Revisiting the Pinatubo Eruption as a Test of Climate Sensitivity
By Roy W. Spencer, PhD.
The eruption of Mt. Pinatubo in the Philippines on June 15, 1991 provided a natural test of the climate system to radiative forcing by producing substantial cooling of global average temperatures over a period of 1 to 2 years. There have been many papers which have studied the event in an attempt to determine the sensitivity of the climate system, so that we might reduce the (currently large) uncertainty in the future magnitude of anthropogenic global warming.
In perusing some of these papers, I find that the issue has been made unnecessarily complicated and obscure. I think part of the problem is that too many investigators have tried to approach the problem from the paradigm most of us have been misled by: believing that sensitivity can be estimated from the difference between two equilibrium climate states, say before the Pinatubo eruption, and then as the climate system responds to the Pinatubo aerosols. The trouble is that this is not possible unless the forcing remains constant, which clearly is not the case since most of the Pinatubo aerosols are gone after about 2 years.
Here I will briefly address the pertinent issues, and show what I believe to be the simplest explanation of what can — and cannot — be gleaned from the post-eruption response of the climate system. And, in the process, we will find that the climate system’s response to Pinatubo might not support the relatively high climate sensitivity that many investigators claim.
Radiative Forcing Versus Feedback
I will once again return to the simple model of the climate system’s average change in temperature from an equilibrium state. Some call it the “heat balance equation”, and it is concise, elegant, and powerful. To my knowledge, no one has shown why such a simple model can not capture the essence of the climate system’s response to an event like the Pinatubo eruption. Increased complexity does not necessarily ensure increased accuracy.
The simple model can be expressed in words as:
[system heat capacity] x[temperature change with time] = [Radiative Forcing] – [Radiative Feedback],
or with mathematical symbols as:
Cp*[dT/dt] = F – lambda*T .
Basically, this equation says that the temperature change with time [dT/dt] of a climate system with a certain heat capacity [Cp, dominated by the ocean depth over which heat is mixed] is equal to the radiative forcing [F] imposed upon the system minus any radiative feedback [lambda*T] upon the resulting temperature change. (The left side is also equivalent to the change in the heat content of the system with time.)
The feedback parameter (lambda, always a positive number if the above equation is expressed with a negative sign) is what we are interested in determining, because its reciprocal is the climate sensitivity. The net radiative feedback is what “tries” to restore the system temperature back to an equilibrium state.
Lambda represents the combined effect of all feedbacks PLUS the dominating, direct infrared (Planck) response to increasing temperature. This Planck response is estimated to be 3.3 Watts per sq. meter per degree C for the average effective radiating temperature of the Earth, 255K. Clouds, water vapor, and other feedbacks either reduce the total “restoring force” to below 3.3 (positive feedbacks dominate), or increase it above 3.3 (negative feedbacks dominate).
Note that even though the Planck effect behaves like a strong negative feedback, and is even included in the net feedback parameter, for some reason it is not included in the list of climate feedbacks. This is probably just to further confuse us.
If positive feedbacks were strong enough to cause the net feedback parameter to go negative, the climate system would potentially be unstable to temperature changes forced upon it. For reference, all 21 IPCC climate models exhibit modest positive feedbacks, with lambda ranging from 0.8 to 1.8 Watts per sq. meter per degree C, so none of them are inherently unstable.
This simple model captures the two most important processes in global-average temperature variability: (1) through energy conservation, it translates a global, top-of-atmosphere radiative energy imbalance into a temperature change of a uniformly mixed layer of water; and (2) a radiative feedback restoring forcing in response to that temperature change, the value of which depends upon the sum of all feedbacks in the climate system.
Modeling the Post-Pinatubo Temperature Response
So how do we use the above equation together with measurements of the climate system to estimate the feedback parameter, lambda? Well, let’s start with 2 important global measurements we have from satellites during that period:
1) ERBE (Earth Radiation Budget Experiment) measurements of the variations in the Earth’s radiative energy balance, and
2) the change in global average temperature with time [dT/dt] of the lower troposphere from the satellite MSU (Microwave Sounding Unit) instruments.
Importantly — and contrary to common beliefs – the ERBE measurements of radiative imbalance do NOT represent radiative forcing. They instead represent the entire right hand side of the above equation: a sum of radiative forcing AND radiative feedback, in unknown proportions.
