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## “Blah blah blah” vs Equations

It is not surprising that the people most confused about basic physics are the ones who can’t write down an equation for their idea.

The same people are the most passionate defenders of their beliefs and I have no doubts about their sincerity.

I’ll meander into what it is I want to explain..

I found an amazing resource recently – iTunes U short for iTunes University. Now I confess that I have been a little confused about angular momentum. I always knew what it was, but in the small discussion that followed The Coriolis Effect and Geostrophic Motion I found myself wondering whether conservation of angular momentum was something independent of, or a consequence of, linear momentum or some aspect of Newton’s laws of motion.

It seemed as if conservation of angular momentum was an orphan of Newton’s three laws of motion. How could that be? Perhaps this conservation is just another expression of these laws in a way that I hadn’t appreciated? (Knowledgeable readers please explain).

Just around this time I found iTunes U and searched for “mechanics” and found the amazing series of lectures from MIT by Prof. Walter Lewin. A series of videos. I recommend them to anyone interested in learning some basics about forces, motion and energy. Lewin has a gift, along with an engaging style. It’s nice to see chalk boards and overhead projectors because they are probably no more in use (? young people please advise).

These lectures are not just for iPhone and iTunes people – here is the weblink.

The gift of teaching science is not in accuracy – that’s a given – the gift is in showing the principle via experiment and matching it with a theoretical derivation, and “why this should be so” and thereby producing a conceptual idea in the student.

I haven’t got to Lecture 20: Angular Momentum yet, I’m at about lecture 11. It’s basic stuff but so easy to forget (yes, quite a lot of it has been forgotten). Especially easy to forget how different principles link together and which principle is used to derive the next principle.

What caught my attention for the purposes of this article was how every principle had an equation.

For example, in deriving the work done on an object, Lewin integrates force over the distance traveled and comes up with the equation for kinetic energy.

While investigating the oscillation of a mass on a spring, the equation for its harmonic motion is derived.

Every principle has an equation that can be written down.

Over the last few days, as at many times over the past two years, people have arrived on this blog to explain how radiation from the atmosphere can’t affect the surface temperature because of blah blah blah. Where blah blah blah sounds like it might be some kind of physics but is never accompanied by an equation.

Here’s the equation I find in textbooks.

Energy absorbed from the atmosphere by the surface, Ea:

Ea = αRL↓ ….[eqn 1]

where α = absorptivity of the surface at these wavelengths, RL↓ = downward radiation from the atmosphere

And this energy absorbed, once absorbed, is indistinguishable from the energy absorbed from the sun. 1 W/m² absorbed from the atmosphere is identical to 1 W/m² absorbed from the sun.

That’s my equation. I have provided six textbooks to explain this idea in a slightly different way in Amazing Things we Find in Textbooks – The Real Second Law of Thermodynamics.

It’s also produced by Kramm & Dlugi, who think the greenhouse effect is some unproven idea:

Now the equation shown is a pretty simple equation. The equation reproduced in the graphic above from Kramm & Dlugi looks a little more daunting but is simply adding up a number of fluxes at the surface.

Here’s what it says:

Solar radiation absorbed + longwave radiation absorbed – thermal radiation emitted – latent heat emitted – sensible heat emitted + geothermal energy supplied = 0

Or another way of thinking about it is energy in = energy out (written as “energy in – energy out = 0“)

Now one thing is not amazing to me –  of the tens (hundreds?) of concerned citizens commenting on the many articles on this subject who have tried to point out my “basic mistake” and tell me that the atmosphere can’t blah blah blah, not a single one has produced an equation.

The equation might look something like this:

Ea = f(α,Tatm-Tsur).RL↓ ….[eqn 2]
where Tatm = temperature of the atmosphere, Tsur = temperature of the surface

With the function f being defined like this:

f(α,Tatm-Tsur) = α, when Tatm ≥ Tsur and

f(α,Tatm-Tsur) = 0, when Tatm < Tsur

In English, it says something like energy from the atmosphere absorbed by the surface = 0 when the temperature of the atmosphere is less than the temperature of the surface.

I’m filling in the blanks here. No one has written down such ridiculous unphysical nonsense because it would look like ridiculous unphysical nonsense. Or perhaps I’m being unkind. Another possibility is that no one has written down such ridiculous unphysical nonsense because the proponents have no idea what an equation is, or how one can be constructed.

