Climate - In-depth/technical discussion

[jethro]

This thread is for technical, in-depth discussion on the science of Climate Change. Please keep it on topic, please only post with supporting peer review evidence (even if it's only a free abstract) to support your stance.

Keep it civil folks.

[VillagePlank]

I think that we can start positively with something almost everyone can agree with

Svante Arrhenius published the root paper₁ that clearly demonstrated, by scientific means, a relationship between temperature and CO₂, although the idea had been suggested by Fourier, some years earlier. The simplified equation₂ which demonstrates this relationship is:

ΔF = α ln(C/C₀)

Although disputed at the time with reference to absorption rates, the mean temperature of the moon, and flawed assumptions with regard to spectroscopic data, there is, now, little doubt that this relationship holds, at least in the clinical world of a lab or indeed your kitchen.

Essentially, this means that the more CO₂ you have the more is required to see a temperature increase of the same magnitude. In old school money, this is called an arithmetic progression.

1: On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, Svante Arrhenius, Philosophical Magazine and Journal of Science, Series 5, Volume 41, April 1896, pages 237-276.

2: http://en.wikipedia.org/wiki/Svante_Arrhenius, Sat 13 Feb, 2010.

Edited February 13, 2010 by VillagePlank

[Methuselah]

Yes VP...So long as my memory serves me correctly - and I have the right group of functions: http://images.google.co.uk/imgres?imgurl=http://schools-wikipedia.org/images/300/30060.png&imgrefurl=http://schools-wikipedia.org/wp/n/Natural_logarithm.htm&usg=__mc9eCYwa6FOU9b-3jbR2bYSRYiQ=&h=256&w=256&sz=7&hl=en&start=38&itbs=1&tbnid=qTJxbpzEA_VGbM:&tbnh=111&tbnw=111&prev=/images%3Fq%3Dinverse%2Blogarithmic%2Bfunction%26gbv%3D2%26ndsp%3D21%26hl%3Den%26safe%3Doff%26sa%3DN%26start%3D21 ?

The amount of forcing due to CO₂ concentration works like a law of diminishing returns...

[Thundery wintry showers]

Furthermore, as Captain_Bobski discussed a long time ago, there are question marks over the specific value of α, which is significant in that it governs the raw amount of forcing that CO2 generates.

Here's an updated version of the link to the site which discusses this in some detail (the old link was broken):

http://www.aps.org/units/fps/newsletters/200804/marsh.cfm

The sensitivity of the climate to a doubling of carbon dioxide concentration could be in error. The change in forcing due to a change in carbon dioxide concentration is given by

ΔF = α ln(C/C₀) w/m2,

where C₀ and C are the initial and final carbon dioxide concentrations. Since 1990, the estimate by the Intergovernmental Panel on Climate Change (IPCC) of the coefficient α changed by 15% (Δα/α = 0.15) and “implicitly include the radiative effects of global mean cloud cover” [12], and estimates of the radiative effect of clouds are quite uncertain. If the actual sensitivity is significantly lower than current estimates, that would elevate the concentration of carbon dioxide needed to extend the current interglacial.

I think this is also highly relevant to first principles.

[Methuselah]

Furthermore, as Captain_Bobski discussed a long time ago, there are question marks over the specific value of α, which is significant in that it governs the raw amount of forcing that CO2 generates.

Here's an updated version of the link to the site which discusses this in some detail (the old link was broken):

http://www.aps.org/units/fps/newsletters/200804/marsh.cfm

I think this is also highly relevant to first principles.

Aye, Ian, it's very relevant. But, ss I've said before, my memory of these functions is very rusty, so I'm not very qualified to 'stick my oar in,' so-to-speak...So I'll remain on the sidelines and let you guys take the lead...