In fact, this net radiative imbalance (forcing + feedback) is all we need to know to estimate one of the unknowns: the system net heat capacity, Cp. The following two plots show for the pre- and post-Pinatubo period (a) the ERBE radiative balance variations; and (b) the MSU tropospheric temperature variations, along with 3 model simulations using the above equation. [The ERBE radiative flux measurements are necessarily 72-day averages to match the satellite’s orbit precession rate, so I have also computed 72-day temperature averages from the MSU, and run the model with a 72-day time step].
As can be seen in panel b, the MSU-observed temperature variations are consistent with a heat capacity equivalent to an ocean mixed layer depth of about 40 meters.
So, What is the Climate Model’s Sensitivity, Roy?
I think this is where confusion usually enters the picture. In running the above model, note that it was not necessary to assume a value for lambda, the net feedback parameter. In other words, the above model simulation did not depend upon climate sensitivity at all!
Again, I will emphasize: Modeling the observed temperature response of the climate system based only upon ERBE-measured radiative imbalances does not require any assumption regarding climate sensitivity. All we need to know was how much extra radiant energy the Earth was losing [or gaining], which is what the ERBE measurements represent.
Conceptually, the global-average ERBE-measured radiative imbalances measured after the Pinatubo eruption are some combination of (1) radiative forcing from the Pinatubo aerosols, and (2) net radiative feedback upon the resulting temperature changes opposing the temperature changes resulting from that forcing– but we do not know how much of each. There are an infinite number of combinations of forcing and feedback that would be able to explain the satellite observations.
Nevertheless, we do know ONE difference in how forcing and feedback are expressed over time: Temperature changes lag the radiative forcing, but radiative feedback is simultaneous with temperature change.
What we need to separate the two is another source of information to sort out how much forcing versus feedback is involved, for instance something related to the time history of the radiative forcing from the volcanic aerosols. Otherwise, we can not use satellite measurements to determine net feedback in response to radiative forcing.
Fortunately, there is a totally independent satellite estimate of the radiative forcing from Pinatubo.
SAGE Estimates of the Pinatubo Aerosols
For anyone paying attention back then, the 1991 eruption of Pinatubo produced over one year of milky skies just before sunrise and just after sunset, as the sun lit up the stratospheric aerosols, composed mainly of sulfuric acid. The following photo was taken from the Space Shuttle during this time:
There are monthly stratospheric aerosol optical depth (tau) estimates archived at GISS, which during the Pinatubo period of time come from the SAGE (Stratospheric Aerosol and Gas Experiment). The following plot shows these monthly optical depth estimates for the same period of time we have been examining.
Note in the upper panel that the aerosols dissipated to about 50% of their peak concentration by the end of 1992, which is 18 months after the eruption. But look at the ERBE radiative imbalances in the bottom panel – the radiative imbalances at the end of 1992 are close to zero.
But how could the radiative imbalance of the Earth be close to zero at the end of 1992, when the aerosol optical depth is still at 50% of its peak?
The answer is that net radiative feedback is approximately canceling out the radiative forcing by the end of 1992. Persistent forcing of the climate system leads to a lagged – and growing – temperature response. Then, the larger the temperature response, the greater the radiative feedback which is opposing the radiative forcing as the system tries to restore equilibrium. (The climate system never actually reaches equilibrium, because it is always being perturbed by internal and external forcings…but, through feedback, it is always trying).
A Simple and Direct Feedback Estimate
Previous workers (e.g. Hansen et al., 2002) have calculated that the radiative forcing from the Pinatubo aerosols can be estimated directly from the aerosol optical depths measured by SAGE: the forcing in Watts per sq. meter is simply 21 times the optical depth.
Now we have sufficient information to estimate the net feedback. We simply subtract the SAGE-based estimates of Pinatubo radiative forcings from the ERBE net radiation variations (which are a sum of forcing and feedback), which should then yield radiative feedback estimates. We then compare those to the MSU lower tropospheric temperature variations to get an estimate of the feedback parameter, lambda. The data (after I have converted the SAGE monthly data to 72 day averages), looks like this:
The slope of 3.66 Watts per sq. meter per degree corresponds to weakly negative net feedback. If this corresponded to the feedback operating in response to increasing carbon dioxide concentrations, then doubling of atmosphere CO2 (2XCO2) would cause only 1 deg. C of warming. This is below the 1.5 deg. C lower limit the IPCC is 90% sure the climate sensitivity will not be below.