### My Prediction

No one will produce an equation which shows how no atmospheric energy can be absorbed by the surface. Or how atmospheric energy absorbed cannot affect internal energy.

This is because my next questions will be:

1. Please supply a textbook or paper with this equation
2. Please explain from fundamental physics how this can take place

### My Challenge

Here’s my challenge to the many people concerned about the “dangerous nonsense” of the atmospheric radiation affecting surface temperature –

Supply an equation.

If you can’t, it is because you don’t understand the subject.

It won’t stop you talking, but everyone who is wondering and reads this article will be able to join the dots together.

### The Usual Caveat

If there were only two bodies – the warmer earth and the colder atmosphere (no sun available) – then of course the earth’s temperature would decrease towards that of the atmosphere and the atmosphere’s temperature would increase towards that of the earth until both were at the same temperature – somewhere between the two starting temperatures.

However, the sun does actually exist and the question is simply whether the presence of the (colder) atmosphere affects the surface temperature compared with if no atmosphere existed. It is The Three Body Problem.

### My Second Prediction

The people not supplying the equation, the passionate believers in blah blah blah, will not explain why an equation is not necessary or not available. Instead, continue to blah blah blah.

## The Coriolis Effect and Geostrophic Motion

The coriolis effect isn’t the easiest thing to get your head around, but it is an essential element in understanding the large scale motions of the atmosphere and the oceans.

If you roll a ball along a flat frictionless surface it keeps going in the same direction. This is because objects that have no forces on them continue in the same direction at the same speed. (The combination of direction and speed is known as velocity, which is a vector. A vector consists of a magnitude (e.g. speed) and a direction).

Well, that statement was not strictly true – because it wasn’t specific enough.

If you get onto a merry go round and launch your same ball in one direction you observe it move away in a curved arc. But someone above the merry go round, perhaps someone who had climbed up a pole and was looking down, would observe the ball moving in a straight line.

It’s all about frames of reference.

Now we live on planet that is rotating so we have to consider the “merry go round” effect.

There are two approaches for a mathematical basis (and we will keep the maths separated):

• consider everything from an inertial frame – as if all motion was viewed from space (note 1)
• consider everything from the surface of the planet

If we considered everything from space then the problem would actually be more difficult. On the plus side thrown balls would go in a straight line (as normal). On the minus side the boundaries of the oceans, mountains and everything else important would be constantly on the move and we would need mathematical trickery beyond most people’s comprehension.

So everyone goes for option b – consider motion from the surface of the planet. This means the frame of reference is constantly on the move.

### Coriolis

The excellent Atmosphere, Ocean and Climate Dynamics by Marshall & Plumb (2008) comes with a number of accompanying web pages most of which have some videos.

See GFDLab V: Inertial Circles – visualizing the Coriolis force for some detail and the video link, or click on the image below for the video link:

Figure 1 – Click for the video

• the left hand video is the inertial frame of reference – stationary camera
• the right hand video is the rotational frame of reference – the camera is moving with the turntable

This is the best video I have found for making clear what happens in a rotating frame.

With some relatively simple maths, the equations of motion in an inertial frame get transformed into a rotating frame of reference.

Two new terms get introduced:

• the Coriolis acceleration = “stuff appears to veer off to the side as far as I can tell” effect
• centrifugal acceleration = “things get thrown outwards like on a merry-go-round that goes very fast” effect

The centrifugal acceleration is not so significant, just a slight modifier of magnitude and direction to the very strong gravitational effect. But the Coriolis effect is very significant.

Now the Coriolis effect is easy to demonstrate on a rotating table, but we live on a rotating sphere and so there are some complexities that require the use of vector maths to calculate.

Mathematically it is easy to show that the Coriolis effect is modified by a factor relating to latitude. Specifically the effect is multiplied by the sine of the latitude, which means that at the equator the Coriolis effect is zero (sin 0° = 0), and at 30° it is half the maximum (sin 30°=0.5) and at the poles it has the full effect (sin 90° = 1.0).

I found it difficult to come up with a conceptual model which helps readers see why this is so. Readers who have had to think about the effect of resolving forces and rotations into orthogonal directions might be able to provide a conceptual picture – so please add comment if you think so. (Note 2).

