The LI Revisited (Climate Modelling Using a leaky integrator)

[VillagePlank]

With the ocean heat content still rapidly rising, how does that fit in the the LI concept?

Sorry I missed this bit.

The LI concept is remarkably simple. The essential idea is that the warmer it gets the harder it is to warm, and cooler it gets the harder it is to cool. From Newton's Law of Cooling, this seems factual, and this is supported by anecdotal evidence from Petite et al whose ice-core studies demonstrated a 'maximum' and a 'minimum' for the temperature of the Earth, historically; in this respect there is evidence, and physical law to back the idea up. It is a convenient by-product of my interest in neural networks, my interest in climate and weather, and Bobski's constant bothering questions that led us down a road to trying to get a theory together. Actually, theory is too strong, a hypothesis, or even lemma, is a much more accurate description.

Also, I dealt with only surface temperatures as demonstrated by HadCru (v3 I think) That ocean content might be 3km down dramatically warming at this stage in the analysis is irrelevant. I understand that the top 2m of the oceans are warming, and this contributes to the warming of the the surface temperature measurement, but is only considered in the grand scheme of things.

The grand scheme of things: without a shadow of doubt, the current state of the climate is reflected in the temperature readings. If the ocean is warming the surface it is going to show up on some thermometer somewhere, for instance. The leaky integrator, in my view (I know that's a weak turn of phrase), models the entirety, not the detail.

Hope this helps, even if only a little.

Edited January 9, 2013 by Boar Wrinklestorm

[Gray-Wolf]

Hi B.W.!

I don't think we can ignore the deep ocean warming as we are now entering a time where some of the early warming, subducted into the deep oceans, is now starting to return to the surface. This means that all the waters to come will be progressively milded out,

We know that the atmosphere is being primed to hold onto more heat than it used to but I'm concerned about changes to the way energy is used around the planet under warming. It is easy enough to look at the Arctic Basin ans see a place where once energy was spent melting ice all summer now experiencing a period where those energy drains no longer span all of summer (freeing up energy to be utilised in other areas), or the fringes of Greenland where energy used to be utilised in melting all summer long but now is freed up for other tasks from May through Sept, but what of the energy of the oceans that used to be spent equalising the temp of cold bottom waters as they re-surfaced once those waters are no longer as cold (demanding less energy to bring them up to surface temps?)

To me it appears that warming is 'feeding back' on itself by allowing large increases in 'free energy' where once the balance was maintained by 'cold' needing to be warmed?

Add into that any energy 'lost' due to dimming (NASA puts the figure as high as 50%!) as Asia cleans up it's act we can see that warming is not just about GHG's and their increasing concentrations in the atmosphere but the redistribution of energies, once in balance, now warming is altering the planet?

As I recall LI had a near constant input but the 'tap' filling the bucket is now running at an ever increasing rate whilst the hole in the base is narrowing due to CO2 sink failures/ice loss/Albedo flip.

The period of climate inertia (where Mother N had checks an balances to hold back change) is ending.If this 'inertia' was an elastic band then it has reached it's limit and will now spring back to it's new state (further increasing the rate of change)

[Admiral_Bobski]

As I recall LI had a near constant input but the 'tap' filling the bucket is now running at an ever increasing rate whilst the hole in the base is narrowing due to CO2 sink failures/ice loss/Albedo flip.

As a point of order, the "tap" filling the bucket was the Sun, which is not a near-constant input - it varies over the sunspot cycle, and sunspot cycles vary from cycle to cycle. The whole point of the LI was that we had a large peak in sunspot activity around the middle of last century, and we considered what might happen if this increased solar activity was equivalent to a sudden increase in the "tap's" input. Since the 1950s we have had sustained high sunspot cycles, right up until this current one, which is more in keeping with cycles prior to the 1950s.

Also, the LI made no mention of CO2. CO2 was not considered to be a cause of a "narrowing hole" - my initial desire was to see what would happen if we didn't take CO2 into account...and we got a pretty nice comparison between the LI and real world temperatures. The assumption was that maybe CO2's effects are not as large as has been presumed, due, perhaps, to some balancing or mitigating natural effect.

As a final point, I would like to just reiterate that the LI predicted temperatures to remain pretty much level over the next several years (barring natural year-to-year variations) before starting to drop off, if solar activity does not pick back up! So, as is now something akin to my catchphrase, I guess we'll just have to wait and see.

