# 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
November 29, 2010 3:09 pm

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

George E. Smith
November 29, 2010 3:26 pm

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.

November 29, 2010 3:29 pm

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.

November 29, 2010 3:45 pm

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?

tallbloke
November 29, 2010 3:55 pm

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
November 29, 2010 3:57 pm

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
November 29, 2010 4:06 pm

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
November 29, 2010 4:07 pm

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.

November 29, 2010 4:12 pm

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
November 29, 2010 4:23 pm

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.

tallbloke
November 29, 2010 4:31 pm

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
November 29, 2010 4:31 pm

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.
November 29, 2010 4:35 pm

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…
Apparently, they’re expecting to get a REAL Nobel prize this time [heh]…

November 29, 2010 4:40 pm

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
November 29, 2010 4:43 pm

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
November 29, 2010 4:44 pm

‘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?

tallbloke
November 29, 2010 4:54 pm

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
November 29, 2010 4:54 pm

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
November 29, 2010 5:03 pm

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
November 29, 2010 5:18 pm

Hmm…like a PID tuning loop….

Steve Fitzpatrick
November 29, 2010 5:18 pm

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
November 29, 2010 5:25 pm

“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
November 29, 2010 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.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.

November 29, 2010 5:57 pm

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
November 29, 2010 5:58 pm

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
November 29, 2010 6:14 pm

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
November 29, 2010 6:28 pm

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
November 29, 2010 6:36 pm

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
November 29, 2010 6:43 pm

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.
(You have my email address if you want to see my old NCDC chart)

Bill Yarber
November 29, 2010 7:05 pm

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
November 29, 2010 7:26 pm

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

ldlas
November 29, 2010 8:58 pm
Barry Day
November 29, 2010 9:22 pm

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 .”
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.

November 29, 2010 9:23 pm

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

Jim Steele
November 29, 2010 10:36 pm

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
November 29, 2010 11:05 pm

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
November 30, 2010 12:39 am

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
November 30, 2010 12:53 am

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
November 30, 2010 12:58 am

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
November 30, 2010 12:58 am

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
November 30, 2010 1:02 am

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
November 30, 2010 1:21 am

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
November 30, 2010 2:59 am

That overshoot in 95 is probably just positive ENSO.

Dave Springer
November 30, 2010 3:08 am

@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
November 30, 2010 4:00 am

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
November 30, 2010 6:06 am

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

November 30, 2010 9:21 am

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
November 30, 2010 10:27 am

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

Mike S.
November 30, 2010 10:30 am

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
November 30, 2010 10:49 am

“”””” 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.

George E. Smith
November 30, 2010 11:13 am

“”””” Dinostratus says:
November 30, 2010 at 12:58 am
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. “””””
Well Dinostratus, except when I screw up; which is quite often, I am usually very careful with the words that I use; and the organisation of those words into descriptions.
So it is beneficial to read the words that I actually use, and not read any words that I didn’t use. Then you would appreciate, that nowhere did I mention any “non linear propagation delays”.
What I did say was “”””” being limited only by other non linear effects “””””
Now while propagation delays certainly could be non-linear (say some hail Mary’s if you find a system where they are not) I was referring to “other” non-linearities. These usually are the result of limits to the dynamic range of the system variables; the maximum possible output for example. In the case of a simple op amp system which might employ feedback, the output response is limited to some values set by the power supplies being employed. It is an unfortunate fact of life (for the electronic engineer) that ALL of our active devices “pull”, and we don’t have ANY that can “push”. So they are like strings in that respect.
Just try pushing a sack of potatoes with a four metre long piece of rope.
So our electronic circuits are limited to static conditions that lie between the range of the energy sources (power supplies), and our active elements can only pull up or down from those sources of energy. Think about it; if we had “pusher” devices, we wouldn’t need ANY power sources; just a pusher and a puller to make things go up and down.