### Some Maths

The Coriolis effect has to be seen in the light of the other terms in the equation of motion.

The intimidating version, for those not used to the equations of motion for fluids in a Lagrangian formulation (note 3):

Du/Dt + 1/ρ.∇p∇φ + fz x u = Fr …..[1]

where bold characters are vectors, z is the unit vector in the upward direction, u = velocity vector (u,v,w), φ = gravitational potential modified by the centrifugal force, ρ = density, p = pressure and f = Coriolis parameter.

And in not-quite-plain English, the change in velocity with time (following a moving parcel of fluid) plus pressure force plus gravitional force plus the coriolis force equals the frictional force (note that the terms are effectively for unit mass).

The Coriolis parameter:

f = 2Ω sinφ …..[2]

where Ω = the rotational speed of the earth (in radians/sec) = 2 π / (24*3600) = 7.3 x 10-5 /s

And the simpler version in each local x,y,x direction with some simplifications applied (like the hydrostatic equilibrium approximation):

Du/Dt + 1/ρ . ∂p/∂x –  f.v = Fx ….(local x-direction) …[3a]

Dv/Dt + 1/ρ . ∂p/∂y + f.u = Fy ….(local y-direction) …[3b]

1/ρ . ∂p/∂z  + g = 0 ….(local z-direction) …[3c]

### Geostrophic Balance and the Magnitude of the Coriolis Effect

Analysis of fluid flows is often carried out via non-dimensional ratios.

The Rossby number is the ratio of acceleration terms to the Coriolis force, and in the atmosphere at mid-latitudes is typically 0.1.

Another way of saying this is that the acceleration terms in equation 3 are a lot smaller than the Coriolis term. And in the free atmosphere (away from the boundary layer with the earth’s surface) the friction terms are negligible. This simplifies equation 3:

ug = – 1/fρ . ∂p/∂y ….[4a]

vg =   1/fρ . ∂p/∂x ….[4b]

With ug, vg defining the solution – geostrophic balance – to these simplified equations. This tells us that the E-W wind speed is proportional to the pressure change in the N-S direction, and the N-S wind speed is proportional to the pressure change in the E-W direction.

From Marshall & Plumb (2008)

Figure 2 – Colored text added

What might be surprising is the instead of the wind flowing from high to low pressure, it flows at right angles – along the lines of constant pressure.

So of course we have to ask whether these simplifications are justified..

Here is a sample of the 500 mbar wind and geopotential height:

From Marshall & Plumb (2008)

Figure 3

We can see that the wind at 5oo mbar (about 5km high) is quite close to geostrophic balance.

By contrast, if we look at surface winds:

From Marshall & Plumb (2008)

Figure 4

Here we see that the wind is flowing more across the pressure field from high to low pressure – this is because of the effect of friction at the surface. The friction term in equation 3 cannot be ignored when we want to calculate the motion near boundary layers.

### Conclusion

This is just an interesting part of climate science. The large scale atmospheric and oceanic motion is fascinating and also necessary for understanding the science of climate.

### Notes

Note 1: Even watching the planet from space is not an inertial frame of reference as the earth is rotating around the sun, and the sun is rotating around the center of the galaxy, etc, etc.. To avoid this article being a 100 page unfathomable treatise on rederiving the equations of motion, there are necessarily many simplifications, offered without caveat or explanation.

Note 2: The components of the Coriolis force on the surface of a sphere are calculated from Ω x u (where the “x” is the vector cross product, not “times”).

Ωu = (0,  Ωcosφ,  Ωcosφ) x (u,  v,  w)

= (Ωcosφ.w – Ωsinφ.v,   Ωsinφ.u,  -Ωcosφ.u)

w is the vertical component of wind and is generally very small compared with horizontal components. So when at the equator (φ=0°), then:

Ωu = (Ωcosφ.w,   0,  -Ωcosφ.u)

the u-direction (W-E) is very small because w is very small, and the w-direction (vertical) is not important because it competes with the much larger gravity term

Note 3: The term D/Dt has a specific meaning that might be new to many people. This is the Lagrangian differential, which is the change in the property of a fluid following that element of fluid. Rather than the change in property of a fluid at a fixed point in space.