[Gray-Wolf]

But surely this is the 'thing'? Over the coming years the amount of 'shielding' from the sun, that particulate pollution has brought to TSI and pan evap rates, will fall away as Newly developing nations clean up their acts (as we did from 50yrs ago). NASA again posted an article stating quite clearly that you could not blame the sun for the warming as it only varies 0.1% in output over the solar cycle?

The data would have us believe that many areas of the planet have a net reduction of over 5% incoming energy due to the 'Dimming' impacts so if we clean up only 50% of that mess we end up with an increase of solar of 2.5% or 25 times the influence that the solar cycle brings to the planet? Even if we look to other soar outputs which may have a ten fold greater variability than the energy we measure over the solar cycle that is still less than half of what cleaning 50% of current particulate pollution brings to the planet?

I have never argued that solar variability does not have impact upon the climate system it just appears that the variations in output appear dwarfed by what man has introduced into the system?

And , in the background, climate inertia is increasingly overcome as the 'extra energy' ice loss/early snow loss/albedo flip/ocean warming brings us speeds the process ever faster (we used to use the oil tanker as an analogy of climate inertia......I believe we are now in motion so the energy used up driving the initial change is now available on movement alone and not 'hidden' overcoming the inertia?).

The planet is now losing the heat sink that helped keep temps down whilst man steadily increases the atmosphere ability to hold onto heat. Mother N. is now also joining in this atmospheric outing by re-introducing part of the carbon cycle long dormant (now that inertia has been overcome) so even if we cease our production of GHG's we still stand to inherit a fair chunk more over the years.

Oil Tanker or collapsing Dam...things occur very slowly, almost imperceivably, to begin with but once ongoing changes rapidly appear.

[VillagePlank]

But surely this is the 'thing'? Over the coming years the amount of 'shielding' from the sun, that particulate pollution has brought to TSI and pan evap rates, will fall away as Newly developing nations clean up their acts (as we did from 50yrs ago). NASA again posted an article stating quite clearly that you could not blame the sun for the warming as it only varies 0.1% in output over the solar cycle?

The LI used sunspot data as a proxy to a hitherto unknown mechanism; it didn't use TSI; indeed, what mainstream says about TSI is as far as I am concerned completely correct (I reviewed the literature, and I agree with it) However, beneath all of the guff and bravado is the implicit assumption that TSI is the only possible way the sun can influence the earth's climate. I don't agree with that.

[jonboy]

The LI used sunspot data as a proxy to a hitherto unknown mechanism; it didn't use TSI; indeed, what mainstream says about TSI is as far as I am concerned completely correct (I reviewed the literature, and I agree with it) However, beneath all of the guff and bravado is the implicit assumption that TSI is the only possible way the sun can influence the earth's climate. I don't agree with that.

Hi BW this was on Space Weather this morning. Clearly others agree with you.

SOLAR VARIABILITY AND TERRESTRIAL CLIMATE: A new report issued by the National Research Council, "The Effects of Solar Variability on Earth's Climate," lays out some of the surprisingly complex ways that solar activity can make itself felt on our planet. Get the full story from Science@NASA.

[VillagePlank]

Yep

In a concluding panel discussion, the researchers identified a number of possible next steps. Foremost among them was the deployment of a radiometric imager. Devices currently used to measure total solar irradiance (TSI) reduce the entire sun to a single number: the total luminosity summed over all latitudes, longitudes, and wavelengths. This integrated value becomes a solitary point in a time series tracking the sun’s output.

In fact, as Peter Foukal of Heliophysics, Inc., pointed out, the situation is more complex. The sun is not a featureless ball of uniform luminosity. Instead, the solar disk is dotted by the dark cores of sunspots and splashed with bright magnetic froth known as faculae. Radiometric imaging would, essentially, map the surface of the sun and reveal the contributions of each to the sun’s luminosity. Of particular interest are the faculae. While dark sunspots tend to vanish during solar minima, the bright faculae do not. This may be why paleoclimate records of sun-sensitive isotopes C-14 and Be-10 show a faint 11-year cycle at work even during the Maunder Minimum. A radiometric imager, deployed on some future space observatory, would allow researchers to develop the understanding they need to project the sun-climate link into a future of prolonged spotlessness.