The Time History of Forcing and Feedback from Pinatubo
It is useful to see what two different estimates of the Pinatubo forcing looks like: (1) the direct estimate from SAGE, and (2) an indirect estimate from ERBE minus the MSU-estimated feedbacks, using our estimate of lambda = 3.66 Watts per sq. meter per deg. C. This is shown in the next plot:
Note that at the end of 1992, the Pinatubo aerosol forcing, which has decreased to about 50% of its peak value, almost exactly offsets the feedback, which has grown in proportion to the temperature anomaly. This is why the ERBE-measured radiative imbalance is close to zero…radiative feedback is canceling out the radiative forcing.
The reason why the ‘indirect’ forcing estimate looks different from the more direct SAGE-deduced forcing in the above figure is because there are other, internally-generated radiative “forcings” in the climate system measured by ERBE, probably due to natural cloud variations. In contrast, SAGE is a limb occultation instrument, which measures the aerosol loading of the cloud-free stratosphere when the instrument looks at the sun just above the Earth’s limb.
Discussion
I have shown that Earth radiation budget measurements together with global average temperatures can not be used to infer climate sensitivity (net feedback) in response to radiative forcing of the climate system. The only exception would be from the difference between two equilibrium climate states involving radiative forcing that is instantaneously imposed, and then remains constant over time. Only in this instance is all of the radiative variability due to feedback, not forcing.
Unfortunately, even though this hypothetical case has formed the basis for many investigations of climate sensitivity, this exception never happens in the real climate system
In the real world, some additional information is required regarding the time history of the forcing — preferably the forcing history itself. Otherwise, there are an infinite number of combinations of forcing and feedback which can explain a given set of satellite measurements of radiative flux variations and global temperature variations.
I currently believe the above methodology, or something similar, is the most direct way to estimate net feedback from satellite measurements of the climate system as it responds to a radiative forcing event like the Pinatubo eruption. The method is not new, as it is basically the same one used by Forster and Taylor (2006 J. of Climate) to estimate feedbacks in the IPCC AR4 climate models. Forster and Taylor took the global radiative imbalances the models produced over time (analogous to our ERBE measurements of the Earth), subtracted the radiative forcings that were imposed upon the models (usually increasing CO2), and then compared the resulting radiative feedback estimates to the corresponding temperature variations, just as I did in the scatter diagram above.
All I have done is apply the same methodology to the Pinatubo event. In fact, Forster and Gregory (also 2006 J. Climate) performed a similar analysis of the Pinatubo period, but for some reason got a feedback estimate closer to the IPCC climate models. I am using tropospheric temperatures, rather than surface temperatures as they did, but the 30+ year satellite record shows that year-to-year variations in tropospheric temperatures are larger than the surface temperatures variations. This means the feedback parameter estimated here (3.66) would be even larger if scaled to surface temperature. So, other than the fact that the ERBE data have relatively recently been recalibrated, I do not know why their results should differ so much from my results.
[SNIP]
Interesting. Thank you, Dr. Spencer.
It will be interesting to learn why your results are different to those by Forster and Gregory.
Is there any indication of the size of the error in your lambda estimation? I did notice that that scatter diagram has a lot of variation.
Dr. Spencer: I am having some difficulty interpreting the following statement:
If you have time, I would appreciate some expansion on the meaning of this.
/dr.bill
Any areosols added would do for cooler temperatures, never for warmer temperatures, as the atmosphere, that mix of gases called AIR, cannot “hold” heat as water (The Oceans) does: Nobody can change this fact. Air heat volumetric capacity=0.00192 joules, water=4.186 (3227 times than that of AIR).PERIOD.
Sorry if I repeat this fact too many times but it makes all models simply stupid…unless you prefer to warm your feet with a bottle filled with hot air, instead of water!!
The net reduction in solar radiation as a result of Pinatuba is on the order of 2.9 W/m2 (from GISS) to as high as 5 W/m2. 18 months later, 50% of the reduction was still in effect. Temperatures fell by about 0.4C. The Ocean Heat Content numbers don’t show any particular large decline.
So there is no way to take -3.0 W/m2 (from ERBE) (reduced by 50% 18 months later) which then translated into a reduction of 0.4C and say that is consistent with global warming’s predicted long-term lambda value of 1.25 W/m2/K (or 3.7 W/m2 results in 3.0C of warming). Just taking the short-term impact into consideration, Pinatuba gives very low sensitivity values.
The reason the papers find the Pinatuba numbers to be consistent with global warming’s propositions is because they are very bad at basic math (or because they didn’t want to end up on some “List”).
Must have touched a nerve with David.