D/Dt ≡ ∂/∂t + u∂/∂x + v∂/∂y + w∂/∂z, where u = (u,v,w) is the velocity vector

## The Rotational Effect

Climate scientists think that the rotation of the earth is responsible for a lot of the atmospheric and ocean effects that we see. In fact, most climate scientists think it is easy to prove. (Although not as simple as proving that radiatively-active gases affect the climate).

Now suppose the earth’s rotation speed was reducing by X% per year as a result of some important human activity (just suppose, for the sake of this mental exercise) and had been for 100 years or so.

Then atmospheric physics papers and textbooks would comment on the effect of the current speed of rotation of the planet – quantifying its effect by analyzing what climate would be like without rotation. This would be just as an introduction to the effect of rotation on climate. Let’s say that the mean annual equator-arctic temperature differential is currently 35°C (I haven’t checked the exact value) but without rotation it might be thought to be 45°C. So we will describe the rotational effect as being responsible for a 10°C arctic-equatorial temperature differential.

More specifically the rotational effect might be quantified as the number of petawatts of equatorial to polar heat transported vs the value calculated for a “no rotational” earth. But by way of introduction the temperature differential is an easier value to grasp than the change in petawatts.

Various researchers would attempt to calculate the much smaller changes likely to occur in the climate as a result of the rotational changes that might take place over the next 10-20 years. They would use GCMs and other models that would be exactly like the current ones.

And of course there would be many justifiable questions about how accurate the models are – like now.

And many from the general public, not understanding how to follow the equations of motion in rotational frames, or the thermal wind equation, or Ekman pumping, or baroclinic instability, or pretty much anything relating to atmospheric & ocean dynamics might start saying:

The rotational effect doesn’t exist

Many of these people would be skeptical about the small changes to climate that could result from an impercetible change in the rotation rate.

Many blogs would spring up with people using hand-waving arguments about the climatic effects of rotation being vastly overstated.

Other blogs would write that climate science makes massively simplistic assumptions in its calculations and uses the geostrophic balance as its complete formula for climate dynamics. Many other people unencumbered with any knowledge from climate science textbooks, or any desire to read one, would curiously label themselves as skeptics and happily repeat these “facts” without ever checking them.

People with some scientific qualifications, but without solid understanding of the complete field of oceanic or atmospheric dynamics, would write poor quality papers explaining how the rotational effect was much less than climate science calculated and produce some incomplete or incorrectly derived equations to demonstrate this.

These scientists and their new work would be lauded by many blogs as being free from the simplistic assumptions that has dogged climate science and yes, finally, accurate and high quality work has been done!

Other blogs would claim that climate science was ignoring the huge effects of absorption and emission of radiation on the climate.

Then some more serious scientists would come along and write lengthy papers to argue that the rotational effect as defined by climate science does not exist because the “no rotation” result is incorrectly defined, or is not possible to accurately calculate.

Papers of incalculable value.

## Kramm & Dlugi On Dodging the “Greenhouse” Bullet

In Kramm & Dlugi On Illuminating the Confusion of the Unclear I pointed out that the authors of Scrutinizing the atmospheric greenhouse effect and its climatic impact are in agreement with climate science on the subject of “back radiation” from the atmosphere contributing to the surface temperature.

No surprise to people familiar with the basics of radiative heat transfer. However, Kramm & Dlugi are apparently “in support of” Gerlich & Tscheuschner, who famously proposed that radiation from the atmosphere affecting the temperature of the ground was a violation of the second law of thermodynamics. A perpetual motion machine or something. (Or they were having a big laugh). For more on the exciting adventures of Gerlich & Tscheuschner, read On the Miseducation of the Uninformed..

The first article on the Kramm & Dlugi paper was short, highlighting that one essential point.

Given the enthusiasm that new papers which “cast doubt” on the inappropriately-named “greenhouse” effect are lapped up by the blogosphere, I thought it was worth explaining a few things from their complete paper.

If I sum it up in simple terms, it is a paper which will annoy climate scientists and add confusion to scientifically less clear folk who wonder about the “greenhouse” effect.

And mostly, I have to say, without actually being wrong – or not technically wrong (note 1). This is its genius. Let’s see how they “dodge the bullet” of apparently slaying the “greenhouse” effect without actually contradicting anything of real significance in climate science.

