Which way to the feedback?

Guest Post by Willis Eschenbach

There is an interesting new study by Lauer et al. entitled “The Impact of Global Warming on Marine Boundary Layer Clouds over the Eastern Pacific—A Regional Model Study” [hereinafter Lauer10]. Anthony Watts has discussed some early issues with the paper here. The Lauer10 study has been controversial because it found that some marine stratocumulus clouds decrease with increasing warming. This is seen as an indication that (other things being equal) clouds are a net positive feedback, that they will amplify any warming and make it even warmer. This finding has engendered much discussion.

I want to do a different analysis. I want to provide a theoretical understanding of the Lauer10 findings. Figure 1 shows the larger picture, within which Lauer’s results make sense. This is the picture of part of the Earth as a solar-driven heat engine.

Figure 1. Very simplified picture of the main driving loop of the tropospheric circulation. A large counter-rotating cell (a “Hadley Cell”) of air exists on each side of the equator. Energy enters the system mostly around the equator. Thunderstorms (shown with rain) drive deep convection currents from the surface to the upper troposphere. Some of the energy is transferred horizontally by the Hadley Cells to the area at 30N/S. There, some the energy is radiated out to space. A large amount of the radiation occurs in the clear dry desert regions. Other parts of the atmospheric circulation not shown.

Lauer10 is discussing the low cloud decks found off the western edges of the continents at around 30°N/S, as illustrated in Fig. 1.

Considering the earth’s climate as a heat engine can lead us to interesting insights. First, we can see how the heat engine works. The thunderstorms in the wet tropics convert some of the incoming solar energy to work. The work consists in part of moving huge amounts of warm air vertically. In the process, most of the moisture is stripped out of the air, producing the rain shown in Fig. 1. After rising, some of this now-drier air travels polewards. It descends (subsides) in the region around 30° north and south of the Equator. This dry descending air forms the great desert belts of the planet. The air then returns equator-wards to repeat the cycle.

A closed system heat engine (like the climate) needs some form of radiator to cool the working fluid before it returns to be recycled through the engine. In the climate, the areas around 30°N/S serve as the main radiators for this loop of the atmospheric circulation. There, excess energy is radiated to space.

Now, here’s the theoretical question:

What would we expect to happen to this flow system if there is an increase in the temperature?

The Constructal Law says that in such a case, a flow system like the climate will rearrange itself to “speed up the wheel”. That is to say, it will change to increase the throughput of the system. The system reorganizes itself to increase the total of work plus turbulence.

How can the circulation shown in Fig. 1 become more efficient and increase its throughput? There are not a whole lot of control points in the system. The main control points are the clouds at both the hot and the cool ends of the heat engine.

The Constructal Law suggests that as the system warms, two things would happen. First, there would be an increase of cumulonimbus (thunderstorm) clouds at the equatorial end of the system. This would increase the speed and volume of the Hadley circulation. Next, there would be a decrease of clouds in the area around 30° latitude. This would increase the amount of radiation leaving the system. These changes would combine to increase the total throughput of the system.

In that light, let us re-consider the results of Lauer10. What they show is that as more heat passes through the system, as expected, the clouds at the radiator end of the system decrease. This increases the amount of energy that can pass through the system in a given time. In other words, they are an expected result of the system warming.

Lauer10 appears to discount this possibility when they say:

The radiative effect of low marine clouds is dominated by their contribution to the planetary albedo as their impact on outgoing longwave radiation is limited because of the small temperature difference between cloud tops and the underlying surface.

I found this doubtful for a number of reasons. First, the cloud top for marine stratiform clouds is typically at an altitude of ~600-700 metres, and the cloud bottom is at around 400-500 metres. The dry adiabatic lapse rate (cooling with increasing altitude in dry air) is about 1°C per hundred metres. This puts the cloud base at around five degrees C cooler than the surface. Then we have 200 metres at the wet adiabatic lapse rate, that’s about another degree. Total of six degrees cooler at the cloud tops.

The annual average surface temperature at 30°N is about 20°C, which puts the cloud tops at about 14°C. While this doesn’t seem like a lot, it gives a blackbody radiation difference of about 30 W/m2 … hardly a “limited” difference. Even if it is “only” half of that, 15 W/m2, that is the equivalent of four doublings of CO2.

Next, the strength of the solar contribution at 30° latitude is only about 60% of equatorial sunshine. This is due to the greater angle to the sun, plus the greater distance through the atmosphere, plus the inherent increase in albedo with decreasing solar angle.

Next, there is a fundamental difference between equatorial clouds (cumulus and cumulonimbus) and the stratocumulus decks of the area at 30° latitude. This difference is ignored by the averaging, with which climate science is unfortunately rife.