[Thundery wintry showers]

NCDC/NOAA has January 2010 as the 4th warmest on record, with the bulk of the excess warmth found over parts of the USA/Canada, the western side of the Arctic, the tropics and low-latitude Southern Hemisphere, more than offsetting the unusually cold conditions over Eurasia:

http://www.ncdc.noaa.gov/sotc/?report=global&year=2010&month=1&submitted=Get+Report

The troposphere, as Phil Jones mentioned in his interviews with the BBC, had its warmest January on record. However, it is important not to confuse the troposphere (as measured by satellite data) with surface temperatures which are more relevant to us humans (the surface has, in general, warmed a lot more than the troposphere in the last 50 years, and also the troposphere cooled a little in the last decade, unlike the surface).

The Arctic interior was warmer than usual but I don't think it was as exceptionally warm as in the Januarys of either 2005 or 2006, according to the NCDC's Global Circulation Map room plots for the 30 days up to the 1st February- in both of those months 10-15C anomalies were widespread near the pole.

El Nino is not far off the strength of the 1998 one:

http://www.cpc.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml

...but is still a little short of it, and given the prevalence of synoptics in the Northern Hemisphere that favour a cold Eurasia and warm oceans (in contrast to winter 1997/98) which tends to result in a lower positive anomaly due to the landmasses being more prone to larger deviations from the mean, I don't think this is inconsistent with there still being a small upward trend in global temperature once the short-term natural variability from ENSO is factored out of the equation.

The real test, for me, will be what happens in Spring 2010 when we lose that short-term natural variability caused by the winter -ve NAO in the Northern Hemisphere, and see the full effects of the El Nino at the start of the year. Notably, NOAA expect it to continue into the spring.

[SleepyJean]

I didn't know this about CO2 (the law of diminishing returns as Pete succinctly put it). I had previously been thinking along the lines of something on a small scale not necessarily behaving in the same way on a large scale (chaos as opposed to fractals, I believe...do correct me if I'm wrong).

Some of the maths/physics is so far beyond what I was able to grasp at school (I failed my A-level maths :S) that I think I will have to go and learn some in order to properly understand what is going on. Put it like this, I saw an Equinox once about the nature of space/time, and I understood it so clearly at the time that I was able to picture it clearly. Sadly, within minutes of the program finishing all I was left with was the knowledge that space and time are the same thing and it's round. If I only had the maths to describe it properly....

Edited February 14, 2010 by SleepyJean

[Thundery wintry showers]

Here's the original source (yes, that 1896 paper):

http://www.globalwarmingart.com/images/1/18/Arrhenius.pdf

Unfortunately it doesn't appear to go into the physics of why the relationship is a logarithmic one, and I can't find any clear-cut explanations elsewhere- the derivation in the initial source involves some trial and error (see around page 263 if you're intereested). There is a very detailed blog entry here which suggests that it's to do with the slowing down of availability of new spectral lines for absorption as concentrations increase, the exponential decrease of CO2 density with height, and the resulting upward movement of the tropopause. However, especially as it's an internet blog, I cannot vouch for the accuracy of this. What's clear, though, is that while I can get my head around most of the maths that's involved, much of the physics involved is well past my level of comprehension!

The IPCC Report 2007, similarly, only mentions the logarithmic relationship's existence in passing and offers no explanation why. The important thing, though, is that all of the major sources appear unanimously agreed on the logarithmic relationship- including the IPCC.

[Iceberg]

NCDC/NOAA has January 2010 as the 4th warmest on record, with the bulk of the excess warmth found over parts of the USA/Canada, the western side of the Arctic, the tropics and low-latitude Southern Hemisphere, more than offsetting the unusually cold conditions over Eurasia:

http://www.ncdc.noaa.gov/sotc/?report=global&year=2010&month=1&submitted=Get+Report

The troposphere, as Phil Jones mentioned in his interviews with the BBC, had its warmest January on record. However, it is important not to confuse the troposphere (as measured by satellite data) with surface temperatures which are more relevant to us humans (the surface has, in general, warmed a lot more than the troposphere in the last 50 years, and also the troposphere cooled a little in the last decade, unlike the surface).

The Arctic interior was warmer than usual but I don't think it was as exceptionally warm as in the Januarys of either 2005 or 2006, according to the NCDC's Global Circulation Map room plots for the 30 days up to the 1st February- in both of those months 10-15C anomalies were widespread near the pole.

