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Sunday, December 18, 2011

Let's Concentrate on the Concentrations

I can compare apples to oranges. Apples make better crisps and pies, oranges make better cocktails and poultry glazes. A little orange zest goes a long way in an apple popover to give it a little zing with coffee in the morning. Small amounts make things happen in life. Carbon dioxide is a small thing that can have a big impact or not depending on the recipe.

I recently recommended that a couple of bloggers join up and do a post on carbon dioxide. Both are bright and knowledgeable with opinions on climate change. DeWitt Payne has been experimenting with a greenhouse effect experiment. He is meticulous in acquiring data to prove that CO2 enhances the performance of a greenhouse. He will find that it does because it does. That is what he is looking for and he will find it.

I mentioned to him before he started that real greenhouses might be a pretty good place to get ideas. He built his experiment around a box with very well insulated sides and bottom avoiding cardboard and wood which would have some moisture content that might out gas when heated, complicating his experiment. Along with his direct measurements, he has also included a little work on the radiant physics of CO2 by determining the change in the mean free path of photons absorbed and emitted by CO2. He stated that the change in the mean free path is dependent only on the change in concentration of CO2. Which is why I want him to clean his work up and publish it online. Carbon dioxide's radiant properties depending only on the concentration is his apples. My oranges is that the change in concentration of CO2 also changes the thermal conductivity of the air.

The apples and oranges thing makes a big difference in what would be a proper evaluation of the greenhouse effect. There are lots of stumbling blocks that can lead to gotcha moments, the first being what is the initial concentration.

If we were only concerned with the radiant properties, any old concentration would do. But since the end result is to compare the results of the box to the Earth, another initial concentration would be in order.

Ice core in the Antarctic have the longest record of temperature and CO2 change that we have. Those ice cores indicate that about 190 parts per million (ppm) is the lowest concentration that has been in the atmosphere for at least the past 400,000 years. So I am of the opinion that about 190 ppm is the place to start and the Antarctic is the benchmark for the comparison. Inferring that some other place on the planet does something based on what happened in the Antarctic, without knowing what really happened in the Antarctic, is not all that smart in my opinion. Let's just stick to the apples and oranges before making ambrosia.

So the concentration in the Antarctic has changed naturally from about 190ppm to about 280ppm. Currently the concentration in the Antarctic is about 370ppm due to man doing manly things (womanly would work but they don't like taking credit for screwing things up, at least in my household).

So there are a few things I would like to consider in this experiment, Temperatures, Conductivity, Radiant interaction, and Nocturnal performance. The nocturnal performance is something I think is pretty important.

The greenhouse effect is not so much about how hot things can get but about how cold they could get. With about six months of no sunlight and about six months of not very intense sunlight, it just seems logical to me to concentrate on the reason we are not freezing our asses off before we figure out how bad being warmer might be. So with an average surface temperature of about -50C or 223K, how much benefit of the greenhouse effect is the Antarctic getting?

Since this post is going to become a little complicated, bear with me while I take a break to do some cipherin' and try to get rid of most of my worst typos and unintentional misspellings.

Antarctic References?

The Antarctic is a pretty brutal environment for any kind of surveying. Good thermodynamic practice requires staring from a solid frame of reference and not making assumptions without seriously thinking about potential consequences. Averages can obscure important signals, but sometimes they are all you have to work with. When using averages, it is not a bad idea to triple check before announcing you have discovered cold fusion or catastrophic global cooling. With the polar vortex, ozone holes and every thing else, about the only constant reference temperature is space, the final frontier, at approximately 2.7 K degrees.

Atmospheric R values, that silly basic reference where temperature and energy flow have a linear relationship, might be useful. With an average surface temperature of 223K versus space, the R value would be 1.57 using the perfect black body emission of 140 Wm-2. This is just to be used as a reference for what should be happening between one point on the surface and space. Things will get complicated, so don't freak out.

If I used the new average surface temperature of 289.1K degrees in the latest Trenberth and Keihl cartoon, the R value to space would be 0.723 down from the 288K value of 0.731 in their older cartoon. The decrease in the R-value some might think indicates an increase in conductivity. That of course would be an assumption which can make an ass out of people. It is something to keep in the back of your mind though. To compare, the older K&T used 235/390 Wm-2 for 0.602 TOA emissivity and the newer 2009 cartoon uses 239/396 Wm-2 for a 0.604 TOA emissivity. Both are based on global averages so both should be considered carefully before leaping to conclusions.

There is a difference between emissivity and the R value, the emissivity only considers radiant flux, R value considers all energy flux. That is the main reason I use R values as a reference, imperfect as it may be.

Now back to concentrations.