rxc
November 30, 2010 11:14 am

In evaluating the performance of models like the GCM, there should be a defined process that starts with a statement of the important phenomena that effect the system being modeled. Then, there should be a detailed statement of how each phenomenon is modeled, based on experimental data. The models of the phenomena should be tested against a wide range of data, at every scale where they are applied, to ensure that they are not being used outside their limits of applicability. Then, the integrated model can be tested against real data to see whether it predicts the data. The best tests of this sort are those where the modeler has not seen the actual data itself. The gold-standard tests are the ones where the modeler is trying to preduct an apparatus whose data/performance he has never seen before. In the case of a GCM, this would be something like modeling the effects of a particular volcano when you haven’t seen any data from similar types of volcanic erruptions before.
These rules were developed by Los Alamos National Laboratory for use in evaluating computer models used to predict the behavior of nuclear power plants during normal operation, transients, and accidents, and are applicable to all sorts of models, from reactors to GCMs to human performance. But it does not appear that they have been actually used for the GCMs. I wonder why not? Probably because most of the important phenomena are not well understood, or even modeled. But instead, they substitute “dials” in the computer models to represent the “best guess” of the analyst for the way that the phenomenon should behave. This can be useful, but it is not science. Engineers do this sort of thing when they cannot do the necessary experiments to gather the appropriate data, but then they include in their designs enough margin to accomodote the uncertainties.
The AGW promoters have bastardized this practice, using the “precautionary principle” to justify all the worst-case scenarios they can come up with and to justify their control of our society. The precautionary principle, while it is superficially very attractive to every right-thinking person who cares about the well-being of society has one fatal flaw – in practice, it devolves into rule by those who tell the scariest stories. And we know where that leads…

Ulric Lyons
November 30, 2010 11:33 am

The problem here is that it was colder (deviations from normals = surface) in Jan/Feb and May/early June 1991, than anytime till Jan 1997.

George E. Smith
November 30, 2010 11:41 am

“”””” feedback says:
November 29, 2010 at 6:14 pm
Friction (some simple assumptions) is negative feedback:
assume the frictional force is linearly related to velocity:
then we have:
which is by definition negative feedback “””””
Well my cut and paste can’t pick up your very nifty math editor; so just imagine the math in your mind.
So you said that A = B which by definition is negative feedback; therefore friction is negative feedback. Simply wunnerful !
But evidently your proof is only for the special case where it is valid to assume that the frictional force is linearly related to velocity. So just what sort of friction results in a force that is linearly related to velocity. The simple microscopic models of ordinary dry sliding friction would say that the friction force is constant, and independent of the velocity of sliding.
In fluids like liquids or air, what is called friction is often an effect of shearing of the fluid , and then you get into the whole question of laminar flow and Reynold’s numbers and the like. Fortunately for me fluid dynamics is not one of those things in my tool kit; so I can claim total ignorance.
But evidently your proof is a tautology; I don’t see anything but your declarative definition, that proves that friction is a negative feedback.

Dinostratus
November 30, 2010 2:21 pm

George, you just missed the ball. That’s okay, we all do from time to time. I will say, most of us have done it enough such that we learn to adjust our internal transfer functions to require a minimum of negative feedback for a positive gain, just one person’s feedback.

feedback
November 30, 2010 2:38 pm

George E. Smith says:
November 30, 2010 at 11:41 am …
(the nifty math was done in latex — which this thing seems to parse)
Yes I did make a simplifying assumption. My point was that the original posts claim that friction (or resistance) is a feedback was correct. If we take as the input F and the output V then feedback is where,
$F = f(V)$ which for linear negative feedback is,
$F = F_{applied} - F_{friction} = F_applied - \alpha V$
I then solved the differential equation for $F=ma$ (by assuming a solution I knew to be correct — like assuming a wave solution to the wave equation) which was a damped exponential just to show that the assumptions were physically reasonable and would produce a result similar to what the post showed. It was not tautological — just a simple case for demonstration.
Of course the real resistance would be more complicated and a non-linear function of V, however, it was perfectly reasonable to say that friction is a feedback. That is indeed what it is. If the frictional force could be modeled as $\alpha V^2$ then the differential equation is more difficult to solve but the basic result would hold.

feedback
November 30, 2010 2:48 pm

Perhaps to further clarify. If as you say the frictional force was a constant — which it is for a simple cases of sliding — then there would be no feedback. However, as long as the resistive force is a function of V (of any form) it is feedback.
Actually, that is interesting the effective mass of an electron can then be seen as feedback due to the influence of the crystal lattice on the electron wave function — but I digress in order to make a totally inappropriate indirect argument to competence.