“Note that even though the Planck effect behaves like a strong negative feedback, and is even included in the net feedback parameter, for some reason it is not included in the list of climate feedbacks. This is probably just to further confuse us.”
=============
Who needs confusion, when you have chaos.
DNA constantly changes, I.E. is in chaos/random mutation.
Why would climate be different, DNA is just trying to adapt to a chaotic system.
A 4 billion year model run, and we end up with Al Gore 😉
Bill Illis: “(or because they didn’t want to end up on some “List”)”
Have you grown cynical?
So, if the weak Solar Activity was to have a negative forcing upon the climate, it would be greeted by a positive feedback of heat energy from 40m depth of the oceans. What we would eventually see is a depleted ocean heat content, as the ocean heat is expended in holding off the loss.
Conversely, high Solar Activity would be compensated for by the oceans absorbing the extra heat (negative feedback.
None of which has anything to do with C02, which is merely along for the ride in this model.
Where is the proof that climate sensitivity is constant like gravity. At least, in this study, the time frame is short. Often you hear people say the climate sensitivity must be high to account for the end of the last ice age. I would like if someone could do a year by year best estimate of sensitivity in the last 500 000 years. I think we would see sensitivity gets lower when the temperature gets over a certain high(compatible with the thermostat hypothesis).
@Enneagram
Some time before, I was intrigued that temperature in the Philippines didn’t seem to have gone down in Summer 1991 compared to other years. Now after this pesentation, it becomes more clear that temperatures during the rainy season in the Philippines depend much more on ocean temperature. It took time for the ocean to cool after the Pinatubo eruption. This seems to be the feedback with the huge time lag that affects the whole world. So to me it doesn’t matter if you take CO2 as a warming forcing or aerosol as a cooling forcing. Aerosols are very effective to cool the oceans but with the opposite effect of an instanteneous positive forcing such a warming event that would decrease cloud optical depth. So I don’t understand your point.
Marc77,
The climate’s sensitivity [temperature response] to CO2 operates on a log scale. So the more CO2 that is added to the atmosphere, the less effect each additional molecule has. That’s why the current climate is indifferent to more CO2. It doesn’t really matter much, beyond ≈100 ppmv.
David says:
June 27, 2010 at 4:33 pm
[SNIP]
—————–
David do you like getting snipped? Argue the science or make a point. There are plenty of commenters who believe in AGW and they argue their case quite well in most cases. Try it!!! Oh, please read WUWT Policy as well.
http://wattsupwiththat.com/policy/
The equation presented seems to leave out one aspect I rarely read about in discussions or even many papers on climate change. That is simply that in the end all – every picojoule – of energy the Earth receives ends up being radiated out into space. All of the fuss, fury and math about the “greenhouse effect” seems to omit that basic fact. I must be missing something, since I don’t have six post-graduate degrees in some variation on “climate science” after my name. Over a relatively short period of time, any increase in carbon dioxide or any other gas which absorbs in-coming or out-going energy originally received from the Sun re-radiates it all back into space. Whatever “warming” is attributable to these gases seems necessarily to be a short-term phenomenom. I ignore the alleged increase in water vapor as having a further warming, simply because the claimed effect cannot exist, else we would have all “fried” – to indulge in a bit of hyperbole, myself – long since. Not to mention we would already have seen any such effect every year, given the temperature changes from winter to spring to summer of at least two orders of magnitude larger than the claimed temperature increases from carbon dioxide. No such “run-away” effect appears in nature.
So what, in my ignorance and skepticism, am I not understanding? This all seems to me to be “much ado about nothing”, were it not that the politicians and their beneficiaries – which apparently includes many of the core of climate scientist who remain intent on alarming us with their “projections, not predictions; but really we’re all doing to die!!” tales – have seized upon this as a means of increasing their political power. By the way, we’re actually reaching a “tipping point” in that area of human activity, but that’s another comment for another blog.
Marc77 says:
June 27, 2010 at 6:46 pm
“Where is the proof that climate sensitivity is constant like gravity.” […]
Good point. It fits well with something anna v wrote several months ago to the effect of, “You can never cross the same river twice.”
As far as I can know from my readings, the earth’s climate has never really been the same twice in geological time scales. From that perspective, the recent spate of NH glaciations and interstadials is just weather.
So, might I add to your post; what must the sensitivity be (oh, and sensitive to what?) to plunge the earth into another ice age or get us out of one?
There always seems to be a misunderstanding that energy systems are the sum of multiple components, which include input (solar, cosmic, etc.) , storage (oceans, land mass, atmosphere, etc.) and dissipation (clouds, water vapor, etc).
