I have seen, read or heard numerous indications saying how the Earth’s Ocean’s will rise as iceberg’s melt. That was quickly refuted via Archimedes and good old fashioned displacement science.
Then came the fear-mongering about Antarctic ice melting. Considering the average temperature on the south pole is anywhere from -37 Celsius to -57 Celsius, I do not think a few degrees of planetary warmth will do much.
So now the environmentalists want to attack Greenland ice shelfs and other glaciers that are overland.
Well here is some science that no one has mentioned that counters rising sea levels.
It is a very well known but not well announced fact that warm air holds more moisture than cold air. By doing a bit of formula manipulation with the Ideal Gas law, I calculated that a cubic meter of atmosphere can hold an extra 0.85 grams of water vapour for every degree Celsius that the temperature rises. This fluctuates a very very small amount depending on what the two temperatures are or how high up in the atmosphere you go.
However, for a good rough estimate, you can assume the lowest 11km of the atmosphere holds about 75% of the Earth’s atmosphere density. Using the Earth’s average radius of 6.37 Million meters, I calculated that that 11km zone around the planet can hold AN EXTRA 851 Billion cubic meters of water. Taking into account the water surface area of the planet is 361 Billion square meters, then simple division would tell us that the planet’s water level would drop approximately 2.36 meters for every degree Celsius of increased average temperature.
Remember this when someone tells you melting ice will raise sea levels.
You can also point out that increased CO2 levels create bigger, stronger and more abundant plant life. These plants will need more moisture for photosynthesis which means they will be taking in more water than plant life in an environment with less CO2 and they will also convert more of that CO2 into O2.
i.e. warmer temperatures and more CO2 creates a buffering environment that counters the high levels with thriving plant life.
I think that’s enough science to last a week. I urge others to doublecheck my math. The data I used included:
The Ideal Gas Law (PV=nRT)
The Earth’s water surface is 361,126,400,000 square meters
The Earth’s average radius is 6.37 Million Meters
The average temperature is 283 Kelvin (or 10 degrees Celsius)
The average air pressure is 1 atmosphere or 101.325 KiloPascals
The weight of one mole of H20 is 18 grams
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is it painful to be this stupid?
and for christ’s sake, don’t send me any of your bloody “followup” comments via email!
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Thanks for that scientific rebuttal Jeff. I am sure you created absolutely NO global warming expending energy thinking up that reply. I, and the planet, appreciate your environmentally friendly (not to mention biodegradable) brain.
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I recommend this theory as an excellent second place in idiocy to Reagans “trickle” economics.
Jeff, it’s not the blog author’s fault. You didn’t unclick the little checkbox.
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For starters, you should elaborate on how you used the ideal gas law (applies to monatomic non-interacting collision-based gas models) to calculate the figure of 0.85g of water for every degree celsius rise. Air is not monatomic, and adding water (H20) molecules makes this approximation worse. Your method and usage of the IGL is suspect without equations and explanations.
My guess is that you should not rush to publish just yet.
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Vapour density (VD), in mg/m^3
Temperature (T), indegrees Celcius
VD=5.018+0.32321*T+8.1847×10^(-3)*T^2+3.1243×10^(-4)*T^3
Thus, a cubic meter of air can hold about a milligram more water for a 1 degree change in the neighbourhood of 20 degrees C.
You got 0.85
Not bad!
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Your statement is correct but your numbers are somewhat off:
“The mean water vapour content of the atmosphere is equivalent to a layer of water 25 mm thick over the whole Earth, or 35 mm over the ocean surface. If we assume that relative humidities do not change, a rise of equatorial temperature of 3 °C and of double that at higher latitudes would lower sea level by around 7 mm due to additional water vapour in the atmosphere.”
http://www.icsu-scope.org/downloadpubs/scope29/chapter07.html
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Most of the rise in sea level will not be due to melting ice. Sure, warm air can hold more water. But guess what? Warm water takes up more space. Most of the projected rise in sea levels isn’t because the air is warmer. It is because the sea is warmer. That will more than offset the added vapour capacity of the air. And this is coming from someone who isn’t concerned about global warming.
