Isaac Held's 2-box model: another failed ocean-equilibration excuse for dismissing solar warming

Guest post by Alec Rawls

Dr. Isaac Held, who models fluid dynamics at NOAA, dismisses a solar explanation for late 20th century warming by invoking a 2-box model of ocean equilibration. In his model an upper upper ocean layer (100m or so deep) exhibits a rapid temperature response to any increase in radiative forcing (about 4 years), as has been observed for this part of the ocean. So far so good.

Below sits Held’s second box: the entire rest of the oceans, all modeled as having the same temperature. To see the effect of this highly unrealistic simplification, look at what would happen if an intermediate ocean layer were also modeled, say from 100 to 500 meters in depth. Following a step-up in forcing the rapid temperature response of the upper ocean layer would commence to warm the intermediate ocean layer on some intermediate time scale—from a few decades to a century perhaps—and the decreasing temperature differential between these two layers would decrease the rate of heat loss from the upper layer to the ocean below, causing the upper ocean layer to continue to warm on the decades-to-century time scale.

This is exactly what Held and others are saying will not happen. Their claim is that the 20th century’s persistent high levels of solar forcing could not have caused continued warming and hence cannot be responsible for late 20th century warming. But these claims always rest on unreliable and often unstated assumptions about ocean equilibration. Held’s assumptions are stated, making his example particularly revealing. His argument against solar warming hinges directly on what is unrealistic about his model.

Isaac Held on Raimund Muscheler

My email correspondence with Held began when I cc’d him on my critique of Raimund Muscheler, who had claimed that because the high levels of solar forcing from 1950 to 2000 were “relatively constant,” they were unlikely to cause continued warming:

Solar activity & cosmic rays were relatively constant (high solar activity, strong shielding and low cosmic rays) in the second part of the 20th century and, therefore, it is unlikely that solar activity (whatever process) was involved in causing the warming since 1970.

This statement by Muscheler was specifically in answer to the possibility of indirect solar forcings that might be much stronger than the slight variation in TSI (Total Solar Insolation). No matter the strength of the forcing Muscheler and others are saying, continued high forcing should not cause continued warming.

Do these people actually think that it is the rate of change in the level of a temperature forcing rather than the level of the forcing that does the forcing? Alternatively, they may be assuming some implausibly rapid ocean equilibration, so that by 1970 or 1980 equilibrium would have been reached, requiring continued forcing of the same magnitude just to maintain that equilibrium.

I thought Held might offer an antidote because at the same meeting that Muscheler had been quoted as dismissing the solar-warming theory, Held had noted that:

“… some 40-70 percent of the [temperature adjustment to a change in forcing] is achieved on a timescale on the order of 4 years, whereas equilibration takes centuries.”

If equilibration takes centuries then it would not have been attained by 1970. Thus continued high levels of forcing should cause continued warming, right?

No, says Held, not in the 2-box model that he was referring to, as he briefly explained to me in his reply:


I believe that you have misunderstood my perspective on this. As I have tried to indicate in some of my blog posts, especially #3, 4 and 27, I think the forced temperature response should follow the forcing with only a small time lag (small enough that, in practice, it only affects the volcanic response), despite the existence of long oceanic time scales — the argument being that these deep reservoirs have not warmed enough to significantly affect the heat uptake.


As Held puts it in his blog-post #4 (where he introduces his 2-box analysis) the heat capacity of the deeper ocean layer is effectively “infinite” in this model on intermediate time-scales. No matter how much heat gets pumped into the oceans, the deeper ocean layer does not warm significantly over mere decades and so there is no significant reduction in the rate of heat loss from the upper ocean layer. All of the heat that goes into the deeper ocean is regarded as simply disappearing, never to have any effect on upper ocean temperatures except on much longer time scales.

The result is a kind of psuedo-equilibrium where the only thing that will cause further change in the temperature of the upper ocean layer is further change in the level of forcing. Persistent high levels of even a strongly enhanced solar forcing would not cause continued warming of the upper ocean layer in this model. There would just be the rapid temperature response of the upper ocean layer then nothing measurable for generations.

Global Mean Atmospheric Surface Temperature (GMAST) is primarily determined by upper-ocean temperatures, thus according to Held’s 2-box model, where persistent forcing only causes brief warming, the late 20th century increase in GMAST could not have been caused by the high level of solar activity over this period. The highest levels of solar activity were reached in the 50s so the warming effect should have wound down by the 60s. But this 2-box argument turns on the known-to-be-wrong assumption that warming of the upper ocean layer does not warm the next few hundred meters of the ocean any more than it warms the abyss.

Simplified models are fine so long as the insights that are gleaned from them are not driven by the simplifications. For instance, it makes no difference that climate models do not include relativistic effects so long as they are not used to analyze relativistic phenomena, but Held takes this basic principle of science and turns it on its head. His argument that persistent enhanced solar forcing would not cause continued warming turns precisely on the unrealistic simplification that creates his 2-box model. Move just to the next simplest model, a 3-box model, and his argument evaporates. The next ocean layer will warm on intemediate time scales, decreasing the rate of heat loss from the upper layer to the deeper ocean, causing the upper layer to warm.