Systems like these are really a hybrid of multiple impulse functions with varying length tails based on the composition and structure of the materials involved.
Looking at these as simple linear systems will always render a sub-optimal understanding because these systems are neither simple or linear, especially when the storage elements are subject to varying principles of fluid dynamics which are dominated by the topology of the environment.
Ike – Planets each have differing capacities to radiate incoming energy back to space. Consider the Moon vs Earth. Approximately the same distance from the Sun, similar composition, very differing abilities to retain radiative energy from the Sun. The Earth then is warmer. Mars less so, Venus more so. It’s all about air and clouds.
Now consider this concern – suppose there is a condition on Earth that, when heated, creates a greater ability of our planet to absorb more energy than it radiates in a given unit of time – say a human lifetime. Say, for example, that component is CO2. Let’s say that some perturbation causes, briefly, the Earth to absorb more energy than it radiates back to space, and that increase in heat causes the release of additional perturbing components that is additive. Oh, say, permafrost over peat bogs. The added heat warms the peat which releases more CO2 which causes more absorption until, finally, the oceans heat up.
Let’s say that this causes seafloor methane mats to become unstable and to begin releasing methane and other GHG’s, and this, added to the earlier warming influences, cause additional warming. Warming to the point that life becomes stressed, the ice caps melt, and Gavin Schmidt utters on his last breath “I was right!”.
You are correct that all these picojoules will ultimately be released to space, but the rate at which this is done can be sufficiently slow as to end life as we know it by allowing heat to build up for a time. Let’s say this goes on for a thousand years.
It’s important to me this not happen before I retire, but after I die I really won’t care and I don’t like shoveling snow that much anyway, but to return to the story…
Perhaps all is not lost meaning it may in fact be true, for example, that adding heat to the system through perturbation will create more clouds which will have a moderating effect on temperature rise and this dooms day scenario is unachievable. Or it may be true that what we see as a perturbation is, in fact, not. The possibility exists for us to be misreading the root cause of warming because we’re not intelligent enough to see the big picture. CO2 and clouds, for example, affect the temperature of the atmosphere. The temperature is changing. CO2 is changing. Is CO2 the cause, or a result? What if it’s actually cosmic rays causing the problem?
Here’s the real problem – clouds and cosmic rays don’t have a political solution. CO2 does. Therefore, CO2 is the problem of choice – no math needed. CO2 is an empowering influence that clouds will never be. There is no shortage of people ready to exploit that. Politicians are empowered by it and they have budget because they create it as needed. Government budgets create markets where markets would not otherwise exist, so there is a growing “green” economy sector. That includes public education as you might guess, so it can perpetuate. The “green” economy sector feeds back by way of lobbying to create greater need for action – and I assure you this far exceeds anything nature can do until the current interglacial period ends – and the loop is closed.
Eisenhower was closer to the truth than Dr. Jones.
re Ike: June 27, 2010 at 7:26 pm
Hi Ike. I do have a bunch of letters after my name, but they’re all in Physics, not ‘climate science’. Given the situation in that area these days, however, that doesn’t make me unhappy. 🙂
Regarding your question, I think the critical issue that sometimes gets forgotten in the ‘input = output’ statement is that this applies only when the system is in equilibrium. If there is a change in input or output, the system will respond by changing something so as to try and direct things either back to the old equilibrium or to a new one, depending on what changes, and in what way.
On another thread last week, Willis Eschenbach used an example to illustrate this notion. The ‘system’ (as I set it up afterwards) consists of an empty cylinder into which a substantial stream of water is directed at the top. There is also a hole at the bottom, through which some of the water escapes. As it happens, this setup can be solved exactly to find things like the height of the water at any time, the amount of water currently in the cylinder, the amount currently leaving it, and the cumulative amount that has passed through the system from start to finish. You can also examine what happens if anything changes.
You can find, for example, the ultimate stable height to which the water will rise, and when it reaches this level, the inflow and outflow rates will be exactly the same. Before reaching that state, however, the cylinder is still filling, and the outflow is less than the inflow. Ultimately there is one cylinder-full of water that is retained in the system, and it will stay there as long as the system stays the same, even though it is never the same water molecules for very long.
Now, if you change the inlow rate, what happens? Well, that creates a new stable level, and the water level will increase or decrease by a certain amount until it reaches that new stable height, after which the ‘input = output’ statement is again true. Same thing happens if the outflow rate is changed (bigger or smaller hole).
