Testing the Core of AGW Theory

[skierinvermont]

Global SSTs have flat lined or slightly fallen during the OHC flat line. Global temps have flat lined. Something doesn't add up. If the ocean is truly absorbing more heat, then sea level rise wouldn't be slowing either.

Your argument would make sense if we actually saw warming SSTs and sea level rise accelerating during the period where OHC/global temps have been flat lining.

As I said before, sea level rise is occurring much faster than the 50-yr average. The 50 year average is 1.8mm/yr. Since 1998 we have seen 2.9mm/yr and since 2002 we have seen 2.3mm/yr. In addition, the Schuckman 0-2000m ARGO analysis supports continued rapid OHC increase.

You seem to think 2.3-2.8mm/yr is slow, even though this is much faster than most of the last 30-50 years. The only period it is slower than is 1992-1998 when we were rebounding from Pinatubo. My guess is you are looking at the satellite record and noticing the slow-down and forgetting that SLR was much slower prior to 1992. Looking at sea level rise alone, one would conclude that OHC has been rising at an alarming rate the last 9-13 years.. over 50% faster than it was 1960-1990.

Now some of this sea level rise is likely due to mass not steric sea level rise.. so that does need to be accounted for.

[ORH_wxman]

It shouldn't be decelerating if OHC is actually increasing as you say it is via a 2008 study using 0-2000m (where about half of the rise was from 2003 to 2004). So either the OHC data is wrong, the sea level data is wrong, the global temperature data is wrong, or the world simply hasn't been gaining much heat the last 8 years.

[skierinvermont]

It shouldn't be decelerating if OHC is actually increasing as you say it is via a 2008 study using 0-2000m (where about half of the rise was from 2003 to 2004). So either the OHC data is wrong, the sea level data is wrong, the global temperature data is wrong, or the world simply hasn't been gaining much heat the last 8 years.

SLR is only decelerating relative to the rapid 1992-1998 recovery from Pinatubo. Relative to the 50 and 100 year average, SLR is still much faster than it was.

We don't have 0-2000m ARGO data prior to 2002 so we don't know by looking at that source whether it has accelerated or decelerated. We can convert SLR into Joules however and compare them directly. We just need an accurate accounting of ocean mass balance.

I don't see the problem... there are two ways of measuring OHC... SLR and buoy. Both rose rapidly 1992-1998 in the recovery from Pinatubo... then both slowed down but still faster than their pre-1992 rate.

[LakeEffectKing]

It shouldn't be decelerating if OHC is actually increasing as you say it is via a 2008 study using 0-2000m (where about half of the rise was from 2003 to 2004). So either the OHC data is wrong, the sea level data is wrong, the global temperature data is wrong, or the world simply hasn't been gaining much heat the last 8 years.

Very much agree Will.

Ultimately, (and I've stated before) I believe it WILL be shown that it is the oceans and the incredible volume and heat storage capability that dampens significantly the proposed atmospheric warming....the physics for the atmosphere seem reasonably well established....the interaction with the HUGE storage capacity (buffer) in the oceans is far less understood/"settled"....

Many temperature reconstructions very much correlate better with oceanic "patterns" than CO2. Our planet owes its remarkably stable temperature regime over the millenia, due to our oceans.....

[ORH_wxman]

SLR is only decelerating relative to the rapid 1992-1998 recovery from Pinatubo. Relative to the 50 and 100 year average, SLR is still much faster than it was.

We don't have 0-2000m ARGO data prior to 2002 so we don't know by looking at that source whether it has accelerated or decelerated. We can convert SLR into Joules however and compare them directly. We just need an accurate accounting of ocean mass balance.

SLR has decelerated during the period in question.

Global temps not rising should mean that OHC is actually accelerating which would mean SLR should be accelerating too. The accumulated heat should be going somewhere. It should be pretty easy to measure because this is not a minute thing.

[skierinvermont]

SLR has decelerated during the period in question.

Global temps not rising should mean that OHC is actually accelerating which would mean SLR should be accelerating too. The accumulated heat should be going somewhere. It should be pretty easy to measure because this is not a minute thing.

First of all, global temps are rising, albeit at a reduced rate of around .1C/decade.

here's the scenario... We were plugging along at a moderate pace of OHC and temperature increase prior to 1991. Then we get a temperature decrease and OHC stall 1991-1992. Temperature and OHC rise rapidly 1992-1998 on the rebound. Once the rebound is over, they continue rising.. OHC at a faster pace than pre-1991. It makes perfect sense. I see no problem.