DocMartyn
November 30, 2010 2:52 pm

As a biological kineticist my is ‘eye’ is rather different from these people, but the data shown in Figure 3 looks live a very nice second order change in a steady state.
This would be best described by ‘optical thickness’, it is a property of the gas/dust from the eruption blocks a discrete amount of the incoming spectrum. At the time of the eruption you have a very thick cloud, but in one area. As the cloud disperses the area affected increases and the incoming light drops over a larger area. The cloud becomes fully dispersed at the low point. Then, as the amount of material in the cloud drops past a threshold, light is again transmitted, and the light reaching the ground increases.
So what you are looking for is something with a narrow absorption band, that has a T=1/2 of about 15 months. SO2 would be my guess.

November 30, 2010 3:29 pm

lgl says:
November 30, 2010 at 2:59 am (Edit)
That overshoot in 95 is probably just positive ENSO.
########
another reason why Its goin to be very hard for a climate model to get transient response and magnitudes correct.

Barry Moore
November 30, 2010 4:59 pm

Richard thank you for pointing out that there is in fact no minimum period for differentiating between weather and climate although I have seen the 30 year period quoted many times, so I was misinformed. However your remarks do illustrate the statement that common sense is not very common any more I know you are very familiar with rolling averages so a 30 year rolling average can be updated once a month if required thus GISS and CRU need not have just 4 points for our climate history since 1880, now who is being silly. To say that any period is adequate to define climate as long as it is specified again can be taken to the absurd extreem, let us study climate on a 1 month time basis then we really would have a useless chaotic result. I think it very realistic to look at a reasonable long term rolling average then decide if there has been a significant change which can legitmately be called a climate change as opposed to a weather cycle or a short term event such as a volcano.
On a different note I am very pleased to see so many intelligent comments regarding control theory and feedback, since control theory is one of my specializations its good to see some accurate definition put forward as opposed to the skewed perspectives that so many people have. Although some of the responses do indicate there are a number of poeple out there who still do not get it even though it has been explained very clearly in a number of posts.

Curt
November 30, 2010 5:52 pm

David L. Hagen says:
November 30, 2010 at 4:00 am
“Willis…
Please work with a control engineer, rewrite and repost sections and withdraw or cancel portions of this post.”
Well, I am a control engineer, and I think Willis has a far better grasp of feedback control theory than his critics here — and than most climate scientists. (I reserve judgment as to his larger arguments here, however.)
I firmly believe, as does “feedback” above, that wind resistance that increases with velocity does constitute a negative feedback to the system. Let’s examine why. First, consider what the primary function of a cruise control system is. It uses a sensor to determine the actual speed of the car, comparing that to the set speed. If the speed is too low, it increases the forward motive force on the car; if the speed is too high, it reduces the forward motive force on the car. I think everyone here would agree that this is a negative-feedback system — it was engineered to do this.
So for a given set speed, consider how the output velocity “feeds back” to the force applied on the car. Higher speeds mean reduced forward force on the car; lower speeds mean increased forward force on the car.
Now consider the effect of wind resistance. Higher speeds mean increased backward force on the car, which is the same as reduced net forward force on the car. Lower speeds mean decreased backward force on the car, which is the same as increased net forward force on the car. This natural effect from the physics of the system is thus every bit as much a negative feedback as the engineered cruise-control’s manipulation of the accelerator pedal.
If you draw a block diagram of the system using transfer functions with Laplace transforms, as you would be required to do in any introductory controls course, both the natural wind resistance effect and the engineered cruise-control effect would show up in the feedback path from the output velocity node to the “force” node summing the various contributory forces on the car.
To get a little more technical, the transfer function of the car from net force to velocity is a single integrator (1/[M*s]), and the wind resistance is basically a proportional feedback term. This kind of damped 1st-order system is very stable, with large “phase margins”.
The dynamics of a cruise control feedback block are more than simply proportional, and so are not necessarily (as) stable. (They also bring in an external energy source that can drive an instability.)
I have some quibbles with Willis’ presentation of the analogy because he does not distinguish properly between how the force varies and how the resulting velocity varies. A good cruise control system may “overshoot” the accelerator force to overcome a perturbation (slope change or wind change), but it will preferably not overshoot the resulting velocity, hopefully bringing the car smoothly back to the set velocity without overshoot in that quantity.
In his climate system, the net W/m^2 radiative flux density is equivalent to the net force node in the cruise-control car system, and the resulting temperature is equivalent to the car’s velocity — again with fundamentally a single integration from heat flow to temperature through a thermal capacitance (grossly simplified, of course). So the overshoot he shows in the radiative flux density is analogous to the overshoot in the accelerator force, not necessarily overshooting the resulting temperatures.
Of course, analogies do not prove anything (although they can provide a good starting point for further examination). As others have noted, there are many possible reasons for the observed overshoot.
By the way, I write this to unwind from a day mostly concerned with the design of a position-tracking control algorithm, specifically how it should recover from velocity and acceleration saturation conditions; when and how it should re-establish “velocity lock” with what it is tracking, and when and how it should re-establish “position lock”. I deal with these issues every day.

