Overshoot and Undershoot

Guest Post by Willis Eschenbach

Today I thought I’d discuss my research into what is put forward as one of the key pieces of evidence that GCMs (global climate models) are able to accurately reproduce the climate. This is the claim that the GCMs are able to reproduce the effects of volcanoes on the climate.

One of the most-cited papers in this regard is the Soden et al. study of the eruption of the Philippine volcano, Mt. Pinatubo. Their study is entitled Global Cooling After the Eruption of Mount Pinatubo: A Test of Climate Feedback by Water Vapor, available as a PDF. [hereinafter “Soden08”]

Figure 1. A NASA graphic showing satellite measurements of the spread of ash and aerosols from Mt. Pinatubo. In the first month (top right), the volcanic emissions had circled the earth (red area, Philippines on right). In six months, they were fairly evenly spread around the planet. Graphic Source NASA

The eruption of Mt. Pinatubo on 15 June 1991 injected aerosols and volcanic ash high into the atmosphere. This measurably changed the climate for a couple of years. It provided a wealth of observational data, as well as a good test for climate models.

Regarding the match between models and volcanic reality, the authors of Soden08 say (emphasis mine):

Because the transient response of the model depends on both its sensitivity and the external radiative forcing imposed on it, we first demonstrate the consistency between the model-simulated radiative forcing with that measured by satellites (Fig. 1 [of Soden08]). Both the observations and model simulations yield very similar reductions in the absorbed solar or shortwave (SW) radiation, which are nearly twice as large as the reduction in emitted LW radiation, a net loss of radiative energy that cools the surface and lower troposphere.

Parenthetically, when a scientist starts talking about “consistency” between observations and model results, I check my wallet. Consistency? What units are used to measure that? But I digress, back to my question.

How do the models actually stack up against the observations shown in their paper, in the Figure 1 they mention?

Before I get to the question and to their Figure 1, a bit of a diversion. For reasons that will become clear shortly, I want to make a distinction between simple negative feedback, and a governor. A governor is a system that keeps a heat engine running at a (relatively) constant speed. The most common example of a governor in daily life is the “cruise control” on a car. It keeps the car going at the same speed regardless of uphill and downhill grades.

Negative feedback is like increasing wind resistance on an accelerating car. Wind resistance slows the car down. Eventually at some speed wind resistance balances the energy pushing the car, and the car goes no faster. It balances out at a certain speed, where increasing feedback matches energy input. Fig. 2 shows how a negative feedback and a governor respond to increasing forcing.

Figure 2. A comparison of the actions of a governor and negative feedback. Qualitative only, numbers are nominal values.

Note that in response to changed forcings, the governor brings the value back to the desired equilibrium value. The governor does this by producing what is called “overshoot”. “Overshoot” is where the action of the governor drives the system past equilibrium (represented in Fig. 2 by the thick horizontal line at zero). This gives the governor the ability to recover quickly from perturbations.

Simple negative feedback, on the other hand, cannot maintain a specified speed. All it can do is reduce the size of a speed increase or a decrease . It cannot produce overshoot. As shown in the right side of the graph, simple negative feedback can create what appears to be a controlled equilibrium situation. This happens when feedback balances forcing so there is no change in speed.

However, this balance of negative feedback is not stable — any change in the forcing will lead to a new equilibrium speed. A governor, on the other hand, maintains the same speed despite changes in forcings.

Overshoot is necessary to control a “lagged” system such as the climate. This is a system where response to inputs is not instantaneous. I have argued elsewhere that the earth has at least one governor system incorporating overshoot which actively controls the temperature. For our current purposes, please take note of the very different shapes of the response curves of negative feedback and of a system with a governor.

With that as prologue, let us now look at the Soden08 Figure 1.

Soden08 Figure 1. ORIGINAL CAPTION. Comparison of the observed anomalies in absorbed SW (top) and emitted LW (bottom) radiative fluxes at the top of the atmosphere from Earth Radiation Budget Satellite observations (black) and three ensembles of GCM simulations (red). The observed anomalies are expressed relative to a 1984 to 1990 base climatology, and the linear trend is removed (30). The results are expressed relative to the pre-eruption (January to May 1991) value of the anomaly and smoothed with a 7-month running mean (thick line). The GCM anomalies are computed as the difference between the control and Mount Pinatubo simulations for each ensemble member. Both the model and observed global averages are from 60N-60S due to the restriction of observed data to these latitudes.

This looks good at first blush, and the authors say that the GCM results (red) are “consistent” with the observations. However, closer examination reveals issues. What struck me immediately about their results is that the actual observations of both the shortwave and longwave anomalies show clear signs of overshoot. After being knocked down by the volcano, after 1994 they both come back higher than pre-eruption. This worked to quickly restore the pre-disturbance state.

None of the GCMs show this sign of overshoot. Instead, the GCMs gradually drift back to the pre-eruption anomaly value of zero. This is similar to the negative feedback balance shown in Fig. 2. Unlike the overshoot in the observations, the GCM results flatline after 1994. While this doesn’t prove anything, it is another piece of evidence that the GCMs are missing some basic climate mechanisms.

How Much Total Difference did Pinatubo Make?

