Stacked Volcanoes Falsify Models

Guest Post by Willis Eschenbach

Well, this has been a circuitous journey. I started out to research volcanoes. First I got distracted by the question of model sensitivity, as I described in Model Climate Sensitivity Calculated Directly From Model Results. Then I was diverted by the question of smoothing of the Otto data, as I reported on in Volcanoes: Active, Inactive, and Retroactive. It’s like Mae West said, “I started out as Snow White … but then I drifted.” The good news is that in the process, I gained the understanding needed to direct my volcano research. Read the first of the links if you haven’t, it’s a prelude to this post.

Unlike the situation with say greenhouse gases, we actually can measure how much sunlight is lost when a volcano erupts. The volcano puts reflective sulfur dioxide into the air, reducing the sunlight hitting the ground. We’ve measured that reduction from a variety of volcanoes. So we have a reasonably good idea of the actual change in forcing. We can calculate the global reduction in sunlight from the actual observations … but unfortunately, despite the huge reductions in global forcing that volcanoes cause, the global temperature has steadfastly refused to cooperate. The temperature hasn’t changed much even with the largest of modern volcanoes.

Otto et al. used the HadCRUT4 dataset in their study, the latest incarnation from the Hadley Centre and the Climate Research Unit (CRU). So I’ll use the same data to demonstrate how the volcanoes falsify the climate models.

Figure 1. Monthly HadCRUT4 global surface air temperatures. The six largest modern volcanoes are indicated by the red dots.

This post will be in four parts: theory, investigation, conclusions, and a testable prediction.

THEORY

Volcanoes are often touted as a validation of the climate models. However, in my opinion they are quite the opposite—the response of the climate to volcanoes clearly demonstrates that the models are on the wrong path. As you may know, I’m neither a skeptic nor a global warming supporter. I am a climate heretic. The current climate paradigm says that the surface air temperature is a linear function of the “forcing”, which is the change in downwelling radiant energy at the top of the atmosphere . In other words, the current belief is that the climate can be modeled as a simple system, whose outputs (global average air temperatures) are a linear function of the SUM of all the various forcings from greenhouse gas changes, volcanoes, solar changes, aerosol changes, and the like. According to the theory, you simply take the total of all of the forcings, apply the magic formula, and your model predicts the future. Their canonical equation is:

Change in Temperature (∆T) = Change in Forcing (∆F) times Climate Sensitivity

In lieu of a more colorful term, let me say that’s highly unlikely. In my experience, complex natural systems are rarely that simply coupled from input to output. I say that after an eruption, the climate system actively responds to reductions in the incoming sunlight by altering various parts of the climate system to increase the amount of heat absorbed by other means. This rapidly brings the system back into equilibrium.

The climate modelers are right that volcanic eruptions form excellent natural experiments in how the climate system responds to the reduction in incoming sunlight. The current paradigm says that after a volcano, the temperature should vary proportionally to the forcing. I say that the temperature is regulated, not by the forcing, but by a host of overlapping natural emergent temperature control mechanisms, e.g. thunderstorms, the El Nino, the Pacific Decadal Oscillation, the timing of the onset of tropical clouds, and others. Changes in these and other natural regulatory phenomena quickly oppose any unusual rise or fall in temperature, and they work together to maintain the temperature very stably regardless of the differences in forcing.

So with the volcanoes, we can actually measure the changes in temperature. That will allow us to see which claim is correct—does the temperature really follow the forcings, or are there natural governing mechanisms that quickly act to bring temperatures back to normal after disturbances?

INVESTIGATION

In order to see the effects of the volcanoes, we can “stack” them. This means aligning the records of the time around the volcano so the eruptions occur at the same time in the stack. Then you express the variations as the anomaly around the temperature of the month of the eruption. It’s easier to see than describe, so Figure 2 shows the results.

Figure 2. Stacked records of the six major volcanoes. Individual records show from three years before to five years after each eruption. The anomalies are expressed as variations around the temperature of the month of the eruption. The black heavy line shows the average of the data. Black vertical lines show the standard error of the average.

The black line is the average of the stacked records, month by month. Is there a signal there? Well, there is a temperature drop starting about six months after the eruptions, with a maximum of a tenth of a degree. However, El Chichon is clearly an outlier in this regard. Without El Chichon, the signal gets about 50% stronger.

Figure 3. As in Figure 3, omitting the record for El Chichon.

Since I’m looking for the common response, and digging to find the signal, I will leave out El Chichón as an outlier.

But note the size of the temperature response. Even leaving out El Chichon, this is so small that it is not at all clear if the effect shown is even real. I do think it is real, just small, but in either case it’s a very wimpy response.

