let’s suppose that the surface temperature change in each latitude band affects almost exclusively only the outgoing radiation over that same latitude band, such that dR_lat/dT_lat is a constant value.  Potentially, we could get an apparent non-linearity in the global radiative response if the relative rate of heating at different latitudes changes.  This is actually an extremely simplified scenario of the more general situation described by Dr. Held.  Unfortunately, my simplified case here does not hold:

    
Clearly, there are significant changes in dR_lat/dT_lat over the two periods.  This is NOT to say that the differential warming pattern alone isn’t responsible for the apparent non-linearity, but rather that surface temperatures at one latitude must significantly affect the TOA imbalance at another latitude (circulation and cloud changes) or the spatial pattern within a particular latitude must be important, if we are to maintain this idea.  It is possible that using broader regions (rather than single latitude bands) could better capture this, which I will explorer in the future.  

Here is how each latitude warms per 1 degree of global increase in the differing periods:

And for reference, in those periods, here is what the radiative response strength looks like relative to the global temperature increase:

Northern vs. Southern Hemisphere Warming

While looking at this experiment, I also want to harken back to a previous post on the NH vs. SH rate of warming.  Here is how the two hemispheres warm in this experiment:

 

The ratio of NH to SH trends for 30, 50, 100, and 220 years respectively are 2.2, 1.3, 1.3, and 1.5.  This would seem to suggest that, at least in this model, it is unlikely that GHG would account for the ratio of around 3.3 we have seen in recent GISS temperatures, particularly given that aerosols produce the stronger negative influence in the NH.

Code and data (you’ll need to download the runs from PCMDI)

CMIP5 Effective Sensitivity vs. Radiative Response in Last 40 Years

This post forms part 2 of the series I started in the last post, which focused on using the energy balance over the period of 0-2000m OHC data to estimate sensitivity.  As you recall, I noted that using the radiative response over this shorter period actually overestimated temperature sensitivity in the GISS-ER and GFDL CM2.1 model runs, so I wanted to test how the radiative response over this shorter period compares to the “effective sensitivity” in all the CMIP5 runs. 

1. Effective Sensitivity in CMIP5 Runs

Note that I am using “effective sensitivity” here in the sense of Soden and Held (2006)…the net radiative response to an increase in surface temperature over a long term scenario (units W/m^2/K).  In my specific case, I am using the RCP4.5 scenario runs from the CMIP5 models, which hold fixed a 4.5 W/m^2 anthropogenic forcing change in 2100.  In addition to the forcing difference, I use the difference in net radiative imbalance and temperature between the two periods 1860-1880 and 2080-2100. 

The data I grabbed from Climate Explorer using a script (you’ll need to register and insert your own e-mail address), which I developed with some help from this Climate Audit post that cut down the learning curve.  This is not a complete set of all CMIP5 models available at Climate Explorer at the time, as some seemed to be missing radiation fields and others caused my script to choke, but it is *almost* all of them.  Anyhow, here are the diagnosed “effective sensitivities” in the individual model runs (note again that if you were assuming a constant radiative response, you could determine the equilibrium climate sensitivity based on 3.7/effective_sensitivity):

I have not compared these results to Andrews et al. (2012), but if anybody has a copy of this paper I would love to do so.  Anyhow, as you can see, each of the model runs are pretty tightly clustered with other runs within the model, which is to be expected.  One exception was CESM1-CAM5, but after looking at several of the runs it was clear that they had an offset in the splicing of the beginning of the RCP4.5 run onto the end of the historical run.  Looking at this chart again, I’m noticing something suspicious in one of those CCSM4 runs, with 5 runs very closely clustered and then 1 “rogue” one.  I will need to check if that is an offset error as well.  Anyhow, here is a look at the mean “effective sensitivities” and number of runs for each model:

 

2. Shorter-Term Radiative Response (from last 40 years) in CMIP5 Runs

In order to test the method I used in the last post, here we will determine the radiative response based on the difference (in TOA imbalance and surface temperature) between the the 2005-2011 period and the 1965-1974 period.  The latter period was determined by finding the best correlation between the resulting radiative response diagnosed for the models and the longer “effective sensitivity” for those same models. 

