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Earth's energy budget

...or balance...

This article is mostly about the new evidence supporting global warming by Hansen et al. But let me start with an idealized energy budget of the Earth.

The average (over the surface, day, and year) energy coming from the Sun in the form of solar radiation is 342 Watts per squared meter - and almost exactly the same amount of energy is leaving the Earth. Note that 342 is exactly one quarter of the solar constant 1370 W/m^2 (the inflow of solar energy near the Earth) - it's because the radiation is only absorbed by the cross section "pi.R^2" of the planet, while we attribute it to the whole surface "4.pi.R^2" of the Earth by the averaging process.



These 342 W/m^2 may be divided in various ways - see, for example, this PDF file (which I think is, by the way, much more rational than the paper I will discuss below):

  • 67+168+107: here, after the 342 W/m^2 approach the Earth, 67 is absorbed in the visible and UV spectrum by oxygen, ozone, and water in the atmosphere; 168 is absorbed by the surface; 107 is scattered to space in the UV and visible spectrum
  • 107+235: here, 107 is the reflected UV and visible radiation, as explained above; 235 is the total IR radiation emitted to space; the total radiation leaving the Earth is again 342

Where do these 235 W/m^2 of "infrared" energy in the atmosphere come from?

  • 67+66+78+24; here, 67 is the UV and visible solar radiation absorbed by the atmosphere, as mentioned above; 66 is IR radiation emitted by the surface and absorbed by the atmosphere; 78 is latent heat flux from the surface to the atmosphere (typically flowing in the rain or wet conditions); 24 is conduction and convection (from the surface to the atmosphere)

Note that the Earth's energy budget as summarized above works pretty nicely. I did not even have to consider 40 W/m^2 - a subset of those 66 W/m^2 above - which are "atmospheric windows" and may be viewed as direct IR radiation of the surface to the space.




How precisely do we know the numbers above? Of course, much less precisely than indicated. For example, the number "67" counting the UV rays absorbed by the atmosphere is just a result of simulations (which rely on hundreds of assumptions and which become extremely subtle especially once we need to include the effects of clouds). The observed absorption is by up to 30 W/m^2 higher than the predictions of the models - this is known as the absorption anomaly (see also Climate Audit or a description of cloud absorption anomaly of "unprecedented magnitude"). Let me emphasize that this is a UV absorption; greenhouse gases absorb IR radiation from the surface and their effects belong to a different term.

You can see that we roughly know the major energy flows through the atmosphere, as long as you allow for the uncertainties of order 30 W/m^2 (up to ten percent of the energy flows). Now, open the paper by Hansen et al.:

James Hansen is one of the people who started the paradigm that "climate change is one of the most important threats facing the humankind" two decades ago. In the paper above, they "derive" many new catastrophic scenarios. The only reason why you should believe these scenarios based on these specific computer models is the following "consistency check":

  • Their favorite computer models happen to claim that the Earth absorbs "0.85+-0.15 W/m^2" more energy than it emits; the same number "0.85 W/m^2" is calculated from the increasing temperature of oceans as the average extra energy stored by the oceans.

You can see that their advertised error margin is roughly 100 times smaller than the error margin of any conceivable calculation that someone may want to do today or in the near future. A computer model can, of course, calculate certain numbers quite accurately - but when we make a contact with reality, we must also include the errors and uncertainties of the model itself - the model uncertainties which are large. The scientific significance of the number "0.85" is zero. One may obtain numbers between -30 and +30 (or between -10 and -10, to say the least) by various small changes of the assumptions - and any number between -2 and +3 W/m^2 is as probable as 0.85 W/m^2. Of course that if one would derive that the energy imbalance is several (or tens of) Watts per meter squared, something would have to be wrong with the calculation because this would predict a huge, unobserved change in the mean temperature. Only calculations that lead to a plausible cancellation survive.

Gavin Schmidt could tell you that the large uncertainty of the individual terms does not matter because their sum is known accurately. He may try to deduce the number 0.85 W/m^2 from the observed warming in the last 100 years (about 0.5 degrees), given a certain conversion ratio between the imbalance and the temperature anomaly - this conversion ratio is called "sensitivity". Incidentally, James Hansen himself has recently changed his idea about the value of sensitivity roughly by a factor of two, so don't expect miraculous accuracy on this front either.

But even in the highly hypothetical case that the number "0.85 W/m^2" is close to the true imbalance, the climate science is very far from attributing it to some particular effects or from justifying the currently fashionable models. You don't know how to attribute this number exactly because you don't know accurately enough how the number 0.85 is divided to the individual terms.

This imbalance could be a standard discrepancy that always occurs in this era of the glaciation cycles, for example. Once again, the obvious warning is that one cannot verify models based on hundreds of arbitrary assumptions and parameters by looking at one predicted number, especially if the error margin in determining this number makes even its sign uncertain. Even more clearly, neither of their arguments or experiments is able to make any connection with the carbon dioxide.

Global temperature and cosmological constant

This potential for flawed reasoning is just like the cancellation of the cosmological constant (the energy density in the vacuum that curves the space and accelerates its expansion) and the anthropic reasoning. We know that the total cosmological constant is much smaller than the individual terms we imagine as contributions - and in fact, it must be so if galaxies could have formed (but we don't really need this observation since we have simply measured Lambda). But it is just one number. One cannot derive the existence of googols of universes and their properties from this single number, for example. One cannot calculate the mass of the Higgs particle from the small cosmological constant either. The cancellation is something that must occur and we do not know exactly why it occurs, but the fact that it does occur is too small a piece of information to imply anything else.