To properly judge the response, however, we need to compare it to the expected response under various scenarios. Figure 3 shows the same records, with the addition of the results from the average models from the Forster study, the results that the models were calculated to have on average, and the results if we assume a climate sensitivity of 3.0 W/m2 per doubling of CO2. Note that in all cases I’m referring the equilibrium climate sensitivity, not the transient climate response, which is smaller. I have used the lagged linear equation developed in my study of the Forster data (first cite above) to show the theoretical picture, as well as the model results.

Figure 4. Black line shows the average of the monthly Hadcrut temperatures. Blue line shows the average of the modeled annual temperatures from the 15 climate models in the Forster paper, as discussed here. The red line shows what the models would have shown if their sensitivity were 2.4°C per doubling of CO2, the value calculated from the Forster model results. Finally, the orange line shows the theoretical results for a sensitivity of 3°C per doubling. In the case of the red and orange lines, the time constant of the Forster models (2.9 years) was used with the specified sensitivity. Tau ( τ ) is the time constant. The sensitivity is the equilibrium climate sensitivity of the model, calculated at 1.3 times the transient climate response.

The theoretical responses are the result of running the lagged linear equation on just the volcanic forcings alone. This shows what the temperature change from those volcanic forcings will be for climate models using those values for the sensitivity (lambda) and the time constant (tau).

Now here, we see some very interesting things. First we have the model results in blue, which are the average of the fifteen Forster models’ output. The models get the first year about right. But after that, in the model and theoretical output, the temperature decreases until it bottoms out between two and three years after the eruption. Back in the real world, by contrast, the average observations bottom out by about one year, and have returned to above pre-eruption values within a year and a half. This is a very important finding. Notice that the models do well for the first year regardless of sensitivity. But after that, the natural restorative mechanisms take over and rapidly return the temperature to the pre-eruption values. The models are incapable of making that quick a turn, so their modeled temperatures continue falling.

Not only do the actual temperatures return to the pre-eruption value, but they rise above it before finally returning to the that temperature. This is the expected response from a governed, lagged system. In order to keep a lagged system in balance, if the system goes below the target value for a while, it need to go above that value for a while to restore the lost energy and get the system back where it started. I’ll return to this topic later in the post. This is an essential distinction between governors and feedbacks. Notice that once disturbed, the models will never return to the starting temperature. The best they can do is approach it asymptotically. The natural system, because it is governed, swings back shortly after the eruption and shoots above the starting temperature. See my post Overshoot and Undershoot for an earlier analysis and discussion of governors and how they work, and the expected shape of the signal.

The problem is that if you want to represent the volcanoes accurately, you need a tiny time constant and an equally tiny sensitivity. As you can see, the actual temperature response was both much smaller and much quicker than the model results.

This, of course, is the dilemma that the modelers have been trying to work around for years. If they set the sensitivity of their models high enough to show the (artificially augmented) CO2 signal, the post-eruption cooling comes out way, way too big. If they cut the sensitivity way, way down to 0.8° per doubling of CO2 … then the CO2 signal is trivially small.

Now, Figure 4 doesn’t look like it shows a whole lot of difference, particularly between the model results (blue line) and the observations. After all, they come back close to the observations after five years or so.

What can’t be seen in this type of analysis is the effect that the different results have on the total system energy. As I mentioned above, getting back to the same temperature isn’t enough. You need to restore the lost energy to the system as well. Here’s an example. Some varieties of plants need a certain amount of total heat over the growing season in order to mature. If you have ten days of cool weather, your garden doesn’t recover just because the temperature is now back to what it was before. The garden is still behind in the total heat it needs, the total energy added to the garden this season is lower than it would have been otherwise.

So after ten days of extra cool weather, your garden needs ten days of warm weather to catch up. Or perhaps five days of much warmer weather. The point is that it’s not enough to return the temperature to its previous value. We also need to return the total system energy to its previous value.

To measure this variation, we use “degree-days”. A degree-day is a day which is one degree above from some reference temperature. Ten degree-days could be five days that are two degrees warmer than usual, or two days that are five degrees warmer than usual. As in the example with the garden, degree-days accumulate over time, with warmer (positive) degree days offsetting cooler (negative) degree days. For the climate, the corresponding unit is a degree-month or a degree year. To convert monthly temperature into degree-months, you simply add each months temperature difference from the reference to the previous total. The record of degree-months, in other word, is simply the cumulative sum of the temperature differences from the date of the eruption.

What does such a chart measure? It measures how far the system is out of energetic balance. Obviously, after a volcano the system loses heat. The interesting thing is what happens after that, how far out of balance the system goes, and how quickly it returns. I’ve left the individual volcanoes off of this graph, and only shown the stack averages.