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Here is a citation…
http://www.cru.uea.ac.uk/cru/info/slr/
It should also be noted that while arctic sea ice retreat doesn’t add to the volume of water contained in the oceans it does significantly lower global albedo (not libido which is unaffected). Lower albedo results in an enhanced positive feedback loop. So the melting of the arctic sea ice doesn’t directly impact sea levels it does accellerate global warming.
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anon (#4) I simply calculated n for particular temperatures, assumed the difference to keep the same pressure was the added molar mass in grams and got about 0.85.
After reading a few more comments like Tenebris’ I see that I should probably be looking at the vapour density formulas. i.e. read up on my Dumas a bit more.
Tenebris (#5) thanks, but if your math is correct, I am off by a factor of 850 (Holy smokes!!). I got .85 Grams which is 850 milligrams.
On that note, if the 1 mg is accurate, then the added height would be more like 2.7 millimeters, lining up with what Joe Johnston (#6) points out.
Joe, I appreciate the great link, but for a site that has so much math on it, the one section that seems to be a statement on faith is the atmosphere one you quoted. Do you know where the math is behind the statement?
I appreciate the input from all who are commenting constructively.
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The IPCC report(s) claim, (although I have yet to find any of their calculations to back up their claim) that the warming of the oceans (and their concomitant density-based expansion) is the primary cause of their rise.
And that the melting of land-based ice (and reductions in land-based bodies of water) is a secondary cause. (Although no calculations are given when such melting is discussed.)
I have also not found in the IPCC reports any evidence of a clear study of deep ocean warming (most measurements only include near-surface temperatures) to back up the theory, coupled with tidal theory.
I have also not found any study from the IPCC reports of the change in atmospheric water vapour content over the past several centuries, although they do note that water vapour is a very strong GHG.
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Paul (#10) thanks. I did scan the IPCC website when you linked to it a couple of weeks ago here in the comments of another post.
The link Joe Johnston above connects to is very interesting reading too.
I have also been keeping my eyes open on how much water would be taken out of the system for the increased plant life too. If you come across something like that in your readings, please let me know.
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For greater certainty, I think you might want to refer to Chapter 11 of the IPCC “Basis” Report (of the so-called Third Assessment Report), which discusses ocean levels, as well as Chapter 2 (Sections 5, 7) of that same TAR Basis Report.
Relevant questions include: do measurements of Sea Surface Temperature (SST) correspond to measurements of deep-sea temperature, to justify the conclusions of total oceanic heating? How do the observed measurements of atmospheric water vapour (Ch.2) correlate with observed measurements of sea level? (What is the implied total global water content?) How are regionally diverse measurements explained (e.g. rise of 2mm in one area, 5mm in another)?
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Paul, that chapter 11 is a lot more interesting than the tax law chapter 11 (haha). I got a couple of pages in and skimmed a few more. I need to get some more blank paper and print this one out to read. Thank you.
I don’t want to sound like I am grasping at straws, but I wonder how many other water “tanks” are out there that would compensate any ice masses melting off land. i.e. water content in the growing human population, plants, the number of swimming pools being built vs. those being filled in or torn down, empty aquafir that will refill, etc.
Chapter 11 has a section called “Terrestrial Storage” but it doesn’t give a clear indication of what this means. (page 658 of the report)
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I suspect one might have to dig into some of the Reference materials to find a clearer definition of “Terrestrial storage”; although it probably includes lake and river water, I haven’t seen any clear current or historical inventories of puddles, plants, soil, and water table volume content.
It is also worth noting that water vapour might also be formed chemically, e.g. as methane (CH4) reacts with oxygen (O2) in the atmosphere to form Carbon (C) and H2O. Again, I have not seen studies incorporating this (and other chemical reactions) into the global budget and inventories of the relevant elements and compounds.
I’ve also come across this USGS site (which excludes chemical reactions from the cycle, but does include some inventory calculations – scroll to the bottom):
http://ga.water.usgs.gov/edu/watercyclesummary.html
http://ga.water.usgs.gov/edu/watercycleatmosphere.html
Finally, as an aside, one indicator of precipitation is taken from streamflow measurements; however, improved drainage from both urban and agricultural lands has probably increased streamflow for a given level of precipitation as water spends less time in fields and in traversing the water table.