## Tuesday, July 15, 2014

### ATS - Insufficient Heat Is Stored

1. Part 1: ATS

It has been theorized that the use of anthropogenic (man-made) carbon dioxide is the reason for the recently observed warming trend from ca. 1960-1998.
The present level of CO2 in the troposphere is stated by multiple sources as being on the order of 380 ppmv[1] or 0.038% of the atmosphere. This represents an increase, based on the most liberal estimates I have uncovered for pre-industrial levels of 280 ppmv[2], of 100 ppmv or 0.01%. Since this base point is considered to be 'safe and natural', it would logically follow that any warming would have to be associated with the 0.01% increase and it alone.
All heat energy reaching the earth is from the sun, in the form of solar irradiance. Heat reflected back into space is a result of this solar irradiance, and can therefore be considered the same in energy calculations. Solar irradiance can and has been quantified. The amount of energy reaching the planet is on the order of 1366 W/m²[3]. The planet presents a more or less circular profile to the sun, so the area of the earth normal to solar irradiance can be calculated as this circle. The earth is an average of 6371 km[4], with a troposhere layer surrounding it that averages 17km in height[5], which also must be included since it is the location of the atmospheric carbon dioxide.
That means a circular area of: r = 6371 + 17 = 6388 km
A = π r² = π (6388)² = 128,197,539 km²
We can now calculate the amount of energy which is thus intercepted by the earth (including the troposphere):
1366 W/m² = 1,366,000,000 W/km²
1,366,000,000 W/km² • 128,197,539 km² = 175,117,838,274,000,000 W (equivalent to J/s)
175,117,838,274,000,000 J/s = 175,117,838,274,000 kJ/s
That result in in Joules (or kiloJoules) per second. Since most climate predictions are based on much longer time intervals, I will now calculate how much energy would be available during such a longer time interval such as the commonly used 100-yr. period:
100 yr = 36,525 days = 876,600 hr. = 52,596,000 minutes = 3,155,760,000 s
We can now multiply this time interval by the rate of energy influx to obtain the total energy that the planet will recieve from solar irradiation over the next 100 years:
175,117,838,274,000 kJ/s • 3,155,760,000 s/100yr =
552,629,869,311,558,240,000,000 kJ/100yr
Now we must calculate exactly how much of that energy will be affected by the increase in the amount of carbon dioxide in the troposphere. Remembering that the increase from pre-industrial levels is 0.01% of total atmospheric volume, we multiple this total energy by 0.0001:

552,629,869,311,558,240,000,000 kJ/100yr • 0.0001 =
55,262,986,931,155,824,000 kJ/100yr intercepted by anthropogenic CO2
2. Part 2: ATS

Now let us turn to the question of how much energy is needed to increase global temperatures. Of course, the first and most obvious area to be heated is the troposphere itself. Air under average atmospheric conditions has a specific heat capacity of 1.012 J/g•°K[6] and an average density of 1.2 kg/m³[7]. The troposphere itself can be calculated by using the information presented earlier (average radius of earth = 6371 km[4] and a troposhere extending 17 km above the surface[5]). Thus the area of the troposphere can be determined by calculating the volume of a sphere of 6388 km radius and subtracting a sphere of 6371 km radius from it:
V(tot) = 4/3 π r³ = 4/3 π • 6388³ = 1,091,901,171 km³
V(earth) = 4/3 π r³ = 4/3 π • 6371³ = 1,083,206,917 km³
V = V(tot) - V(earth) = 1,091,901,171 km³ - 1,083,206,917 km³
= 8,694,154 km³
Now we can calculate how much energy it would require to raise the temperature of the troposphere by a single degree Kelvin:
1.012 J/g•°K = 1.012 kJ/kg•°K
1.012 kJ/kg•°K • 1.2 kg/m³ = 1.2144 kJ/m³•°K
1.2144 kJ/m³•°K = 1,214,400,000 kJ/km³•°K
Since our calculations are based on a single degree Kelvin temperature rise, we can write this as
1,214,400,000 kJ/km³
1,214,400,000 kJ/km³ • 8,694,154 km³ = 10,558,180,617,600,000 kJ
But to be accurate, the troposphere is not the only thing warming up. It has been often claimed (correctly) that the oceans are a major heat sink. So let us now calculate the amount of energy required to raise the ocean temperature by a single degree Kelvin. The volume of water on the surface of the Earth is an estimation, but several estimations are available and all of them are close.
Therefore, in the interests of conservatism, I am using the smaller of the estimated values: 1,347,000,000 km³[8]. The specific heat capacity of water by volume is 4.186 J/cm³•°K[6] at 25°C. Thus, in order to raise the temperature of the oceans by a single degree Kelvin:
4.186 J/cm³•°K = 4,186,000,000,000 kJ/km³•°K
4,186,000,000,000 kJ/km³•°K • 1,347,000,000 km³
= 5,638,542,000,000,000,000,000 kJ/°K
As before, since we are considering a single degree Kelvin temperature rise, this is equal to
5,638,542,000,000,000,000,000 kJ
We now add the values for the troposphere and the oceans together to obtain the amount of energy required to raise the temperature of these two areas combined by a single degree Kelvin:
5,638,542,000,000,000,000,000 kJ + 10,558,180,617,600,000 kJ
= 5,638,532,558,180,617,600,000 kJ
Now, remember from earlier calculations the total amount of energy that is available from the solar irradiance that can intercept anthropogenic carbon dioxide:
55,262,986,931,155,824,000 kJ
3. Part 3 ATS