El Nino is not far off the strength of the 1998 one:

http://www.cpc.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml

...but is still a little short of it, and given the prevalence of synoptics in the Northern Hemisphere that favour a cold Eurasia and warm oceans (in contrast to winter 1997/98) which tends to result in a lower positive anomaly due to the landmasses being more prone to larger deviations from the mean, I don't think this is inconsistent with there still being a small upward trend in global temperature once the short-term natural variability from ENSO is factored out of the equation.

The real test, for me, will be what happens in Spring 2010 when we lose that short-term natural variability caused by the winter -ve NAO in the Northern Hemisphere, and see the full effects of the El Nino at the start of the year. Notably, NOAA expect it to continue into the spring.

Just a few points, it's the lower troposphere which is the warmest on record, not just the troposphere, there is very good correlation >90 between TLT and surface temps, so it does pretty much mirror the ground temps see below.

The troposphere has warmed in the last decade (using a 10 year avg or straight trend line (with the least warming being in the upper reaches of the troposphere), the stratosphere has cooled.

Re ENSO sorry I have to disagree again we are realistically speaking nowhere near the 98 El Nino, this has 6 months above 2C, we have had none and only 1 month even approaching 2C.

98 was really a super super El Nino. I've put alot of this on the ENSO thread with some very good contributions from Kold, but essentially yes, it was was 2nd warmest EL Nino in the last 20 years, it was the warmest western based (zone 4) on record. But didn't really compare to 98 in strength or persistance of strength.

If you breakdown the global temps you can see that in 98 temps in the tropics made up alot of warming, this is less so the case in the recent record breaking months.

Cheers

Edited February 15, 2010 by Iceberg

[sunny starry skies]

Am mainly just checking in here, this is a great idea - I'll look forward to posting more in here in the future, but I've been too busy enjoying the Winter Olympics in my free time at the mo! So far as I can see the logarithmic relationship of CO₂ is fully acknowledged by the major research and modelling efforts, which makes sense as it's hardly new information! What I haven't seen yet (partly because I've not done enough digging to look for it) is information on quite where we sit on that logarithmic curve. I suspect that's a moot point as it will be coded into the modelling efforts for future projections, and so should already be taken account of. I also suspect that there isn't a significant change in the 'later' rates of CO₂-induced warming (say, post-550ppm compared to present rates), as I would have thought that this would either be the subject of scientific debate, or highlighted more prominently in publications such as AR4. Sorry about lack of supporting information though!

Something else I'd like to move my own understanding forward on is the difference between the spatial pattern of observed impacts of AGW and observed impacts of solar forcing. So far as I'm aware, they are not the same - my understanding is:

- solar should lead to warming at all altitudes, and more warming at lower latitudes.

- AGW should lead to more warming at high latitudes, tropospheric warming and stratospheric cooling due to the radiative properties of the CO2. [this is the observed pattern]

Is that right?

sss

Edited February 17, 2010 by sunny starry skies

[VillagePlank]

Here's the consequences of,

ΔF = α ln(C/C₀)

Here's the data (with the doubling in bold). The terms are (from right to left)

% = Percentage change of CO

C₀ = Starting CO₂ concentration (ppmv)

C = Ending CO2 concentration (ppmv)

alpha = constant

delta F = change to forcing (w/m²)

lambda = climate sensitivity

delta T_s = change to surface temperature (^oC)

lambda is the key₁ to converting the delta F from w/m² to ^oC. Actually, it's in Kelvin, but a degree increase in Kelvin is the same as a degree increase in Celsius.

And this what the chart looks like:

This (very) minor study of mine, I think, leads to two important points in my view. How is alpha (as TWS has already pointed out), and lambda derived? For instance if alpha is halved you need a 300% increase in CO₂ to get the same 3^oC increase. Similarly, with lambda. Of course, the inverse is also true - should these constants be too low, then delta T_s increases much more rapidly correspondingly with percentage increases.

So these constants look all important to me (or I am doing something horrendously wrong!) Does anyone know how to derive these constants from first principles?

