Comments on Dr. Ollila’s Claims that Greenhouse Effect Calculations Violate Energy Conservation

Once again I am being drawn into defending the common explanation of Earth’s so-called “greenhouse effect” as it is portrayed by the IPCC, textbooks, and virtually everyone who works in atmospheric radiation and thermodynamics.

To be clear, I am not defending the IPCC’s predictions of future climate change… just the general explanation of the Earth’s greenhouse effect, which has a profound influence on global temperatures as well as on weather.

As we will see, much confusion arises about the greenhouse effect due to its complexity, and the difficulty in expressing that complexity accurately with words alone. In fact, the IPCC’s greenhouse effect “definition” quoted by Dr. Ollila is incomplete and misleading, as anyone who understands the greenhouse effect should know.

As we will see, in the case of something as complicated as the greenhouse effect, a simplified worded definition should never be the basis for quantitative calculations; instead, complicated calculations are sometimes only poorly described with words.

What is the “Greenhouse Effect”?

Descriptions of the Earth’s natural greenhouse effect are unavoidably incomplete due to its complexity, and even misleading at times due to ambiguous phrasing when trying to express that complexity.

The complexity arises because the greenhouse effect involves every cubic meter of the atmosphere having the ability to both absorb and emit infrared (IR) energy. (And almost never are the rates of absorption and emission the same, contrary to the claims of many skeptics – IR emission is very temperature-dependent, while absorption is not).

While essentially all the energy for this ultimately comes from absorbed sunlight, the infrared absorption and re-radiation by air (and by clouds in the atmosphere) makes the net impact of the greenhouse effect on temperatures somewhat non-intuitive. The emission of this invisible radiation by everything around us is obviously more difficult to describe than the single-source Sun.

The ability of air and clouds to absorb and emit IR radiation has profound impacts on energy flows and temperatures throughout the atmosphere, leading to the multiple infrared energy flow arrows (red) in the energy budget diagram originally popularized by Kiehl & Trenberth (Fig. 1).

[As an aside, contrary to the claims of the 2010 book Slaying the Sky Dragon: Death of the Greenhouse Gas Theory, this simplified picture of the average energy flows between the Earth’s surface, atmosphere, and space is NOT what is assumed by climate models. Climate models use the relevant physical processes at every point on three-dimensional grid covering the Earth, with day-night and seasonal cycles of solar illumination. The simplified energy budget diagram is instead the best-estimate of the global average energy flows based upon a wide variety of observations, model diagnostics, and the assumption of no natural long-term climate change.]

If the Earth had no atmosphere (like the Moon), the surface temperature at any given location would be governed by the balance between the rate of absorbed solar energy and the loss of thermally-emitted infrared (IR) radiation. The sun would heat the surface to a temperature where the emitted IR radiation balanced the absorbed solar radiation, and then the temperature would stop increasing. This general concept of energy balance between energy gain and energy loss is involved in determining the temperature of virtually anything you can think of.

But the Earth does have an atmosphere, and the atmosphere both absorbs and emits IR radiation in all directions. “Greenhouse gases” (primarily water vapor, but also carbon dioxide) provide most of this function, and any gain or loss of an IR photon by a GHG molecule is almost immediately felt by the non-radiatively active gases (like nitrogen and oxygen) through molecular collisions.

If we were to represent these infrared energy flows in Fig. 1 more completely, there would be a nearly infinite number of red arrows, both upward and downward, connecting every vanishingly-thin layer of atmosphere with every other vanishingly thin layer. Those are the flows that are happening continuously in the atmosphere.

The most important net impact of the greenhouse effect on terrestrial temperatures is this:

The net effect of a greenhouse atmosphere is that it keeps the lower atmospheric layers (and surface) warmer, and the upper atmosphere colder, than if the greenhouse effect did not exist.

I have often called this a “radiative blanket” effect.

Interestingly, without the greenhouse effect, the upper layers of the troposphere would not be able to cool to outer space, and weather as we know it (which depends upon radiative destabilization of the vertical temperature profile) would not exist. This was demonstrated by Manabe & Strickler (1964) who calculated that, without convective overturning, the pure radiative equilibrium temperature profile of the troposphere is very hot at the surface, and very cold in the upper troposphere. Convective overturning in the atmosphere reduces this huge temperature ‘lapse rate’ by about two-thirds to three-quarters, resulting in what we observe in the real atmosphere.