There is a second problem with the Soden08 model results, one which is less theoretical and more mathematically demonstrable. This has to do with the cumulative energy deficit from the volcanic eruption.

As you can see in the Soden08 Fig. 1 above, after the eruption the amount of incoming solar energy (SW, or shortwave radiation) dropped about twice as much as outgoing energy (LW, or longwave radiation). As a result, after the volcano there was a global net energy deficit. There was less energy entering the system than there was leaving the system. This deficit continued for some months.

The total magnitude of this deficit is an important indicator of the overall impact of the Pinatubo eruption on the climate system. It is a basic measurement of the phenomenon, answering the fundamental first question everyone asks — how big is it? We can investigate the total magnitude of the volcanic disturbance by looking at the cumulative energy deficit created by the eruption.

To do that, I first digitized the data in the Soden08 Figure 1. The data is available here as an Excel worksheet. Results in the worksheet for the GCMs are the average of the three runs shown in their Figure 1.

I then calculated the net energy balance (solar energy absorbed minus longwave energy emitted to space) for each month. I then started a cumulative total at zero, and added each month’s net energy balance to the cumulative total. This cumulative total shows how far out of balance the system was each month.

The resulting curve shows the size of the total disturbance caused by the volcano, as well as showing the path of recovery. The units are Watt-months/metre^2 (for convenience, since the data is monthly). For example, a two-Watt/m2 deficit that continued for three months would give a cumulative deficit of six Watt-months/m2. Fig. 3 illustrates the problem with the GCM results.

Figure 3. Cumulative effect of the Pinatubo eruption. Red line shows data from the average of the models (GCMs) shown in Soden08 Figure 1 above. Blue line shows data from the ERBS observations shown in Soden08 Figure 1 above.

So what does this result mean? Well, among other things it means that in this case the general “first glance” similarity of observations and models is misleading. A closer examination shows that the models did a very poor job at being consistent with the observations.

• The models greatly underestimated the magnitude of the peak impact of the eruption.

• They showed recovery starting much sooner than the observations show.

• They greatly underestimated the speed of the recovery once it started.

• They greatly underestimated the total impact of the eruption.

To put some numbers on those statements:

• The peak energy deficit in the observations was -42 Watt-months/m^2. This is more than twice the -18 Watt-months/m2 in the model results.

• The models show recovery starting about a year and a half after the eruption. The observations show about two and a half years before things turn around.

• The observed speed of the recovery is more than five times that of the modelled speed of recovery (post-1994 linear trends).

• The total impact of the eruption on the global energy balance is given by the area underneath the curves. Alternatively, it can be expressed as the average value of the energy deficit over the time period of the curves (1991-1995). The observed average energy deficit over that period is -21 Watt-months/m2. Again, this is more than twice the models’ estimate of -10 Watt-months/m2.

My conclusion? These models are not doing a credible job of representing Pinatubo’s effect on the global energy balance. The total size of the disturbance is a fundamental, basic measure of the accuracy of a simulation. Both the observed peak energy deficit and the observed total impact of the volcano were more than double the model results.

An error where the raw observed size of the phenomenon is more than double the model estimate? That sounds like a government project. Bad model, no cookies. Clearly, there is some fundamental problem with their simulation — they are showing the eruption of Mt. Minitubo, the half-size model.

When models show that kind of error in the raw size, peak size, and timing of the effects of a volcanic eruption … are the models “consistent” with the observations? Would you pay good money for a model that gave that size of error?

In addition, model results do not show the observed “overshoot” that leads to a speedy recovery from a disturbance. The results of this observed overshoot are seen in the difference between modelled and observed recovery rates. Driven by overshoot, the observed recovery rate is five times that shown by the models.

In short, I see no support for their implied claim that the models are an accurate representation of reality. Far from that, I don’t even see support for their vague claim of “consistency”. Their idea of consistency reminds me of the line from the old song, “She could easily pass for forty-threeeeee … in the dusk … with the light behind her.”

Their model results are inconsistent with observations. I do not see the Soden08 study as support for the idea that GCMs can successfully model the changes from volcanic eruptions.

Regards to all,

w.

PS – A final note for clarification. As the title suggests, the main thrust of Soden08 is concerned with whether the models perform better if they include a water vapor positive feedback. It finds that the GCMs do in fact perform better if there is positive feedback from a warming.

My analysis of the model results and observational data above is completely separate from the Soden08 analysis. We are simply using the same results and data. I make no claim that their analysis is right or wrong. In fact, I strongly suspect they are right, that the models do perform better if there is positive feedback from warming, although I have my own ideas what that demonstrates. But that is distinct from my analysis above.

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R. de Haan

Anything to make CO2 the center of the AGW consensus.
Great article.