My second email exchange with Dr. Held

Isaac Held’s remarks to me were very brief and his blog posts are focused on a CO2 driver of late 20th century warming rather than the possibility of a solar driver. I wanted to nail down his position on the latter so I pulled together what his posts seem to imply about solar forcing and asked him to please let me know if I had his position right.


I got a chance to look at the blog posts of yours that you mentioned (3, 4, 6, and 27, and I read a few others too). All very interesting stuff.

On attribution for 20th century warming the focus of these posts is on WMGGs [Well Mixed Greenhouse Gases] and how, by adjusting the climate sensitivity estimate in the GCMs, variation in WMGG can be seen to account pretty well for 20th century temperature history. This doesn’t really get at my specific question, which is whether Raimund Muscheler’s statement can be supported. He was addressing the hypothesis that there might be some enhanced solar forcing effect, as by GCR or uv effects on cloud cover, and he claimed that even a persistent high level of such forcing could not cause warming [or continued warming].

You do make two comments that seem to imply a position here, but please let me know if I’ve got you right on this. First, you left a comment in your post #27 that specifically applies to the question of attribution for late 20th century warming:

“The assumption is not that the climate in 1980 is in equilibrium but that the heat uptake is proportional to the temperature anomaly from some (pre-industrial) equilibrium — ie. the system is in what I called the intermediate regime in post #3. (Actually post #4 — IH 5/17/12)”

As I understand your position, the heat capacity of the second ocean layer is effectively infinite in the intermediate regime and this regime easily persists for multiple decades and even centuries, even for quite substantial heat input into the deeper oceans. This is a direct implication of the 2-box model. Given the vast size of the second ocean layer it’s going to take a long time for this layer to warm enough to take a significant bite out of the rate of heat transfer from the upper ocean layer. As you put it to me in your email response:

“I think the forced temperature response should follow the forcing with only a small time lag (small enough that, in practice, it only affects the volcanic response), despite the existence of long oceanic time scales — the argument being that these deep reservoirs have not warmed enough to significantly affect the heat uptake.”

So with the temperature of the deep oceans essentially fixed over a broad intermediate time scale, the temperature of the upper ocean layer on this time scale is driven entirely (or virtually entirely), by forcings from above, which it responds to rapidly. Thus the only way to get continued warming of the upper ocean layer (necessary for continued warming of GMAST), is for temperature forcings to continue to rise.

CO2 forcing did continue to rise post 1970 while solar forcings were (to use Musheler’s phrase) “relatively constant.” Thus as analyzed by your 2-box model, CO2 is a viable explanation for late 20th century warming while solar-activity driven effects (no matter the mechanism) are not.

Am I understanding you correctly? Is this the argument you are making, or would make?



In response, Held seemed to be satisfied with my account of his position:

It sounds like you understand


I also understand how Held’s 2-box model fails catastrophically in this application

Add the least bit more realism—an intermediate ocean layer—and a persistent high solar forcing will cause continued warming on intermediate time scales. Isaac Held must understand this too. After all, he has a doctorate in this stuff and has spent his life studying it. Anything that is obvious at first glance to a non-scientist like myself cannot have eluded Dr. Held entirely, making it hard not to suspect that he might be treating this failing of his simplified model as feature rather than a bug. The “consensus” position that late 20th century warming was caused by CO2 depends on finding some way to dismiss the rival solar theory and Held’s hyper-symplified model provides one.

On the other hand, this application is not what Held has been using his 2-box model for. In his blog posts Isaac argues for the utility of the 2-box model entirely on the grounds that it does a remarkably good job of mimicking the behavior of the mainline GCMs, which are never used to examine what kind of behavior enhanced solar forcing might produce. These models are driven pretty much entirely by CO2. That is what Held is fixated on and I have no indication that he had ever used his 2-box model to dismiss a solar explanation for late 20th century warming until I urged him to weigh in on Raimund Muscheler’s typical/outlandish statement that a persistent high level of forcing should not cause continued warming.

All the consensus scientists are doing the same thing. The only models they look at are CO2 driven. The only hypothesis they actually try to work through, or even consider, is the CO2-warming hypothesis. When it comes to the possibility of late 20th century warming having been caused by the sun they content themselves with the most unscientific statements imaginable and simply refuse to look deeper.

I have compiled more than a dozen instances of leading IPCC scientists all making simple unconditional statements that because solar activity was not going up in the late 20th century it cannot have caused late 20th century warming. You’d think this was Newton’s Fourth Law: temperature is driven by the trend in the temperature forcing, not the level of the forcing. They all just pretend it is obvious that persistent high levels of forcing cannot cause continued warming.

Only when pressed do these scientists admit that they are making implicit assumptions about ocean equilibration, which they then try to justify with various half-considered rationales. Unfortunately, the only person who has been pressing these scientists on their unstated assumptions is me, so the unscientific statements continue to flow.

When the alternative is to hack-up an untenable excuse, avoidance is much preferred, and that’s where these guys all hang out, Held included. To make sure, I asked him about it: had the implications of his 2-box model for solar warming ever been pulled together and stated explicitly by anyone but me? Had it ever been published as a grounds for dismissing the solar-warming theory? Had it been discussed at meetings or passed around by email? Were people familiar with this argument?

