There seems to be a good amount of confusion about what the "missing heat" refers to, as well as what implications the Balmaseda et al (2013) paper has for this missing heat. So first, here is my quick summary:
In many ocean datasets, there seems to be a discrepancy in the rate of ocean heat uptake up to the mid 2000s, and the uptake afterwards, with this more recent rate of uptake appearing to be smaller. However, neither models nor satellites show a decrease in the TOA imbalance (as the increased forcing should only exacerbate this imbalance). The "missing heat" means that theoretically, there should be more heat going into the ocean (that is, at the same rate as before). The other possibility is that there was "extra heat" before – that is, the discrepancy in the ocean heat uptake is an illusion, and that prior calculations were overestimating this heat uptake. This latter assumption would imply that the GCMs are generally overestimating the TOA imbalance.
Now let’s look at this within the context of Balmaseda et al., (2013):
Indeed, you can see that even in the purple line, the slope in the early part of the 2000s is larger than that of the later part of the decade. After digitizing this and calculating the TOA imbalance, I get 1.23 W/m^2 for the first part of the decade (2000-2004), and 0.38 W/m^2 for the last half (2005-2009). That is a huge discrepancy. So let’s see if we see something similar in the satellites(CERES SSF1 degree net TOA imbalance annual anomaly):
A drop of ~ 0.85 W/m^2 should be quite obvious in this graph, but there is no sign of that at all. Rather, the average imbalance from 2005-2009 is about 0.17 W/m^2 *larger* than that from 2000-2004. If we called the combined discrepancy of ~ 1 W/m^2 imbalance for 5 years the "missing heat", we are talking somewhere around 8 * 10^22 J.
Note that we are only using the satellites in this context in terms of *relative* TOA imbalance. Some are under the misconception that we are able to measure the absolute TOA imbalance via satellite, and that using ocean heat content is just a secondary check (that is, we know that the extra heat is somewhere in the earth system from satellites, and just need to look harder to find it in the ocean). This view is incorrect. As explained in Stephens et al., 2012:
The combined uncertainty on the net TOA flux determined from CERES is ±4 Wm–2 (95% confidence) due largely to instrument calibration errors. Thus the sum of current satellite-derived fluxes cannot determine the net TOA radiation imbalance with the accuracy needed to track such small imbalances associated with forced climate change
In other words, in terms of determining the absolute energy budget, ocean heat content is really the only game in town. Satellites instead provide a check in terms of the evolution of this ocean heat content data, and have managed to raise a red flag in the ocean heat uptake slowdown. In this much, I don’t see that Balmaseda et al. 2013 hasn’t really solved the case of the "missing heat", as we still see a large unexplained discrepancy in the rate of ocean heat uptake. While surface winds and deep ocean heat warming may help explain a pause in surface warming, it does not explain this lower implied TOA imbalance.
Loeb et al. 2012 essentially “solved” this problem by noting the large uncertainties in the ocean heat datasets, which implied that the apparent discrepancy was likely an artifact of inaccurate ocean measurements. Given the vastly larger coverage of ARGO from 2005 on, and the fact that these estimates range from implied TOA imbalances of ~ 0.38 W/m^2 to 0.6 W/m^2 (von Shuckmann and Le Traon, 2011; Stephens et al, 2012; Hansen et al, 2011, Masters 2013), and that we actually see a slight increase in TOA imbalance towards the later part of the CERES decade, I suspect that the huge rate of heating in the early part of the decade in Balmaseda et al. 2013 may be an artifact as well. Such would imply that the B13 primary published ocean warming of 1.19 +/- 0.11 W/m^2 in the 2000s (0.84 W/m^2 globally) may be 1.5x to 3x too high.
In the next post, I hope to look at this last point in some more depth , and at "missing heat" in terms of TOA imbalance relative to various GCMs.