1: http://en.wikipedia.org/wiki/Radiative_forcing, retrieved 17 Feb 2010

Edited February 17, 2010 by VillagePlank

[VillagePlank]

Before we go onto discussing the constants, I thought it might be nice to add something which Arrhenius did note₁ (and it's an excuse to draw a pretty chart) and that was the differing effect of CO₂ on temerature depending on latitude.

Certainly something to consider, I think, because the ramifications of that are, to say the least, interesting.

Here's the data:

Here's the chart:

It looks pretty obvious that the following seems true: the higher the concentration of CO₂ the more pronounced the effect on temperature, at the surface, between the equator and higher latitudes.

1: On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, Svante Arrhenius, Philosophical Magazine and Journal of Science, Series 5, Volume 41, April 1896, pages 237-276. Table VII, p266

Edited February 17, 2010 by VillagePlank

[sunny starry skies]

Before we go onto discussing the constants, I thought it might be nice to add something which Arrhenius did note₁ (and it's an excuse to draw a pretty chart) and that was the differing effect of CO₂ on temerature depending on latitude.

Certainly something to consider, I think, because the ramifications of that are, to say the least, interesting.

Here's the data:

Here's the chart:

It looks pretty obvious that the following seems true: the higher the concentration of CO₂ the more pronounced the effect on temperature, at the surface, between the equator and higher latitudes.

1: On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, Svante Arrhenius, Philosophical Magazine and Journal of Science, Series 5, Volume 41, April 1896, pages 237-276. Table VII, p266

If I'm not much mistaken, is this not just indicative of the greater effect of CO2 at higher latitudes, in line with modern thinking? (and there's not data there for latitudes above 70 or below -40). Some evidence there for the greatest change in influence being between 20-40 degrees too, indicating that the tropical regions are least sensitive. Or was there another point you were making?

sss

[VillagePlank]

If I'm not much mistaken, is this not just indicative of the greater effect of CO2 at higher latitudes, in line with modern thinking? (and there's not data there for latitudes above 70 or below -40). Some evidence there for the greatest change in influence being between 20-40 degrees too, indicating that the tropical regions are least sensitive. Or was there another point you were making?

sss

The missing data is a point to note about the paper, itself - I just typed it into Excel.

Arrhenius₁ made some observations himself that seem, on the face of it, reasonable - but, for me, not necessarily obvious.

Firstly, the nebulosity (I had to look it up - it means cloudiness) of the southern hemisphere, presumably on account of the southern oceans, means the effect will be less than the Northern hemisphere (important implications in measuring global temperature: should we, or do we, account for this?)

Secondly, an increase in C0₂ will reduce diurnal range of temperatures. He fleets over this, and I don't understand why, and I can't find any source that explains it, either.

Thirdly, that the difference between the equator and the poles are different because "those places ... alter their albedo by the extension or regression of the snow-covering" So temperature increases at the poles are larger with the same C0₂ differential₂.

Add that lot together, and, it seems to me, at least one of the constants, probably alpha, needs to be some function of albedo. Not a great surprise, but I didn't expect to see it.

(Sorry if this is excess to requirements - this is the sort of thing that, ahem, gets me going, one might say. The hunt for the alpha function is on!)

1: On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, Svante Arrhenius, Philosophical Magazine and Journal of Science, Series 5, Volume 41, April 1896, pages 237-276. page 265

2: As above, page 257

Edited February 17, 2010 by VillagePlank

[Thundery wintry showers]

I take Iceberg's good points regarding the strength of the El Nino, which only approached 1998 levels for a single month. Interestingly the global warmth of January 2010 was most emphasised in the Southern Hemisphere landmasses and not the tropics/oceans according to NCDC/NOAA, with record-breaking warmth over Australia.

The elevated winter warmth over the Northern Hemisphere relative to the Southern, according to a Brian Hoskins paper back in 2002, is accentuated by the recent trend for a strongly positive NAO, leading to a pattern of warm anomalies over Eurasia and cold anomalies over the oceanic Atlantic sector, a point also picked up on by the contributors to the "Global and regional climate in 1996" article in Weather. This is because the continents are more prone to larger temperature anomalies than the oceans, and it was a large part of the reason why 1996 was a much cooler year in the Northern Hemisphere than either 1995 or 1997. It also shows up the Northern Hemisphere warmth in January 2010 to be remarkable, because January 2010 had the 1996-style pattern of a cold Eurasia and a warm Atlantic- most recent months with that pattern (e.g. December 2002, January 2006) have had Northern Hemisphere temperatures not far above the long-term average.