Isaac just offered the modest answer that he found the 2-box model worthwhile because of how well it captures the response of the full-fledged GCMs to rising CO2. So that’s good. It means there has been no worked-out deception on Held’s part, and it means that Held’s excuse for dismissing a solar explanation for late 20th century warming is stillborn. In the first instance where Held has ventured to misapply his two-box model to the solar-warming hypothesis it now dies.

This makes FOUR off-the-cuff attempts to support the claim that persistent forcing can’t cause continued warming, all now dead and buried

1. Mike Lockwood cites Stephen Schwartz’ even more unrealistic one-box model of ocean equilibration.

2. Solanki and Schuessler argue that, since the solar-temperature correlations they have found are strongest with short time lags, rapid temperature responses are all they have evidence for and need to consider. Wrong. Rapid temperature responses of imply longer period responses (just as the solar warming of the day is evidence that the lengthening of the day will warm the season), especially in a system with large heat sinks.

3. Muscheler, Schmidt and others point to the pattern of warming. Since temperatures dipped between 1940 and 1970, the oceans must have equilibrated to the high level of solar forcing that began in the 1920s by at least 1940 they suggest, as if the mid-century wiggle in GMAST means there was a similar wiggle in ocean heat content, despite the apparent domination of GMAST by ocean oscillations.

It is perfectly possible that ocean heat content continued to rise when GMAST dipped and this is what the little heat-content data we have from the mid-20th-century suggests. There was no fall-off in the rate of sea level rise over this period and since surface temperatures were slightly down the melt-rate should not have increased, suggesting that thermal expansion remained steady.

4. Now add Isaac Held’s 2-box fail.

All four have been presented as reasons why a solar explanation for late 20th century warming can safely be dismissed as a significant possibility when in actuality not a one of these rationales stands up to the least bit of scrutiny. Besides internal variability, enhanced solar forcing is the alternative hypothesis to the CO2-warming theory, and the consensus has been falsely claiming to have ruled it out.

GCMs are multi-thousand box models

If going from 2 to 3 ocean layers changes model behavior so that persistent forcing does cause continued warming on intermediate time scales then a fortiori models with “as many as 30 [ocean] layers” will also exhibit this continued-warming behavior. In full-fledged GCMs convection, ocean currents and even ocean oscillations are all modeled. Heat that gets poured into the oceans for extended periods of time will come back out on similar time scales.

Have GCM tests with enhanced solar effects been run? There are some strong indications that they have not. In particular, if such tests had been run, and if they supported the claim that that continued strong solar forcing would not cause continued warming, then surely these tests would have been cited by the many scientists who make this claim, but no such citations are ever offered.

I’m trying to verify now whether these tests have been run and will do a full post on the subject in the future. In the meantime, if anyone has any information about whether GCM models with enhanced solar forcing have been tested and where any results might be found, please email me (alec-at-rawls-dot-org) or leave a note in the comments.

Conceptually there is no obstacle. Svensmark, for instance, hypothesizes that solar variance might be responsible for a 1% or 2% variation in low cloud cover. Adding this solar response to existing GCMs would be easy. To get the best fit for a given level of cloud effect climate sensitivity would have to be reduced an offsetting amount (which at the same time would reduce the warming effect of CO2). It’s just a matter of actually running the tests.

It the tests have been run, the lack of citations suggests that the results do not support the “consensus” position. There are three scandalous possibilities. 1) That contrary results were found and are being kept secret. 2) That contrary results were found and are available but are going un-cited because they contradict the statements that many scientists are making. 3) That despite over $100b in public funding for climate research the “consensus” never bothered to test the alternate hypothesis (in the “post-normal science” sense of seeing how well the hypothesis performs in model runs).

The only innocent possibility is that the IPCC has simply neglected to cite model-tests that support its otherwise unsupported claims that late 20th century warming cannot have been caused by the sun, but that really isn’t possible, not just because the “consensus” doesn’t behave this way, but because no legitimate GCM would behave this way. Persistent high levels of forcing must tend to create continued surface warming on intermediate time scales, and it must take quite some doing for a scientist to convince himself otherwise.


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David L. Hagen

By contrast, David Stockwell at Niche Modeling in his Solar Accumulation Theory finds solar forcing dominates.
e.g. Key evidence for the accumulative model of high solar influence on global temperature
Note especially his Pi/2 (90deg) or 2.75 year lag between the 11 year solar cycle forcing and ocean temperature.


As a registered professional engineer, specializing in fluid dynamics, heat transfer, and experimental testing, and with over 20+ years experience, i will say, the greater “number of boxes” or mixing cells yield results closer to the real world, providing the simulation includes the important and encompassing physics and the pertinent initial and time varying conditions. I would not use “two boxes” to represent the ocean. However, if i decided to, there would be graphical comparisons between the 1) real world data, 2) and the predictions of the many ocean layer model, and 3) the two layer model to reveal that possibility.