Troy's Scratchpad 
The observations actually suggest that the anomalous uptake of heat in the oceans during the early 2000’s was in fact fact real. You could, of course, legitimately argue over the magnitude, but not over whether this happened. This can be confirmed by looking at Svedrup transport, in other words, the transport of ocean volume (currents) from the equator toward the poles (meridional). As the wind-driven ocean circulation intensified in the early 2000’s, it spun up all the subtropical ocean gyres. The intensified Ekman pumping in the Taylor columns at the centre of the gyres would have caused a vertical displacement of isopycnals (stronger warming of the deep ocean) and a slight equatorward shift of the gyre axis. A stronger return of ocean volume in the subsurface layers toward the equator, would have been balanced by stronger surface poleward transport in the swift and deep western boundary currents, and stronger poleward return in the weaker, shallower, eastern boundary currents. The intensified easterly trade winds near the equator (where the Coriolis Force is zero) would have forced stronger upwelling (Ekman suction) of deep cold water in the eastern tropical Pacific.
All this has been observed and described in the scientific literature over the last decade, and cannot be simply handwaved away. The ocean-based observations suggest that the theoretical underpinnings of oceanography are largely correct.
As for the top-of-the-atmosphere (TOA) imbalance, yes, ocean heat content is what we have to work with, but you appear to be guilty of oversimplifying this. Ocean heat uptake is a good measure of the TOA imbalance over time, but not so over short intervals. The reason should be obvious – clouds. Indeed, satellite and ground-based observations suggest that a strong reduction in solar radiation reaching the Earth’s surface (predominately the Southern Hemisphere) did in fact happen between about 2004-2007. This is not only supported by the ocean temperature measurements, but by Svedrup Transport slowdown and the accompanying spin-down of the subtropical ocean gyres from around 2004 onwards. Another supporting piece of evidence are the trends in ocean heat content for the respective 0-700 and 700-2000 layers. A short-term reduction in surface solar radiation at the ocean’s surface should cause a slowdown in the rate of warming in the surface layers, but not so in the deeper layers. Why? Think of it in terms of volume transport. Less heat will be going into the 0-700 layer, but the rate of heat loss, from the upper layer into the 700-2000 metre layer below, will still be occurring for a time. There should, of course, be a slowdown in warming of the deeper layer when the cooler water eventually reaches the deep ocean. Then there’s the trend in global oceanic evaporation – it nosedives around 2004 too.
I will be interested to see what you come up with, but there’s a whole lotta evidence to indicate that the anomalous ocean warming in the early 2000’s, followed by a slowdown, was in fact real (and I didn’t get to discussing the sea level trends which support this too). Whether this is connected to the large-scale shift of industrial sulfate pollution to Asia, or to increased sulfate emissions from tropical volcanoes, is still being debated in the scientific literature. But ocean heat uptake has increased again (after the mid-2000’s slowdown, and industrial sulfate pollution has shown a dramatic decline since around 2007-2008.
If you really want to ascertain whether the complex evolution in ocean heat content during the 2000’s was real, I would suggest you look at the sea surface height anomalies over that decade.
Comment by Rob Painting — July 19, 2013 @ 4:26 pm
Hi Rob, thanks for stopping by. To address your points:
To be clear, I am suggesting that if the satellite data are to be believed, we should be dubious of the apparent drop in the rate ocean heat uptake around the mid-2000s. There would need to be an unusually high ocean heat uptake in the early part of the decade even if this were the case that the pre-2005 rate was an artifact, to maintain the relatively stationary surface temperature in spite of the positive TOA imbalance (let’s say approximately 0.4 W/m^2). I would be interested to read something that quantifies the effect the phenomenon you describe…that is, based on the observation of these events, what level drop should we have expected in the rate of ocean heat uptake during that time?
I disagree. Clouds have a profound effect on regulating the Earth’s temperature, both in terms of albedo and OLR absorbtion, but this happens at TOA…you seem to be suggesting they can explain the divergence between the TOA imbalance and the rate of ocean heat uptake. If we truly had ~ 1.4 W/m^2 “deficit” in the rate of ocean heat uptake relative to what we’d expect at TOA, the extra 8 x 10^22 J over this time would require on the order of a ~ 10 K rise in atmospheric temperatures if it were “hidden” in the atmosphere. Obviously nothing like this was observed.