### Goody & Yung’s Big Mistake

Regular readers of this blog will know that I have a huge respect for Richard M. Goody, who wrote the seminal Atmospheric Radiation: Theoretical Basis in 1964. (The 2nd edition from 1989 is coauthored by Goody & Yung).

However, they have a mistake in a graph on p.4:

Kramm & Dlugi say:

..This figure also shows the atmospheric absorption spectrum for a solar beam reaching the ground level (b) and the same for a beam reaching the temperate tropopause (c) adopted from Goody and Yung [30]. Part (a) of Figure 5 completely differs from the original twin-peak diagram of Goody and Yung. We share the argument of Gerlich and Tscheuschner [2,4] that the original one is physically misleading..

I have the same argument about this one graph from Goody & Yung’s textbook. You can see my equivalent graph in 4th & 5th figures of The Sun and Max Planck Agree – Part Two.

There is nothing in the development of theory by Goody & Yung that depends on this graph. Kramm & Dlugi don’t demonstrate anything else in error from Goody & Yung. However, I’m sure that someone who wants to devote enough time to the subject will probably find another error in their book, or at least, an incautious statement that could imply that they have carelessly tossed away their knowledge of basic physics. This is left as an exercise for the interested reader..

To clarify the idea for readers – the energy emitted by the climate system to space is approximately equal to the energy absorbed from the sun by the climate system. This is not in dispute.

Kramm & Dlugi point out that one should be careful when attempting to plot equal areas on logarithmic graphs. Nice point.

### Kepler & Milankovitch

Kramm & Dugli spend some time deriving the equations of planetary motion. These had been lost by climate science so it is good to see them recovered.

They also comment on Milankovitch’s theory in terms that are interesting:

Thus, on long-term scales of many thousands of years (expressed in kyr) we have to pay attention to Milankovitch’s [33] astronomical theory of climatic variations that ranks as the most important achievement in the theory of climate in the 20th century [10].

The theory definitely has a lot of mainstream support as being the explanation for the ice ages. However, as a comment to be developed one day when I understand enough to write about it, there isn’t one Milankovitch theory, there are many, and of necessity they contradict each other.

Interesting as well to suggest it as the most important achievement in the theory of climate last century – as the consequence of accepting Milankovitch’s theory is that climate is very sensitive to small peturbations in radiative changes in particular regions at particular times. In essence, the Milankovitch theory appears to rely on quite a high climate sensitivity.

Anyway, I’m not criticizing Kramm & Dugli or saying they are wrong. It’s just an interesting comment. And excellent that Kepler’s theories are no longer lost to the world of climate science.

### Energy Conversion in the Atmosphere & at the Surface

The authors devote some time to this study (with no apparent differences to standard climate science) with the conclusion:

..Note that the local flux quantities like Q(θ, φ), H(θ, φ), G(θ, φ) and RL↑(θ, φ) are required to calculate global averages of these fluxes, but not global averages of respective values of temperature and humidity.

An important point.

They also confirm – as noted in Kramm & Dlugi On Illuminating the Confusion of the Unclear – that the energy balance at the surface is affected by the energy radiated by the atmosphere. Just helping out the many blog writers and blog commenters – be sure to strike Kramm & Dlugi off your list of advocates of the imaginary second law of thermodynamics.

### The Gulags for Everyone? – Climatology Loses Its Rational Basis

The authors cite this extract from the WMO website about the “greenhouse” effect:

In the atmosphere, not all radiation emitted by the Earth surface reaches the outer space. Part of it is reflected back to the Earth surface by the atmosphere (greenhouse effect) leading to a global average temperature of about 14°C well above –19°C which would have been felt without this effect.

This website statement is incorrect as the radiation emitted by the Earth’s surface is absorbed and re-emitted by the atmosphere – not reflected. This is a very basic error.

Kramm & Dlugi say:

Note that the argument that “part of it is reflected back to the Earth surface by the atmosphere” is completely irrational from a physical point of view. Such an argument also indicates that the discipline of climatology has lost its rational basis. Thus, the explanation of the WMO is rejected..

Well, we could argue that if one person writing a website for one body writes one thing that is not technically correct then that whole discipline has lost its rational basis. We could.