kse
November 30, 2010 5:56 pm

OMG what crap…
It seems like Willis and most of the commenters do not have a slightest idea about systems with feedback of any kind – like basic signal processing circuits or automated control systems (btw. what the f* is governor? I did majors in signal processing & microsystems and I never heard that term). I have only one suggestion – please, do not circulate any links or other references to this page in any climate change related site. Otherwise, them alarmistas will get yet another clear indication of the stupidity of us “denialists”.
F.Y.I. overshooting or lack of it does not proove that there are two systems operating with different paradigms – it only tells that the feedback in the first system allows some oscillation while the other system possibly over-dampens the input signals. So the system could be the same – it only depends on the feedback factor how the system reacts.
REPLY: ah the “crap” pronouncement from on high, from an anonymous coward no less. – A

George E. Smith
November 30, 2010 6:18 pm

“”””” Dinostratus says:
November 30, 2010 at 2:21 pm
George, you just missed the ball. That’s okay, we all do from time to time. I will say, most of us have done it enough such that we learn to adjust our internal transfer functions to require a minimum of negative feedback for a positive gain, just one person’s feedback.
Well I’m a bit too long in the tooth to bother with having my work reviewed in private. I’m just not that proud; so have at it Dinostratus. You said:- “”””” George, you just missed the ball. That’s okay, we all do from time to time. “””””
Well that is perhaps the most elegant scientific proof I have seen in a long time; a simple declarative thrust; and the demon is dead !
So for those of us not quite as up to speed as you; perhaps you could show some of your intermediate steps leading to your bottom line: “”””” George, you just missed the ball. ….. “””””
Like right out here in public; “open Kimono” as they say; be my guest.

Harpo
November 30, 2010 6:40 pm

kse said
(btw. what the f* is governor? I did majors in signal processing & microsystems and I never heard that term).
That comment sums up the problem we have.

November 30, 2010 7:10 pm

I think this thread has become an argument about semantics. Although, I have to admit I have no idea what “kse’s” point is. I do agree with Curt though, both natural phenomena (e.g. drag) and engineered features (e.g. throttle response) must be included in models. It is semantics in my view to argue that drag is not a feedback just because it is not an engineered feedback.