The reasons why ocean heat content may not be a good measure of TOA imbalance over the short term are a) the measurements carry a lot of uncertainty, or b) the ocean heat uptake over that time may be comparable to the heat exchange between the observed ocean and: deeper ocean, cryosphere, land, or atmosphere. However, 8 x 10^22 J is > 5 times the TOTAL heat estimated taken up since 1970 by the cryosphere+land+atmosphere…there’s no way any of those could hide anywhere near that amount of heat (I do not think). Thus we are left with (a), uncertainty in ocean heat measurements, which is what Loeb et al. suggested (and I’ve noted) in reconciling with satellites.
From the global perspective, the satellites do not appear to show such a change in CRF…see figs 1 and 2 here:
http://www.earth-syst-dynam.net/3/97/2012/esd-3-97-2012.pdf. Perhaps a small reduction in surface solar radiation occured, but given the lack of evidence that a corresponding TOA change occurred, I am dubious that when averaged globally this would come anywhere near explaining the apparent change in rate of ocean heat uptake that B13 suggests.
Again, can you explain a bit more quantitatively how this trend relates to the problem of “missing heat”. Because without noting a TOA imbalance that would show up with the satellites, there is limited capacity for the atmosphere “hiding” the extra heat from the ocean uptake.
From the latest publications (e.g. Guemas et al 2013, Watanabe et al 2013), neither of those explanations seem to be finding much favor. This is because based on stratospheric optical depth, volcanic activity seems to account for at most ~0.1 W/m^2 in the second half of the decade. Similarly, Murphy (2013, Nature Geosciences) suggests a small global effect from the regional distribution of aerosols. Obviously, neither of these is the last word, but I also want to point out that any huge effect from these would occur at TOA and thus should be apparent in the satellite record. These explanations do little to solve the discrepancy between the satellits and ocean measurements that is the basis for the “missing heat”.
I would be happy to hear quantative arguments over what this implies, but sea surface anomalies seem like they would be affected by a variety of sources – ice melt, groundwater runoff, etc. – and only a portion of that is the steric component.
You mentioned that we could “argue over the magnitude” of how much larger the 2000-2004 ocean heat uptake could be relative to that after…perhaps we could agree on a maximum amount that would remain consistent with satellite observations. As of right now, without a quantitative argument, I don’t see that it could be anywhere near the amount that B13 implies (I’m not saying their estimate shouldn’t be published, only that it highlights an inconsistency with satellites).
Comment by troyca — July 22, 2013 @ 8:30 am
Troy – It’s rather too long-winded to explain in detail here, but here are my thoughts:
You are using the ocean heat content as a proxy for the TOA imbalance, but this may be too simplified. The OHC results from the TOA imbalance and the capacity of the ocean to absorb sunlight in the surface layers. When the wind-driven ocean circulation spins up, it removes a large amount of heat from the surface of the tropical ocean through the intensified transport of water (containing properties such as heat) both downward into the ocean interior, and poleward. Strong upwelling (Ekman suction) in the eastern tropical Pacific, which accompanies the spin-up, and the diminished cloud cover, create conditions where the tropical ocean can absorb a large amount of heat. It is, afterall, where the majority of the incoming energy is received. It just so happens that the Earth switched to the negative phase of the Interdecadal Pacific Oscillation – a period where the wind-driven circulation intensifies – around 2000. This came right on the heels of a monster El Nino in 1997-1998 – where the tropical ocean discharged a non-negligible amount of heat into the atmosphere. These two acting in tandem would have primed the tropical oceans to absorb anomalous heat. This anomalous uptake of heat would imply a large TOA imbalance if the OHC was presumed to be a diagnostic of the TOA imbalance alone. However this overlooks the contribution of the huge, but temporary, ocean heat uptake (OHU) efficiency.
The dimming of surface solar radiation, indicated by satellite and ground-based instruments, which intensified after 2004 only complicates the picture – some of the heat was never there in the first place. This reduction in sunlight reaching the surface layers of the ocean, resolves some of the discrepancy in sea level rise through the 2000’s, i.e. the temporary slowdown in the middle of the decade. It may also explain why the wind-driven ocean circulation spun down so quickly from 2004 onwards – there was less energy going into the surface layers. Recent combined observational/modelled estimates may be biased low because of this underestimation of the negative aerosol forcing through the 2000’s. Very broadly-speaking the CERES data seem to agree with this hypothesis – as the data show an increase in the TOA imbalance after 2007.