George E. Smith

Well I don’t like your example of “wind resistance” as being a case of “negative feedback”. It isn’t; nor is friction in the car’s transmission.
One thing you can say about a vehicle (say a car) beset by wind resistance or friction in the transmission is that IT CAN NEVER OVERSHOOT.
Wind resistance (and I presume that in your model the wind resistance effect relates only to the speed of the vehicle through the air, and its drag coefficient. It’s a trivial case of output energy dissipation; and has nothing whatsoever to do with feedback.
“Feedback”, as its name implies calls for taking a sample of the OUTPUT and FEEDING IT BACK to THE INPUT.
All that wind resistance does is increasingly LOAD the output, until the net force available for further acceleration is zero; and the system approaches that point assymptotically, and in theory never reaches the steady state.
But Feedback goes back to the system input to also be acted upon by the open loop system transfer function. And part of that transfer function is a PROPAGATION DELAY. The output doesn’t occur until sometime AFTER the input happens; which means that the feedback signal also is returned to the input; after the original input signal started the change of state.
It is the DELAY going through the system that is the cause of the overshoot; the control does not act fast enough to prevent an overshoot.
And in severe cases of propagation delay, the system is quite unstable and oscillates; being limited only by other non linear effects; such as banging into the power supply rails in the case of well understood amplifier feedback or process control loop feedback systems.
I’m not a chemist; but if my memory serves, doesn’t “le Chatalier’s Principle” say that a system disturbed from an equilibrium condition, will react in such a way as to oppose the disturbing influence.
An electric motor sent spinning by the application of a Voltage to its terminals, will act as a generator, and generate an induced EMF that is ALWAYS opposite in phase to the input Voltage; thus reducing the net driving voltage that determines the current in the windings. In the end, the net power generated is just the current flowing multiplied by the DIFFERENCE between the applied Voltage, and the induced EMF.
Likewise a generator to which a resistive load is applied, thus allowing a current to flow, will now act as a motor and in such a way that the motor effect tries to stop you from turning the generator; so now you have to do real work to keep it turning.
High efficiency LEDS have the same problem. They generate a lot of internal flux; but optical TIR effects stop the light from escaping from the die, and since the LED is also an effective photodetector, the excess light banging around inside the die and crossing the junction region gets absorbed and generates a photo-current that is in a direction to oppose the drive current being applied at the terminals.
NONE of those things result in oscillation or overshoot.
And the trouble with the climate models seems to be that they assume some sort of steady state; and they don’t pay much attention if any, to the propagation delays of whatever physical processes are going on.
If the Temperature input to CO2 change output is of the order of 800 years as the paleo record (ice cores) suggests; and the system truly was a feedback system, you would have one singing oscillator that would slam up against the stops going from runaway cooling to runaway heating.

Willis,
I believe what you have called simple negative feedback is not a feedback at all. It is just nonlinear resistance. Feedback involves the output modifying the input somehow.
It’s not clear that the volcano response should be seen as involving feedback either. The ash etc goes up, and eventually dissipates. There’s no reason why this cause should be seen as responsive to its effect.
Your evidence for overshoot is thin – just one following peak. OK, it is consistent with overshoot, but could have happened for any number of other reasons.

Mt. Minitubo, lol
So what engine drove the re-filling of the cumulative energy deficit? And more to the point, what was the governor that put the brake on the re-filling once it overshot?
It would seem that incoming short wave radiation would not have been able to re-fill the ‘lost’ energy as solar output doesn’t increase due to volcanic eruptions, so I expect energy was taken from somewhere else due to the fact that the previous equilibrium was re-attained (and a large amount of energy it would have been). Was there a large freeze somewhere, or perhaps a cooling current introduced into the oceans?

Hi Willis,
I’ll read this fully tomorrow (it’s late here) but I just want to mention a potential confounding factor. Solar activity took a pretty steep dive from mid ’91 just after the eruption and headed down to minimum in ’94.
http://www.woodfortrees.org/plot/pmod/from:1990/to:1994
Although some say solar activity variation doesn’t affect climate more than 0.15C or so over the cycle, Nir Shaviv discovered a terrestrial amplification due probably to cloud albedo variation:
http://sciencebits.com/calorimeter
Rapid falloffs in solar activity cause a bit of a bounce around in SST’s as the ocean takes the opportunity to offload excess heat content when the sun goes quiet.
Anyway, just sayin.

Barry Moore

Willis I really do not mean to be overcritical but we have just waded through a sea of smoke and mirrors theoretical mumbo jumbo about a hypothetical shell which was either 100% transparent or 100% opaque and with a fixed global average W/m2 radiation.
Now we have a post which mirrors many of the comments to your previous post explaining that the energy arriving at the earths surface and leaving the surface is extremely variable for a number of reasons. In my maths 101 course I learned that if you have 14 variables in an equation you must be able to derive from independant formulea the values of 13 before you can evaluate the 14th. Therin lies the complete falsification of the claim that we know how much CO2 effects our climate or how much anthropogenic emissions have contributed to the worlds atmospheric CO2 content there are just too many unknown variables. As a very wise man said once correlation does not prove causation. It may provide some good hints but nothing more.
Last point, again a little bit of nit picking, you can not refer to a 2 year event as a climate event this takes a shift over 30 years before it can be considered a climate change but volcanos do effect weather.

Michael Larkin

Very good presentation, Willis. Surprising myself, I understood more or less every word. I wish everyone who writes about the science could be as articulate.

jack morrow

Yes Willis, I like that song too about “she looks better with the light behind her”-but I never like these reports and models that these people come up with. I just cannot understand their motive other than it must be for money.
Like everyone else–I love your posts.

