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Roger's Equations

This blog features weekly an equation, formula, or constant that occurs frequently in Engineering or Science. I will try to present the subject matter in a nonformal, conversational style that can be easily followed. Criticism and corrections are encouraged, as are suggestions for future discussions.

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Global Warming (Part 2 of 3)

Posted July 26, 2006 5:42 PM by Roger Pink

Last journal entry I examined whether the world is getting warmer. I used the qualitative evidence that the ice on practically every corner of the planet is receding at an accelerating rate, to justify that in fact the Earth is warming.

This entry I'd like to examine the mechanisms involved in warming the Earth and the possibility that the current shift in climate is the result of human activity, specifically increasing Carbon Dioxide and Methane emissions over the past 150 years.

There are two significant sources of heat for Earth. The first is the Sun which provides 170,000 TeraWatts of power to the Earth. The second is fission reactions in the core of the Earth producing 25 to 50 TeraWatts of power. Since the sun provides much more power (4000x more), I will ignore the contribution from the core and focus on how the power from the Sun is converted to heat on Earth.

If you were to look at our Sun, you would see it's yellow in color (don't look at the sun, you'll damage your eyes). The sun is yellow because its peak emissions are in the visible range. The Sun also has sizeable emissions all the way from gamma rays, x-rays, and Ultraviolet rays, to the far infrared and microwaves. The high energy gamma rays, x-rays, and UV are blocked by the upper atmosphere and middle atmosphere. The lower energy UV, Visible, and IR frequencies make it to ground level. The lower IR frequencies are absorbed by the lower levels of the atmosphere and converted to heat. The middle frequencies of UV, Visible, and NIR are the frequencies that make it to the Earth's surface and make the largest contribution to heating the Earth.

At this point I think it makes sense to take a step back and define what we mean by "Heating the Earth". That's because when we human beings talk about global warming, what we really mean is the warming of the region of Earth we inhabit. The core of the Earth recieves very little heating from the Sun, and although the -60C of the upper Troposphere is quite balmy as compared to the 3k (-270C) of space, we aren't too interested in temperature fluctuations there aside from the indirect consequences they might have on our region of the Earth. The steady 4C of the deep ocean, and by deep I mean beyond 1000 meters, is of little consequence to us as well unless it effects us in our region. So when we talk about the "heating of the Earth" what we mean is the heating of the Earth in our nice little habitable region which is from a depth of about 1000 meters in the ocean to an altitude of about 10 miles in the atmosphere.

The surface of the Earth consists of 71% Oceans and 29% land. The oceans have roughly 4.5x the heat capacity of the land, which means land will heat up and cool down much more quickly than the oceans(or lakes). 75% of the Atmosphere is located in the first 10 miles. This atmosphere consists of 78% Nitrogen, 20.9% Oxygen, .934% Argon, .0381% Carbon Dioxide and Water Vapor will vary from less than a percent up to about 3%.

Our region of Earth is heated in several ways. A small amount of heating comes from infrared light being absorbed by the atmosphere, warming the atmosphere. The majority of the heating comes from the Earth absorbing the UV and Visible light from the sun and emitting light at Infrared wavelenths. It's important to know that UV and Visible light interacts with matter by producing electron transitions whereas Infrared interacts with matter by producing vibration transitions. The higher the vibration energy, the higher the random motion of the molecule. The higher the random motion of the molecule, the higher the temperature by definition. So Infrared radiation is converted to heat. When the Earth emits Infrared radiation, it is partially absorbed by the atmosphere, which heats the air. If the Earth had no atmosphere, it would have an average temperature similiar to the moon's average temperature of 0C instead of 17-18C the Earth has.

Greenhouse gases are the gases in the atmosphere that absorb infrared radiation well. Nitrogen and Oxygen do not absorb infrared well at all. A minor portion of the atmosphere consisting of carbon dioxide, water vapor, methane, and ozone, and some others accounts for almost all the Infrared absorbtion. Water vapor is the largest contributor, accounting for 40-70% of the heat retained. Carbon Dioxide is next accounting for 10-25%, Methane 5-10%, Ozone 2-7%, and the rest making small contributions. Water vapor has another mechanism that slightly offsets it's greenhouse contributions. Water vapor forms clouds that can reflect light back into space before it can get to the ground. Also, the water vapor, which absorbs heat when it evaporates from the oceans, releases heat when it forms rain (or snow) into the atmosphere. We should note that warmer air can hold more water vapor.