Comment by Rob Painting — July 24, 2013 @ 3:09 am
Rob,
I believe this is where you are getting hung up. Apart from the relatively small heat uptake by the cryosphere, land, and atmosphere, the OHC (to the degree the measurements are accurate) IS a diagnostic of the TOA imbalance alone. The ocean heat uptake efficiency does NOT have to do with the relationship between total ocean heat content and TOA imbalance…rather, it relates the *surface temperature* to the TOA imbalance (i.e. ocean heat content tendency). The OHU efficiency is shorthand to refer to the relative distribution of ocean heat uptake at various layers…a higher efficiency generally implies the deeper ocean heat is increasing faster relative to the surface layers than normal, which means that you can get a larger TOA imbalance without the corresponding surface temperature increase. But since we’re using the ocean heat content of “all depths”, again, this does not affect the relationship between ocean heat uptake and TOA imbalance. There is simply no place for that heat to hide!
While the CERES data do not exclude the possibility of a small aerosol contribution, I do not think they generally support it either. The large 2008 TOA imbalance generally has to do with the large La Nina that year, and we would expect an increase in the TOA imbalance throughout decade regardless of aerosols, given the continued increase of GHG emissions without a large surface temperature increase to offset it. But this is really now ancillary to the point we were discussing above…I hope you agree there is nothing in the satellite record to corroborate the apparent change in ocean heat content tendency that the B13 dataset (and some others) imply.
Comment by troyca — July 24, 2013 @ 8:25 am
Troy – do you happen to know how deep “total depth (purple on the graph)” is in this paper?
Comment by JCH — July 23, 2013 @ 3:13 pm
I couldn’t say for sure, but I am assuming they are estimating the entire ocean. I would imagine that the contribution below 2000m is relatively small though.
Comment by troyca — July 24, 2013 @ 8:32 am
Troy, i can see that you are particularly fixated on the idea that heat is hiding somewhere. That’s because you won’t allow the possibility that a reduction in the amount of sunlight reaching the Earth’s surface, over the early 2000’s did indeed happen. I think the Goddard Institute for Space Studies (GISS) radiative forcing over the 2000’s pretty much tallies with the various observations. You are finding inconsistencies because you are beating up on a strawman.
The change in OHU (due to the spin-up of the wind-driven ocean circulation, and coming soon after the monster El Nino) occurred when the dimming appears to have started. That’s why the oceans could soak up a vast amount of heat despite a decline in the radiative forcing. You even allude to this in your last comment , where you state: “The large 2008 TOA imbalance generally has to do with the large La Nina that year” Now look back at the CERES data. Why do the El Nino in the early part of the decade of the decade exhibit such a muted response compared to the latter part? The CERES data actually supports what I have already stated – the early decade is muted because of the substantial negative aerosol forcing. It takes off like a scolded cat once the negative forcing declines (2007), and you get a big response to both El Nino and La Nina. That’s because there is suddenly more energy coming into the climate system. Is it just a conicidence that industrial sulfate pollution peaked around 2006-2007 and has been declining since? Maybe.
As it stands your hypothesis is at odds to various data sets and tells us nothing. Now you could be right of course, but there is a substantial body of evidence against it. My hypothesis, however, does explain a lot – ocean heat content, the evolution of change in the ocean layers, sea level change, ocean circulation response, the CERES data.
Comment by Rob Painting — July 24, 2013 @ 12:56 pm
Rob,
I am certainly *not* fixated on the idea that the heat is hiding somewhere…in fact I mentioned that it would be impossible for the implied quantity (if the 2000-2004 OHC of B13 is to be believed) of heat to “hide” from the apparent lack of variability in the CERES TOA imbalance measurements. This is the problem of “missing heat” that currently exists – I suggest reading Loeb et al. 2012 (http://xa.yimg.com/kq/groups/18383638/336597800/name/ngeo1375.pdf) for a primer on what the “problem” is. L12 essentially just argues for uncertainty in the early 2000 OHC measurements to primarily resolve this issue. Trenberth did not agree that this was much of a solution, and continues to feel that we haven’t closed the budget. Again, here is the “problem”:
1) CERES TOA measurements show no large drop in the TOA imbalance from the first half of the 2000s to the second half of the 2000s.