One huge difficultly with determining this radiative response for a model is that the TOA forcing data is simply not available (at least, in my experience).  It requires a special fixed SST run to do this calculation***, and I don’t believe this is included in the CMIP5 archive.  Thus, I have decided to simply use the GISS forcings for ALL the calculations, and this will cause some slight inaccuracy in the diagnosed radiative response for other models.  Nonetheless, here is the radiative response as diagnosed:

For reference, using the GISS estimate for the aerosol forcing (and not the IPCC one, which is of smaller magnitude), my test in the previous post resulted in a –2.4 +/- 0.8 W/m^2/K response over this same period, which is a good deal stronger than most model runs.  

***The Forster and Taylor (2006) method uses the inverse of the long-term radiative response to estimate forcing, but we can’t do that here because we are testing the relationship between the shorter-term and long-term response, and the assumption that these would be the same would be begging the question. 

3. Relationship between 40 year Radiative Response and Effective Sensitivity

The plot below shows the relationship between the 40-year response and the effective sensitivity.  The r^2 value is 0.36, which is pretty strong despite the fact that I have essentially ignored the difference in aerosol forcing between the models. 

So, what can this knowledge, combined with the previous test, tell us about effective sensitivity of the real world system?  The chart below includes red lines showing the least/likely/most radiative response from observations over that same period (–2.4 +/- 0.8 W/m^2/K, again assuming GISS forcings rather than the IPCC): 

If we were confident in that regression, our “likely” estimate for “effective sensitivity” would be right around –2.0 W/m^2/K, which would correspond to an ECS of ~ 1.85 K if we assumed a negligible difference between the “effective sensitivity” radiation response and that response over the full time it takes to equilibrate.   However, I don’t think much stock can be placed in that regression, given that we have not used particularly accurate forcing data for the individual model aerosols, and the radiative response is well outside the main cluster of models.  I think this latter fact is the more interesting qualitatively – there IS a fairly strong underlying relationship between this 40 year radiative response and the longer term “effective sensitivity”, and only 3 model runs of all the model runs looked at here have this radiative response fall within the 2.5%-97.5% uncertainty range as diagnosed from OHC in my last post.  Of those, 1 of those “compatible” runs is a rogue CCSM4 run that is almost certainly affected by an offset issue.  I am curious about the other 2 models/runs that diverged from the pack as well, but these don’t seem likely to be “rogue” runs because their corresponding effective sensitivities (which would also be affected by an offset issue) are normal.  Regardless, given that the modeled aerosol forcings tend to be larger in magnitude than in satellite estimates, this line of evidence would suggest it is even more likely that the effective temperature sensitivity of almost all CMIP5 models is too high.

This presents an additional test to just comparing temperature trends to models, because temperature and radiative imbalance will be negatively correlated if all else is kept equal.  So in the event that you get a lower temperature trend in the real world than models due to La Nina conditions towards the end of the period, you should see an increase in TOA imbalance relative to models as a consequence of this unforced cooling, assuming the radiative response between the real world and models are about the same.  However, as both the temperature trend AND TOA imbalance trend are smaller than almost all CMIP5 models over this period, La Nina would not serve to explain the situation.  This leaves some combination of the following possibilities that I can see: 1) incorrect diagnosis of TOA imbalance from 0-2000m OHC, 2) aerosol forcing greatly exceeds that of GISS (which itself greatly exceeds the IPCC best estimate), 3) some other unknown forcing, 4) too high of effective temperature sensitivity in the CMIP5 models.    

Data and Code

The following script, ProcessCMIP5Data.R, accesses the CMIP5 data in my public folder and creates the figures for the above post.  HOWEVER, it is quite a few files, and processing will be slow if you run the above turnkey script.  Instead, I recommend you download the data to your local machine first, unzip it, and then change “baseURL” in the above script to point to your specific folder you unzipped it into.