Figure 5. Cumulative record of degree-months of energy loss and recovery after the eruptions. Circles show the net energy loss in degree-months four years after the eruption. 

Remember that I mentioned above that in a governed system, the overshoot above the original temperature is necessary to return the system to its previous condition. This overshoot is shown in Figure 3, where after the eruptions the temperatures rise above their original values. The observations show that the earth returned to its original temperature after 18 months. The results in Figure 5 show that it took a mere 48 months to regain the lost energy entirely. Figure 5 shows that the actual system quickly returned to the original energy condition, no harm no foul.

By contrast, the models take much larger swings in energy. After four years, the imbalance in the system is still increasing.

Now folks, look at the difference between what the actual system does (black line) and what happens when we model it with the IPCC sensitivity of 3° per doubling, or even the model results … I’m sorry, but the idea that you can model volcanic eruptions using the current paradigm simply doesn’t work. In a sane world, Figure 5 should sink the models without a trace, they are so very far from the reality.

We can calculate the average monthly energy shortage in the swing away from and back to the zero line by dividing the area under the curve by the time interval. Nature doesn’t like big swings, this kind of response that minimizes the disturbance is common in nature.  Here are those results, the average energy deficit the system was running over the first four years.

Figure 6. Average energy deficit over the first four years after the eruption.

In this case, the models are showing an average energy deficit that is ten times that of the observations … and remember, at four years the actual climate is back to pre-eruption conditions, but the models’ deficit is still increasing, and will do so for several more years before starting back towards the line.

CONCLUSIONS

So what can we conclude from these surprising results?

The first and most important conclusion is that the climate doesn’t work the way that the climate paradigm states— it is clearly not a linear response to forcing. If it were linear, the results would look like the models. But the models are totally unable to replicate the rapid response to the volcanic forcings, which return to pre-existing temperatures in 18 months and restore the energy balance in 48 months. The models are not even close. Even with ridiculously small time constant and sensitivity, you can’t do it. The shape of the response is wrong.

I hold that this is because the models do not contain the natural emergent temperature-controlling phenomena that act in concert to return the system to the pre-catastrophic condition as soon as possible.

The second conclusion is that the observations clearly show the governed nature of the system. The swing of temperatures after the eruptions and the quick return of both temperature and energy levels to pre-eruption conditions shows the classic damped oscillations of a governed system. None of the models were even close to being able to do what the natural system does—shake off disturbances and return to pre-existing conditions in a very short time.

Third conclusion is that the existing paradigm, that the surface air temperature is a linear function of the forcing, is untenable. The volcanoes show that quite clearly.

There’s probably more, but that will do for the present.

TESTABLE PREDICTION

Now, we know that the drops in forcing from volcanoes are real, we’ve measured them. And we know that the changes in global temperature after eruptions are way tiny, a tenth of a degree or so. I say this is a result of the action of climate phenomena that oppose the cooling.

A corollary of this hypothesis is that although the signal may not be very detectable in the global temperature itself, for that very reason it should be detectable in the action of whatever phenomena act to oppose the volcanic cooling.

So that was my prediction, that if my theory were correct, we should see a volcanic signal in some other part of the climate system involved in governing the temperature. My first thought in this regard, of course, was the El Nino/La Nina pump that moves warm Pacific water from the tropics to the poles.

The snag with that one, of course, is that the usual indicator for El Nino is the temperature of a patch of tropical Pacific ocean called the Nino3.4 area. And unfortunately, good records of those temperatures go back to about the 1950s, which doesn’t cover three of the volcanoes.

A second option, then, was the SOI index, the Southern Oscillation Index. This is a very long-term index that measures the difference in the barometric pressures of Tahiti, and Darwin, Australia. It turns out that it is a passable proxy for the El Nino, but it’s a much broader index of Pacific-wide cycles. However, it has one huge advantage. Because it is based on pressure, it is not subject to the vagaries of thermometers. A barometer doesn’t care if you are indoors or out, or if the measurement location moves 50 feet. In addition, the instrumentation is very stable and accurate, and the records have been well maintained for a long time. So unlike temperature-based indices, the 1880 data is as accurate and valid as today’s data. This is a huge advantage … but it doesn’t capture the El Ninos all that well, which is why we use the Nino3.4 Index.

Fortunately, there’s a middle ground. This is the BEST index, which stands for the Bivariate ENSO Timeseries. It uses an average of the SOI and the Nino 3.4 data. Since the SOI has excellent data from start to finish, it kind of keeps the Nino3.4 data in line. This is important because the early Nino3.4 numbers are from reanalysis models in varying degrees at various times, so the SOI minimizes that inaccuracy and drift. Not the best, but the best we’ve got, I guess.