Michael Tremblay

Just a question. Does his model take into account the temperature/density differences of water? I ask this because fresh water is at its densest at 4C and the temperature at the bottom of a deep fw lake will be 4C despite what the outside temperature is. The water will be less dense and rise as it’s temperature increases or decreases. I know that the effect is the same for salt water but I’m not sure of the temperature. This phenomenon is responsible for the creation of the thermocline, whose depth will vary depending on what climate zone it is in, the season, and even whether it is day or night. This is primarily where the heat exchange takes place and its depth (as I noted) is dynamic going down as much as 1300 meters is some places. The mixing that that causes is enough to transfer enough oxygen from the surface to depths capable of keeping fish alive through long winters when lakes are ice covered.

What Did I Tell You!?

There wasn’t much warming anyway. Temperatures only just BARELY got out of the standard deviations over time and we’re, just as predicted by every classical model before Gore’s “Go Ahead And Install My Policies in Spite of the Election’ tour,
headed joyfully back into our cooling half-cycle.
Magic Gas and Global Warming are a myth.
Magic Gas and climatic impacts other than normal are a scam.
Magic Gas is a hoax being perpetrated by a relatively, select group of power grant application writers who claimed to be trying to discover whether the rising CO2 in the air might impact the atmosphere in some strange way.
When Al OUTED their SCAM(s – there were several people doing it when Big Al outed them) they were forced to either recant and admit fraud or plunge forward with Al Gore’s political power protecting their scamming.
So you have people claiming science when even Al Gore’s own experiment on the internet, adding CO2 to a bottle, as re-done uninterrupted by Tony Watts, showed cooling.
You have people claiming science when the ventilation systems of nuclear submarines have dealt with 4,000 ppm of CO2 in the atmosphere there so they don’t have to scrub it out. There aren’t any special ventilation system parts to account for Magic Gas holding heat some unusual way.
You have people claiming they believe in CO2’s Magic Gas properties who simultaneously admit to you, they don’t think it’s possible or humanity to array the equipment, to measure whether a narrow spectrum of infrared light – some heat – is rising in our atmosphere, globally.
Do YOU really believe, there’s no way to check to see if CO2 has magical heat handling properties?
So: anything you read that comes from government-touched data is likely to have false physics in it, because in order to invent a MAGIC GAS the scientific method has to be stretched out on railroad tracks and de-limbed, both arms and legs, by a locomotive of magic-gas research money.

Earl Smith

The real world is not in accord with these models.
Instead of heat conduction down through the water what happens is that ocean storms mix the waters down to about 300 feet (10x 30ft winter storm wave height). It is below this turbulent mixing zone that you see conduction; and water is a very poor conductor of heat. In a stratified system all the normal heat flow is by convection, but with heat applied at the top there is very little heat flow down through the water, so you are left with poor conduction as the only heat flow method.
Thus the cold arctic water that descends to the depths stays at roughly the same temperature even as it travels to the equator where it is forced to the surface after a 1000 year journey. As any submariner could tell you, waters below 300 feet are COLD.


Off topic.
Does any model take into account of underwater thermal activity? We know for a fact that there are underwater volcanic activities and we know that these energy release cannot go anywhere except absorbed by the sea. Given enough time this bound to have some effect. Or could it be assumed that vertical convection would transport this heat to the surface.
Nevertheless be it a short or long term heat transfer it would be unthinkable to neglect its effect on land temperature.
Am I dead wrong?

Alec – You need to explicitly ask Isaac Held to repeat the study using the 3-box model. It’s no good communicating with him in a way that only requires him to verify that you have understood him correctly, and then sniping at him from the sidelines. Get him to address the real problem directly, and maybe everyone can progress.


A model should only be as complicated as it takes to prove your point of view, and no more so.

Bill Hunter

Nice post! 4 years? One has to ask what the implications of the 2 box model are for Foster and Ramstorf, 2011, since its now been 7 years since solar minimum arrived.


I think Held’s model is reasonable. Not necessarily correct, but not prima-facie unreasonable. The flaw in it is not a lack of an intermediate layer, but that the depth of the top layer is held to be constant.
As should be obvious, it takes the same amount of energy to raise the top layer – 100m deep – by .25 degrees as it does to raise 1 metre of water by 25 degrees.
I’m not sure what the temperature difference between surface waters and deep water is, but presumably it’s about 20 or 25 degrees.

Paul Vaughan

1. Multidecadal Sea Level
2. Solar Cycle Deceleration — via:
(a) International Sunspot Numbers
(b) Ironed Sun Total Solar Irradiance (ISTSI) (Svalgaard)
3. Sea Surface Temperature
(a) Pacific Ocean
(b) Northern Hemisphere


Yes, there are many unstated assumptions about late 20th century warming. Keep at it. This is good stuff. There is no reason why the deep ocean won’t continue to absorb heat during and after periods of high solar activity.

Stephen Wilde

It is good to see Alec pressing the climate professionals on this matter since it is simple common sense and logic.
Previously raised as an issue here:
back in 2008 where I referred to TSI as a proxy for whatever might then amplify the solar effect and since then it has become increasingly likely that the amplification effect arises from global cloudiness and albedo responses to solar variations which then alter the amount of solar energy able to enter the oceans.
“It is true that, as the alarmists say, since 1961 the average level of TSI has been approximately level if one averages out the peaks and troughs from solar cycles 19 through to 23.
However, those solar cycles show substantially higher levels of TSI than have ever previously occurred in the historical record.
Because of the height of the TSI level one cannot simply ignore it as the IPCC and the modellers have done.
The critical issue is that having achieved such high levels of TSI by 1961 the sun was already producing more heat than was required to maintain a stable Earth temperature. On that basis alone the theory of AGW cannot be sustained and should now die.
Throughout the period 1961 to about 2001, there was a steady cumulative net warming effect from the sun. The fact that the TSI was, on average, level during that period is entirely irrelevant and misleading.”