OHC has only decelerated relative to 1992-1998. Relative to pre 1992 it has accelerated.

[ORH_wxman]

First of all, global temps are rising, albeit at a reduced rate of around .1C/decade.

here's the scenario... We were plugging along at a moderate pace of OHC and temperature increase prior to 1991. Then we get a temperature decrease and OHC stall 1991-1992. Temperature and OHC rise rapidly 1992-1998 on the rebound. Once the rebound is over, they continue rising.. OHC at a faster pace than pre-1991. It makes perfect sense. I see no problem.

OHC has only decelerated relative to 1992-1998. Relative to pre 1992 it has accelerated.

You keep insisting on comparing stuff to the 1990s...it doesn't matter what we did in the 1990s when we are talking about rates decelerating in the wrong direction since 2003-2004.

If global temps decelerate, then OHC should accelerate. It is not happening unless the data is all wrong. Both have decelerated. Where is the accumulated heat going?

[skierinvermont]

You keep insisting on comparing stuff to the 1990s...it doesn't matter what we did in the 1990s when we are talking about rates decelerating in the wrong direction since 2003-2004.

If global temps decelerate, then OHC should accelerate. It is not happening unless the data is all wrong. Both have decelerated. Where is the accumulated heat going?

OHC hasn't decelerated since 2003. It has continued at a fairly linear rate. A rate slower than we saw 1992-1998 in the rebound from Pinatubo, but a rate faster than pre 1991. Indicating that AGW has generally accelerated over the last 50 years.

[ORH_wxman]

OHC hasn't decelerated since 2003. It has continued at a fairly linear rate. A rate slower than we saw 1992-1998 in the rebound from Pinatubo, but a rate faster than pre 1991. Indicating that AGW has generally accelerated over the last 50 years.

Yes it has.

Even the 2000m chart showed that a huge portion of the jump was from 2003 to 2004 and nearly flat lined the last couple years on it going through 2008. Its a poor data set anyway of only 5 years, but the 0-700m has most definitely slowed since 2003. It has hardly gone up at all.

[skierinvermont]

Yes it has.

Even the 2000m chart showed that a huge portion of the jump was from 2003 to 2004 and nearly flat lined the last couple years on it going through 2008. Its a poor data set anyway of only 5 years, but the 0-700m has most definitely slowed since 2003. It has hardly gone up at all.

There's barely enough precision to give an estimate of the absolute trend 2003-2008.. never mind enough information to say whether 2003-2005 was faster or slower than 2006-2008. Knowing something like that requires even more precision than knowing the 2003-2008 period as a whole.

Plus your description of Schuckman is just wrong. The large majority of the rise occurs post 2004. The trends 2003-2005 are nearly the same as 2006-2008.

Looking at this graph we see:

2003-2008: .77 +/- .11 W/m2 (near the expected value)

2003-2005: .7 +/- .3 W/m2

2006-2008: .85 +/- .3Wm2

[WeatherRusty]

Let's not forget about the reduced total forcing resulting from the prolonged solar minimum through the latter half of the 2000's, enough to offset about 7 years of greenhouse warming. Also, growing aerosol pollution from the developing world, particularly China and India.

I just read an article presenting a study which finds the Indian monsoon has been reduced in total rainfall over the past decade by 10% due to increasing aerosol pollution and a consequential slackening of the north to south temperature gradient. Those aerosols strongly affect weather patterns and radiative forcing.

[skierinvermont]

Notice how the argument over the years has gone

it's not warming fast enough since 1998 2002 2005

[ORH_wxman]

There's barely enough precision to give an estimate of the absolute trend 2003-2008.. never mind enough information to say whether 2003-2005 was faster or slower than 2006-2008. Knowing something like that requires even more precision than knowing the 2003-2008 period as a whole.

Plus your description of Schuckman is just wrong. The large majority of the rise occurs post 2004. The trends 2003-2005 are nearly the same as 2006-2008.

Looking at this graph we see:

2003-2008: .77 +/- .11 W/m2 (near the expected value)

2003-2005: .7 +/- .3 W/m2

2006-2008: .85 +/- .3Wm2

You are putting a lot of faith in this data set which doesn't match SLR either. 2007-2008 is basically a flat line in that graph which is the final two years.

