On Models

I have seen a number of comments over the years disparaging models. Here are two models:

F=ma
PV=nRT

Did you know that, ultimately, all models are mathematical relations?

So here I’ve shown two models. Very simplified, but still models. Both wrong by the way. BUT both are very usefull because they are predictive. I’ve been told that all of mechanical engineering can be summarized as “F=ma and you can’t push on a rope, everything else can be derived”. THAT is the measure of a model. Can you use it to predict an outcome successfully?

Don’t disparage models. Generally, there is nothing wrong with models, even wrong models. Disparage instead the inability of a model to predict. THAT is the problem with the general circulation models. They are not particularly successfull at prediction.

HEY. Wait a minute! What’s wrong with F=ma? To understand that, google special relativity. As for PV=nRT, that is the “ideal” gas law. All gases deviate from this in extreme conditions. So. Both are, in an absolute sense, wrong. Extremely useful, but not exactly right, hence, strictly speaking, wrong.

We’d better be right

A number of years ago I posted a comment on slashdot that “as scientists, we had better be right about global warming, because if we are wrong, it will provide ammunition to every crank and huckster who would demean science”. In all of the following, the “They” is us. Scientists. If we, the science communithy, are wrong about global warming, what will be our defence when Jenny McCarthy says “see! they were wrong about global warming and they are wrong about vaccines too!” or a fundementalist says “see! they were wrong about global warming and they are wrong about evolution too!”. Yes. We the science community had better be right because in this case, and only in this case, science has said: There is NO doubt. This is truth. We can argue about the rest mass of a proton, but we brook no argument about the chaotic impacts on climate of increasing one of hundreds of variables that impact climate. Such certainty is hubris, pure and simple. Science will out. The truth will be known. If it assures us that increasing carbon dioxide increases temperature, hooray! We are safe. If it does not. . . Who knows.

More on “Why Is The Ocean So Cold?”

I need some help here. In particular, I’m looking for people who have at least an undergraduate level of training in thermodynamics generally and energy flow specifically, or self taught equivalent. (I have studied energy transfer in a number of university courses, but that was many years ago now. I’m pretty confident in my ability to perform an energy balance, but I’m stumped by this one).

Here, in a nutshell, is my conundrum:

Why is the ocean so cold?

Our friends at BEST, CRU, GISS, etc. going all the way back to Fourier, all agree that the “surface temperature” of the earth is more than 10 celcius or 283 kelvin. Further, it is  hypothesized that the “surface temperature” of the earth has always been at least 10 celcius and often more.

So how is it that the temperature of the ocean, which is in direct contact with this “surface” is at least 6 degrees colder than the “surface temperature”? Not only is the ocean in direct contact with this “surface”, but the earth itself is constantly shedding thermal energy into the ocean from the crust.

If someone can show me a complete energy balance that allows the ocean to be at a steady state temperature that is lower than the “surface temperature”, I would be grateful. If there isn’t such a balance, one of two things must be true. The “surface temperature” is colder than estimated or the laws of thermodynamics don’t apply to the oceans.
Just to be clear, it is an absolute certainty that the laws of thermodynamics
apply to the oceans.

No hand waving allowed. I’ve seen a number of debating point style arguments. I would like to see some math on this. I’m working on my math on this. My first run approximation has the oceans boiling away a few billion years ago, so something is not right. If you are not sure how the oceans should have boiled away billions of years ago, add 0.1 W/m² of energy to a 4 km column of  water for 1 billion years and determine what the temperature that of the water should be. That is lower than the approximation of the rate of energy transfer from the crust to the bottom of the ocean.

Update:

I’ve had two exchanges with Dr. Gavin Schmidt at RealClimate. Thanks Dr. Schmidt. His short answer is there is no short answer. In order to understand the mechanisms for the heat transfer that occurs, I must first learn a GCM. This answer is exactly correct and exactly useless. So it seems the answer is: The ocean is so cold because of reasons that are too complicated to explain.

I am going back to my little explanation of the greenhouse effect using engineering methods for now. When that is done I’ll look at the ocean again.

Carbon Sinks

I was thinking about carbon sinks and the like in the universe. On our planet, it took about 5 billion years for life to get to the point that it could communicate with the universe. At this time, a spectacularly large amount of carbon is tied up in limestone and hydrocarbons. Consider what would have happened without humans. Eventually, the amount of carbon, naturally sequestured, would have reached the point that photosynthesis would no longer be possible. I think, prior to man, the planet was very close to that point. If CO2 levels drop to the point that photosynthesis stops, then life on the planet is hooped. Especially the more evolved forms of life, such as man. Could this be why there are no other civilizations in the universe? Death from lack of CO2?

UN Wants to ban CFC light bulbs

These guys:

http://www.unep.org/hazardoussubstances/Mercury/Negotiations/INC3/tabid/3469/Default.aspx

Want to ban mercury. If they have vaccines on the table, then CFC’s are on the table too. If these people have a wit of sense, they will let this whole thing drop, like the 1970’s call to ban chlorine.

Why is the ocean cold?