Stephen Wilde

I think a post of mine has just gone to the spam filter due to a link which I included.
Please have a look and retrieve it for me (assuming the link is unobjectionable).

David Young

You know, I would actually be interested in a calculation with a 3 layer ocean to show that it does indeed change Held’s conclusion. I don’t think your post shows that in any quanatative way.

Robert A. Taylor

What of upwelling; downwelling; non horizontal currents; turbulence between static areas, currents, and different currents at different depths?

Robert A. Taylor

OOPS! I failed to include:
Every time I find new details of climate models they are obviously so over simplified as to be essentially no better, possibly worse, than simple curve matching.

“He was addressing the hypothesis that there might be some enhanced solar forcing effect, as by GCR or uv effects on cloud cover”
Or possibly UV period?

Michael Tremblay

Thanks Alec, this is an interesting piece. It’s nice to see someone examining someone’s experiments with a critical eye and pointing out their mistakes. This is a very complex issue and it requires more than a simplistic model to explain what is happening.


Here is an interesting quote from Science, 26 October 2012:
Detecting Causality in Complex Ecosystems
“Identifying causality (I) in complex systems can be difficult. Contradictions arise in many scientific contexts where variables are positively at some times but at other times appear unrelated or even negatively coupled depending on the system state (movie S1).”
This would seemingly apply to Climate Science …


You’re all missing the elephant in the room here, I think. The creature of course being the natural process of ENSO. It controls the temporal and spatial distribution of, among other climatic variables such as pressure gradients and winds, cloud cover, not just in the tropical Pacific but by atmospheric teleconnections also in the Atlantic and Indian Oceans. By far the most important of all ocean basins though, when it comes to the year-to-year uptake of solar energy, is the Eastern Tropical Pacific Ocean, the West Pacific Warm Pool (in the Western Tropical Pacific Ocean) being its prime reservoir.
It is quite easy to show how the evolution in global OHC (0-700m) since about 1970 (when it started to rise) is simply governed by ENSO. All one has to do is split the world ocean into two subsets, one ‘following’ the East Pacific (NINO) and one ‘following’ the West Pacific (WPWP). These two subsets swing in remarkable counterphase. But during the course of specific ENSO events along the time line (that is, major La Niñas, when the cloud cover above the Central and Eastern Tropical Pacific is at a minimum) there arises a skewness between energy gain in the one subset and energy loss in the other. This occasional (but at very distinctive sequential intervals) asymmetry explains the entire rise in OHC since the early 70s.
There is no need for any increased TSI or a sustained high level of solar output to explain the net accumulation of heat in the oceans. Only specific, ENSO-driven cloud cover variations in the tropics.
I’m not saying, though, that the Sun isn’t a factor in all this. Only that it’s probably rather a puppet master, pulling the strings through some mechanism other than direct output (although, like Stephen Wilde said, this can be used as a proxy) on the fairly regular decadal and multidecadal regime shifts that occur in Earth’s climate system (also, maybe particularly, affecting the ENSO).


Alec Rawls says:
November 15, 2012 at 10:38 pm
“What of upwelling; downwelling; non horizontal currents; turbulence between static areas, currents, and different currents at different depths?”
It will take GCM test runs of enhanced solar forcing to get an idea of how these complexities might play out. In general, these mechanisms will transport energy into and out of the oceans and should operate on intermediate time scales.
And don’t forget the jellyfish and their ability to mix the ocean waters, apparently, as much as storms and tides.
See –


Having only recently woken up to the idea of deep time and the existence of the world before 1850 (e.g. discovery of the Ordovician high-CO2 ice age problem), the climate community appear to have woken up to the existence of the deep ocean also. At least this is good.
But they are still locked into a paradigm where everything is driven from the atmosphere and the newly discovered ocean is a passive player only, simply responding to atmospheric forcings. IF radiative forcings really do exist, and IF there are no opposing feedbacks (two significant ifs) then yes in the long term the amount of heat energy in the system will change.
However they are excluding or ignoring one important component. What if the ocean itself decides to become a player? Taking for the sake of argument Held’s 2-box ocean model, the top box is warm, the bottom box is cold. Vertical mixing between the 2 boxes will cool the top box (with an insignificant effect on the bottom box). This will cool the earth’s climate, which is influenced by the sea surface temperature, but with no change to the total energy in the system.
So vertical ocean mixing is a mechanism for climate change without (necessarily) any forcing driven change in the system’s heat energy budget.
So what kind of dynamics could control ocean mixing in a thermodynamically open dissipative far-from-equilibrium system ….? Anyone?

