### Global Warming - Atmospheric Analysis

This is an extension of my Atmospheric Composition page - but with more technical data.

It is generally agreed that, at sea level, the atmospheric pressure is 14.7 psi and that about 0.035% of the atmosphere is CO2 - but what does that mean. This page will present those facts in a slightly different manner.

Note - the first 2 sections are highly technical and fairly boring. However, they are necessary to understand the rest of the document.

Basic Data | Air Column | NOVA's Bogus CO2 Experiment | Global Warming in 1900
Venus Air Column | Problems with this Method of Analysis | Closing Thoughts

### Basic Data

This table presents a few facts related to Earth's atmosphere. Some of these are used on this page - others will be used in future pages.
Data for the Earth Metric English
Atmospheric pressure at sea level 1014 mb 14.71 psi
Atmospheric density at the surface 1.217 kg/m3 0.07597 lb/ft3
Total mass of atmosphere 5.1 x 1018 kg 5.6 × 1015 short tons
Total mass of hydrosphere 1.4 x 1021 kg 1.5 × 1018 short tons
Mean molecular weight of atmosphere 28.97 g/mole
Specific Heat of Air (typical) 1.012 J/g*K [2]
1.005 J/g*K [3]

Specific Heat of Water - gas (100 °C) 2.080 J/g*K
Specific Heat of Water - liquid (25 °C) 4.1813 J/g*K

Table References

1. NASA's Planetary Fact Sheets for Earth
2. U.S. Standard Atmosphere, 1976 - NOAA, NASA, USAF
3. Specific heat capacity - the given values are for constant pressure and are dependent on the actual temperature
4. Specific heat capacity of Carbon Dioxide - This shows how the values vary with temperature
5. To convert the values, I just used Google's calculator and rounded to the correct number of significant figures, for instance
`    1.217 kg/m^3 in lb/ft^3 = 0.075974828 pound / (ft^3)`
Note: The values differ slightly based on the reference and its date. Standards, by definition, depict average values measured under specific conditions. Real world values will vary considerably. This is one reason the equations and models are very complicated.

### Air Column

The equations that describe the atmosphere are relatively complex - mostly because the atmosphere itself is very complex. The most obvious problems are

• The pressure decreases with altitude
• The temperature changes with altitude (lapse rate)
Even more complex
• Water vapor - none of the existing models handle this adequately
• Gases that directly absorb IR radiation
• Wind and storms
For steady state analysis, it is useful to consider the air column above you as though it was placed in a horizontal tube at a single pressure. Air is known to weigh about 0.076 pounds per cubic foot (0.07597 lb/ft3) at sea level. In order to determine the length of a column of air that produces 14.7 pounds per square inch (14.7 psi - the pressure at sea level) simply involves dividing the pressure by the density (and converting the units).
```14.71 psi = 14.71 lb/in2

(14.71 lb/in2 * (12 in)2/(1 ft)2) / 0.07597 lb/ft3 = 27,880 ft
= 5.280 miles
= 8.498 kilometers
```
What this means is that the 100 or so miles of atmosphere above your head contains the same amount of gas as a horizontal tube 5.280 miles long (8.498 km).

Since CO2 is about 0.035% of the atmosphere, that accounts for about 9.8 ft of that tube.

```27,880 ft * 0.00035 =  9.76 ft  The value found in some references
27,880 ft * 0.00038 = 10.59 ft  Current value
27,880 ft * 0.00045 = 12.55 ft  Reasonable expected maximum after ALL oil is burned
27,880 ft * 0.00070 = 19.52 ft  Burning coal can provide a higher value
27,880 ft * 0.00100 = 27.88 ft  IPCC projects values higher than this
```
Using historical data, 30 years produced an increase of about 44 ppm. Using that as a basis, and the fact that the increase is linear, the concentration in 2100 should be
```369 ppm + 100/30 * 44 ppm = 516 ppm  (0.0516%)
```
not more than 1,000 ppm the IPCC is predicting.

Note - the fact that the CO2 increase is linear, while at the same time the amount of CO2 released by humans has grown exponentially, is the primary proof that humans are NOT responsible for the change in CO2 concentration or climate change.