2) OHC measurements (particularly those of B13) DO imply a huge drop in TOA imbalance from the first half of the 2000s (primarily XBT) to the 2nd half (when ARGO was fully deployed) based on the differing rates of ocean heat uptake.
Obviously, there is a conflict here between two datasets. This is not my “hypothesis”, this is the problem that scientists have and are working to resolve.
In one of your previous responses, you argued against #2, saying that we could not be sure that the rate of ocean heat uptake would be an indicator of TOA imbalance over short periods due to the change in ocean heat uptake efficiency. As I pointed out in my last response, OHU efficiency has nothing to do with the relationship between OHU and TOA imbalance, but instead with the relationship between TOA imbalance and surface temperatures. Do you agree now that this is the case, and that there is a conflict between #1 and #2?
My tentative “hypothesis” was to suggest that the CERES TOA measurements and ARGO measurements were more accurate than the early 2000s XBT, and that for the early part of the decade, the rate of ocean heat uptake was overestimated. This is similar to the argument by L12.
This is not responsive on several counts. First of all, if we had a *reduction* in the amount of sunlight in the early 2000s, this would imply a *smaller* TOA imbalance in the early part of the decade than in the second part, which is the opposite of what the B13 data show. In fact, this would generally agree with my thought that the early 2000s larger TOA imbalance was an artifact. Nevertheless, the GISS radiative forcing data does not speak to this for a couple reasons, the primary one being that the TOA imbalance is a function of both F and the radiative response (lambda*T), with lambda being the strength of radiative response that is itself unknown. That is a whole other tangent though…
If the “dimming” occurred in the early part of the decade, this would *decrease* the TOA imbalance over that time. Again, this is the opposite of what the B13 data shows, and presumably the opposite of what you were previously arguing.
The data sets are “at odds” with one another, unless you add huge uncertainties, as L12 does. Again, this is why it is a problem and researchers are actively investigating. My “hypothesis” is to favor the satellites and ARGO over early 2000s XBT measurements, as one of those three must be the odd man out.
Your hypothesis, from your first post, was: “the observations actually suggest that the anomalous uptake of heat in the oceans during the early 2000′s was in fact real.” The B13 dataset (if you are choosing this set for your “observations”) indeed shows an implied 0.85 W/m^2 drop-off in TOA imbalance from the first half of the decade to the second. On the other hand, the CERES dataset shows no such drop. In that sense, your resolution to the “problem” is to discard the CERES data.
You then went on to argue that there was dimming from aerosols in the early part of the decade, implying a *lower* TOA imbalance in the early part of the decade, which is nominally consistent with CERES data…but of course this completely contradicts the B13 dataset (and hence what appeared to be your original point).
To move this into the quantitative realm, and perhaps help clarify both of our positions, I suggest we both state our rough estimates of the following: 2000-2004 TOA imbalance, and 2005-2009 TOA imbalance. For the sake of argument, here’s mine:
2000-2004: 0.4 W/m^2
2005-2009: 0.5 W/m^2
This is consistent with the CERES data, and with subsequent ARGO estimates of OHC. It is *inconsistent* with the B13 OHC data from 2000-2004…as I pointed out before, this is because any estimate will be inconsistent with one of the 3 pieces of data.
Comment by troyca — July 24, 2013 @ 3:22 pm
I really don’t understand the obsession with uncertainty. It’s a dagger that cuts both ways. And yes I have read, and written, a blog post about Loeb et al. The basic gist of which was that the error bounds were huge. You seem to be arguing that uncertainty only works in one direction. That certainly isn’t the case. Let’s just agree that the uncertainty is very large.
” If the “dimming” occurred in the early part of the decade, this would *decrease* the TOA imbalance over that time. Again, this is the opposite of what the B13 data shows, and presumably the opposite of what you were previously arguing.”