Dr. Isaac Held, who models fluid dynamics at NOAA, dismisses a solar explanation for late 20th century warming by invoking a 2-box model of ocean equilibration.
Only yesterday I was looking at files at the NOAA website and came across this,
very relevant to the subject..
Perhaps NOAA’s models would be more adequate if they examined more closely their data files.
It appears that one side wants to exclude solar factor all together and the other is convinced that sunspot record alone are the answer.
Oceans are the main absorber and reservoir of heat. How much solar energy is absorbed and when and how much of it is released is determined by both the sun and the Earth


Lets remember the first rule of climate science, when the models and reality differ its reality which is in error. Once you done that can see why is right we they say ‘His argument against solar warming hinges directly on what is unrealistic about his model.’ , but wrong with what it means to Held. With reality coming a poor second to models .

Alan Millar

The warmists like it both ways though.
All the ‘missing’ energy from the last 15 years or so is ‘hiding’ in the deep ocean where we can’t measure it they say. However, this energy magically gets there without heating any intermediate layers on the way down apparently.
Like I say, magic. It makes you wonder how these people can look at themselves in the mirror.
However, reality is closing in on them and most of them will have realised this. They will now have realised that their predictions and models are a fail and that they were fooled by the natural variability heating in the late 20th century adding to what looks a fairly minor CO2 effect. Heck the PDO cycle was not identified until 1996, long after most of them had leaped aboard the good ship AGW, thrown of their life jackets and nailed themselves to the mast!
The ship is sinking but they are going to keep bailing out with everything they have got to delay the day it finally sinks beneath the waves taking them with it.
The crafty ones amongst them will start to edge towards the life rafts and it will be interesting to see who are the first to start issuing slightly ameliorated predictions.

We often here:
Solar output now is same as in the early 1900’s ,
but temperatures are radically different (Svalgaard)
So what has changed since 1900’s.
The Earth has changed !
You may not know it but NOAA scientists do !
Here is the change as NOAA knows it:
For the global temperature change you might say
“It takes two to tango”
Where the sun takes the lead and the Earth follows

This man works (?) for NOAA and ignores solar input? idiot.


“… some 40-70 percent of the [temperature adjustment to a change in forcing] is achieved on a timescale on the order of 4 years, whereas equilibration takes centuries.”
If 40-70 is important does its inverse 30-60 inconsequential?


And if you nail a plank of wood to a block of wood in the shape of a cross you have have a simple model of an aeroplane that proves powered flight is impossible.

kadaka (KD Knoebel)

From Stephen Wilde on November 15, 2012 at 9:09 pm:

Previously raised as an issue here:
back in 2008 where I referred to TSI (…)
“It is true that, as the alarmists say, since 1961 the average level of TSI has been approximately level if one averages out the peaks and troughs from solar cycles 19 through to 23.
However, those solar cycles show substantially higher levels of TSI than have ever previously occurred in the historical record.”

I have checked the source data you used, as given on your graph, originating from Lean J. 2000:
Clearly you have selected “11yrCYCLE+BKGRND” instead of “11yrCYCLE”.
This has been superseded by the historical TSI reconstruction based on Wang, Lean, and Sheely 2005, available on the SORCE site:
Both show an oscillation of about 90 yrs duration. However, as Leif Svalgaard previously stated:

The SORCE reconstruction is based on two assumptions [both likely to be false]:
1) the Group Sunspot Number is correct
2) there is a ‘background’ variation which is equal to the 11-year moving average of the Group Sunspot Number on which TSI rides.

As shown in Leif’s recent WUWT post, the GSN has been demonstrated to be flawed, do not use it. The adding in of the made-up background variation is shown to be in error as well by the graph at “2”.
Leif has already supplied his “best guess” of the TSI values that should be used, based on reconstructed sunspot number. They notably do not have the background variation:
This result is similar to what is found in your original source of Lean 2000 if you select “11yrCYCLE”, but instead you had selected the values with the background variation added in.
Your choice is shown to have been in error, and since your fancifully-titled “The Death Blow to Anthropogenic Global Warming” article was based on notably higher TSI levels from 1961 to 2001, which only exist with the background variation added, your article is invalidated. Lean 2000 “11yrCYCLE” shows the 1961-2000 average to be only 0.25 W/m2 higher than the 1610-1960 average, 0.018%, hardly enough to support your results.
Although the small increase possibly could have been a contributor to late-20th century warming.

Peter Miller

I suppose ignoring the existence of slow moving, deep ocean, currents aka the Great Marine Conveyor Belt, is just another factor essential for the findings of Dr Isaac Held’s model.
Still, we mustn’t let facts get in the way of the model’s findings – after all, if you did that, it wouldn’t be climate science.

Martin Lewitt

It sounds like you and Held are not familiar with the climate commitment studies of Wigley, et al and Meehl, et al, for an explanation of how even a continuation of an already achieved level of new forcing can take decades for most of the land temperature adjustment and sea level will continue to rise as heat is stored into the oceans for perhaps a millenia or more. If I recall correctly both studies found that the unrealized climate commitment alone will account for another 1 degree C of warming over the next century. While they claim it is due to CO2, it could just as easily apply to the high levels of forcing achieved during the recent solar grand maximum.
I’ve never found evidence that solar forcing was seriously considered. The TAR stated that the uncertainty in solar variation was a factor of two, yet we never read of model runs where the solar variation histories of Lean, et al, were doubled to test the solar hypothesis. If the solar contribution is eventually found to be responsible for more of the recent warming, I suspect that it won’t be due to under estimating the radiative forcing, but due to the differences in solar coupling to the climate, magnetic (cosmic rays), chemical (stratospheric and tropospheric creation of ozone, a GHG), or vertical (land surface, ocean penetration) and horizontal distribution effects (tropics) on a dynamic nonlinear system.

vukcevic says:
November 16, 2012 at 2:28 am
The Earth has changed !
You may not know it but NOAA scientists do !
Here is the change as NOAA knows it:

From Rikubetsu, Hokaido [the coldest place in Japan]:
That the Earth’s main field changes does not impact the climate one bit.