### atm-cm

The total amount of a gas in a column of air is sometimes expressed in
```atm-cm at STP
```
Given a column of gas at STP, this is the length in centimeters.

Note: STP - Standard temperature and pressure - zero degrees C and one atmosphere pressure

When discussing ozone, Dobson Units (DU) are used, partly because Dobson was the first person to study atmospheric ozone and partly because there is very little ozone in the air.

```1 DU = 1 milli-atm-cm (also shown as 1 m atm-cm)

ozone concentration = 0.3 atm-cm = 300 m atm-cm = 300 DU
```
This means that all the ozone in a column of air, when placed in a single layer at 0 degrees C and one atmosphere, would produce a layer of gas only 3mm thick.

Without correcting for temperature and pressure, the following are approximate values for CO2 (based on the table above). Corrected values should be about 9% less (because the temperature would be lower).

``` 350ppm   9.76 ft -> 297 atm-cm  The value found in some references
380ppm  10.59 ft -> 323 atm-cm  Current value
450ppm  12.55 ft -> 383 atm-cm  Reasonable expected maximum after ALL oil is burned
700ppm  19.52 ft -> 595 atm-cm  Burning coal can provide a higher value
1000ppm  27.88 ft -> 850 atm-cm  IPCC projects values higher than this
```
```
9.76 ft at 1 atm * 12 in/ft * 2.54 cm/in = 297 atm-cm  (when rounded to 3 significant figures)
```

### NOVA's Bogus CO2 Experiment

A few years ago, NOVA and Frontline cooperated to produce an "end of the world" piece on CO2. In it was an experiment where a closed chamber was placed between a person and an IR camera. When CO2 was added to the chamber, the image of the person completely disappeared. At the time, I was upset because they never indicated when the concentration in the chamber
• Was equivalent to the concentration in the air before the modern industrial society began
• Was what was equivalent to today's value
• Was what was projected at various dates in the future
Well ... reviewing the video, it appears that the tube was about 3 feet long - HEY, that's less than 1/3 of the current value. (This experiment is why I performed the calculations above. Based on my calculations, the tube needs to be 10.5 feet long to simulate the current amount of CO2 in the atmosphere.)

This demonstration was supposed to illustrate what was GOING to happen, how adding CO2 to the atmosphere would destroy the Earth ... but it actually showed ... without a doubt ... that the atmosphere is already totally opaque.

Let me be very clear about this - their totally bogus demonstration showed that adding more CO2 to the atmosphere will have absolutely no effect - and this was in a propaganda film.

Ok, why do I call it propaganda and bogus

• Before the demonstration was presented, it was pointed out that the atmosphere of Venus is mostly CO2 - incorrectly implying that Venus is hot because the atmosphere is CO2.

• If you look at the IR monitor, the temperature range is restricted to an extremely narrow range. With a different range, the effect may have been negligible. (I spent some time developing IR monitoring systems - it is surprising what you can do if you play with the settings.)

• Adding CO2 to a chamber from a compressed source significantly reduces the temperature of the gas. (That is how dry ice was discovered.) Since the chamber appears to be insulated, it is probable that they were relying on the reduced temperature to get the desired results. It is also highly likely that water condensed on the transparent plates used to seal the ends of the chamber.

• They never indicated how the change in the image related to an equivalent atmospheric concentration (which, of course, it never did).

• Actually, there was no real data at all.
So, I'll still call it bogus ... for now.

By the way, there may be ways, other than simply blocking IR, that permit additional CO2 to raise the Earth's temperature - but this is the mechanism presented by NOVA.

### Global Warming in 1900

This is not the first time that scientists have thought human produced CO2 might change the climate - during the Industrial Revolution (late 1800's), lots of coal was being burned.
In 1900, Knut Ångström sent infrared radiation through a tube filled with carbon dioxide. He put in as much of the gas in total as would be found in a column of air reaching to the top of the atmosphere. The amount of radiation that got through the tube scarcely changed when he cut the quantity of gas in half or doubled it. The reason was that CO2 absorbed radiation only in specific bands of the spectrum, and it took only a trace of the gas to produce bands that were "saturated" — so thoroughly opaque that more gas could make little difference. Reference
The Ångström unit of length, still used to measure the wavelength of light, was named for Knut's father.
```4,000 Ångstroms = 400 nm
```