Carbon Dioxide and Methane are the 2nd and 3rd strongest greenhouse gases. Levels of these gases can and have changed throughout history. Over the last last million years ago, Carbon Dioxide levels have fluctuated from low levels during ice ages and higher levels in the periods between ice ages. The Carbon Dioxide atmospheric levels during ice ages typically are around 180-210 muL/L and between ice ages are typically 280-300 muL/L. We are currently between ice ages and up until 150 years ago, Carbon Dioxide levels were 260 to 280 muL/L, typical of the past million years. In 2006, Carbon Dioxide levels have reached 380 muL/L. Methane has varied as well in a predictable manner over the previous million years. During Ice ages, Methane levels were around 320-350ppbv and between Ice ages were around 650-770ppbv. Methane levels are currently around 1750ppbv. Clearly both Methane and Carbon Dioxide levels are much higher than the average values of the past million years. The increase corresponding exactly with the industrial revolution.

With such a dramatic increase in greenhouse gases, why hasn't there been a violent increase in temperatures? To answer that, we must remember that the Earths surface is 71% Ocean and 29% Land. The oceans act like huge heat sink that moderates temperature change. In the short term this prevents the Earth from the temperature extremes found on the moon during night and day. Over a large time scale, oceans slow the warming (or cooling) of the planet by absorbing heat. The surface area of the Earth's oceans are 361 million square kilometers, with a volume of roughly 1.34 billion cubic kilometers and a total mass of 1.4 x 10^21 kilograms. The specific heat of water is 4.186 (joule/gram)*C. To raise the temperature of all the water in the ocean 1 degree Celsius would require 10^25 joules or 10^22 BTUs. Melting ice also removes heat from the atmosphere. Ice has a latent heat of 334 j/g and the Earth has roughly 2.4x10^19 kg of ice. This means that it would take 8.0 x 10^21 joules (8.0 x 10^18 BTUs) of heat to melt all of the ice on the planet. To give an idea of how much energy that is, the sun provides 5.6x10^19 BTUs to the entire Earth every day. So if you turned the Sun off for a day, the ocean would only cool 1 degree Celsius. A heat imbalance caused by increased atmospheric absorption of infrared due to increased levels of greenhouse gases will take a long time to show up as noticable air temperature increases. All the heat is being used to heat the ocean and melt ice.

So if you want to know if there is a heat imbalance due to increased levels of greenhouse gases, you should should look for the following signs:

Is Global Ice levels declining? (yes)
Are the oceans warming (yes)
Have there been changes in long standing weather patterns (weather is fueled by ocean currents)? (yes)

It's scary when you start to think about it. For instance, consider these facts:

Atmospheric CO2 levels and Methane levels are far beyond anything the atmosphere has seen in over 1 million years.
These increased greenhouse gases in the atmosophere are a direct result of industrialization and the levels are expected to rise significantly over the next hundred years.
There is a delay (hysteresis) between increases in greenhouse gases and and air temperature changes due to the moderating effect of water.
Water and ice act as heat resevoirs meaning that temperature changes are difficult to start and once started, difficult to stop. When the ice is gone, temperatures will rise more quickly.

Last entry I argued that the melting of ice on all continents is evidence that global warming is occuring. Over the last million years there has been a correlation between atmospheric levels of CO2 and Methane and Climate. I think it's unreasonable to ignore this correlation now. With the levels of CO2 and Methane way beyond the average levels and increasing and a global melt underway, I think there is little question that industrialization and the green house gases it has placed in the atmosphere has altered our climate.

Next journal entry I will examine the question "Can we do anything about global warming?"


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Join Date: May 2006
Posts: 15
#1

Re: Global Warming (Part 2 of 3)

09/19/2006 4:59 PM

Indeed the Oceans are warming. Not only is the surface warming, the depths are also warming (at a slower rate).Marine scientists are surprised at the rate of warming in the very deep waters.

Of great interest to me is the vast quantities of methane ices 'sequestered' in the deeper ocean levels.

The point on the temperature/pressure curve where methanes become stable is starting to shift as the oceans warm. (oceans getting warmer, pressure remaining the same) means the point where the methane ices revert to gas is moving deeper into the ocean.

We can expect an increase of methane release which will accellerate the rate of warming, which.....

If we were to harvest the methane just below the freezing point, we could use it to fire our gas fired power plants. The CO2 released is the lesser evil if is allowed into the atmosphere or it could be sequestered underground or in the greater depths of the ocean where the pressure/temperature keeps it a liquid.

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