[Gray-Wolf]

As I mentioned I do not have issues with other solar processes, more impacting than TSI and it's cyclical variation, just the scale of those impacts compared to the human induced ones? As mentioned in my last post any lessening of the current load of 'dimming' pollutants would appear to offer far greater forcing than anything we know of from the sun (as seen in physical and proxy records)?

Even without humankind cleaning up it's pollutants from the combustion of fossil fuels we are now seeing important 'state changes' impacting the way the planet consumes it's energy and the heat budget of the planet.

When you look at the period of time that the Arctic region is now accepting over 80% of incoming solar, instead of reflecting back into space 90%, you can see a net 'gain' from outside the system. when you factor in the energy, already in the system, that was formally spent melting ice into water over summer you start to see how important this shift is. When you then take on board the findings on first year ice's abilities to transmit energy into the ocean below (over 3 times that of older ice) and the continued thinning of the winter pack allowing more energy into that ocean from 'sun up' (and not just once the ice has formed melt pools) makes me wonder what scale of reduction in the energy budget we would need to offset that alone?

Though only a few years ago that we debated the LI some of the concerns I voiced back then are beginning to now add into the system and other impacts appear to now be queued up in the wings (portions of our dormant carbon cycle re-animating and soil drying/rain forest drought/peat wetland destruction ect.).

I continue to support your efforts in highlighting the importance of the LI theory but feel that the impacts of AGW were not accurately portrayed (due to lack of data?) and that now that we are overcoming the long period of climate inertia positive feedbacks will exaggerate the rate of change allowing temps to attain the level current GHG levels dictate?

[Admiral_Bobski]

Actually, the "impacts of AGW" were not portrayed at all - that was kind of the point of the whole exercise - and not for lack of data but rather as an exploration of the possibilities of there being no significant AGW effect.

I am very wary of this whole "positive feedbacks" issue, which is kind of why I keep on saying "Time Will Tell", but I would like to call you out on your use of the word "dictate" and offer the use, instead, of the word "suggest".

[VillagePlank]

I have never argued that solar variability does not have impact upon the climate system it just appears that the variations in output appear dwarfed by what man has introduced into the system?

As a point model - I assume you realise what that is - one can model a series of feedforward and feedback mechanisms and whole host of complex science, or one can accept that hysteresis (hysteresis may well be caused by a complex series of feed back and forward mechanisms!) has it's place (and thus amplification of the primary culprit is simply a mathematical artefact), and it's all rather simple. William of Occam had a point. However, it could be the case that the reason why the LI works is even more complex. Capn did some good work with the quantum mechanics side of things, for instance ....

I should add that in no way do I, and I think Cap'n as well, dismiss the GH effect of GhG, only their magnitude. There is no need to rewrite ANY science to accept the LI postulate, simply alter it's conclusions. That it might have socio-political ramifications, to me, is neither here nor there.

Edited January 11, 2013 by Boar Wrinklestorm

[BornFromTheVoid]

I used a gradient descent algorithm to derive the weightings, and treated the parameters as a system of equations on the basis that climate is deterministic, and will shown as such if we ever slay Laplace's demon, it is the emergent behaviour of climate that is chaotic. I never published the math, well, frankly, because it would have put a lot of people of seeing all these alien sort of symbols flying around everywhere. I also used custom software which wot I wrote to do the job. I alluded to the techniques throughout, however, but only one person ever asked, but he seemed like a PhD student, so I told him/her, to, ahem, sod off...

...And, you'll note, most people who read this post, have now gone to sleep. You'll also note that some things were purposefully held back since I was eventually hoping to publish.

I think it may take me quite a while to get my head around some of the maths involved!

Is there anyway you could explain the gradient descent method in layman's terms? I have a very slight idea of how it works within the LI, but not good enough to be able to really comment on it.

Sorry I missed this bit.

The LI concept is remarkably simple. The essential idea is that the warmer it gets the harder it is to warm, and cooler it gets the harder it is to cool. From Newton's Law of Cooling, this seems factual, and this is supported by anecdotal evidence from Petite et al whose ice-core studies demonstrated a 'maximum' and a 'minimum' for the temperature of the Earth, historically; in this respect there is evidence, and physical law to back the idea up. It is a convenient by-product of my interest in neural networks, my interest in climate and weather, and Bobski's constant bothering questions that led us down a road to trying to get a theory together. Actually, theory is too strong, a hypothesis, or even lemma, is a much more accurate description.