Seems uncharitable to me. Although I have to confess that on occasion I am a little bit uncharitable. I wrote that Gerlich & Tscheuschner had lost their marbles, or were having a big laugh, with their many ridiculous and unfounded statements. We all have our off days.

I think if we want to uphold high standards of defendable technical accuracy we would say that the person that wrote this website and the person that reviewed this website are not technically sound as far as the specifics of radiative physics go. I’m hard pressed to think it is justified to cast stones at say Prof. Richard M Goody for this particular travesty. Or Prof. R. Lindzen. Or Prof. V. Ramanathan. Or Prof. F.W. Taylor. Otherwise it might be a bit like Stalin with the Gulag. Everyone and their mother gets tarred with the sins of the fellow down the road and 30 million people wind up digging rocks out of the ground in a very cold place..

But let’s stay on topic. If indeed there is one.

### The Main Point

Now that we have found a graph in Goody that is wrong, a website that has a mistake and have rediscovered Kepler’s equations of motion, we turn to the main course.

Kramm & Dlugi turn to perhaps their main point, about the surface temperature of the earth with and without radiatively-active gases.

As a clarification for newcomers, average temperature has many problems. Due to the non-linearity of radiative physics, if we calculate the average radiation from the average temperature we will get a different answer compared with calculating the radiation from the temperature at each location/time and then taking the average.

For more on this basic topic see under the subheading How to Average in Why Global Mean Surface Temperature Should be Relegated, Or Mostly Ignored

First citing Lacis et al:

The difference between the nominal global mean surface temperature (TS = 288 K) and the global mean effective temperature (TE = 255 K) is a common measure of the terrestrial greenhouse effect (GT = TS – TE = 33 K).

The authors develop some maths, of which this is just a sample:

Using Eq. 3.8 and ignoring G(θ,φ) will lead to:

<Ts> = 23/2Te/5 ≈ 144K (3.9)

for a non-rotating Earth in the absence of its atmosphere, if S = 1367 W/m² , α (Θ0, θ, φ) = αE = 0.30 and ε(θ, φ) = ε = 1 are assumed [2]

Ts = 153 K if αE = 0.12 and Ts = 155 K if αE = 0.07

It might surprise readers that these particular points are not something novel or in contradiction to the “greenhouse” effect. In fact, you can see similar points in two articles (at least) on this blog:

– In The Hoover Incident we had a look at what would happen to the climate if all the radiatively-active gases (= “greenhouse” gases) were removed from the atmosphere. Here is an extract:

..And depending on the ice sheet extent and whether any clouds still existed the value of outgoing radiation might be around 1.0 – 1.5 x 1017 W. This upper value would depend on the ice sheets not growing and all the clouds disappearing which seems impossible, but it’s just for illustration.

Remember that nothing in all this time can stop the emitted radiation from the surface making it to space. So the only changes in the energy balance can come from changes to the earth’s albedo (affecting absorbed solar radiation).

And given that when objects emit more energy than they absorb they cool down, the earth will certainly cool. The atmosphere cannot emit any radiation so any atmospheric changes will only change the distribution of energy around the climate system.

What would the temperature of the earth be? I have no idea..

Notice the heresy that without “greenhouse” gases we can’t say for sure what the surface temperature would be.. (It’s definitely going to be significantly lower though).

..The average for 2009 [of outgoing longwave radiation] is 239 W/m². This average includes days, nights and weekends. The average can be converted to the total energy emitted from the climate system over a year like this:

Total energy radiated by the climate system into space in one year = 239 x number of seconds in a year x area of the earth in meters squared..

ETOA= 3.8 x 1024 J

The reason for calculating the total energy in 2009 is because many people have realized that there is a problem with average temperatures and imagine that this problem is carried over to average radiation. Not true. We can take average radiation and convert it into total energy with no problem..

The point here is that the total emitted top of atmosphere radiation is much lower than the total surface emitted radiation. It can be calculated. In that article I haven’t actually attempted to do it accurately – it would require some work (spatial and temporal temperature across a year and the longwave emissivity of the surface around the globe) – it is a straightforward yet tedious calculation. (See note 2).