Bloke down the pub

This sounds like the Mr McCawber principle.
“Annual income twenty pounds, annual expenditure nineteen nineteen six, result happiness. Annual income twenty pounds, expenditure twenty pounds nought and six, result misery.”
As long as energy going in exceeds energy being lost, the temperature will go up, regardless of whether the level of energy in is up, down, or stable.

Henry Clark

Solar activity & cosmic rays were relatively constant (high solar activity, strong shielding and low cosmic rays) in the second part of the 20th century
That “relatively constant” falsehood keeps getting repeated.
While the Modern Maximum in the second part of the 20th century did not replicate the rise of solar activity during the first half of the century and before (and unsurprisingly, for example, average sea level rise rates dropped from 2.03 mm/yr over 1904-1953 to 1.45 mm/yr over 1954-2003 — ), what really happened was this:
When solar activity relatively dropped in the 1960s relative to the mid-20th-century high, there was major global cooling, with the global cooling scare occurring for a reason as seen in the temperature graphs of the time (like ), and only later recent revisionism for the CAGW movement rewrote historical temperature records to delete almost all of the inconvenient drop then.
Then solar activity substantially rose, including a major 3% change in average cosmic ray deflection for solar cycles 21 and 22 of 1976 to 1996, compared to the cycle before, and that coincided with the global warming scare. Atmospheric temperatures peaked with the 1998 El Nino which released much recently-stored ocean heat back to the atmosphere.
Finally, solar activity started to relatively go down with cycle 23 (1998-2008) and beyond, while global temperatures have not been warming but rather cooling as the trend from 1998 to now ( ).
As the article here implies, there is also a partial time lag due to the oceans being far from zero thermal latency. That further improves the match (including making the downward slope of 1998-now slower net atmospheric cooling less than it would have been otherwise). The bulk of the picture, though, most of all just requires something few even on WUWT do: use solar and temperature data which has not been fudged in recent CAGW-convenient revisionism.

Isaac, but not Newton this time.
Up to now, no climatologist or climate model offered an explanation for North Atlantic temperature variations, which give the shape to the “global” temperature record. Model is obviously out of reality. Please Mr. Isaac, what caused the early 20th century warming? Do not say solar forcing, since it is included in the model and shows almost nothing. Until you have no answer, do not play wise over late century warming, indistinguishable from the early one. And, it ended few years ago.

lsvalgaard says: November 16, 2012 at 3:34 am
From Rikubetsu, Hokaido [the coldest place in Japan]:
That the Earth’s main field changes does not impact the climate one bit

Hi Doc
(Sapporo winter Olympics?) Keep warm.
You say:
That the Earth’s main field changes does not impact the climate one bit.
and likewise one could state:
The climate change does not impact the Earth’s main field changes one bit.
Both of the above are considered to be correct.
However, in the old tradition, it is to some of us to question, and that is what I do.
Thus: either of two statements or both could be also wrong .
My link was actually inspired by your visit to Japan. I will email you details assembled in a pdf file, but if Alec Rawls would like to contact me I will email it to him too (e. address is on the graph)
Nature is full of surprises.

David L. Hagen

Roy Spencer has been developing an alternative diffusion model for ocean temperatures.
Is Gore’s Missing Heat Really Hiding in the Deep Ocean?
Deep Ocean Temperature Change Spaghetti: 15 Climate Models Versus Observations

The following comparison between the 20th Century runs from most (15) of the IPCC AR4 climate models, and Levitus observations of ocean warming during 1955-1999, further bolsters the case for a relatively low climate sensitivity: estimated here to be about 1.3 deg. C for a future doubling of atmospheric CO2. This is quite a bit lower than the IPCC’s best estimate of 3 deg. C warming.

On filing their paper, Spencer highlights the importance of requiring 1st law energy conservation

We used a 1D forcing-feedback-diffusion model of ocean temperature change to 2,000 meters depth to explain ocean temperature variations measured since 1955. . . .
The 1D model has the advantage that it conserves energy, which apparently is still a problem with the IPCC 3D models which exhibit spurious temperature trends (peer reviewed paper here). Our own analysis has shown that at least 3 of the IPCC models actually produce net (full-depth) ocean cooling despite positive radiative forcing over the 2nd half of the 20th Century.
After all, if a climate model can’t even satisfy the 1st Law of Thermodynamics, and global warming is fundamentally a conservation of energy process (net accumulation of energy leads to warming), how then can 3D models be used to explain or predict climate change? . . .