Dr. Ollila’s Claims

The latest installment of what I consider to be bad skeptical science regarding the greenhouse effect comes from emeritus professor of environmental science, Dr. Antero Ollila, who claims that the energy budget diagram somehow violates the 1st Law of Thermodynamics, i.e., conservation of energy, at least in terms of how the greenhouse effect is quantified.

His article is entitled, How The IPCC’s Greenhouse Definition Violates the Physical Law of Conservation of Mass & Energy. He uses a modified version (Fig. 2) of the Kiehl-Trenberth diagram:

It should be noted that these global average energy budget diagrams do indeed conserve energy in their total energy fluxes at the top-of-atmosphere (the climate system as a whole), as well as for the surface and atmosphere, separately. If you add up these energy gain and loss terms you will see they are equal, which must be the case for any system with a stable temperature over time.

But what Dr. Ollila seems to be confused about is what you can physically and quantitatively deduce about the greenhouse effect when you start combining energy fluxes in that diagram. Much of the first part of Dr. Ollila’s article is just fine. His objection to the diagram is introduced with the following statement, which those who hold similar views to his will be triggered by:

“The obvious reason for the GH effect seems to be the downward infrared radiation from the atmosphere to the surface and its magnitude is 345 W/m2. Therefore, the surface absorbs totally 165 (solar) + 345 (downward infrared from the atmosphere) = 510 W/m2.“

At this point some of my readers (you know who you are) will object to that quote, and say something like, “But the only energy input at the surface is from the sun! How can the atmosphere add more energy to the system, when the sun is the only source of energy?” My reading of Dr. Ollila’s article indicates that that is where he is going as well.

But this is where the problem with ambiguous wording comes in. The atmosphere is not, strictly speaking, adding more energy to the surface. It is merely returning a portion of the atmosphere-absorbed solar, infrared, and convective transport energy back to the surface in the form of infrared energy.

As shown in Fig. 2, the surface is still emitting more IR energy than the atmosphere is returning to the surface, resulting in net surface loss of [395 – 345 =] 50 W/m2 of infrared energy. And, as previously mentioned, all energy fluxes at the surface balance.

And this is what our intuition tells us should be happening: the surface is warmed by sunlight, and cooled by the loss of IR energy (plus moist and dry convective cooling of the surface of 91 and 24 W/m2, respectively.) But the atmosphere’s radiative blanket reduces the rate of IR cooling from the warmer lower layers of the atmosphere to the upper cooler layers. This alteration of average energy flows by greenhouse gases and clouds alters the atmospheric temperature profile.

A related but common misunderstanding is the idea that the rate of energy input determines a system’s temperature. That’s wrong.

Given any rate of energy input into a system, the temperature will continue to increase until temperature-dependent energy loss mechanisms equal the rate of energy input. If you don’t believe it, let’s look at an extreme example.

Believe it or not, the human body generates energy through metabolism at a rate that is 8,000 time greater than what the sun generates, per kg of mass. But the human body has an interior temperature of only 98.6 deg. F, while the sun’s interior temperature is estimated to be around 27,000,000 deg. F. This is a dramatic example that the rate of energy *input* does not determine temperature: it’s the balance between the rates of energy gain and energy loss that determines temperature.

If energy has no efficient way to escape, then even a weak rate of energy input can lead to exceedingly high temperatures, such as occurs in the sun. I have read that it takes thousands of years for energy created in the core of the sun from nuclear fusion to make its way to the sun’s surface.

Since this is meant to be a critique of Dr. Ollila’s specific arguments let’s return to them. I just wanted to first address his central concern by explaining the greenhouse effect in the best terms I can, before I confuse you with his arguments. Here I list the main points of his reasoning, in which I reproduce the first quote from above for completeness:

[begin quote]

The obvious reason for the GH effect seems to be the downward infrared radiation from the atmosphere to the surface and its magnitude is 345 Wm-2. Therefore, the surface absorbs totally 165 + 345 = 510 Wm-2….

The difference between the radiation to the surface and the net solar radiation is 510 – 240 = 270 Wm-2...

The real GH warming effect is right here: it is 270 Wm-2 because it is the extra energy warming the Earth’s surface in addition to the net solar energy.

The final step is that we must find out what is the mechanism creating this infrared radiation from the atmosphere. According to the IPCC’s definition, the GH effect is caused by the GH gases and clouds which absorb infrared radiation of 155 Wm-2 emitted by the surface and which they further radiate to the surface.

As we can see there is a problem – and a very big problem – in the IPCC’s GH effect definition: the absorbed energy of 155 Wm-2 cannot radiate to the surface 345 Wm-2 or even 270 Wm-2. According to the energy conversation law, energy cannot be created from the void. According to the same law, energy does not disappear, but it can change its form.