This supposed warming should be showing up beyond that period in the 0-700m data and it is not. SLR shouldn't be decelerating. You are going into semantics again which still circumnavigates the overall question of where this heat should be going. We shouldn't have to nitpick data sets to find it. A global temp rise deceleration should be quite clear in the OHC/SLR data but it most certainly is not if we are truly storing all that heat.

[WeatherRusty]

You are putting a lot of faith in this data set which doesn't match SLR either. 2007-2008 is basically a flat line in that graph which is the final two years.

This supposed warming should be showing up beyond that period in the 0-700m data and it is not. SLR shouldn't be decelerating. You are going into semantics again which still circumnavigates the overall question of where this heat should be going. We shouldn't have to nitpick data sets to find it. A global temp rise deceleration should be quite clear in the OHC/SLR data but it most certainly is not if we are truly storing all that heat.

We recently made note of a study which explained recent SLR trends as a result of excessive continental precipitation the past several years. This is just one more reason why it is folly to focus on every short term rise or dip in some parameter as if these represent anything pertaining to a longer term trend.

[ORH_wxman]

We recently made note of a study which explained recent SLR trends as a result of excessive continental precipitation the past several years. This is just one more reason why it is folly to focus on every short term rise or dip in some parameter as if these represent anything pertaining to a longer term trend.

I agree its dangerous to say anything about short term trends which is why the recent flat lining of these things are only preliminary questions...not making absolute statements about how our climate is changing. But its certainly note-worthy when we see this happening on a scale that may reach a decade soon...perhaps it's just a blip. But the longer it goes, the more questions will be asked.

[skierinvermont]

You are putting a lot of faith in this data set which doesn't match SLR either. 2007-2008 is basically a flat line in that graph which is the final two years.

This supposed warming should be showing up beyond that period in the 0-700m data and it is not. SLR shouldn't be decelerating. You are going into semantics again which still circumnavigates the overall question of where this heat should be going. We shouldn't have to nitpick data sets to find it. A global temp rise deceleration should be quite clear in the OHC/SLR data but it most certainly is not if we are truly storing all that heat.

I'm not putting faith in the data at all.. I'm the one saying the precision is barely adequate for 2003-2008 as a whole,, and certainly not enough to make statements about even shorter periods such as 2007-2008 or 03-05 vs 06-08.

Also a slowdown in surface warming would not show up in OHC immediately. Over time if the surface failed to warm while net radiative forcing continued to increase, then OHC would have to rise faster and faster. But that could take 20 years of zero surface warming combined with continued net radiative forcing increases to have a big impact. All we have experienced is 10 years of slightly slower than expected warming.

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Here is the math:

net radiative forcing has increased by about .4W/m2 since 2000 ignoring the solar minimum.

Including the solar minimum we're talking about .25W/m2 of net radiative forcing since 2000.

Given surface temperatures have continued to increase (helping to balance off the net radiative forcing), the rate of OHC uptake would be expected to increase only about .1W/m2, perhaps less. Perhaps Rusty can tell us exactly how much .1C of surface warming increases OLR.

Let's say the oceans were supposed to be gaining heat at .7W/m2 if the surface continued warming. Instead, we would now expect the oceans to gain heat at a new rate of .8W/m2 instead of .7W/m2. Thus 10 years of slowly rising temperatures would only have a small effect on ocean heat uptake. An increase from .7 to .8W/m2.

Compare this to if we had 20 years of ZERO surface warming with constant solar input:

-net radiative forcing would increase .8W/m2

- there would be zero surface warming to counterbalance this

- the rate of ocean heat uptake would increase from .7W/m2 to 1.5W/m2. In other words, OHC would rise over 2X as fast.

Thus we see the effect on OHC of 20 years of zero warming with constant solar input is 800% greater than 10 years of slow warming with declining solar input.

If we had 50 years of no surface warming in which net radiative forcing increased 2W/m2.. we would now expect the oceans to warm at 2.7W/m2 instead of .7W/m2. The oceans would soon boil. You get the idea. This goes back to my original point regarding storage of heat in the deep ocean. It quickly becomes an ineffective way to keep the earth cool. It can work for a short period but eventually the surface MUST warm or else the rate of heat gain accelerates.

[skierinvermont]

How's my math Rusty?

Can you tell us how much .1C of surface warming since 2000 would increase the radiation emitted by earth?

[WeatherRusty]

How's my math Rusty?

Looks good in the hypothetical situation where the oceans did not pass any energy onto the atmosphere. I take it you have based your forcing figures on a 4W increase over 100 yrs?