You are not grasping this at all. I have blogged about this many times before, so contrary to your assertion I have been very consistent. Consider this thought experiment:
Around 2000 the climate switched into a mode where capacity of the ocean to take up heat increased sharply. Coincidentally, the amount of solar radiation reaching the ocean surface declined (global dimming). Around 2004, the surface solar radiation (SSR) declined further – until around 2007, whereupon the surface solar radiation began to increase. We measure the amount of heat taken up by the ocean as a proxy for the TOA imbalance – seeing as we can’t measure this precisely with satellites. The ocean will be taking up heat due to the (temporarily) enhanced efficiency, but at the same time less heat will be going into the ocean. The OHC (TOA proxy) is a consequence of both processes.
If this is true, and I’ve collected together research which supports my hypothesis, then a whole raft of observations makes sense. For instance:
1. The oceans take up anomalous heat in the early decade despite a dimming in SSR.
2. OHC as a proxy for TOA is unable to distinguish between the two processes as they are occurring simultaneously.
3. This anomalous heat uptake is supported by the observations of the rapid spin-up of the wind-driven ocean circulation – which transports heat downward and poleward.
4. This is further supported by the changes in sea surface height – anomalous bulges indicating water mass transport in key areas of the wind-driven ocean circulation – such as the centre of the sub-tropical ocean gyres.
5. Global oceanic evaporation should also be affected by the amount of sunlight entering the surface layers. As the SSR declines global evaporation weakens.
6. This affects the interannual variability in sea level caused by La Nina & El Nino because the spatial distribution of heat in the surface layers alter global rainfall patterns. In other words, the exchange of water mass between the oceans and continents weakens and we observe less year-to-year variability in sea level rise.
7. Around 2004 the dimming reveals itself because it strengthens.
8. As a consequence the wind-driven ocean circulations spins down and the SSH anomaly rapidly declines.
9. Because of this relative change of heat going into the upper layer versus the lower layer, the heat content in each rapidly diverges. The upper layer slows quickly, but the lower layer does not because heat is still being transported down from the bottom of the upper layer – the ‘cooling signal’ takes time to reach down that far.
10. Strengthened dimming causes a sharp drop off in global oceanic evaporation around 2004.
11. Year-to-year sea level variability dramatically diminishes between 2003-2007 because evaporation off the surface oceans has nosedived.
12. Sea level rise slows despite an acceleration in the contribution of water volume from disintegrating land-based ice.
13. 2006-2007 sulfate emissions from industrial activity peak, and then begin to decline.
14. Coincidentally, we see the CERES data begin to show large swings associated with ENSO – suggestive of more energy once again coming into the climate system.
15. With more energy available once more, global ocean evaporation increases again (haven’t actually confirmed that yet).
16. The above is suggested by the year-to-year variability in sea level rise picking up once again.
17. Ocean heat content begins to trend upwards once again, and so does sea level rise – as the thermosteric component veers upward.
18. Climate sensitivity estimates based upon ‘recent’ observations & models diverge from paleo and climate model estimates because they underestimate the negative forcing by aerosols -particularly during the 2000’s. According to some research the observations imply a stronger negative forcing than even the climate models simulate.
19. This may explain why these estimates are biased low.
I’ve left out a bunch of other stuff, but I don’t see any broad inconsistency with Balmaseda et al. I could, of course, be wrong.
Comment by Rob Painting — July 25, 2013 @ 1:37 am
Rob,
I fear that by using qualitative terms without consideration of magnitude or equations to explain it, you are convincing yourself that something impossible (i.e. having a high rate of ocean uptake while simultaneously having a low TOA imbalance) is in fact possible. This is why I suggested in my last post we try to quantify these things.
Consider your statement:
Your first process, “heat uptake efficiency” (k below), refers to the relationship between the energy going into the ocean and the *surface temperature* change. That is:
(1) dOHC/dt = k * dT/dt
This “efficiency” is what you got hung up on before. It refers only to the relative uptake of ocean vs. the surface layer…since the surface layer heat capacity is substantially smaller, we are generally unconcerned with this ocean uptake efficiency for global energy balances, and only care when the analysis is of surface temperature trends (not relevant to the post or the “problem” I have mentioned with the B13 dataset).
