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Monday, January 10, 2011

Getting it wrong: George White's argument against AGW (Pt 2)

Continuing my critique of George White's argument against AGW*, I must first note its general structure.  After the introduction, White proceeds to analyse the various energy flows into, and out of the the Earth's atmosphere as revealed by satellite data.  He does this in the sections on Albedo Effects and Energy Flux.  He then mounts an argument that Thermal Lag does not influence the rate at which the Earth warms or cools due to changes in forcings.  White claims this result is itself an argument against AGW, but this is not so.  Rather, if he could make his case, it would be a necessary auxiliary hypothesis to the argument he mounts in his introduction, and to a lesser extent, his second argument.    That second argument uses the same data and an unusual method to determine the Earth's climate sensitivity, and is presented in the section on Climate Sensitivity.  I had hoped to deal with both of those discussions in one post, but on reflection I will require two (making this a four part series).

Turning to his argument on Thermal Lag, White first collects the data on energy flows at the surface for the globethe northern hemisphere, and the southern hemisphere.  In reading the graphs, it is important to realise that the scale for each measure is indicated by two limit lines, which are each an equal distance from the mean value, that distance being given on the key.  White derived the values on the graphs from calculation or direct plotting data from NASA, and I have assumed he has made no error in doing so.

From the data presented in the graphs, White determines the energy flux, ie, the net energy flow into or out of the Earth's surface.  The energy flux is just energy coming in minus the energy going out.  White includes a term, Pw, for energy used to drive weather systems or used in biology, which he says is not available to warm the planet.  That is not correct.  Energy is neither created or destroyed; and energy that drives the wind is dissipated as heat.  Most energy used in biology is also eventually dissipated as heat, though a very small fraction is stored by burial in the first stage of the process that leads to the creation of fossil fuels.  As it happens, humans are releasing that stored energy far faster than nature is packing it away; so the net balance of Pw should be to heat the surface, though the amount of energy involved is so small compared to solar flux that it is reasonable to ignore it.

Now comes the crux of his argument.  Having determined the energy flux for each hemisphere, White determines the volume of water that will be heated by that energy flux by 5 degrees (5.3 in the northern hemisphere), ie, the average change in sea surface temperature over the seasonal cycle.  It turns out, in White's calculations to approximate closely to the volume of water above the thermocline.  The thermocline, White says, "is an insulating layer" that prevents heat from flowing to the deep ocean.  In other words, according to White, over the seasonal cycle, the total amount of water heated and cooled by changes in energy flux is the total amount of water available to be heated and cooled by that flux.  It follows, according to him, that thermal lag in the ocean is not a factor in determining the effect of CO2 on global temperatures.

So, how does this argument fare?

The first thing to notice is that all White has demonstrated, even if we accept all his values and calculations, is that the ocean obeys the principle of conservation of energy.  The amount of water heated to a given temperature is the amount of water that could have been heated.  Unless White is claiming that the basic theory of the Greenhouse Effect violates the first law of thermodynamics, it is difficult to see an argument here.

Second, and again assuming all his values and calculations are correct, White is ignoring how the Green House Effect works.  Essentially, the effect of an increase in green house gasses is to reduce outgoing radiation at the top of the atmosphere.  To restore the balance with energy coming in from the sun, this means the Earth must warm to increase its energy output.  Doubling of CO2 will reduce the outgoing radiation by 3.7 watts per meter squared.  Ignoring feedbacks, to restore this would require an increase in temperature of at the surface from 288 to 288.7 degrees if all radiation came from the surface. However, the additional 3.7 w/m^2 squared will only heat the surface waters (using White's values and formulas) by 0.6 degrees assuming the increasing temperature did not result in an increase in outgoing radiation in the interim.

As a result of the previous calculation, it is clear that thermal equilibrium will not be restored in one year so there is some thermal lag, even if we dispute no other aspect of White's argument.  Of course, the difference between 0.6 and 0.7 is small, so you may wonder what the fuss is all about.  However, that difference is small only because of a number of assumptions made in White's favour.

To start with, not all outgoing radiation comes from the surface.  A significant amount comes from CO2 high in the atmosphere, and with an average temperature of about 220 K.  If all radiation came from that altitude then an increase of 1.5 degrees K would be needed to restore radiative balance.  As all levels of the troposphere are tied to equivalent temperature increases by the adiabatic lapse rate, the result is that the surface must warm by a greater amount to compensate for the smaller increase in radiation with rise in temperature at higher altitudes.  The net effect is that the surface must warm by 1.2 degrees in the no feedback case, not by 0.7.

Further, the outgoing radiation will increase with every increase in temperature, reducing the net energy flux available to heat the ocean.  By the time the surface temperature rises by 0.6 degrees, the net flux difference due to the doubling of CO2 (still in the no feedback scenario) is approximately 0.3 w/m^2.  At that flux rate, the ocean surface would only warm at about 0.05 degrees per anum (using White's figures and formulas).  In other words, just given the considerations to date, it would take more than ten years to warm just the surface waters of the ocean sufficiently to restore radiative balance.

And, of course, all this has assumed no feedback.  Given that the feedback response is expected to be a 2.8 degree increase, that will increase further the time taken to reach equilibrium.  Further, the feedback scales with temperature so although it does increase the final effective change in flux, it does so gradually and therefore does not significantly increase the rate of warming.  So if the feedback is as expected by the IPCC, the thermal lag scales out to several decades, even if we assume White made no other mistakes than ignoring the need to restore radiative balance.  Of course, the feedback response is controversial in the pseudo debate on global warming, with some commentators putting it a around 0.5 degrees (which would reduce the thermal lag to around 5 years).  For those commentators, the facts in this paragraph will only show that they cannot rely on a presumed lack of thermal lag to prove a low feedback, for doing so will constitute a circular argument.