190/1,000,000 is my choice for the base concentration of CO2. For the radiant impact we can assume the nitrogen and oxygen have little impact on emissivity. Not a bad assumption for the NOCTURNAL condition I recommended earlier. For conductivity, we would assume a base of 0.024 Wm-1.K-1 at STP for N2 and O2 which make up basically the rest of the atmosphere. CO2 has a non-linear impact on conductivity. At colder temperatures than STP, its conductivity increases to a peak value at -20 C or 253K. For the change in emissivity due to CO2, DeWitt assumes that only the change in concentration matters. I disagree, but we have to start somewhere, so for now that is the assumption.

The Properties of Carbon Dioxide list the Thermal Conductivity of CO2 as 0.086 W/m-1.K-1 at -50C or 223K degrees. Roughly the same as 293K (20C), so for initial comparison we can assume that conductive is also only dependent on concentration. At 190ppm, you have to go to five decimal places to see the CO2 impact of 0.02401 and at 280ppm that changes to a whopping 0.02402 which for most purposes would be negligible.

Obviously there is no reason to consider a change in conductivity since using the Arrhenius relationship, dF=5.35ln(280/190) = 2.1 Wm-2 of addition CO2 forcing of the 140Wm-2 emission from the surface. Assuming twice the forcing impact at the surface, 4.2Wm-2 for a surface increase in flux to 144.2 Wm-2, the surface temperature would increase to 224.5 K approximately. That new temperature and flux would change the -50C R value to -48.5 which would be 1.54 instead of 1.57, a 1.9% decrease which should be noted.

Assuming the current concentration of 370 is indicative of change from the maximum 280 ppm in the ice cores, conductivity would only increase to 0.024017 at 223K while the change in forcing, dF=5.35ln(370/190) = 3.56EWm-2, with the same assumptions as before, would produce an average surface flux of 147.1Wm-2 with an approximate average surface temperature of 225.7 degrees K. So if the Antarctic were its own little planet, nearly doubling the CO2 concentration would produce 2.7 degrees of warming. The new R value would be 1.534, a 2.3% decrease from the 190ppm value. The conductivity at this point would have increased to a whopping, 0.024023 Wm-1.K-1 which is an increase of only 0.05 percent.

This was all estimated assuming that the base conductivity was 0.024 and that only concentration mattered. The Antarctic would have warmed some where in the ballpark of 2.7 degrees with the rise in CO2 from 190ppm to 370ppm. The Vostok Ice Cores indicate about 8 degrees of temperature change from about 190 ppm to 280 ppm.

Vostok, where the ice core was drilled, has a range of temperatures from -21C to -89C. That is a fairly wide range of temperatures. In degrees K, that range is from 252K to 184K with a black body flux range from 228Wm-2 to 65Wm-2. For 7.1Wm-2 of additional forcing to produce about 8 degrees C change, the temperature would have to be lower than the -50C used in the estimates above. At the lower temperature, 184K @ 65Wm-2, and increase to 192K @ 77Wm-2 would be a 12Wm-2 increase for an 8 degree increase in temperature.

This brings to what are the proper assumptions?

The thermal conductivity of CO2 increases from 0.086 @ -50C to 0.115 @ -20C. The impact of an assumed concentration only dependent change in CO2 forcing increases as temperature decreases. Oxygen at low temperatures exhibits magnetic properties and Vostok is near the southern geomagnetic pole. At 197.5 K and 1 atmosphere, carbon dioxide can jump from gas to solid and back at will. Last but not least, at 184 K the relationship between thermal conductivity and electrical conductivity may be blurred in a magnetic field.

It would be nice if a simple change in concentration of a trace gas could answer all the questions. It doesn't quite look like it explains if the Vostek ice cores indicate global climate change or geomagnetic changes in the past, which may be partial drivers of climate change.

Since I was cruising the internet I ran across a post on Watts Up With That. I take most post with a grain of salt, this one did have an interesting graph on the Last Glacial Minimum (LGM) which I will see if it will post here as a link or photo.

Cool. The post is CO2 Sensitivity is Multi-Modal - All Bets are Off, by Ira Glickstein. I haven't checked out the post completely, but the general premiss agrees with my line of thinking. I do note that the Arctic part of the plot is not consistent with with what I would expect, which would be closer to -6 C on average with a great deal of regional fluctuation because of the Gulf Stream.

The interesting part is the southern temperate LGM temperature change which I think agrees with the expected temperature and CO2 relationship in the Vostek ice cores, not the Antarctic relationship which I pointed out above. O18 concentration in the Antarctic are unlikely to be produced locally, but transported from the southern temperate zone and southern tropical convective zone. How the ratios are amplified is the question, which I still think is due to the southern magnetic field fluctuations.

But before I wander too far astray, how about More on Let's Concentrate on Concentrations?

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