Doug Badgero

Not to nitpick, but a cruise control returns an auto to the same speed because it is a proportional-integral controller. A proportional controller by itself will operate with an offset in the process parameter from setpoint. The integral function returns the process parameter to setpoint. Other than that, I think your analysis contains many interesting observations. In particular, the GCMs inability to model the overshoot…….just as you observed.

INGSOC

Dee mountain, she done blowed up! Make me cold. Now she done make me thinking. If all dee mountain blowed up, me get really cold? Me no like cold… No make mountain blowed up. Me needing mountain offsets. Me making big bucks! Buy big jacket.

I first digitized the data in the Soden08 Figure 1. The data is available here as an Excel worksheet. Results in the worksheet for the GCMs are the average of the three runs shown in their Figure 1.
I then calculated the net energy balance (solar energy absorbed minus longwave energy emitted to space) for each month.

Willis, I think you need to be careful here. Were you able to confirm that the detrending done to Fig1 was the same for each of the two graphs contained in it?
ORIGINAL CAPTION. Comparison of the observed anomalies in absorbed SW (top) and emitted LW (bottom) radiative fluxes at the top of the atmosphere from Earth Radiation Budget Satellite observations (black) and three ensembles of GCM simulations (red). The observed anomalies are expressed relative to a 1984 to 1990 base climatology, and the linear trend is removed (30).
Maybe footnote (30) can help?
Cheers
t b

INGSOC

Like some other commenters, I pretty much blew my cerebral cortex on your last mystery post. I have been reduced to giggling to myself, and making buzzing noises with my lips when spoken too. Perhaps you could repeat everything after “Today I thought…” I understood that part. I got lost when the mountain she blowed up.

Frank K.

So yet again when I see the letters “GCM” in a report, I go seeking the actual differential equations they use, and again I come up empty. I looked at the supplemental materials, and again nothing (that I could see).
However, in my searching, I did come across the Los Alamos CMIP website and this funny little link…
http://pcmdi-cmip.llnl.gov/awards.html?submenuheader=3
Apparently, they’re expecting to get a REAL Nobel prize this time [heh]…

Sigh,
1991  Aug 12  5+
Global Volcanism Program | Cerro Hudson | Eruptive History
http://www.volcano.si.edu/world/volcano.cfm?vnum=1508-057&volpage=erupt&format=expanded#E199188
Well, everyone leaves it out. I just pray we don’t get two bad eruptions like those, within three months of each other, now. We might be in deep do.

Bill Illis

Really nice article, Willis.
What I find the most interesting is that the net reduction in forcing is -3.0 watts/m2 as a result of Pinatubo but temperatures only declined -0.4C to -0.5C. This forcing measurement would also include all the feedbacks which respond on a short-term basis so there is no “you forgot to include the feedbacks of X, Y, Z etc.”
That means the short-term climate sensitivity is only 0.13C to 0.17C per watt/m2. Slightly less that what the Stefan-Boltzmann equations says it should be for the surface at 0.18C/watt/m2 and only about half of what the climate models assume it to be at 0.265C per watt/m2.
So lets expand this actual sensitivity response to the forcing assumed for a doubled GHGs of +3.7 watts/m2 and also include all the extra long-term response feedbacks that the theory says should occur of +7.8 watts/m2 and we have only +1.53C to +1.9C per doubling of GHGs in the long-term.
Whenever the pro-AGW scientists write a paper like this, it is always sounds like the theory and the climate models are consistent with the results. But if you actually look at the data, you find nothing of the sort. It is willful blindness and distortion and some people just buy it and/or play along.

John from CA

‘Their model results are inconsistent with observations.”
Hit the Nail on the Head but for all the wrong reasons.
The point is “they” are incapable of objective observation and any attempt to program “it” is equally flawed and thus subjective. Observational data is a converse fallacy in climate science logic.
They don’t understand the climate system, the idea of a “Climate Model” is absurd.
Do we need to go further than this?

Willis, you can probably disregard my comment at November 29, 2010 at 4:31 pm
I now see the linear trend they removed is relative to the baseline period, not the period of the data depicted.
Time for kip.

Steve in SC

Willis,
I think in your governor example you have overshoot and undershoot reversed.
Feedback implies a closed loop system and what we may have here is an open loop system with perturbations and lags. The final result of which is limited only by the energy input and output. Of course no one ever implied that climate scientists have ever had a smattering of control theory.

John from CA

Actually Willis [with great respect],
What is it that they “Claim” to know and agree upon as fact? And here’s the part that’s going to give you an itch, if “they” agree did they make it a module of the Peer Reviewed Climate Model?
Its fun to spin on WUWT about the “science” but where is the logic we can trust?

MattN

Hmm…like a PID tuning loop….