### Venus Air Column

This is a similar Air Column calculation for Venus - assuming that the atmosphere is 100% CO2 and ignoring nitrogen. The factor of 100 is to account for the increased pressure on Venus - this value can easily be disputed. I have seen both 90 and 92 used.
```1.98 kg/m3 = 0.1236 lb/ft3  (Density of CO2 at stp)

(14.71 lb/in2 * (12 in)2/(1 ft)2) * 100 / 0.1236 lb/ft3 = 1,713,786 ft
= 324.6 miles
= 522.4 kilometers
```
On Earth, a horizontal column of air at sea level that represents all the air in the column of air above you is 5.3 miles long.

On Venus, a similar column of atmosphere, if located at sea level on Earth, would be about 60 times longer - about 324 miles long.

On Earth, a 10 foot chamber containing 100% CO2 represents the total amount of CO2 between the surface and free space.

A chamber that represents the amount of CO2 on Venus will be about 312 miles long (96.5% of 324).

To be completely clear, these propagandist want us to believe that increasing 10 feet of CO2 to 20 feet will cause Earth to be like Venus which is equivalent to about 1,680,000 feet of CO2.

Air Column Feet of CO2
Earth 5.3 miles 10 feet
Venus 324 miles 1,680,000 feet

And you want to know why I am skeptical.

Note - The first calculations in this section assume that the atmosphere of Venus is 100% CO2, and the last calculation uses the value 96.5%. As a result, there is a small error - but with 5 orders of magnitude difference ... it really doesn't matter.

### Problems with this Method of Analysis

To a certain point, considering the atmosphere as though it is at a constant pressure provides excellent data. Particularly, it demonstrates that the atmosphere is already saturated with CO2 and it provides a very good way to compare the Earth with Venus. However, there is a significant problem with this approach.
When gases absorb or emit radiation, the widths of the spectral lines are dependent on the temperature and pressure.
The experiment described above completely hides this effect.

Note - While the spectra of each gas is different, the absorption and emission spectra for a specific gas are usually identical. (The primary exception is fluorescence.) Though it is seldom mentioned, this means that CO2 absorbs and emits IR radiation at exactly the same frequencies. Note however that all the radiation in a spectral line is not at exactly a single frequency, but instead in a small range (band) of frequencies. It is the width of these spectral lines that is affected by temperature and pressure.

Basically, at ground level the spectral bands are at their maximum widths. (Maximum pressure - but not always the maximum temperature.) It is here that CO2 can absorb more energy than it emits. As you get farther from the Earth, the temperature and pressure both decrease and the bands get narrower.

This means that when CO2 emits energy towards space, only some of it will be absorbed by the CO2 above it. However, a very very small amount will not be absorbed because the absorption bands are narrower.

The rate of this cooling is partly related to the mean free path - how far the radiation travels before it is reabsorbed. Basically, the farther radiation travels toward space (lower temperature and pressure) before being reabsorbed, the narrower the absorption band and the more heat is lost to space.

The funny thing is that when this band spreading is taken into effect, it quickly becomes apparent that carbon dioxide is actually the only gas that cools the atmosphere. That's right, without carbon dioxide the atmosphere has no way to release its energy to space and the planet quickly over heats.

Up to about 11,000 feet (top of the troposphere), water vapor provides this capability. But above that level, there are few, if any, gases to cool the atmosphere.

Another point is that as the amount of CO2 in the atmosphere increases, the mean free path for CO2 released IR radiation decreases. This is offset, at least in part, by having more emitters. It is not clear to me if this will have a positive or negative effect. The evidence from Venus indicates that more CO2 will have a cooling effect ... but there is definitely room for more research on this.

Eventually, I plan to develop a page on just this effect. At that time, I may change my position on this ... but I don't think so. The analysis I've done to date is fairly solid.

### Closing Thoughts

Let me be clear that this is not a fully rigorous analysis - there are a LOT of other situations to consider. But this is a good, and I think fair, start.

I have additional original work on

• Heat - explains how water vapor creates heat pipes that cool the planet
• Venus - discusses the real reason Venus is hot ... and why the Earth is cool

Author: Robert Clemenzi