The problem is that the timing of clouds is often more important than the amount. Consider someplace in the tropics that has say eight hours of clouds per day. If those clouds are in the afternoon, the reflection of the sunlight will dominate the effect of the clouds on radiation. The clouds will cool the afternoon, as we all know from our common experience.

If that same eight hours of clouds occurs at night, however, the situation is reversed. Clouds are basically an impervious black body to outgoing longwave radiation. Because of this, they increase the downwelling LW when they are overhead. During the day this is usually more than offset by the reduction in solar radiation.

But at night there is no sun, so the effect of night-time clouds is almost always a warming. Again this is our common experience, as clear winter nights are almost always colder than winter nights with clouds.

However, all of this is obscured by the averaging. In both the day and night cases above, we have the exact same amount of clouds, eight hours per day. At night the cloud warms the earth, during the day the same cloud cools the earth, and averages can’t tell the difference.

The relevant difference between stratocumulus at 30° latitude and the equatorial clouds is that the equatorial clouds die out and vanish at night. This allows for free radiation from the surface. The stratocumulus deck, on the other hand, persists day and night. This means that it has much more effect on radiation than equatorial cloud.

Finally, I think that there is a fundamental misunderstanding in their claim that the maritime stratocumulus cloud “impact on outgoing longwave radiation is limited” because of the small temperature difference.

It is true that between the upwelling longwave from the surface and from the low clouds is about 10% (30W/m). The temperatures are not hugely dissimilar. But the internal energy flows are very different under the two conditions (clear and cloudy).

Consider a night-time hour with cloud. The cloud is radiating through clear dry air above to space at something like 370 W/m2. In addition, the cloud is radiating roughly the same amount back to the surface, something like 370 W/m2. Meanwhile, the ocean surface is radiating (losing) around 400 W/m2.

So the ocean loses 400 and gains 370 W/m2, so it is losing 30 W/m2 in this part of the transaction.

Now take away the cloud for an hour. The surface is still radiating something like 400 W/m2, this time out to space. So the authors of Lauer10 are correct, there’s not much change in outgoing LW, “only” 15 to 30 W/m2. But what they are neglecting is that the ocean is no longer receiving 370 W/m2 of LW from the cloud. Instead, above the ocean is mostly dry air, which provides little downwelling radiation to the surface. In this case the surface itself is losing about 400 W/m2.

So despite having identical energy flows to space, these two conditions have two very different net internal energy flows. When the sky is clear, the ocean is losing energy rapidly. When it is overcast with marine stratocumulus, the ocean loses energy much more slowly. The difference in ocean loss is 370 W/m2, which is a large difference. That is why I don’t agree that the clouds make little difference to the radiation balance. They make a big difference to net energy flows (into and out) of the ocean.

And why are oceanic net energy flows important to the outgoing radiation? It is the long-term balance of these flows across the ocean surface that determines the oceanic (and therefore the atmospheric) temperature. As a result, small sustained imbalances can cause gradual temperature shifts of the entire system.

I think I notice the problem because of my training as an accountant. A small difference in the amount of payments can mask a huge difference in the source of those funds. And a small amount of income or expense adds up over time.

My conclusions?

1. I think it quite possible that Lauer’s findings are correct, that increased warming in the area of the persistent marine stratiform layers at 30°N/S leads to decreased clouds in those areas.

2. I think that Lauer’s finding are an expected effect when we consider the Earth as a heat engine operating under the Constructal Law. With increasing heat, the Constructal Law says the system will adapt by increasing throughput. Reduced cloudiness at the cold end of the heat engine is an expected change in this regard, just as we expect (and find) increased cloudiness at the hot end of the heat engine with increasing heat.

3. Of course, for this study to truly be science I need to insert the obligatory boilerplate. So let me note that mine is a preliminary study, that “further investigation is warranted”, that I could use a big stack of funds to do just that, that I will require a personal assistant to undertake the onerous task of archiving a few datasets per year, and that Exxon has been most dilatory in their payment schedule …

FURTHER INFORMATION

Constructal Theory Web Portal

Constructal Law and Climate (Adrian Bejan, PDF)

The constructal law of design and evolution in nature (Adrian Bejan, PDF)

A previous post of mine on Constructal Law and Flow Systems

The constructal law and the thermodynamics of flow systems with configuration (Adrian Bejan, PDF)

Addendum before posting. After writing the above, I noted today a new paper published in Science (behind a paywall) entitled Dynamical Response of the Tropical Pacific Ocean to Solar Forcing During the Early Holocene, Thomas M. Marchitto et al. It is discussing one of the geographical areas that Lauer10 analyzed, the eastern Pacific off of Mexico. The abstract says:

We present a high-resolution magnesium/calcium proxy record of Holocene sea surface temperature (SST) from off the west coast of Baja California Sur, Mexico, a region where interannual SST variability is dominated today by the influence of the El Niño–Southern Oscillation (ENSO). Temperatures were lowest during the early to middle Holocene, consistent with documented eastern equatorial Pacific cooling and numerical model simulations of orbital forcing into a La Niña–like state at that time. The early Holocene SSTs were also characterized by millennial-scale fluctuations that correlate with cosmogenic nuclide proxies of solar variability, with inferred solar minima corresponding to El Niño–like (warm) conditions, in apparent agreement with the theoretical “ocean dynamical thermostat” response of ENSO to exogenous radiative forcing.