Another interesting question is, while the Arctic perfectly fits the "expected" AGW pattern with huge warming at high latitudes, Antarctica does not, with rapid warming in the Peninsula but not much of a trend in the interior. There have been a number of papers in Nature recently analysing the amount of warming in the centre of Antarctica, including one which was riddled with confirmation bias suggesting that there had been a lot of recent warming in West Antarctica that could only be explained via AGW- ignoring the large fluctuations in temperature there since the 1940s.

Interestingly VP's stats suggest that the enhanced warming at higher latitudes, from the AGW contribution from CO2, would only be expected to become substantial with high amounts of AGW (for a global warming of about 3.3C, the values range from 3.5C at the pole to 3.1C at low latitudes) so in that case the pattern over Antarctica may not be entirely inconsistent with AGW, while the rapid warming of the Arctic may be heavily assisted by cyclical factors.

[sunny starry skies]

Interesting points TWS and VP. (BTW, VP, I was aware the data came from Arrhenius and not because you'd missed it out).

Just been having a look at the 'polar amplification' issue in a reference from IPCC, and it seems that Holland and Bitz (2003) suggest that much of the amplification is albedo-related, cloud cover may also play a part.

http://www.cgd.ucar.edu/oce/pubs/03pubs_files/Holland-ClimDyn.pdf [found in AR4, regional climate]

That to me makes sense with sea ice reduction and snowpack reductions in the Arctic, but I wonder about Antarctica. It's a different system altogether with the isolating effect of the circumpolar storms and currents, and with a large ice sheet in the centre, rather than sea ice. Is it the case that the Peninsula warming is as expected, as albedo at those latitudes is affected by sea ice, while the interior's albedo remains little changed as much of it is kilometres-thick ice? There seems to be a lot of uncertainty about Antarctic trends and the reasons why - just not enough hard data.

sss

[VillagePlank]

Interesting points TWS and VP. (BTW, VP, I was aware the data came from Arrhenius and not because you'd missed it out).

Just been having a look at the 'polar amplification' issue in a reference from IPCC, and it seems that Holland and Bitz (2003) suggest that much of the amplification is albedo-related, cloud cover may also play a part.

http://www.cgd.ucar.edu/oce/pubs/03pubs_files/Holland-ClimDyn.pdf [found in AR4, regional climate]

Thanks for the paper. I've had a quick peruse, and it seems to be quite a good review of the issue in it's relation to a selection of climate models. I'll read it properly at some point over the weekend.

Physically, albedo's part to play in all of this₁, is almost certainly related to some kind of interaction of physical matter and physical geometry. I was hoping to avoid such mathematics until a later date, but it looks like we need to start considering the ellipsoid₂, now, too. Could this be the the missing alpha function such that our current assumption that it is a constant is incorrect, but it can be modelled as such since we can take pictures from space, and generate a mean albedo for the Earth?

It looks as if there is a NASA document₃ that deals with how we measure albedo from space. It looks very in depth, and looks like it may take a while (at least for me) to get my head around it.

1:http://en.wikipedia.org/wiki/Albedo, retrieved 19 Feb 2010

2:The ellipsoid and the Transverse Mercator projection, Geodetic information paper. No 1 2/1998 (version 2.2), Ordnance Survey, here

3:MODIS BRDF/Albedo Product: Algorithm Theoretical Basis Document Version 5.0,A. H. Strahler, J.-P. Muller, MODIS Science Team Members, here, retrieved 19 Feb 2010

Edited February 19, 2010 by VillagePlank

[Gray-Wolf]

Wasn't the extensive warming of the upper trop. in antarctica put down to heat capture by GHG's? If I can remember the paper correctly they measured the highest temp increases across the globe there and I'm sure the reflected solar was that which was captured?