Steve Fitzpatrick

Willis,
Nice post. My guess is that there is more going on here than first meets the eye.
Having worked many times (hundreds?) with control loops, I am a little puzzled how an active control (one that leads to oscillations around an equilibrium value) would develop in Earth’s atmosphere/oceans in response to a volcanic eruption. Maybe this is clear to you, but if so, please explain where you think the active control comes from in the system.
Some of Earth’s natural systems do seem inclined to natural oscillation; for example, the ENSO, where the strength of trade winds control the pushing of very warm tropical Pacific water to the Far East (exposing cooler water), while at the same time the strength of the trade winds themselves depend on the average warmth of the tropical ocean. In this circumstance, the lag between cause (the sea movement and sea surface temperature) and effect (the strength of trade winds) leads to the potential for overshoot and oscillation. The lag between cause and effect is always key to induce oscillation/overshoot in any system.
I am just not sure how the Pinatubo eruption can lead to this same tendency to overshoot/osciallate.

Ed_B

“open loop system with perturbations and lags”
The ash is the pertubation. The lag is the time for the ash to be washed out by rain. The global climate system returns to ‘normal’ quickly, because the negative feedback of the cloud system makes it happen.(the heat dumping equitorial thunderstorm system turns down, allowing for a quick build up of heat in the ocean)
Nice thought process Willis!

harrywr2

George E. Smith says:
November 29, 2010 at 3:26 pm
““Feedback”, as its name implies calls for taking a sample of the OUTPUT and FEEDING IT BACK to THE INPUT.”
In electrical engineering.
In climate positive feedback is often referred to an amplifying effect. A negative feedback is a dampening effect.
I.E.
The sun shines on the ocean, heating the water resulting in more water vapor, which itself is a GHG, which results in even more heating. This is a ‘positive feedback’
Alternatively
The sun shines on the ocean, heating the water resulting in more water vapor which forms into a cloud, which acts as a sunshade, resulting in cooling. This is a negative feedback.

Doug Badgero

I think the lag operator in climate will depend on the nature and location of the perturbation also. I always knew there was a lag, as we all do if we think about it…..the warmest days of the NH summer occur a many weeks AFTER the summer solstice. However, I didn’t realize until I read Lindzen’s congressional testimony how long that lag could be. That is, warming in the deep South Pacific not seen in Greenland until 4000 years later. Not to say these are cause and effect, they may be two effects to a not yet fully understood cause. I think we don’t understand a lot more than we understand.

walt man

Negative FB in a circuit tends to a stable output (phase shift lt 180) It lessens the efects of pertubations
Positive FB in a circuit tends toward instability (loop gain gt 1)
A governor is just the application of negative feedback to control output to a stable value. This can use many methods to obtain stability as others have said (e.g. PID). A slow response adds phase shift to the feedback causing neg to become pos!
You can play with electronic version of simulation for free with this application:
LTspice IV
http://www.linear.com/designtools/software/#Spice

feedback

Friction (some simple assumptions) is negative feedback:
assume the frictional force is linearly related to velocity:
F_f = \alpha V
then we have:
a = \frac{dV}{dt} = \frac{(F - \alpha V)}{m}
which is by definition negative feedback and a solution is:
V =  V_f (1-e^{-t/\tau})
which can be shown by,
\frac{dV}{dt} = V_f \frac{e^{-t/\tau}}{\tau}
and
V_f \frac{e^{-t/\tau}}{\tau} = \frac{(F - \alpha V_f (1-e^{-t/\tau})}{m}
and
\frac{m}{\tau}V_f e^{-t/\tau} = F - \alpha V_f (1-e^{-t/\tau})
which gives for a valid solution and the curve that was given,
V_f = \alpha F and \tau = \alpha V_f/m

R. de Haan

Bristlecone pine tree rings and volcanic eruptions over the last 5000 yr
Matthew W. Salzer ⁎, Malcolm K. Hughes
Laboratory of Tree-Ring Research, The University of Arizona, Tucson, Arizona 85721, USA
http://media.longnow.org/files/2/Salzer_Hughes_2007.pdf

Baa Humbug

Bill Illis says:
November 29, 2010 at 4:43 pm
“That means the short-term climate sensitivity is only 0.13C to 0.17C per watt/m2. Slightly less that what the Stefan-Boltzmann equations says it should be for the surface at 0.18C/watt/m2 and only about half of what the climate models assume it to be at 0.265C per watt/m2.”
Hi Bill. Interesting comment. Similar calculation was made by John L Daly about 7 years ago…
6) Observe and measure the effect of major radiative disturbances in the atmosphere:
The most common events of this type are explosive volcanic eruptions. Recently, we have had the eruption of the Phillipine volcano Mount Pinatubo in June 1991, the most powerful eruption this century. It has been possible to observe the radiative disturbance caused by Pinatubo, using remote sensing from satellites.
The results of these observations was that the blocking and scattering of solar radiation by the stratospheric aerosols temporarily reduced solar radiation to the earth’s surface by -4.7 wm-2 .
The Earth cooled, according to CRU, by about -0.5 degC during 1992. The Goddard Institute in New York estimated the cooling at -0.6 degC., while the satellite estimate was about -0.7 degC. So, if we take the average of these three estimates for the 1992 cooling (ie. -0.6 degC.) divided by the change in energy :-
0.6/4.7 = 0.128 degC per wm-2
This gives a very similar sensitivity result to Idso’s 0.113 deg per wm-2 in Method [5]. Applied to the +1.5 wm-2 scenario of doubled CO2, this suggests that global temperature will rise by only +0.16 degC.”
The above was number 6 of 6 different ways climate sensitivity could be deduced with observations as opposed to GCMs
All 6 ways gave similar results, i.e. a sensitivity of 0.2DegC per doubling of CO2, (including all feedbacks) much much lower than the IPCC estimates of 1.5-4.5DegC
Details at http://www.john-daly.com/miniwarm.htm