This may seem like an odd question, but I am beginning to wonder if there may be something interesting in the answer. Here is why I wonder. We are told that the average temperature of the surface of the planet is about 15 celsius. The oceans overlay the thinnest part of the earth’s crust. Hence they should be warm at the bottom too. Even if the geothermal forcing is relatively small (my estimate is about 0.2W/(m.k), it is still positive. So why is the average temperature of the ocean around 4 or 5 celsius? Given that the first 14.5 meters of the ocean (or 0.4% of the total mass of water on the surface of the planet) contains as much mass as the entire atmosphere, the average energy content of the fluid surface of the planet (oceans plus atmosphere) may be low enough that there is no need for a greenhouse effect to explain the temperature as it is very close to where it should be for a black body radiator. I am missing something simple I am sure, but can’t place it exactly.

How well do you understand radiant heat transfer?

A problem for the physics minded among you:
Given:
• Two parallel plates, separated by a distance of 20 meters.
• The first plate is continuously heated to maintain a temperature of 350 k
• The second plate is continuously cooled to maintain a temperature of 300 k
• The space between the plates is at atmospheric pressure, 20% oxygen, 80% nitrogen
• Under all conditions, total pressure is constant at 1 bar.

Assume that the plates are sufficiently large that all energy transfer is between the plates only and the plates are black body radiators/absorbers. UPDATE And assume the only mechanism for heat transfer between the plates is radiant transfer. And assume there is no absorption of radiant energy by oxygen or nitrogen. And for the pedantic amoung you, please realize that in engineering there is a field of study called heat transfer. We don’t call it “enthalpy transfer” because it deals with thermal energy only and enthalpy can be transferred by other mechanisms.
Anyway.
Find:
The (UPDATE steady state) temperature of the intervening gas, the energy input to the first plate and the energy removed from the second plate under the following conditions.
1% of the original atmosphere is displaced by CO2
2% of the original atmosphere is displaced by CO2
5% of the original atmosphere is displaced by CO2
10% of the original atmosphere is displaced by CO2
20% of the original atmosphere is displaced by CO2
50% of the original atmosphere is displaced by CO2

Plot the results.

CO2 absorption is not xeno’s paradox

One argument for CO2 absorption continuing to increase is that,
each layer of the atmosphere radiates onto the next, while the pressure of the
atmosphere drops, hence one can never get to saturation. This is similar to
Xeno’s paradox of the tortoise. Given that Achiles eventually passes the
tortoise, there must be a fundamental flaw in the initial argument.

In combustion calculations, there are also gradients of CO2
concentration. There are (massive) gradients in temperature. Compared to
climate, the gradients are orders of magnitude higher. At a fundamental level,
there is NO difference with between the atmosphere of combustion engineering
(which includes things that are not burning these days) to the atmosphere of
climate science. The atmosphere is the atmosphere.

 

390 ppm atmospheric CO2 – A Little or A Lot?

The short answer is – A lot.

If you are performing calculations of CO2 impacts, you look at how much CO2 there is in any one bit of air (concentration) and how far it is from heat source to cool thing (distance). The product of these two things determines how much radiant energy is absorbed by the CO2.

We will use ‘bar’ for pressure (1 bar = 100 kPa) and meters for length, though we will use bar cm for the product (for reasons that will become apparent).

We will start with normal air, 80% N2, 20% O2.

First, displace air with CO2 until the mixture becomes 50% CO2, 40% N2, 10% O2. Let’s all agree that a 50% atmosphere of CO2 is a lot of CO2.

4 meters of this mixture will have a “Path Length” of 200 bar cm.

Now only displace 10% of the air, so 10% CO2, 72% N2, 18% O2

20 meters of this mixture will have a “Path Length” of 200 bar cm and absorb as much radiation as 4 meters of the 50% concentration.

Now only displace 0.039% of the air. Thus about 80% N2, 20% O2, 390 ppm CO2.

5,128 meters of this mixture (at the surface of the earth) will have a “Path Length” of 200 bar cm and absorb as much radiation as 4 meters of the original mixture that was 50% CO2. So over a very long length, 390 ppm is a LOT of CO2.

The atmospheric pressure drops as elevation increases. For the total atmosphere (40 kilometers for calculation purposes), at 100 ppm CO2 throughout, the path length will be somewhere around 67 bar cm (using the ‘standard atmosphere’ equation for change in pressure with elevation). At 390 ppm, the path length is somewhere around 261 bar cm, or more than a 50% CO2 atmosphere over 4 meters. At one time, one could review Leckner’s curves for CO2 absorbance on google books. The page with the curves has been removed from the review of the reference (Bejan, Adrian; Kraus, Allan D. Heat Transfer Handbook. John Wiley &Sons., 2003 Page 618 ). If you go to that book in a library, you will see that at 200 bar cm, the emissivity is nearly identical to that at 100 bar cm and the increase to 500 bar cm is less than that from 100 to 200, over a temperature range from 0 celsius to 2,000 celsius. Beyond 500 bar cm, there is no further impact from increasing CO2. It is at about 100 bar cm that the growth begins to flatten out from the logarithmic that is used in climate models. I will be happy to provide a photocopy of the individual page to anyone who asks, as that is ‘fair use’, but will not post such a photocopy here as that might be construed as copyright violation.

A summary of things still hidden by the climate science clique.

1: Data related to Yamal.

From:
University of East Anglia:
“URALS” (which includes the Yamal and Polar Urals long chronologies, plus other shorter ones).

Can be solved by providing a followable link to:
The digital version of this series together with a list of all the measurement data sets used to make this composite, denoting each data set by ITRDB identification or equivalent.

2: Feel free to comment and add to this list.