[sunny starry skies]

Wasn't the extensive warming of the upper trop. in antarctica put down to heat capture by GHG's? If I can remember the paper correctly they measured the highest temp increases across the globe there and I'm sure the reflected solar was that which was captured?

Are you thinking of this one?:

Turner et al, 2006: Significant warming of the Antarctic winter troposphere. Science 311, 1914-1917

http://www.sciencema...t/311/5769/1914 [abstract]

http://www.sciencema...l/311/5769/1914 [full text, may not be accessible]

Looks like observations of remarkable upper tropospheric warmth in Antarctica, as well as stratospheric cooling. They conclude that while this is the pattern expected from GHG warming (no reference annoyingly as I'm really interested in the expected patterns and why), they cannot attribute it directly as the models show too much variability in expected pattern over Antarctica. I wonder, does ozone depletion factor into this (am not sure off the top of my head)?

sss

Edited February 19, 2010 by sunny starry skies

[VillagePlank]

Are you thinking of this one?:

Turner et al, 2006: Significant warming of the Antarctic winter troposphere. Science 311, 1914-1917

http://www.sciencema...t/311/5769/1914 [abstract]

http://www.sciencema...l/311/5769/1914 [full text, may not be accessible]

Looks like observations of remarkable upper tropospheric warmth in Antarctica, as well as stratospheric cooling. They conclude that while this is the pattern expected from GHG warming (no reference annoyingly as I'm really interested in the expected patterns and why), they cannot attribute it directly as the models show too much variability in expected pattern over Antarctica. I wonder, does ozone depletion factor into this (am not sure off the top of my head)?

sss

Surely it's a consequence of Arrhenius, and therefore a physical manifestation of albedo? (Thanks for the paper, I'll get it when I have a mo')

[Iceberg]

The missing data is a point to note about the paper, itself - I just typed it into Excel.

Arrhenius₁ made some observations himself that seem, on the face of it, reasonable - but, for me, not necessarily obvious.

Firstly, the nebulosity (I had to look it up - it means cloudiness) of the southern hemisphere, presumably on account of the southern oceans, means the effect will be less than the Northern hemisphere (important implications in measuring global temperature: should we, or do we, account for this?)

Secondly, an increase in C0₂ will reduce diurnal range of temperatures. He fleets over this, and I don't understand why, and I can't find any source that explains it, either.

Thirdly, that the difference between the equator and the poles are different because "those places ... alter their albedo by the extension or regression of the snow-covering" So temperature increases at the poles are larger with the same C0₂ differential₂.

Add that lot together, and, it seems to me, at least one of the constants, probably alpha, needs to be some function of albedo. Not a great surprise, but I didn't expect to see it.

(Sorry if this is excess to requirements - this is the sort of thing that, ahem, gets me going, one might say. The hunt for the alpha function is on!)

1: On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, Svante Arrhenius, Philosophical Magazine and Journal of Science, Series 5, Volume 41, April 1896, pages 237-276. page 265

2: As above, page 257

Going back to this post (sorry a bit of jumping around), as I rarely get time to look in on this thread.

I think it's important to note that Svante Arrhenius's work is old and predates alot of what is known nowadays about global temperature re-distribution, so although I have a lot of respect for him we have moved on lot, with atmospheric cell placement (i.e hemisphere triple cell, Jet Stream, Ocean conveyors etc).

albedo was pretty much the only mechanism known back then, not so now.

WRT to climate sensitivity (Lambda?), we are not talking about a simple formula IMO, which is why climate modelling is so important everything from the percentage of GHG to the age of the GHG (atmospheric lifetimes reduce GHG effectiveness on a range of scales depending on the molecule.), through to the height of the GHG in the atmosphere through to distribution within the atmosphere, CFC's are a good example here.

you can then role in various factors such as albedo, WV etc.

[Admiral_Bobski]

I think it's important to note that Svante Arrhenius's work is old and predates alot of what is known nowadays about global temperature re-distribution, so although I have a lot of respect for him we have moved on lot, with atmospheric cell placement (i.e hemisphere triple cell, Jet Stream, Ocean conveyors etc).