AusieDan

Hi Willis,
Last year I took a look at the NCDC global land and ocean temperature series (1880-2009).
My interest was in the long term trend (0.7 degrees per century) and particularly at the 60 odd year oscillations, which seem to be somehow tied up with the 11 / 22 year solar spot cycles.
I found that I could ignore the yearly chaotic (ie undefined) fluctiations, the periodic Le Nino an La Nina distubances AND the various sposmatic volcano eruptions.
I was able to draw a zig zag channel based on 30 odd year linear trends (half the 60 year complete cycle – each 30 year half cycle going relatively down or up) plus and minus 0.15 degrees up and down from this channel, which was superimposed on the long term linear 130 year trend.
All the el ninos an lja ninas and volcanoes fitted into this channel with no year’s data outside its confines.
I felt very smart for a while.
However, I was disconcerted when attempting to updata my chart earlier this year, to find NCDC had completley recalibrated the whole series and my channels no longer fitted.
I gave up in disgust and have since concentrated on examing only individual locations.
The point of all this however is that, to my recconing, the temperature (which I acknowledge is a different horse to energy) seems to bounce back quite quickly after major volcanic and Le/La interruptions as if they had not occurred.
A 100% feedback reaction.
Any comments?
(You have my email address if you want to see my old NCDC chart)

Bill Yarber

Willis
What you are talking about is proportional (P), integral (I) and derivative (D), or PID control. It requires P+D to achieve overshoot. Negative feedback is representative of P only, where the response I’d “proportional” to the offset or disturbance (error). A governor or cruise control for an auto requires all three, P+I+D for best results. Microprocessors make this type of control easy and relatively inexpensive. I seriously doubt that Earth’s climate system has any feedbacks which act as a governor, but several feedbacks acting in tandem might effectively produce the same, or similar results. However, these feedbacks may or may not always act the same way when the initial conditions or the upsets are changed.
That is why I have said repeatedly that any process control engineer can look at the temp vs CO2 curves and easily say it is OBVIOUS that CO2 concentration changes are not the cause of recent warming, or the cooling from ’44 to ’75 for that matter. AGW is BS, pure and simple.

Brian H

Good work on the feedback. IMO, there’s no more important issue in GCC.

Barry Day

How on Earth can climate models even come even close to representing,help anyone’s understanding or to reproduce “accurately”??? the effects of volcanoes on the climate while ignoring a possible>>>85 times more activity going on at the bottom of the Oceans.
“These mid-ocean ridges combine to form a global undersea mountain system known as the mid-ocean ridge system. Extending more than 40,000 miles (64,000 kilometers), it is the longest topographic or surface feature on Earth. Snaking its way between the continents, the ridge system encircles the planet like the seams on a baseball.”
“The largest fracture zone occurs along the Mid-Atlantic Ridge, offsetting it by 590 miles (950 kilometers).”
“Geologists estimate that 75 percent of the molten rocks or magma reaching Earth’s surface does so through mid-ocean ridges .”
Read more: http://www.scienceclarified.com/landforms/Ocean-Basins-to-Volcanoes/Ocean-Basin.html#ixzz16jvgIZNB
Read more: http://www.scienceclarified.com/landforms/Ocean-Basins-to-Volcanoes/Ocean-Basin.html#ixzz16juPLUtD
Read more: http://www.scienceclarified.com/landforms/Ocean-Basins-to-Volcanoes/Ocean-Basin.html#ixzz16jtlEgRF
AND THERE ARE SOME THAT WONDER HOW/WHY CO2 CAN RISE WITHOUT OUR HELP JUST LIKE IT HAS IN THE PAST.
Geologists estimate that there may be as many as>>> 85 million sea-mounts on the floors of the world’s oceans.
Read more: http://www.scienceclarified.com/landforms/Ocean-Basins-to-Volcanoes/Ocean-Basin.html#ixzz16jxGWgEq

Doesn’t GCM actually stand for “Global Circulation Model”?

Jim Steele

Temperature changes in the tropical Pacific really do not show any response to Pinatubo. So I have long thought the volcano-cooling theory is overstated.

jorgekafkazar

Steve Fitzpatrick says: “…Some of Earth’s natural systems do seem inclined to natural oscillation; for example, the ENSO, where the strength of trade winds control the pushing of very warm tropical Pacific water to the Far East (exposing cooler water), while at the same time the strength of the trade winds themselves depend on the average warmth of the tropical ocean. In this circumstance, the lag between cause (the sea movement and sea surface temperature) and effect (the strength of trade winds) leads to the potential for overshoot and oscillation. The lag between cause and effect is always key to induce oscillation/overshoot in any system….”
The pile up of water in the Western Pacific is allowed to slosh eastward when El Nino is triggered. The overshoot feature is obvious: once the mound (1/2 meter high, or thereabouts) starts to move eastward, it gains momentum. Vwallah! Overshoot.
Regarding overshoot mechanisms in eruptions, I think the primary one may also be obvious. Ash high in the atmosphere prevents incident radiation from reaching the earth, raising the effective albedo. Where does the ash end up? In the ocean, increasing its absorptivity. Overshoot?

wayne Job

Thank you Willis you have just proved to me my simple robust climate control mechanism. The world indeed has a very good thermostat, totally unaffected by this CO2 non sense.