Also, I dealt with only surface temperatures as demonstrated by HadCru (v3 I think) That ocean content might be 3km down dramatically warming at this stage in the analysis is irrelevant. I understand that the top 2m of the oceans are warming, and this contributes to the warming of the the surface temperature measurement, but is only considered in the grand scheme of things.

The grand scheme of things: without a shadow of doubt, the current state of the climate is reflected in the temperature readings. If the ocean is warming the surface it is going to show up on some thermometer somewhere, for instance. The leaky integrator, in my view (I know that's a weak turn of phrase), models the entirety, not the detail.

Hope this helps, even if only a little.

The upper and lower temperature limit only applies to the geologically recent past though, doesn't it? The glacial/interglacial period. As GW has mentioned a number of times here, at the moment (to a clearly arguable extent) we are raising the Earth's temperature by releasing CO2 that was mostly buried deep within the planet. As the Earth's biosphere begins to adjust it's carbon cycle to the new warmer temperatures (permafrost melt, clathrates, ocean CO2 release, etc.) more "natural" carbon will be added to the system as well as our own likely continued contributions. I think this would be enough to over-ride the cycle of glacial/interglacial we've been in over the last million years or so.

From looking through the old LI threads, the prediction showed a drop to near average global temperatures by 2014, but with the assumption that sea ice levels would remain relatively static, and that sunspot counts would be higher than reality. It seems that going by the latest MO output, that temps are likely to rise to new record highs though?

Also, while you hindcasted the LIA, it hasn't been shown to be a strong global phenomena, but mainly a north Atlantic one? Are there not any global temperature data sets extending back into the 1700s with which to correlate? The dip in the hindcast around the late 1830s though seems to tie in with some very cool year for the northern hemisphere though!

[VillagePlank]

I think it may take me quite a while to get my head around some of the maths involved!

Is there anyway you could explain the gradient descent method in layman's terms? I have a very slight idea of how it works within the LI, but not good enough to be able to really comment on it.

I don't know how much maths you know .... I will give it a go.

On a time series graph you have the dependent variable, time, and you have some independent quantity such as temperature. By convention, we could call time, x, and the temperature y; in calculus we can convey the information that y depends on x, or, that y is a function of x, by writing y=f(x). Now, we can represent anything we damn well like with a line, including say how far out we are - ie the error. The greater the y the greater the error. By simple deduction, then, and by basic algebra and calculus, the idea is that we can move down the slope on the line, just a bit, and try again. We can iterate though this process until the y=f(x) goes back up, and then we have the local minima to the function - or the local point at which the error is at it's least. The hard bit is determining if that local minima is representative fo the global function. It is reasonably trivial (you need to know matrix and vector linear mathematics to get high order polynomials) to use least squares to get a polynomial of the form y=f(x) for any time series graph. The minimum values for y are the weightings. Widrow and Stearns (1985) proved that if the descent rate is sufficiently small then this leads to a convergent solution although I, perhaps significantly, adapted their delta rule.

From looking through the old LI threads, the prediction showed a drop to near average global temperatures by 2014, but with the assumption that sea ice levels would remain relatively static, and that sunspot counts would be higher than reality. It seems that going by the latest MO output, that temps are likely to rise to new record highs though?

Yes, that's true. The arctic ice was considered constant (it hasn't been) and the median of volcanic eruptions was taken forward (it's has a far less cooling effect) and so on and so forth. If I had the code - and I've checked, now, and I haven't - I would rerun it, and my supposition is that it would be a pretty good match. What I mean by that is using real sea-ice, sunspot, volcanic, and enso values would result in a fairly good match without any changing the model (ie if we can predict sea-ice, sunspot, volcanic and enso values, the LI might act as a good predictor of the climate)

Also, while you hindcasted the LIA, it hasn't been shown to be a strong global phenomena, but mainly a north Atlantic one? Are there not any global temperature data sets extending back into the 1700s with which to correlate? The dip in the hindcast around the late 1830s though seems to tie in with some very cool year for the northern hemisphere though!

Yes, I agree. And, of course, most of the land mass on the planet is in the Northern Hemisphere, thus most of the temperature archives/proxy, and the match is to the HadCru NH set - I wanted to avoid the ocean/atmosphere boundary conditions, and since the largest part of the warming seems to be happening in the NH, it seemed to me a good place to start.