Another thing you can do is to give the system a ‘one time shot of extra water’, perhaps by dumping in a bucketful at the top all at once. This makes the level rise right away, but the ‘regular’ inflow hasn’t changed, so the stable level will be the same, and what happens is that the outflow speeds up a little, and after a while the water level is back down to normal, and things are as they were before. If you had scooped out a bucket of water, the outflow would have slowed down a bit until the water level was back up to normal, and you can calculate the amount of time needed for these things to happen.
This cylinder of water isn’t, of course, a ‘climate model’, but it illustrates the behaviour of a large number of systems in Nature, including biological and thermodynamical ones, and many, many others. If you wanted to, you could think of the water height as analogous to temperature, the inflow and outflow as radiation, and the water currently in the cylinder as the energy stored in various ways on the planet, including the bit that makes the atmosphere livable.
One notable difference is that it is quite possible, at least in principle, to maintain this cylinder in a state of equilibrium (they do it all the time in mixing vats in factories), whereas the Earth is never in such a state, if for no other reason than the fact that we spin on our axis every 24 hours. On the other hand, it is quite possible for the Earth to ‘hunt’ up and down towards a stable level as the inputs and outputs change back and forth. As far as anyone can tell, it has been doing this for vast periods of time, and in a manner that has given an acceptable place for biological organisms to exist and evolve.
In any case, I have no reason to think that this will change because we inject a bit of CO2 into an already vast system. The CO2 system is just about max’ed out anyway, and while anything we, or the whales, or the ants, or the volcanoes might do, will have some kind of temporary effect, it is likely to be as significant as painting the water cylinder a different colour.
/dr.bill
Rapid cooling following certain volcanic eruptions create wide spread suffering. The Year without a Summer in 1816 is an example. Can any case be made that higher CO2 levels may act as a buffer against the cooling effect of SO2 and other volcanic aerosols?
Bravo:
“[…] but we do not know how much of each. There are an infinite number of combinations of forcing and feedback that would be able to explain the satellite observations.”
–
Credibility is eroded when confidence in allocation is projected authoritatively. Climate scientists throw linear decompositions around far too haphazardly.
“As can be seen in panel b, the MSU-observed temperature variations are consistent with a heat capacity equivalent to an ocean mixed layer depth of about 40 meters.”
But this author, using the same model, talks about 700 m:
R. W. S., “The Great Global Warming Blunder”, p. 115-116
Did I miss something, or is this the current state of the science?
It seems to me that the Cp*[dT/dt] would be better estimated using the ocean temperature anomaly rather than the troposphere temperature anomaly or better yet using the buoy system temperature vs depth profiles to estimate the change in energy. We will have better data for the next major eruption in the tropics.
rbateman says:
June 27, 2010 at 6:35 pm (Edit)
So, if the weak Solar Activity was to have a negative forcing upon the climate, it would be greeted by a positive feedback of heat energy from 40m depth of the oceans. What we would eventually see is a depleted ocean heat content, as the ocean heat is expended in holding off the loss.
Conversely, high Solar Activity would be compensated for by the oceans absorbing the extra heat (negative feedback.
None of which has anything to do with C02, which is merely along for the ride in this model.
Someone else gets it. Nice one Rob.
Bill Illis says:
June 27, 2010 at 5:55 pm
The net reduction in solar radiation as a result of Pinatuba is on the order of 2.9 W/m2 (from GISS) to as high as 5 W/m2. 18 months later, 50% of the reduction was still in effect. Temperatures fell by about 0.4C. The Ocean Heat Content numbers don’t show any particular large decline.
I doubt Pinatubo affected the level of solar radiation at all, the sun being 93,000,000 miles away from the erruption. It would have had a big effect on insolation though, as you enumerate. We need to avoid conflating the two as some people round here exploit the confusion in small changes of total solar irradiation and changes in the insolation, energy recieved at the surface of Earth, and specifically the ocean.
I have calculated that the ocan was getting around 4W/m^2 nore than the long term average from the sun (and lowered cloud cover) in the 93-2003 decade. This would be around enough to offset the cooling from Pinutubo. There was a big El nino around ’89. I think the ocean would have been heading into a negative anomaly around Pinutubo’s erruption anyway, given the timing of it’s general ocscillations.
The “compensation” of the additional heat going into the ocean either side of the erruption explains why Ocean Heat Content didn’t drop much as a result of Pinatubo.
This should be posted in volcanism category, not… whatever the heck vulcanism is?