“Bill Hunter says:
November 15, 2012 at 8:26 pm
Nice post! 4 years? One has to ask what the implications of the 2 box model are for Foster and Ramstorf, 2011, since its now been 7 years since solar minimum arrived.”
F&R2011 shows that solar equilibrium is reached at 1 month:
“An interesting result is the time lags found. For volcanic
eruptions the resulting cooling lags by about half a year,
whereas the warming associated with El Ni˜no events lags
the multivariate ENSO index by 2–5 months. For ENSO the
largest lag is found in the lower troposphere, whereas for solar
forcing the lag in the surface data is larger. This is consistent
with ENSO forcing the climate system from below (via ocean
heat release) while solar irradiance forces the system from the
top. The lags found here are consistent with those from Lean
and Rind (2008) for the longer period 1889–2006, namely 6
months for volcanoes, 4 months for ENSO and 1 month for
solar variations.” – F&R2011, Section 5.1
We know from real world that this is absolutely false. The variations they’re considering were a few w/m^2. The real world, when trying to locally equalize over a season, has a much longer response time than one month (NH solar forcing starts dropping – albeit rather slowly at first- on June 22nd, but the temperatures rise for another 4-6 weeks) with a much greater forcing function (forcing between summer and winter is ~100+ w/m^2)
I know this is just a localized phenomenon, but even so, the physics of how the oceans equilibrate doesn’t change based on the timeframe you examine. The result that F&R report – that solar equilibrium is reached in 1 month – is wrong.

David L. Hagen

Re: “it is unlikely that solar activity (whatever process) was involved in causing the warming since 1970.”
That appears to include an “argument from ignorance”. e.g., the steady solar heating is assumed and dismissed because of the change in trends around 1970 – while ignoring variations in solar, the Pacific Decadal Oscillation, and changes in galactic cosmic rays/cloud cover. Each or all of those ignored features could cause the major change in trends, such as the solar heating such as shown by Stockwell. e.g. see:
A 39-Year Survey of Cloud Changes from Land Stations Worldwide 1971-2009 Ryan Eastman, Stephen G. Warren J. Climate eview (May 2012 preprint)

Global average trends of cloud cover suggest a small decline in total cloud cover, on the order of -0.4 % per Decade. Declining clouds in middle latitudes at high and middle levels appear responsible for this trend.

Declining clouds = warming.


lsvalgaard says:
November 16, 2012 at 3:34 am
From Rikubetsu, Hokaido [the coldest place in Japan]:
You’re not w/the program at all, Dr S. You’re supposed to be holding conferences in Hawaii, Tahiti, French Riviera, Cancun, Bahamas, etc, etc. 🙂


I agree with one aspect of Held’s story. The whole ocean probably is a near infinite heat sink.
However, I suspect from experience with testing heat sinks for LED packages that the all important thermal settling time he is calculating depends directly on the depth he assigns to box1. Double the artificial definition of box1 to 200 meters, leave everything else in box2, and … its a miracle, the settling time doubled to 8 years!
Volume times thermal capacitance of a uniform material. No, it is not really uniform, but whatever.

kadaka (KD Knoebel)

*sigh* Is my lost comment ever going to get out of the spam filter?

There’s no comment in the spam filter -Anthony

Crispin in Waterloo

“You’d think this was Newton’s Fourth Law: temperature is driven by the trend in the temperature forcing, not the level of the forcing.”
The core error in this mis-direction is so close to my own experience in my field that I am pasting quotes into current texts (with attribution, Alec). It boils down to an even simpler error, or an error that can be stated in a simpler fashion: they are confusing temperature with heat. They are by subterfuge taking the first derivative of the temperature curve and pretending it is the temperature then saying you need an increase in heat input to keep the ‘temperature’ constant.
What may be surprising is how few people will notice such errors of logic. If you listen to enthusiasts talk about how they have increased the heat transfer efficiency because of this or that change in temperature you soon hear this type of mistake. The rate of change in temperature and the temperature and the quantity of heat and the efficiency are not interchangeable metrics, guys! To some of them it is a big mish-mash and you lift out what you want.
I am surprised to see a specialist in this field advising his non-specialist colleagues to use a 2-box model knowing full well it does not bear any slight resemblance to reality. The obvious ENSO-driven changes (see Bob Tisdale’s excellent animations!) and that something-or-other called the ‘overturning circulation’ for heaven’s sake show that a two box approach has to be misleading. It boils down to a cleverly hidden cover that makes it appear more likely that CO2 has been causing the 1975-1995 temperature increase.
Of course it all ends in tears when the eggshell of increasing CO2 collides with the concrete wall of temperature stasis. It is Humpty Dumpty all over again. All of Mann’s horses and all Hansen’s men will never put Humpty together again.

kadaka (KD Knoebel)

I check, it’s still not there, I send the comment I wrote asking asking about my lost comment… And there it is with the after-posting reload!
Wow, that was fast work by the moderators! Thanks!

Matthew R Marler

Add the least bit more realism—an intermediate ocean layer—and a persistent high solar forcing will cause continued warming on intermediate time scales.
How do you know that? It would depend on the rate constants for transfer between the layers, would it not? It would seem to me that you ought to run your model with a variety of rate constants for the various parameters and see where your models differ from his, and where they agree.