Please remember, I was a rank amateur (and probably still am) at the start of all this, and it's been years since I looked at any of this. All of this is from memory so errors and ommisions omitted!!!!!

Edited January 11, 2013 by Boar Wrinklestorm

[Admiral_Bobski]

The upper and lower temperature limit only applies to the geologically recent past though, doesn't it?

Depends on what you mean by "Geologically Recent"!

Is 600 million years long enough?

Edited January 12, 2013 by pottyprof

[BornFromTheVoid]

I think myself and BW were more discussing the cyclic nature seen in the Vostok ice core record.

I suppose we could go back even further still and discuss the faint young sun paradox!?

Edited January 12, 2013 by pottyprof

[Admiral_Bobski]

Perhaps he could clarify - we had discussed, way back in the early days of the LI, how the Earth has varied between a minimum of about 10C and a maximum of about 25C over the past 600 million years. Obviously the Vostok core doesn't even cover one half of one million years, so those extremes are only variations around the "current" average temperature of about 12C. Although those variations are obviously of interest, of more interest still (to me, at least) is that there seems to have been, for over half a billion years, some kind of cap on Earth's possible temperature extremes.

I suppose we could go back even further still and discuss the faint young sun paradox!?

A discussion of the faint young sun paradox would be interesting....it might be nice, one day, to find some proxies for the LI's various inputs going back many hundreds of millions of years and see what happens, but I don;t know if there's any way of extrapolating ENSO information back that far, or even reliable sunspot data for that matter. Please bear in mind that I haven't really thought much about the LI in about 3 years now and I'm a bit out of practice!

Edited January 12, 2013 by pottyprof

[songster]

it might be nice, one day, to find some proxies for the LI's various inputs going back many hundreds of millions of years and see what happens, but I don;t know if there's any way of extrapolating ENSO information back that far

How can you even think ENSO could have any relevance to palaeoclimate? Depending on the configurations of the continents, there wasn't even a SO, let alone an EN.

Edited January 12, 2013 by pottyprof

[VillagePlank]

How can you even think ENSO could have any relevance to palaeoclimate? Depending on the configurations of the continents, there wasn't even a SO, let alone an EN.

And you think that the continental positions are considered in paleoclimate? You've got about 1/2 million years of climate to deal with before we get into continental shift.

Edited January 12, 2013 by pottyprof

[Admiral_Bobski]

How can you even think ENSO could have any relevance to palaeoclimate? Depending on the configurations of the continents, there wasn't even a SO, let alone an EN.

Begging your pardon, sir, that I didn't say "Oceanic Overturning/Oscillating/Currents Etc.," for there must have been some movement of the planet's oceans even 600 million years ago (we still had a Moon back then). We used the facility that ENSO has of swallowing up and spitting out heat in cycles (El Nino, La Nina) as a moderating factor in our refinement of the LI output. Now, even if there was no El Nino or La Nina a hundred million years ago, due to the configuration of continents, this facility must have existed in some format or other because - and here's the shocker - the oceans move! (gasp!)

Edited January 12, 2013 by pottyprof

[Devonian]

My, sketchy, knowledge of things ocean circulation is that the world is very different when we have ocean right around the equator than it is now when various continents interrupt such motion.

Edited January 12, 2013 by pottyprof

[BornFromTheVoid]

I think the main issue with trying to extend any ENSO like feature back more than a few centuries, is that as an oscillation, overtime it's effect is equal to pretty much zero. It's only on shorter time scales that ENSO's impact on global temperatures can be seen.

Edited January 12, 2013 by pottyprof

[Admiral_Bobski]

I think the main issue with trying to extend any ENSO like feature back more than a few centuries, is that as an oscillation, overtime it's effect is equal to pretty much zero. It's only on shorter time scales that ENSO's impact on global temperatures can be seen.

While I agree that, in and of itself, an ocean oscillation has a presumed net effect of zero, the issue becomes more complicated when introducing the concept of lag.

If heat is stored during a period of higher solar activity, retained through a period of low solar activity, and then released during another period of high solar activity then it affects the outcome differently from the way it would if the heat was released during the earlier (or a later) period.

Where the heat actually is at any given moment in time potentially makes a difference.

Regardless of the particular arrangement of continents, the ocean must always have had some kind of rolling heat capacitance, due to its gravitationally-induced motion - the way this motion would affect retention and emission of heat may be different, further complicating matters, but there would have been an effect.