So if we know the energy required to raise a single degree, and we know how much energy can be intercepted by the anthropogenic carbon dioxide, we can calculate how many degrees of temperature rise could possibly happen. Remember, please, that we are making the following assumptions in these calculations:
We only include the energy required to raise the temperatures of the troposphere (where the carbon dioxide is) and the oceans (climatic heat sink). No energy calculations are included to this point for land masses or for upper atmospheric levels, each of which would, in reality, contribute in some way to the amount of energy required.
We are assuming that 100% of the available solar irradiance is being absorbed by anthropogenic carbon dioxide. This includes shortwave solar irradiation which is actually reflected back into space without being absorbed, and it also includes radiation that is absorbed through other means such as photosynthesis.
We are assuming 100% conversion of that intercepted energy by anthropogenic carbon dioxide into heat, and not calculating how much of that heat is dissipated back into space through emission.
All of the above are extremely conservative assumptions. Inclusion of them will only decrease the expected temperature increases due to anthropogenic carbon dioxide.
Now, the actual calculation we have been waiting for:
Energy(required) / Energy(available) = Ratio
5,638,552,558,180,617,600,000 kJ / 55,262,986,931,155,824,000 kJ = 102.03
It would require 102 times as much energy as is available now to raise the temperature 1°K in 100 years.
In other words, if ALL of the solar irradiance that the anthropogenic CO2 could intercept were converted into heat, and if it took no energy to warm the land masses and the upper atmosphere, the temperature of the planet would only warm by about 0.01°K in 100 years.

Ignorance denied.

Response:

The accurate CO2 level today is right at 400 ppm (the most recent measurements from the Scripps Institute of Oceanography Keeling Curve webpage). This makes CO2 .004% of the atmosphere. The preindustrial level is quoted as being 280 ppm, or .028% of the atmosphere. That is an increase of .012%, or about a 43% increase in CO2 levels. You used the increase of (approximately) .01% of the atmosphere as the factor of how much extra energy is being stored and that was incorrect. You should have used the 43% figure.

You go through a lot of calculations to determine the amount of solar energy reaching the Earth's surface. Why didn't you just look it up? A NASA Cosmicopia site quotes 1.8 x 10^17 J/s, very close to what you calculated, 1.75 x 10^17 J/s, which comes out to be 1.5 x 10^22 joules per day. That is equal to 5.5 x 10^24 joules per year and 5.5 x 10^26 joules per century. That is consistent with your figure above.

The next part is where your fatal flaw comes in to play. You assumed that increasing the amount of atmospheric CO2 from 280 ppm to 400 ppm was a .01% increase. That is only the amount of increase of the fraction of the atmosphere, not the increase in CO2. In fact, the increase in CO2 levels was 43% ((400-280)/280 x 100%). If you were correct about a linear change in CO2 concentration resulting in a linear change in heat absorbed (you weren't, thank goodness), then this would result in an increase of 2.4 x 10^26 joules of extra energy being absorbed over the next 100 years. You quoted 5.5 x 10^22 joules for the next century. So, you are short by a factor of 4300.

It is estimated that global warming has increased the efficiency of the planet's greenhouse effect by 1%. Using that figure (and your calculations), that would mean an additional 5.5 x 10^21 joules per day being added to the environment. Over 100 years that would come out to be 5.5 x 10^24 joules total.

I have some issues with your calculations into how much energy would be needed to heat the atmosphere and oceans. We will return to that issue later. Let's work with your numbers for right now.

You calculated it would take 5.7 x 10^24 joules of energy to raise the temperature of the ocean and atmosphere by 1 Kelvin.

Using the stored heat numbers I found above, I get the following:

Using the linear approach: A temperature increase of 42 Kelvins (42 degrees C).

Using the increased efficiency number: A temperature increase of about 1 Kelvin (1 degree C).

Both of these numbers are far in excess of what your calculated.

Let's return to the issue of how much energy it takes to raise the temperature by 1 K. By your calculations, it would take more than 534,000 times as much energy to heat the oceans as the atmosphere. This is not realistic. Part of the problem is you assumed the entire ocean volume would be heated by the same amount and this is not a true statement. Not all of the ocean will be heated and it will probably not be heated by the same amount throughout. There is another way to figure this. Of all absorbed energy, about 93% goes into the oceans and 7% goes into the air/land/ice system. I am going to start with your figure for heating the troposphere. I disagree with it, but the percentage of error is acceptable for this discussion. What I did then was to divide this by 7 and then multiply it by 100. The air/land/ice system absorbs 7% of the energy and the oceans absorb 93%. Using that ratio, and your figure of 1.06 x 10^19 joules to heat the troposphere, I get a figure of about 1.5 x 10^20 joules needed to raise the temperature of the air and oceans by 1 K. The figure you calculated was about 38,000 times as large as that. Then, using that figure along with the amount of extra energy being absorbed over a century, we get the following:

Using your numbers: A temperature increase of 367 degrees.

Using the linear number I found above: A temperature increase of 1.6 million degrees.

Using the increased efficiency number from above: A temperature increase of 37,700 degrees.

No, we are not going to heat up by even anything like those numbers over the next century. In fact, we probably will see a temperature rise close to 3 or 4 degrees total. I am not preaching doom and gloom. I am just making the point that the energy budget certainly supports the greenhouse scenario.
Fortunately, most of the solar energy never reaches the ground and doesn't end up heating the planet. Some of the other numbers are back of the envelope type, so there will be some flaws in the outcomes. But, the point is proven - using your method, we can see that global warming is most definitely possible and is a serious issue.
Your basic premise was correct. You used the idea of the using the expected total amount of energy stored and determined how much heating could be done with that energy. The flaws were in your calculations into the amount of extra energy retained due to the greenhouse effect and the amount of energy needed to raise the temperature.
You did not prove man made global warming is not real.