The Planck Response (black body) is 0.3C/watt

So 0.1C would increase surface radiation by about 0.33W.

[ORH_wxman]

I'm not putting faith in the data at all.. I'm the one saying the precision is barely adequate for 2003-2008 as a whole,, and certainly not enough to make statements about even shorter periods such as 2007-2008 or 03-05 vs 06-08.

Also a slowdown in surface warming would not show up in OHC immediately. Over time if the surface failed to warm while net radiative forcing continued to increase, then OHC would have to rise faster and faster. But that could take 20 years of zero surface warming combined with continued net radiative forcing increases to have a big impact. All we have experienced is 10 years of slightly slower than expected warming.

...

.

.

Here is the math:

net radiative forcing has increased by about .4W/m2 since 2000 ignoring the solar minimum.

Including the solar minimum we're talking about .25W/m2 of net radiative forcing since 2000.

Given surface temperatures have continued to increase (helping to balance off the net radiative forcing), the rate of OHC uptake would be expected to increase only about .1W/m2, perhaps less. Perhaps Rusty can tell us exactly how much .1C of surface warming increases OLR.

Let's say the oceans were supposed to be gaining heat at .7W/m2 if the surface continued warming. Instead, we would now expect the oceans to gain heat at a new rate of .8W/m2 instead of .7W/m2. Thus 10 years of slowly rising temperatures would only have a small effect on ocean heat uptake. An increase from .7 to .8W/m2.

Compare this to if we had 20 years of ZERO surface warming with constant solar input:

-net radiative forcing would increase .8W/m2

- there would be zero surface warming to counterbalance this

- the rate of ocean heat uptake would increase from .7W/m2 to 1.5W/m2. In other words, OHC would rise over 2X as fast.

Thus we see the effect on OHC of 20 years of zero warming with constant solar input is 800% greater than 10 years of slow warming with declining solar input.

If we had 50 years of no surface warming in which net radiative forcing increased 2W/m2.. we would now expect the oceans to warm at 2.7W/m2 instead of .7W/m2. The oceans would soon boil. You get the idea. This goes back to my original point regarding storage of heat in the deep ocean. It quickly becomes an ineffective way to keep the earth cool. It can work for a short period but eventually the surface MUST warm or else the rate of heat gain accelerates.

Your hypothetical solutions are ignoring a lot of questions we have about the ocean/atmosphere relationships.

We have seen virtually zero atmospheric warming in the time OHC barely moved. You still do not explain this. You use some math from 2000 to try and support your idea, but it still says nothing about the period in question post-2000.

As of now, we'll just blame shoddy data on OHC, but if it continues for another 5-8 years, then it will become even more problematic.

[skierinvermont]

Looks good in the hypothetical situation where the oceans did not pass any energy onto the atmosphere. I take it you have based your forcing figures on a 4W increase over 100 yrs?

The .4W/m2 since 2000? Has it really risen 4W in 100 years? I thought it was less than that.. I was looking more at the post-1970 rate which is faster.

Also, I was assuming the atmosphere warms some... that's how I go from .25W/m2 net forcing since 2000 (including solar min) to .1W/m2 for ocean heat uptake ( the global imbalance grows .1W/m2).

But I was wondering if you could tell us how much .1C of surface warming would increase earth's outgoing radiation? That would give a more exact number.. I was guessing .15W/m2 (which is how I go from .25W/m2 net forcing to a .1W/m2 imbalance). But I think it is probably more than .15W/m2, in which case earth's energy imbalance might not grow much at all.

[skierinvermont]

The Planck Response (black body) is 0.3C/watt

So 0.1C would increase surface radiation by about 0.33W.

Aha thank you... was busy looking for that... my guess of .15W was way off

so assuming the surface has warmed .1C over the last decade, and that net forcing has increased by .25W/m2.. then the global energy imbalance has actually decreased by .08W/m2 (.25-.33= -.08)and the rate of OHC uptake should be expected to decrease (ever so slightly).

Just goes to show the powerful effect a solar min has on OHC uptake.

[matthewweatherwatcher]

Aha thank you... was busy looking for that... my guess of .15W was way off

so assuming the surface has warmed .1C over the last decade, and that net forcing has increased by .25W/m2.. then the global energy imbalance has actually decreased by .08W/m2 (.25-.33= -.08)and the rate of OHC uptake should be expected to decrease (ever so slightly).