Once again, I wanted to look at the cumulative degree-months after the eruptions. If my theory were correct, I should see an increase in the heat contained in the Pacific Ocean after the eruptions. Figure 6, almost the last figure in this long odyssey, shows those results.

Figure 6. Cumulative index-months of the BEST index. Positive values indicate warmer conditions. Krakatoa is an obvious outlier, likely because it is way back at the start of the BEST data where the reconstruction contains drifts.

Although we only find a very small signal in the global temperatures, looking where the countervailing phenomena are reacting to neutralize the volcanic cooling shows a clearer signal of the volcanic forcing … in the form of the response that keeps the temperature from changing very much. When the reduction in sunlight occurs following an eruption, the Pacific starts storing up more energy.

And how does it do that? One major way is by changing the onset time of the tropical clouds. In the morning the tropics is clear, with clouds forming just before noon. But when it is cool, the clouds don’t form until later. This allows more heat to penetrate the ocean, increasing the heat content. A shift of an hour in the onset time of the tropical clouds can mean a difference of 500 watt-hours/m2, which averages over 24 hours to be about 20 W/m2 continuous … and that’s a lot of energy.

One crazy thing is that the system is almost invisible. I mean, who’s going to notice if on average the clouds are forming up a half hour earlier? Yet that can make a change of 10 W/m2 on a 24-hour basis in the energy reaching the surface, adds up to a lot of watt-hours …

So that’s it, that’s the whole story. Let me highlight the main points.

• Volcanic eruptions cause a large, measurable drop in the amount of solar energy entering the planet.

• Under the current climate paradigm that temperature is a slave to forcing with a climate sensitivity of 3 degrees per doubling of CO2, these should cause large, lingering swings in the planet’s temperature.

• Despite the significant size of these drops in forcing, we see only a tiny resulting signal in the global temperature.

• This gives us two stark choices.

A. Either the climate sensitivity is around half a degree per doubling of CO2, and the time constant is under a year, or

B. The current paradigm of climate sensitivity is wrong and forcings don’t determine surface temperature.

Based on the actual observations, I hold for the latter.

• The form (a damped oscillation) and speed of the climate’s response to eruptive forcing shows the action of a powerful natural governing system which regulates planetary temperatures.

• This system restores both the temperature and the energy content of the system to pre-existing conditions in a remarkably short time.

Now, as I said, I started out to do this volcano research and have been diverted into two other posts. I can’t tell you the hours I’ve spent thinking about and exploring and working over this analysis, or how overjoyed I am that it’s done. I don’t have a local church door to nail this thesis to, so I’ll nail it up on WUWT typos and all and go to bed. I think it is the most compelling evidence I’ve found to date that the basic climate paradigm of temperatures slavishly following the forcings is a huge misunderstanding at the core of current climate science … but I’m biased in the matter.

As always, with best wishes,

w.

APPENDICES

UNITS

Climate sensitivity is measured in one of two units. One is the increase in temperature per watt/m2 of additional forcing.

The other is the increase in temperature from a doubling of CO2. The doubling of CO2 is said to increase the forcing by 3.7 watts. So a sensitivity of say 2°C per doubling of CO2 converts to 2/3.7 = 0.54 °C per W/m2. Using the “per doubling” units doesn’t mean that the CO2 is going to double … it’s just a unit.

DATA

Let’s see, what did I use … OK, I just collated the Otto and Forster net radiative forcings, the Forster 15 model average temperature outputs, the GISS forcing data, and the dates of the eruptions into a single small spreadsheet, under a hundred k of data, it’s here.

METHOD

The method depends on the fact that I can closely emulate the output of either individual climate models, or the average output of the unruly mobs of models called “ensembles” using a simple lagged linear equation. The equation has two adjustable parameters, the time constant “tau” and the climate sensitivity lambda. Note that this is the transient sensitivity and not the equilibrium sensitivity. As you might imagine, because the earth takes time to warm, the short-term change in temperature is smaller than the final equilibrium change. The ratio between the two is fairly stable over time, at about 1.3 or so. I’ve used 1.3 in this paper, the exact value is not critical.

Using this lagged linear equation, then, I simply put in the list of forcings over time, and out comes the temperature predictions of the models. Here’s an example of this method used on the GISS volcanic forcing data:

Lambda (a measure of sensitivity) controls the amplitude, while tau controls how much the data gets “smeared” to the right on the graph. And sad to say, you can emulate any climate model, or the average of a bunch of models, with just that … see my previous posts referenced above for details about the method.

INDIVIDUAL RECORDS

Here are the most recent six eruptions, eruptions that caused large reductions in the amount of sunlight reaching the earth, with the date of the eruptions shown in red.