Hectic, hectic, hectic at the moment, hence my absence, but time for a quick post!

Arrenhius's work is old, granted, but the whole of AGW science stems from his original paper - to the extent that his Greenhouse Gas law is still used to this day (this one: ΔF = α ln(C/C₀) ).

The validity, or otherwise, of Arrenhius's paper is one of the fundamental building blocks of the theory of AGW. Although we have come a long way since that paper was written it is still a crucial part of AGW theory. If it is wrong in any way then there may be knock-on effects further down the line.

:huh:

CB

[VillagePlank]

The validity, or otherwise, of Arrenhius's paper is one of the fundamental building blocks of the theory of AGW. Although we have come a long way since that paper was written it is still a crucial part of AGW theory. If it is wrong in any way then there may be knock-on effects further down the line.

Hi CB, good to see you back.

Indeed, such that this paper is relevant is that the IPCC say that the relationship is logarithmic. Indeed, it is, but why? I can find no 'audit' trail back of it's heritage - and, therefore, I am working on the notion that is so obvious that an idiot like me must have missed it.

I am doing the background reading at the moment; and some of it seems extremely tricky. As far as I can ascertain the family heritage is something like this:

Maxwell's equations (without the Lorentz abstraction) ->

Beer's law (made me laugh, too) ->

The Arrhenius approximation.

More later next week (am stuck on vector field divergence, and curling at the moment)

albedo was pretty much the only mechanism known back then, not so now.

That may well be so, but the Arrhenius approximation still describes what we are observing to some magnitude or another. If you know of an analysis of a paper that describes Arrhenius' flaws, I am pretty sure that everyone who takes the time to read this thread would be delighted if you'd share the link.

After, we don't ditch Pythagoras simply because it's old - or do we?

Edited February 19, 2010 by VillagePlank

[Admiral_Bobski]

Hi CB, good to see you back.

Indeed, such that this paper is relevant is that the IPCC say that the relationship is logarithmic. Indeed, it is, but why? I can find no 'audit' trail back of it's heritage - and, therefore, I am working on the notion that is so obvious that an idiot like me must have missed it.

I am doing the background reading at the moment; and some of it seems extremely tricky. As far as I can ascertain the family heritage is something like this:

Maxwell's equations (without the Lorentz abstraction) ->

Beer's law (made me laugh, too) ->

The Arrhenius approximation.

More later next week (am stuck on vector field divergence, and curling at the moment)

That may well be so, but the Arrhenius approximation still describes what we are observing to some magnitude or another. If you know of an analysis of a paper that describes Arrhenius' flaws, I am pretty sure that everyone who takes the time to read this thread would be delighted if you'd share the link.

After, we don't ditch Pythagoras simply because it's old - or do we?

Hi VP - nice to be back - my head's a bit crowded at the moment so I've not been able to really focus on in-depth technical discussions, but it's starting to clear slightly...!

With regards to Arrhenius's flaws, I've dug up this old PDF which refers to Angstrom's rebuttal of the original Arrhenius paper:

http://docs.lib.noaa.gov/rescue/mwr/029/mwr-029-06-0268a.pdf

In particular is this comment: "The remainder of Angstrom’s paper is devoted to a destructive criticism of the theories put forth by the Swedish chemist, S. Arrhenius, in which the total absorption of CO[2], ie quite inadmissibly inferred from data which include the combined absorption of CO[2], and the vapor of water."

Subsequent to this, Arrhenius's supporters discredited Angstrom's rebuttal (though whether this was valid or not I don't know) by claiming that his experiments were not a legitimate approximation of the actual atmosphere, and that there were errors in the taken measurements.

I'm not sure how those objections invalidate Angstrom's assertion that Arrhenius had not appropriately distinguished between CO2 effects and water vapour effects, so I shall have to do more reading up on the subject - perhaps if I could find Angstrom's actual paper it might help!

CB

[Admiral_Bobski]

Realclimate give their view on the debate here:

http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/

I've got to go and check on something before I say more...