Perhaps of more importance on these timescales is the albedo effect - long periods occurred when there were no icecaps, while at other times there were periods of enormous ice extent. How much of an effect this may have had on LI-style heat retention and lag effects I am not sure, since I lack the data.

Edited January 12, 2013 by pottyprof

[BornFromTheVoid]

While I agree that, in and of itself, an ocean oscillation has a presumed net effect of zero, the issue becomes more complicated when introducing the concept of lag.

If heat is stored during a period of higher solar activity, retained through a period of low solar activity, and then released during another period of high solar activity then it affects the outcome differently from the way it would if the heat was released during the earlier (or a later) period.

Where the heat actually is at any given moment in time potentially makes a difference.

Regardless of the particular arrangement of continents, the ocean must always have had some kind of rolling heat capacitance, due to its gravitationally-induced motion - the way this motion would affect retention and emission of heat may be different, further complicating matters, but there would have been an effect.

Perhaps of more importance on these timescales is the albedo effect - long periods occurred when there were no icecaps, while at other times there were periods of enormous ice extent. How much of an effect this may have had on LI-style heat retention and lag effects I am not sure, since I lack the data.

Ah, but you can also have the same lag with cooling, which would eventually even things out.

Edited January 12, 2013 by pottyprof

[Admiral_Bobski]

Ah, but you can also have the same lag with cooling, which would eventually even things out.

Yes indeed, you can have the same lag with cooling, but it would not necessarily even things out, depending on the timing and duration of such events - such is the nature of the time lag. The lag issue complicates the issue beyond a simple net-effect cancellation.

Edited January 12, 2013 by Captain_Bobski

[VillagePlank]

Sorry for last night, guys

The most important part of the leaky integrator is that the rate of change is variable depending on what is in the system. Most of the literature does not refer to a leaky integrator, it refers to a leaky bucket, so I shall stick to the analogy. I am stuck with a brain trained in study in a completely different area which is why we call this the leaky integrator.

Lags and hysteresis are a consequence and are not causal.

Assume we have a bucket with some water in it. Now the bucket has a hole in it, so some of the water leaks out, and this is directly proportional to the height of the water because greater pressure means more water per time unit will esacpe. Also there is nozzle that keeps putting water into the bucket.

If the hole is blocked it's clear that the rate of change of the height of the water is directly proportional to the nozzle. If the nozzle is off, but the hole is unblocked then it is again obvious that the rate of change of the height is proportional to it's own height. (by analogy water pressure in the bucket)

The height of the water is the earth's energy, the hole is how much energy manages to escape the earth, and the nozzle is how much energy is coming in. The key concept then is that energy gets topped up in the normal way, but energy is lost proportionallly to how much energy is in the system. The lag in the system is because as the energy drops energy is lost more slowly (ie the rate of change of water in the bucket slows down) and thus still remains. If the energy comes in is constant then the result is gradually increasing energy. So, the lag, is therefore variable depending on the cumulation of states years and years before it, and so the system demonstrates hysteresis.

If this is a reasonable analogy of the earth's climate system as a whole, the current consensus says that the anthropogenic emissions are gradually closing the hole, all other things being equal.

I hope I've got that about right.

Edited January 12, 2013 by Boar Wrinklestorm

[Admiral_Bobski]

That sounds about right, BW (Have to resist the urge to call you VP!)

As a little tidbit of background info, in the LI, greenhouse gases are part of what determines the size of the hole. According to AGW theory, as GHG concentrations increase, the "hole" gets smaller, thereby decreasing the amount of heat that can escape into space.

What got us so excited about the LI (or got me excited, at least) was that we could get a seemingly good match with actual observed real-world temperature without changing the size of the hole!

If the LI were to verify as a legitimate model then it would suggest that changing GHG concentrations in the atmosphere has a negligible effect on temperatures (at least in the concentrations we are talking about).

Now, obviously we met a lot of resistance to this idea, on the basis that we all "know" that GHGs have an effect. But I have always argued that, although GHGs may have a straightforward effect per se, once those GHGs are in an ever-changing, dynamic system like the real world, replete with sinks, checks and balances, the situation becomes less clear-cut.

Discuss...

PS - Changed my name - thought I deserved a promotion!

Edited January 12, 2013 by Admiral_Bobski