Dinostratus

Eschenbach Said,
I want to make a distinction between simple negative feedback, and a governor. A governor is a system that keeps a heat engine running at a (relatively) constant speed. The most common example of a governor in daily life is the “cruise control” on a car. It keeps the car going at the same speed regardless of uphill and downhill grades.
Negative feedback is like increasing wind resistance on an accelerating car. Wind resistance slows the car down.
Response,
Those statement are simply incorrect. Even a third year electrical engineering student knows it not to be true.

Richard S Courtney

Barry Moore:
You mistakenly assert:
“Last point, again a little bit of nit picking, you can not refer to a 2 year event as a climate event this takes a shift over 30 years before it can be considered a climate change but volcanos do effect weather.”
Sorry, but this ’30-year climate length’ meme is a misunderstanding. A period of 2 years or less is perfectly acceptable.
The International Geophysical Year in 1958 established 30 years as a Standard Climate Period to use for comparison purposes. They chose 30 years for the purely arbitrary reason that it was then thought that only 30 years of reliable data existed. So, for example, when establishing global temperature anomalies CRU, GISS, etc. compare an annual datum to the average of a 30-year period (but they use different 30-year periods).
Clearly, if a climate datum were for a minimum time of 30 years then CRU, GISS etc. would each have a maximum of 4 data points for their temperature time series that begin around 1880. In fact, they each provide annual data. Indeed, they provide anomalies for individual months.
The 1994 IPCC Report used 5-year periods for assessment of changes to hurricane frequency.
Any period length can be used for climate assessment so long as the period is clearly stated and explained.
And 30 years would be a silly choice as the minimum climate datum period for several reasons: e.g. 30 years is not a multiple of the Hale Cycle.
Richard

Dinostratus

George E. Smith Said,
And in severe cases of propagation delay, the system is quite unstable and oscillates; being limited only by other non linear effects
Response,
Propagation delay does not necessarily need to be non-linear. Most students of stability analysis aren’t introduced to non-linear effects until graduate school as they are, to my understanding, phenomenological.

Dinostratus

GES also said,
And the trouble with the climate models seems to be that they assume some sort of steady state
Response,
Yes, this has been one of Tennekes objections to GW models.

Dinostratus

Okay, so I read the rest of what George E. Smith wrote. This stood out in the conclusions,
“When models show that kind of error in the raw size, peak size, and timing of the effects of a volcanic eruption … are the models “consistent” with the observations? Would you pay good money for a model that gave that size of error?”
Hell, I’ve paid a whole lot of good money for less accuracy. Sometimes in unsteady fluid models with property changes, we pop the champagne if we only catch the indications of a trend.
Smith is conflating the ability of GW models to adequately capture the response to CO2 increases with their ability to capture the impulse-like input from Mt. Pinatubo. Yes clouds play a role in both but they are different effects and the ability to sufficiently model a transient does not necessarily immune their ability to model the quasi-steady state. The former is a higher order effect and the latter is a zero order effect. Asymptotic solutions to simple non-linear equations will show that the steady state solutions often have little to no bearing on the solutions to the higher order solutions.
For the record, I am skeptical of GWT because of Tennekes objections to the models and because the data record is, at best, suspect.

lgl

That overshoot in 95 is probably just positive ENSO.

Dave Springer

@willis
“It keeps the car going at the same speed regardless of uphill and downhill grades.”
Not always true. Sometimes the car doesn’t have enough power to maintain the set speed going up a steep grade. Perhaps more often simply releasing the accelerator isn’t enough to prevent overspeed going down a steep slope – none of the cruise controls in the many cars I’ve owned could apply the brakes.

David L. Hagen

Willis
Appreciate your enthusiasm in critiquing the paper in terms of active control. Unfortunately much of your “control” explanation appears confusing by misusing control terms with some wrong explanations. That is seriously misleading to most readers.
Please work with a control engineer, rewrite and repost sections and withdraw or cancel portions of this post.
See examples above. George E. Smith, Nick Stokes, Doug Badergo, Steve in SC., Bill Yarber, Dinostratus, Dave Springer etc.
I’m not a control engineer. From my faint recollection, your use of “overshoot” appears to be underdamped closed feedback control. The underdamping results in the “overshoot”. An optimally damped closed feedback control system gives the fastest settling to the desired control with NO “overshoot.”
Your “negative feedback” example appears like open loop control with nonlinearly increasing drag, or closed loop proportional control without “integral” feedback to bring it back to the prescribed control point. You can have “equilibrium” without returning to the desired control point.