The second process (a decrease in forcing, F) indeed affects the TOA imbalance:
(2) TOA_Imbalance = F – lambda*T
Let us call ALC the heat content of the Atmosphere+Land+cryosphere. We can relate TOA_Imbalance *exactly* to ocean heat content (assuming no measurement error) via:
(3) TOA_Imbalance = dOHC/dt + dALC/dt
As you can see, the efficiency term, k, plays almost no role in the relationship between TOA_Imbalance and dOHC, except that dT/dt modifies dALC/dt. However, we usually just drop this efficiency term because the minor effect it has on dALC/dt (and dALC/dt in general) is such a small quantity as to be insignificant the 5-year intervals we are discussing here. However, I will carry it through for the sake of argument, to show you that this increased ocean uptake capacity does not allow the wiggle room you seem to think.
Consider that the CERES satellites show that the average TOA imbalance from 2000-2004 (TOA_first) was ~ 0.15 W/m^2 less than from 2005-2009 (TOA_second). We get
(4) TOA_first – TOA_second = -0.15 W/m^2
On the other hand, B13 shows that the rate of ocean heat content has *decreased* (when averaging globally) by 0.85 W/m^2 over that time:
(5) dOHC_first/dt – dOHC_second/dt = 0.85 W/m^2
Using equation #3 in #4 to relate this, we get:
(6) (dOHC_first/dt + dALC_first/dt) – (dOHC_second/dt + dALC_second/dt) = -0.15 W/m^2
Solving using #5 and #6 we get a solution set of
(7) dALC_first – dALC_second = (-1.0 W/m^2)
So we have found a solution set by including our Atmosphere+Land+Cryosphere heat capacity (and hence implicitly our ocean heat uptake efficiency), right, and all is well? Not quite…this number makes no sense from a physical perspective, as I’ve explained. Over 5 years, this is equivalent to 8 * 10^22 J, and this “solution” implies that this quantity somehow would have had to gone into the cryosphere+land+atmosphere from 2005-2009. Obviously, this is more than a magnitude too large (based on land, atmospheric, and ice measurements, not to mention common sense)…this is what is meant by the “missing heat”, in that order to balance our energy while maintaining consistency between datasets, there is no accounting for this extra implied heat.
Unfortunately, this relates to why your list breaks down at #2:
“2. OHC as a proxy for TOA is unable to distinguish between the two processes as they are occurring simultaneously.”
Forcing affects TOA imbalance (your process 2), but for us to get a rise in the rate of ocean heat uptake while simultaneously seeing a decrease in TOA imbalance (your process 1) at the magnitude these datasets suggest, we would require drawing that from elsewhere in the earth system (ALC above), and would need to draw it in such a magnitude that would have sent the earth into another ice age. Obviously, nothing like this was observed.
By all means, I am not suggesting you trust me on this. I know several of your SkS contributors are physics-trained, and perhaps you can confer with them on this topic.
Comment by troyca — July 25, 2013 @ 8:43 am
Yes, an interesting idea – apart from apparently being impossible. But that still leaves us with various observational datasets that contradict each other. Rapid accumulation of heat in the early part of the 2000’s despite a global dimming trend (as implied by the CERES data figure above too). The magnitude of the early 2000’s warming suggested by Balmaseda et al (2013) may be too high , but the ocean circulation implies anomalous heat uptake then too. Furthermore, Balmaseda et al state that withdrawing the ARGO data makes very little difference – the trend is only slightly reduced. Whether this implies the overall evolution of OHC (i.e. rapid early 2000’s warming) is more or less the same is another matter – they don’t go into that detail. All very much an intriguing puzzle…..
Comment by Rob Painting — July 28, 2013 @ 1:04 pm
Rob,
I agree it is an intriguing puzzle. The only thing I would say is that they note that withdrawing the ARGO data makes little difference in the last decade trend. However, if the entirety of that “difference” results only from the transition period in the early part of the decade, then that could go a little ways towards explaining the discrepancy (if the early decade large ocean heat uptake was an artifact of the XBT to ARGO transition). Of course, that would be assuming that adding in the ARGO data only increases the trend due to this artifact, and not because it is discovering additional warming mixed by the XBT measurements.
Comment by troyca — August 20, 2013 @ 7:49 pm