So much for taking White's argument at face value.  Even in those terms it fails; but it is worse, for he significantly mischaracterizes the structure of the oceans.

(Surface structure of the ocean, by Genny Anderson)

At its upper margins, the ocean has two main layers.  The upper mixed layer is well mixed by turbulence generated by surface winds.  As a result it has close to constant temperature by depth (though the temperature varies significantly by latitude).  This is the layer to which White refers.  However, its average depth is closer to 70 meters than to 60.

Seasonal (and global) warming is not restricted to the mixed layer.  The main thermocline, which contains 9 times the volume of the mixed layer is also heated and cooled on a seasonal basis, although it (obviously) does not maintain a constant temperature change with the mixed layer.  In fact, the nature of the thermocline as a gradient spanning over 100 meters rather than as an abrupt step wise transition, shows that it is formed by the transfer of heat from the mixed layer to the deep ocean.  That transfer is brought about by conduction and diffusion, and is very small at the lower bound of the thermocline, but significantly larger at its upper bound.

Further, the surface waters at the poles also warm and cool seasonally, and also as a result of the Greenhouse Effect.

Overall, then the total amount of water that must be warmed to restore radiative balance following an increase in greenhouse gasses, with more energy going into surface waters outside of the mixed layer than that which goes into the mixed layer.

There is also a loss of heat to the deep ocean due to the thermohaline conveyor, and conduction/diffusion across the thermocline.  Contrary to White, the thermocline is not  an insulator, and is in fact the mark of a slow heat transfer to the depths.  Its unique structure merely marks the transition from rapid heat transfer due to turbulence in the mixed layer to slow heat transfer by conduction and diffusion in the depths.

So, to summarize, George White's argument that there is no significant thermal lag is based on two significant errors.  The second, and least important in terms of magnitude, is that he underestimates by an order of magnitude the volume of the ocean that must be warmed to restore radiative balance.  Far more importantly, he ignores the fact that the Greenhouse Effect is just the requirement that radiative balance be restored once it is disturbed.  Allowing for that, Thermal Lag is shown to be of the order of 5 to 10 years in the no feedback case, and around three times that with feedbacks in the range expected by the IPCC.  These figures must be approximately doubled to account for the additional volume of water that must be heated, and which was not considered by White.

Having said that, White in his calculations effectively relied on a model with a resolution of a single hemisphere, and with two ocean and one atmospheric layers.  That very low resolution necessarily introduced errors into his estimations which will also apply to my estimations.  In contrast, in calculating Thermal Lag, climate scientists have used models with 1.5 degree spatial resolution and with multiple oceanic and atmospheric layers.  Consequently I would be inclined to trust their estimates of Thermal Lag (ie, approximately 30 years) rather than the estimates I have derived here. 

Further reading (Added 4/2/11):  

*  I have recently been made aware that George White has a more extensive argument against AGW than the one I am discussing (thank you Leonard).  Given the length of that argument, I will leave discussing it to a later date.


  1. Tom,
    The thermal conductivity and diffusion of water are so much lower than convective mixing, that for all practical purposes, it can be considered insulating. The temperature of the layer below the thermocline is near constant to the bottom and has stayed near constant for thousands of years. Radiation up is only from the surface, and there is a small temperature gradient even in the upper layer, and changing currents can redistribute heating and location, and clouds can also change, so your argument is not conclusive. Take a look at the following for an example:

  2. Leonard,

    First, even if your claim about heat transfer below the thermocline were correct, White would still significantly have understimated the volume of ocean that is heated and warmed by even seasonal cycles. As indicated above, the region of the thermocline itself varies in temperature of a seasonal basis, with variations potentially being as great as those in the mixed layer, which is all that White considers. See for instance:

    Further, heat transfer to the deep ocean has been measured by Willis et al (see in particular figure 9)

    It has also been measured by Levitus in a variety of papers with different authors:

    In both cases, they show by observation a decadal temperature trend down to 700 meters or beyond that is between 1/5th and 1/4 of that on the surface. That is not inconsequential.

    Gouretski and Kultermann show warming at 750 - 1000 meters that is only half that of that found at the surface (0-10 meters)in the period from 1950 to 2000:

    I must emphasise that these results are not based on models, but on observations. Based on them, and in particular on Levitus, the IPCC AR$ estimates that 30% of the increase in ocean heat content is below 700 meters. That is consistent with the models, with Huan et al showing the increase in heat content in an extended model run to be approximately equal for the layers 0-250 meters, 250 to 700 meters, and below 700 meters:

    So White's assumption that heat is not transfered beyond the mixed layer, very necessary for his argument, is in disagreement with both observation and modelling. There is little to support it beyond his need for it to be true.

    Even had that not been the case, his failure to account for the time needed to raise the oceans surface to restore radiative balance still demolishes his argument - a point you have not adressed.

    Finally, I do not see the point of your discussion complexity. Certainly the ocean is complex, and I might well miss a point as well. For that reason I would much rather rely on detailed modelling to determine the consequences of the application of physical theory in this case. That is not because the models are fallible, but because they remove at least one cause of fallibility from simple calculation.

    Having said that, any problem with simple calculation is not just a problem for me, but for White as well. If you do think the ocean is to complex for my argument to be certain, then you should also have thought the same of White's arguement. To do otherwise is special pleading, yet it was you who introduced me to White's argument, which you have publicly endorsed.

    Finally, I have little to say about Tisdale's article which would take me to far of topic. All that needs to be said, perhaps, is that he appears to think the succesive transfer of energies between ocean and atmosphere can by itself, without any increased energy input, result in a permanent increase in oceanic heat content.