From Figure (2) it is easy to name the two other energy sources which are needed for causing the GH effect namely latent heating 91 Wm-2 and sensible heating 24 Wm-2, which make 270 Wm-2 with the longwave absorption of 155 Wm-2.

When the solar radiation absorption of 75 Wm-2 by the atmosphere will be added to these three GH effect sources, the sum is 345 Wm2. Everything matches without the violation of physics. No energy disappears or appears from the void. Coincidence? Not so.

Here is the point: the IPCC’s definition means that the LW absorption of 155 Wm-2 could create radiation of 270 Wm-2 which is impossible.“

[end quote]

Now, I have spent at least a couple of hours trying to follow his line of reasoning, and I cannot. If Dr. Ollila wanted to claim that the energy budget numbers violate energy conservation, he could have made all of this much simpler by asking the question, How can 240 W/m2 of solar input to the climate system cause 395 W/m2 of IR emission by the surface? Or 345 W/m2 of downward IR emission from the sky to the surface? ALL of these numbers are larger than the available solar flux being absorbed by the climate system, are they not? But, as I have tried to explain from the above, a 1-way flow of IR energy is not very informative, and only makes quantitative sense when it is combined with the IR flow in the opposite direction.

If we don’t do that, we can fool ourselves into thinking there is some mysterious and magical “extra” source of energy, which is not the case at all. All energy flows in these energy budget diagram have solar input as the energy source, and as energy courses through the climate system, they all end up balancing. There is no violation of the laws of thermodynamics.

Is There an Energy Flux Measure of the Greenhouse Effect?

One of the problems with Dr. Ollila’s reasoning is that there really isn’t any of these unidirectional energy fluxes (or combinations of energy fluxes, such as 155, or 270, or 345 W/m2) that can be called a measure of the greenhouse effect. The average unidirectional energy fluxes are what exist after the surface and atmosphere have readjusted their temperature and humidity structures (as well as after the sensible and latent convective heat transports get established).

Even the oft-quoted 33 deg. C of warming isn’t a measure of the greenhouse effect… it’s the resulting surface warming after convective heat transports have cooled the surface. As I recall, the true, pure radiative equilibrium greenhouse effect on surface temperature (without convective heat transports) would double or triple that number.

If the atmospheric radiative energy flows are too abstract for you, let’s use the case of a house heated in the winter. On an average cold winter day, I compute from standard sources that the heating unit in the average house leads to a loss of energy through the walls, ceiling, and floor of about 10 W/m2 (just take the heater input in Watts [around 5,000 Joules/sec] and divide by the surface area of all house exterior surfaces [ around 500 sq. meters]).

But compare that 10 W/m2 of energy flow though the walls, ceiling, and floor to the inward IR emission by the exterior walls, which (it is easy to show) emit an IR flux toward the center of the house that is about 100 W/m2 greater than the outward emission by the outside of the walls. That ~100 W/m2 difference in outward versus inward IR flux is still energetically consistent with the 10 W/m2 of heat flow outward through the walls.

This seeming contradiction is resolved (just as in the case of Earth’s surface energy budget) when we realize that the NET (2-way) infrared flux at the inside surface of the exterior walls is still outward, because that wall surface will be slightly colder than the interior of the house, which is also emitting IR energy toward the outside walls. Talking about the IR flux in only one direction is not very quantitatively useful by itself. There is no magical and law-violating creation of extra energy.

Concluding Comments

If you have managed to wade through the arguments above and understand most of them, congratulations. You now see how complicated the greenhouse effect is compared to, say, just sunlight warming the Earth’s surface. That complexity leads to imprecise, incomplete, and ambiguous descriptions of the greenhouse effect, even in the scientific literature (and the IPCC’s description).

The most accurate representation of the greenhouse effect is made through the relevant equations that describe the radiative (and convective) energy flows between the surface and the atmosphere. To express all of that in words would be nearly impossible, and the more accurate the wording, the more the reader’s eyes would glaze over.

So, we are left with people like me trying to inform the public on issues which I sometimes consider to be a waste of time arguing about. I only waste that time because I would like for my fellow skeptics to be armed with good science, not bad science.

[I still maintain that the simplest backyard demonstration of the greenhouse effect in action is with a handheld IR thermometer pointed at a clear sky at different angles, and seeing the warming of the thermometer’s detector as you scan from the zenith down to an oblique angle. That is the greenhouse effect in action.]