A note in passing that this difference between the top of atmosphere radiation and the surface radiation is also derided by the internet imaginary second law advocates as being a physical impossibility because it “creates energy”.

Now I am not in any way a “representative of climate science” despite the many claims to this effect, it’s just that the basics are.. the basics. And radiative transfer in the atmosphere is a technical yet simple subject which can be easily solved with the aid of some decent computing power. So I have no quarrel with anything of substance that I have so far read in textbooks or papers on radiative physics. Yet I appear to have stated similar points to Kramm & Dlugi.

Perhaps Kramm & Dlugi have not yet stated anything controversial on the inappropriately-named “greenhouse” effect.

They take issue with what I would call the “introduction to the greenhouse effect” where a simple comparison is drawn. This is where the “greenhouse” effect is highlighted as “effective temperature”.

It could more accurately be highlighted as “difference in average flux between surface and TOA” or “difference in total flux between surface and TOA”

Is it of consequence to anything in climate science if we agreed that the difference between the TOA radiation to space and the upward surface radiation is a better measure of the “greenhouse” effect?

Kramm & Dlugi comment on a paper by Ramanathan et al:

“At a surface temperature of 288 K the long-wave emission by the surface is about 390 W/m², whereas the outgoing long-wave radiation at the top of the atmosphere is only 236 W/m² (see Figure 2 [here presented as Figure 17]). Thus the intervening atmosphere causes a significant reduction in the long-wave emission to space. This reduction in the long-wave emission to space is referred to as the greenhouse effect”

As discussed before, applying the power law of Stefan and Boltzmann to a globally averaged temperature cannot be justified by physical and mathematical reasons.

Thus, the argument that at a surface temperature of 288 K the long-wave emission by the surface is about 390 W/m² is meaningless.

Just for interest here is how Ramanathan et al described their paper:

The two primary objectives of this review paper are (1) to describe the new scientific challenges posed by the trace gas climate problem and to summarize current strategies for meeting these challenges and (2) to make an assessment 0f the trace gas effects on troposphere-stratosphere temperature trends for the period covering the pre-industrial era to the present and for the next several decades. We will rely heavily on the numerous reports..

We could assume they don’t understand science basics, despite their many excellent papers demonstrating otherwise. Or we could assume that someone writing their 100th paper in the field of climate science doesn’t need to demonstrate that something called the “greenhouse” effect exists, or quantify it accurately in some specific way unless that is necessary for the specific purpose of the paper.

However, this is the genius of Kramm & Dlugi’s paper..

### Dodging the Bullet

Casual readers of this paper (and people who rely on the statements of others about this paper) might think that they had demonstrated that the “greenhouse” effect doesn’t exist. They make a claim in their conclusion, of course, but they haven’t proven anything of the sort.

Instead they have written a paper explaining what everyone in climate science already knows.

So, to clarify matters, what is the emission of radiation from the top of atmosphere to space in one year?

ETOA= 3.8 x 1024 J

What is the emission of radiation from the surface in one year?

Esurface = ?

My questions to Kramm & Dlugi:

Is  Esurface significantly greater than ETOA ?

Obviously I believe Kramm & Dlugi will answer “Yes” to this question. This confirms the existence of the greenhouse effect, which they haven’t actually disputed except in their few words at the conclusion of their paper.

Hopefully, the authors will show up and confirm these important points.

### Conclusion

The authors have shown us:

• that a graph in the seminal Goody & Yung textbook is wrong
• Kepler’s laws of planetary motion
• that a website describes the “greenhouse” effect inaccurately
• that without any “greenhouse” gases the effective albedo of the earth would be different
• the average temperature of the earth’s surface can’t be used to calculate the average upward surface radiation

However, the important calculations of “radiative forcing” and various effects of increasing concentrations of radiatively-active gases are all done without using the “33K greenhouse effect”.

Without using the 33K “greenhouse” effect, we can derive all the equations of radiative transfer, solve them using the data for atmospheric temperature profiles, concentration of “greenhouse” gases, spectral line data from the HITRAN database and get:

• the correct flux and spectral intensity at top of atmosphere
• the correct flux and spectral intensity of downward radiation at the surface

We can also do this for changes in concentrations of various gases and find out the changes in top of atmosphere and downward surface flux. (Feedback and natural climate variations are the tricky part).

