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:

Alec,

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.

Isaac

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.

Isaac:

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?

Sincerely,

Alec

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

It sounds like you understand

Isaac

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.