Warren in Minnesota

Feedback and overshoot aside, I find the comparison of the observed and modeled cumulative energy deficit interesting.

willis:
you prolly want to spend some more time looking at control theory, as Dinostratus and Nick, and others have pointed out.
I like using the metric you used ( integrating the response) Basically, you see the model having a transeint response that needs work. When modelling highly complex system like this, your first goal is to get the system to respond in right direction. go up when its supposed to go up, go down when its supposed to go down, get the right magnitude of response and the exact transient response correct is a tough problem. So, these results are what one would call “consistent” what would be in consistent.
1. if volcanoes warmed the planet
2. if the planet continued to cool.
3. if the response was a step response.
The unknowns: excactly how a plume of particles disperses, exactly how radiation
interacts with them, exactly how the system rebounds. Those unknowns will drive the kind of mismatch you see. I suspect that if you did GCMs experiements ( more than 3 runs) dedicated to varying the the modelling of these aspects that you could improve the results. But for the purposes of climate science its largely correct and improvements to the models would not drive forecasts, since volcanos cant be forecast.

Dave F

Hmmm…
Your figure 3 would certainly suggest an ‘overshoot’ in the estimate of climate sensitivity used in the GCMs.

Mike S.

I admit to being a little confused by the objections to Willis’ “negative feedback” example. If the input is the force pushing on the car, the output – acceleration – is indirectly generating/increasing an opposing input force (wind resistance) which reduces the net force pushing the car forward. This appears to be in line with the definition over at Wikipedia: “Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated.”
So, apparently I’m missing something in the various commenter arguments.
@Dave: none of the cruise controls in the many cars I’ve owned could apply the brakes.
I actually had one once which would – first car I ever drove that used cruise control, in fact. Nearly wrecked the second one because it didn’t apply the brakes, and I hit 85 downhill before realizing what was(n’t) happening.

George E. Smith

“”””” harrywr2 says:
November 29, 2010 at 5:34 pm
George E. Smith says:
November 29, 2010 at 3:26 pm
““Feedback”, as its name implies calls for taking a sample of the OUTPUT and FEEDING IT BACK to THE INPUT.”
In electrical engineering.
In climate positive feedback is often referred to an amplifying effect. A negative feedback is a dampening effect. “””””
I don’t believe I said anything about “electrical engineering”.
“output” and “input” can refer to almost any system that changes its condition as a result of the alteration of some variable.
Long before we had digital computers, which process numbers, we had “analogue” computers which as their name implies, simulated the behavior of some physical system by substituting analogues of the physical parameters and variables to create a new system, whose behavior is described by the exact same differential equations as the original system.
electrical systems are just a more recent implementation of procedures that have existed for eons. Chemical plant process controllers used hydraulic or pneumatic elements long before they ever went to electronic controls.
Sitting right above my computer screen on my book shelf, I have a complex assemblage of gears, including spiral track gears, that performs a simple mathematical function; it multiplies two numbers. In this case, the numbers happen to be total rotation angles of two different “input” gears; and the product is the total rotation angle of an “output” gear.
This “analogue computer” operates by exploiting a simple algebraic formula:- (A + B)^2 = A^2 + 2.AB + B^2
So don’t go confusing the issue by implying that my remarks apply only to one type of system. It is one of the most important results of Physics, that a very wide variety of Physical systems can be modelled by a range of models that are governed by exactly the same sets of differential equations; so once you have derived solutions for one sytem, those results can be transferred to completely different systems.
Wind resistance to forward motion is NOT any kind of “feedback”. And “amplification” is NOT “feedback” either. Amplification implies the requirement of additional energy input; that’s what “amplifiers” do; they use low energy “signals” to control some much higher energy supply source; usually in some reasonably linear fashion. Ordinary automobile “power steering” is an example of where a small signal is “amplified” by having an auxilliary power source (Hydraulic) that augments the input signal and is also under the control of that input signal. And I don’t have any electrical engineering in my car’s power steering.
As for negative feedback being a “dampening effect”; well I suppose in a climate system you do get dampening effects when it rains; but I don’t see what that has to do with feedback. Well maybe you intended to say a “damping” effect; but then that would be wrong too; because “damping” effects in typical control systems are energy dissipative “resistive” effects; and their purpose is to control the time response of systems. I don’t see how you can describe the capture of LWIR photons by CO2 to be an energy dissipating “damping” effect and it certainly isn’t a dampening effect; since that is restricted to H2O. If anything, the CO2 “greenhouse” effect is an energy storage process; albeit for quite short storage times. But in this day and age of digital computers, short energy storage times are passe; since dynamic computer memory, requiring constant refreshing, is the most common way of doing the computer’s main memory.
It is this willful misuse of well understood Physical principles by those who call themsleves “climate scientists”, that is a big part of the source of this whole problem. These “climatists” invent their own new world of “forcings” and “climate sensitivities” and “anomalies, and “feedbacks” or “amplifications”; and are quite oblivious to the fact that there are centuries of prior investigations of the Physical universe that have developed a formalism that has successfully explained most of what humans have observed about the universe; yet climatists insist on describing “models” of totally unreal things like non-rotating planets with infinite thermal conductivities, that keep the whole thing in an isothermal state, even though it has an input of energy over only a portion of it. Somehow the feel that averaging, and statistical manipulations and trend lines can transform their static equilibrium system into an imitation of the real dynamic and never in equilibrium earth.