The discussions about average temperature are an amusing sideshow.

They are of no consequence for deriving the “greenhouse” effect or for determining the changes that might take place in the climate from increases or decreases in these gases.

### Notes

Note 1: I didn’t check everything, so there could be mistakes. As the full article makes clear, not much need to check. I don’t endorse their last paragraph, as my conclusion – and article – makes clear.

Note 2: The calculation in that article for total annual global surface radiation doesn’t take into account surface emissivity. The value of ocean emissivity is incorrectly stated (see Emissivity of the Ocean). There are probably numerous other errors which I will fix one day if someone points them out.

## Kramm & Dlugi On Illuminating the Confusion of the Unclear

Many people are confused about science basics when it comes to the inappropriately-named “greenhouse” effect.

This can be easily demonstrated in many blogs around the internet where commenters, and even blog owners, embrace multiple theories that contradict each other but are somehow against the “greenhouse” effect.

Recently a new paper: Scrutinizing the atmospheric greenhouse effect and its climatic impact by Gerhard Kramm & Ralph Dlugi was published in the journal Natural Science.

Because of their favorable comments about Gerlich & Tscheuschner and the fact that they are sort of against something called the “greenhouse” effect I thought it might be useful for many readers to find out what was actually in the paper and what Kramm & Dlugi actually do believe about the “greenhouse” effect.

Much of the comments on blogs about the “greenhouse” effect are centered around the idea that this effect cannot be true because it would somehow violate the second law of thermodynamics. If there was a scientific idea in Gerlich & Tscheuschner, this was probably the main one. Or at least the most celebrated.

So it might surprise readers who haven’t opened up this paper that the authors are thoroughly 100% with mainstream climate science (and heat transfer basics) on this topic.

It didn’t surprise me because before reading this paper I read another paper by Kramm – A case study on wintertime inversions in Interior Alaska with WRF, Mölders & Kramm, Atmospheric Research (2010).

This 2010 paper is very interesting and evaluates models vs observations of the temperature inversions that take place in polar climates (where the temperature at the ground in wintertime is cooler than the atmosphere above). Nothing revolutionary (as with 99.99% of papers) and so of course the model used includes a radiation scheme from CAM3 (=Community Atmospheric Model) that is well used in standard climate science modeling.

Here is an important equation from Kramm & Dlugi’s recent paper for the energy balance at the earth’s surface.

Lots of blogs “against the greenhouse effect” don’t believe this equation:

Figure 1

The highlighted term is the downward radiation from the atmosphere multiplied by the absorptivity of the earth’s surface (its ability to absorb the radiation). This downward radiation (DLR) has also become known as “back radiation”.

In simple terms, the energy balance of Kramm & Dlugi adds up the absorbed portions of the solar radiation and atmospheric longwave radiation and equates them to the emitted longwave radiation plus the latent and sensible heat.

So the temperature of the surface is determined by solar radiation and “back radiation” and both are treated equally. It is also determined of course by the latent and sensible heat flux. (And see note 1).

As so many people on blogs around the internet believe this idea violates the second law of thermodynamics I thought it would be helpful to these readers to let them know to put Kramm & Dlugi 2011 on their “wrong about the 2nd law” list.

Of course, many people “against the greenhouse thing” also – or alternatively – believe that “back radiation” is negligible. Yet Kramm & Dlugi reproduce the standard diagram from Trenberth, Fasullo & Kiehl (2009) and don’t make any claim about “back radiation” being different in value from this paper.

“Back radiation” is real, measurable and affects the temperature of the surface – clearly Kramm & Dlugi are AGW wolves in sheeps’ clothing!

I look forward to the forthcoming rebuttal by Gerlich & Tscheuschner.

In the followup article, Kramm & Dlugi On Dodging the “Greenhouse” Bullet, I will attempt to point out the actual items of consequence from their paper.

Further reading –  Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part One and New Theory Proves AGW Wrong!

Note 1 – The surface energy balance isn’t what ultimately determines the surface temperature. The actual inappropriately-named “greenhouse” effect is determined by:

• the effective emission height to space of outgoing longwave radiation which is determined by the opacity of the atmosphere (for example, due to increases in CO2 or water vapor)
• the temperature difference between the surface and the effective emission height which is determined by the lapse rate