Just goes to show the powerful effect a solar min has on OHC uptake.

So the solar "grand minimum" that we're in is enough to do what is observed. Cool. Imagine whats going to occur once we move out of the solar grand minimum.

[WeatherRusty]

So the solar "grand minimum" that we're in is enough to do what is observed. Cool. Imagine whats going to occur once we move out of the solar grand minimum.

Since the solar cycle is known to produce a limited range of variability, it can only lower energy received at Earth by a limited amount. CO2 on the other hand will continue to add to the forcing as it's concentration increases.

[skierinvermont]

So the solar "grand minimum" that we're in is enough to do what is observed. Cool. Imagine whats going to occur once we move out of the solar grand minimum.

Yes.. pretty much.

[WeatherRusty]

SKIER.

I think you may enjoy the discussion going on over at Lucia's Blackboard.

Lord Monckton has tried to overturn the accepted value for the Planck Response.

Also this post is found in the discussion area:

Pinatubo reduced surface solar irradiance by around -3.0 W/m2. Feedbacks occured in all the major climate indices – clouds declined, OLR declined, water vapour declined – Temperatures fell by 0.5C.

Sure, but the decline in ocean heat content (a drop of ~2 x 10^22 joules over about a year) in the aftermath of Pinatubo means that the decline in average surface temperatures was moderated.

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The Earth’s surface is 5.1 X 10^14 square meters, and a year has 3.16 x 10^7 seconds, so 1 watt per square meter for a year is 1.61 * 10^22 joules. Since the actual ocean loss looks closer to 2 X 10^22, that means for the first year the ocean was adding about 1.24 watt per square meter to the surface. Without taking that into account, there is no way to infer a correct sensitivity value.

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That does not mean there are no important feedbacks, only that you have to take into account the heat lost from the ocean in doing any calculation based on the response to Pinatubo. So assuming the Pinatubo effect was in fact -3 watts/M^2 for a year, something like: -3.0 + 1.24 = -1.76; 0.5C implies ~1.76/0.5 = 3.52, not 6. The other complication is knowing the correct Pinatubo effect. You need to use the average aerosol effect for the year following the eruption (while the ocean heat content was falling) to do an ‘apples-to-apples’ calculation. Like most aerosol influences, I strongly suspect there is uncertainty in the Pinatubo effect on net solar energy. Lastly, we can assign all the drop in ocean heat to Panatubo, but who knows… the ocean heat content sometimes changes significantly (up or down) in the absence of a specific identified cause, so we can’t be sure the ocean contribution was all due to Pinatubo.

The Blackboard

[skierinvermont]

SKIER.

I think you may enjoy the discussion going on over at Lucia's Blackboard.

Lord Monckton has tried to overturn the accepted value for the Planck Response.

Also this post is found in the discussion area:

Pinatubo reduced surface solar irradiance by around -3.0 W/m2. Feedbacks occured in all the major climate indices – clouds declined, OLR declined, water vapour declined – Temperatures fell by 0.5C.

Sure, but the decline in ocean heat content (a drop of ~2 x 10^22 joules over about a year) in the aftermath of Pinatubo means that the decline in average surface temperatures was moderated.

.

The Earth’s surface is 5.1 X 10^14 square meters, and a year has 3.16 x 10^7 seconds, so 1 watt per square meter for a year is 1.61 * 10^22 joules. Since the actual ocean loss looks closer to 2 X 10^22, that means for the first year the ocean was adding about 1.24 watt per square meter to the surface. Without taking that into account, there is no way to infer a correct sensitivity value.

.

That does not mean there are no important feedbacks, only that you have to take into account the heat lost from the ocean in doing any calculation based on the response to Pinatubo. So assuming the Pinatubo effect was in fact -3 watts/M^2 for a year, something like: -3.0 + 1.24 = -1.76; 0.5C implies ~1.76/0.5 = 3.52, not 6. The other complication is knowing the correct Pinatubo effect. You need to use the average aerosol effect for the year following the eruption (while the ocean heat content was falling) to do an ‘apples-to-apples’ calculation. Like most aerosol influences, I strongly suspect there is uncertainty in the Pinatubo effect on net solar energy. Lastly, we can assign all the drop in ocean heat to Panatubo, but who knows… the ocean heat content sometimes changes significantly (up or down) in the absence of a specific identified cause, so we can’t be sure the ocean contribution was all due to Pinatubo.