In the case of the oceans, the announced error margin is not only more than 100 times smaller than the uncertainties connected with the absorption anomaly. It is also comparable to many other effects that have been neglected - such as the energy loss from the tidal forces and the heat stored by the "bulk" of the Earth. Nevertheless, the authors construct the model to get an almost perfect cancellation, and they don't hesitate to claim that the finding implies that

  1. additional warming of 0.6 degrees Celsius is now guaranteed even without further changes of the atmosphere, because of "thermal inertia" of the oceans (note that "thermal inertia" is not just an awkward way to talk about heat capacity because heat capacity tends to stabilize the temperature near a constant, not in the state of uniform motion) ;-)
  2. this "thermal inertia" also implies that the atmosphere is "lagging behind", and therefore we must be afraid of the future even in the case when we don't observe the predicted effects
  3. melting icebergs and rising sea levels are guaranteed, as always

I am not 100% sure that the 15 authors will agree with me that their paper is a textbook example of cargo cult science. Something that superficially uses the correct words and sometimes even the correct formulae, but always in a misleading, incomplete, incorrect context. Something essential is missing. The calculations and arguments only pick some mechanisms, formulae, and possible explanations, but they do not worry that the right explanation may be completely different. The "implication 2" moreover shows that their speculations are untestable.

The logical connections between various statements and observations in the paper are flawed, the attribution is unjustified, but it does not matter too much today. What probably matters more is that hundreds of newspapers inform about this "smoking gun" or even "proof" of global warming (fortunately, BBC added quotes to the word "proof" and cited scientists who stated that the evidence supporting Hansen et al. models is weak).

The climate science, something that the U.S. spends 6 billions USD per year for, has become a huge enterprise that does not intend to explain and predict numbers anymore; it is intended to justify the failure to calculate anything correctly and overcompensate the failure by even more sensational predictions that will be shown incorrect in the future - far enough future so that their responsibility for the incorrect predictions will be forgotten. A well-known mainstream climate scientist Hans von Storch, together with Nico Stehr, recently complained about the losing battle of sober analysis against sexy, catastrophic scenarios (well, Hans von Storch - who is a former leading German defender of Donald Duck :-) - keeps on telling me that Fred Singer's translation is lousy and that an authorized translation is here).

Summary of the paper by Hansen et al.: they have demonstrated that the temperature growth in the recent decades is roughly consistent with the temperature growth of the oceans, but they have found no arguments whatsoever that could attribute this growth to any particular mechanism, and the agreement with their particular model is pure chance because of the huge model uncertainties. The warming in the last 100 years may be a statistical fluke, the end of the little ice age, the effect of the solar magnetic field, or anything else. As Roy Spencer wrote later, they just outlined one internally consistent interpretation of the data among many other possible interpretations.

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reader Quantoken said...

It is common practice for nowaday scientists to blow the precision of their experiments completely out of proportion, in shrink their experimental error a couple hundred times smaller so as to make their results look real while in fact they are just random noise.

They have forgotten many important factors, for example there are heat generated by the natural decay of some radioactive elements in the crust of the earth, like U238 and U235. There are 4 ppm of U238, and approximately 1/137 of U235. So that's a huge amount generating a few 10 watts per square meter.

Let's say the 0.85 watts per square meter is the correct imbalance figure. How much can it heat the earth up? The earth is a huge heat reservior if you count all the mass. If you do a little bit calculation it takes a couple of tens of millions of years to heat up even one degree, at a discrepancy of just 1 watts per square meter.

Quantoken


reader John A said...

Lubos,

As usual, you talk too much sense.

I'll put a link to your post on the front page of climateaudit.

Unfortunately, there's a memory problem with the mySQL server and we can't post long articles or save images. We're still waiting for someone to fix it (probably in classic support style by rebooting the thing).


reader Leucipo said...

342 W per surface square meter. Hmm lets see... 342 Joule/sec are 0.095 WattHour per second, and this is by square meter. From the calculation I see we use the total surface of earth, so total input is 48407631 MegaWattHour each second, so "dairy production" of 4182419395114 MegaWattHour.

And did you say there are almost the same quantity leaving the earth? Someone should put a net somewhere. Lets see, sharing equally, it gives a dairy lot of 697 MWh for each person in the Earth.How much do you pay the KWh in your electricity receipt? Money rains, and we do not care...

Well, for more references, I read somewhere that we are burning 0.25 MwH per person and day. Guess this is the kind of "naive temperature analysis" argued to proof that human action is still irrelevant.


reader Alec Rawls said...

Good stuff Luboš. Hansen et al. may have found some indication of ocean warming, but their claim that this supports their physical model--a model that is nowhere near competent to predict temperature variations on such a scale--is absurd. NASA climatologists Hansen and Schmidt adamantly refuse to include best estimates for cosmic-ray/cloud effects (the leading candidate for a natural cause of warming) in their models. For them to then claim that this new non-evidence for their model justifies concluding that warming is human induced is nothing but disingenuous, tendentious, meritricious, cant. (I'd heap on more synonyms if I could think of them.) My post here.