In short, their study reports that when the ocean gets warmer at the equator, it gets cooler at 30°N, and vice versa. They also find that this effect is visible on annual through millennial timescales. Unsurprisingly, this is not found in the GCMs.

Intrigued by the idea of a “ocean dynamical thermostat”, I read on:

Values in the middle of this range are sufficient to force the intermediate- complexity Zebiak-Cane model of El Niño–Southern Oscillation (ENSO) dynamics into a more El Niño–like state during the Little Ice Age (A.D. ~1400 to 1850) (3), a response dubbed the “ocean dynamical thermostat” because negative (or positive) radiative forcing results in dynamical ocean warming (or cooling, respectively) of the eastern tropical Pacific (ETP) (4). This model prediction is supported by paleoclimatic proxy reconstructions over the past millennium (3, 5, 6). In contrast, fully coupled general circulation models (GCMs) lack a robust thermostat response because of an opposing tendency for the atmospheric circulation itself to strengthen under reduced radiative forcing (7).

Now, consider this finding in light of Figure 1. Yes, it is a simple “thermostat” in the sense that as the equator heats up, the area around 30°N/S cools.

But in the light of the climate heat engine it is much more than that. The Constructal Law says in response to increased forcing the climate system will respond by increasing throughput. One way to increase the throughput of a closed cycle heat engine is to cool the radiator.

And that is exactly what their “ocean dynamical thermostat” is doing. By cooling the radiator of the climate heat engine, the engine runs faster, and moves more heat from the tropics. Conversely, when the earth is cooler than usual, the engine runs slower, and less heat is transported from the tropics. This warms the tropics.

I started this by saying that I would provide a theoretical framework within which the Lauer10 findings would make sense. I believe I have done so. My theoretical results were strengthened by my subsequent finding that Marchitto et al. fits the same framework. However, this is only my understanding. Additions, subtractions, questions, falsifications, confusions, expansions, and just about anything but conflagrations gratefully accepted.

Finally, testable predictions lie at the heart of science, and they are scarce in climate science. If I am correct, the kind of study done by Lauer et al. of the persistent stratocumulus decks in e.g. the Eastern Pacific should reveal that in the observations, changes in night-time cloud cover are greater than changes in day-time cloud cover. My check from the Koch brothers must have gotten lost in the mail, so I don’t have the resources for such a study, but that is a testable prediction. It would certainly be a good and very easy direction for Lauer et al. to investigate, they have the records in hand. Here’s their chance to prove me wrong …

My regards to all,

w.

References and Notes for the above quotations from Marchitto et al.

3. M. E. Mann, M. A. Cane, S. E. Zebiak, A. Clement, J. Clim. 18, 447 (2005).

4. A. C. Clement, R. Seager, M. A. Cane, S. E. Zebiak, J. Clim. 9, 2190 (1996).

5. K. M. Cobb, C. D. Charles, H. Cheng, R. L. Edwards, Nature 424, 271 (2003).

6. M. E. Mann et al., Science 326, 1256 (2009).

7. G. A. Vecchi, A. Clement, B. J. Soden, Eos 89, 81 (2008).

PS – Both papers, one discussing the atmosphere and the other the ocean, explicitly note that this thermostatic effect is not correctly simulated by the climate models (GCMs). The Marchitto paper is very clear about exactly why. It is because of one of the most glaring and under-reported shortcomings of the models. Here’s Marchitto again, in case you didn’t catch it the first time through (emphasis mine):

In contrast, fully coupled general circulation models (GCMs) lack a robust thermostat response because of an opposing tendency for the atmospheric circulation itself to strengthen under reduced radiative forcing (7).

Say what? Model circulation strengthens under reduced forcing?

In a natural heat engine, when you add more heat, the heat engine speeds up. We can see this daily in the tropics. As the radiative forcing increases, more and more thunderstorms form, and the atmospheric circulation speeds up. It’s basic meteorology.

In the models, amazingly, as the radiative forcing increases, the atmospheric circulation actually slows down. I might have missed it, but I’ve never seen a modeller address this issue, and I’ve been looking for an explanation since the EOS paper came out. Although to be fair the modellers might have overlooked the problem, it’s far from the only elephant in the model room. But dang, it’s a big one, even among elephants.

So yeah, I can see why the models are missing the proper thermostatic feedback. If your model is so bad that modelled atmospheric circulation slows down when the forcing increases, anything’s possible.