The Blackboard

Yikes Lucia's response is super-long winded but if I understand it correctly I think it can be boiled down to the following:

Monckton and Kimoto have assumed that when surface temperature, and thus surface radiation increases, there will be no corresponding increase in black radiation and all of this increased radiation will make it to the top of the atmosphere and escape.

Of course this is false, if surface radiation increases, so will black radiation. In fact, we see almost none of the energy emitted by the surface makes it to the TOA directly (this is what K&T label the 'atmospheric window'). Almost all of the surface radiation is re-absorbed and re-emitted by the atmosphere. Thus if surface radiation increase, so will 'black radiation,' the 'atmospheric window,' and 'emitted by atmosphere.' As seen below:

Monckton and Kimoto erroneously assume that when surface radiation increases 1W/m2, OLR will increase 1W/m2. Of course, this is completely absurd and isn't worthy of a seconds consideration. They make the completely absurd assumption that 'black radiation' is governed solely by internal variables which they label I_j. To the contrary, black radiation is strongly dependent upon surface radiation. It's like they assume that when the surface emits more energy ALL of this energy is instantly teleported to outer space and doesn't interact with the atmosphere at all. It's a pretty basic dumb error once you boil it down.

Regarding Pinatubo I think you are correct in pointing out that the oceans contributed a forcing of 1.24W/m2. But you also have to remember the earth was not in balance before Pinatubo. If atmospheric forcing decreased by 3W/m2 (including feedbacks) 'ocean forcing' if I can call it that changed by +1.99W/m2 (from -.7 to +1.24). Thus the net change at the surface was only 1W/m2 (-3 from the atmosphere, and +2 from the oceans).

In other words, if the earth had been in balance prior to Pinatubo, the oceans would have released more heat. The fact that oceans went from absorbing energy to releasing energy needs to be accounted for. Your analysis accounts for the fact that they released energy, but doesn't account for the fact that they were absorbing energy before. I think this is correct, but correct me if I'm wrong.

[WeatherRusty]

Yikes Lucia's response is super-long winded but if I understand it correctly I think it can be boiled down to the following:

Monckton and Kimoto have assumed that when surface temperature, and thus surface radiation increases, there will be no corresponding increase in black radiation and all of this increased radiation will make it to the top of the atmosphere and escape.

Of course this is false, if surface radiation increases, so will black radiation. In fact, we see almost none of the energy emitted by the surface makes it to the TOA directly (this is what K&T label the 'atmospheric window'). Almost all of the surface radiation is re-absorbed and re-emitted by the atmosphere. Thus if surface radiation increase, so will 'black radiation,' the 'atmospheric window,' and 'emitted by atmosphere.' As seen below:

Monckton and Kimoto erroneously assume that when surface radiation increases 1W/m2, OLR will increase 1W/m2. Of course, this is completely absurd and isn't worthy of a seconds consideration. They make the completely absurd assumption that 'black radiation' is governed solely by internal variables which they label I_j. To the contrary, black radiation is strongly dependent upon surface radiation. It's like they assume that when the surface emits more energy ALL of this energy is instantly teleported to outer space and doesn't interact with the atmosphere at all. It's a pretty basic dumb error once you boil it down.

Regarding Pinatubo I think you are correct in pointing out that the oceans contributed a forcing of 1.24W/m2. But you also have to remember the earth was not in balance before Pinatubo. If atmospheric forcing decreased by 3W/m2 (including feedbacks) 'ocean forcing' if I can call it that changed by +1.99W/m2 (from -.7 to +1.24). Thus the net change at the surface was only 1W/m2 (-3 from the atmosphere, and +2 from the oceans).

In other words, if the earth had been in balance prior to Pinatubo, the oceans would have released more heat. The fact that oceans went from absorbing energy to releasing energy needs to be accounted for. Your analysis accounts for the fact that they released energy, but doesn't account for the fact that they were absorbing energy before. I think this is correct, but correct me if I'm wrong.

if so:

If we substitute 2.0 for 1.24 we get:

assuming the Pinatubo effect was in fact -3 watts/M^2 for a year, something like: -3.0 + 2.0 = -1.00; 0.5C implies ~2.0/0.5 = 4.0

and Planck Response = 0.4C/watt

then

Planck Response = ~1.5C per 2xCO2

Of course in reality there would be feedbacks contaminating this computation, but the difference of 0.3C over 1.2C would be evidence for positive climate feedback..