George E. Smith
November 30, 2010 7:22 pm

“”””” Curt says:
November 30, 2010 at 5:52 pm
David L. Hagen says:
November 30, 2010 at 4:00 am
“Willis…
Please work with a control engineer, rewrite and repost sections and withdraw or cancel portions of this post.”
Well, I am a control engineer, and I think Willis has a far better grasp of feedback control theory than his critics here — and than most climate scientists. (I reserve judgment as to his larger arguments here, however.)
I firmly believe, as does “feedback” above, that wind resistance that increases with velocity does constitute a negative feedback to the system. “””””
Well you haven’t specifically said what is the INPUT to the system, and what is the OUTPUT. Most people would consider that the OUTPUT of the system is simply the speed (velocity if you like) of the car; adopting your cruise control system as the model.
The INPUT signal would have to be the “Speed set point” that is stored somewhere in the system; and is presumably settable by the driver; but is otherwise a fixed value at any particular time maybe 50 km per hour shall we say. The energy source that powers the “op-amp” would be the car’s engine; and lets’s assume that without ANY feedbacks, (as in the Open loop forward gain) the engine can drive the car up to say 1,000 km per hour. (some op-amp people believe you can never have too much open loop forward gain). If we think of our car’s gain (A) as being analagous to the Voltage gain of an op-amp analogue of our car control system; we can make the gain as high as we like without limit, simply by raising the load resistance at the output node of that amplifier. Of course in a practical case, you would need to raise the output supply Voltage, in order to maintain some finite operating current for the amplifier output devices.
But in any case, it is obvious from the op-amp analogue, that the output node load resistance is a limiting factor on the maximum output Voltage (car speed). A smaller load resistance gives a lower gain and a lower output value (car speed).
Now NOBODY would say that load resistance was a component of any feedback network; it is an essential component of the open loop system with absolutely no feedback applied. And the only reason that such an amplifier could oscillate, would be if there happens to be some parasitic “feedback” from the high output signal swing to some sensitive input terminal; well we assume that our op-amp designers know about shielding from stray capacitive unintended feedback; or it even could be a high leakage resistance feedback; but we took care of that with careful deigns and layout. There simply is no feedback connection from our car’s final speed to the cruise control set point, while the cruise control is switched off; so it can’t oscillate, no matter what forward gain we design in. The load resistance or impedance does NOT comprise a feedback; but it does set a limit to how fast our car can go.
Wind resistance is in no way different from the load resistance of an op-amp analogue to our cruise control system.
With the cruise control turned off, wind resistance still impedes forward motion; but since out car can do 1000 km per hour, it is not a big effect at 50 or 100 km per hour. It doesn’t matter if the wind resistance is constant or linear with speed or varies with the square of the speed; or it could even follow the function y = exp (-1/x^2). That is simply some sort of non-linear but variable load resistance; and all it does is change the open loop gain of our amplifieer; since it feeds back NOTHING to the input (set point) while the cruise control is turned off.
If I turn the cruise control on with the 50 km/hr set point, I now simply enable a sensor to read the car’s forward speed, and feed that to a comparator that compares it with the set point; and that comparator output can be sent to the accelerator (gas supply). Well of course I can add refinements such as acceleration sensors etc to add additional modes of control; but none of those sensors respond IN ANY WAY to the air resistance; they are not even aware of it. The OUTPUT is THE CAR SPEED; and the only thing that the feedback networks read is the car speed and functions of the car speed; they do not sense the air resistance, of which they are totally oblivious. Friction and wind resistance are nothing more than variations in the load impedance of the “amplifier”; which certainly can reduce the forward gain of the amplifier; but they have no effect on the closed loop gain except to the extent that the closed loop gain with only finite amounts of feedback still has small order dependence on the actual value of the forward gain. To the extent that extraneous loads like wind resistance and friction can lower the forward gain; that can only affect the stability of the system if the original dfeedback loop design was lousy so the system is conditionally stable and could oscillate for some range of forward gains. Well hopefully we don’t have control engineers designing cars with conditionally stable cruise control loops.
There isn’t ANY time delay between the system output (car speed) and the frictional or wind resistance opposing “force”, because those factors (wind and friction) act BEFORE the output speed is established not after it is.
So if you guys still want to call wind resistance and friction negative feedback; that’s fine with me; but I’ll take a pass on buying any car with control systems that you designed into it. Maybe that was the problem with the Toyota sudden acceleration problem; somehow the feedback signal from the wind resistance and friction got disconnected and the car went into a runaway mode. Funny how many of those sudden acceleration crashes happened with the accelerator wide open, and the accelerator pedal pushed to the floor (computer said so) and no signal evidence that the brake pedal had ever been pressed.

Barry Moore
November 30, 2010 7:43 pm

George is right but his explanation is a little complicated I agree. I will try to simplify it with the same example.
You set your cruise control at 100 kpm, your speed for whatever reason drops to 97 kpm the SPEED sensor is the feedback mechanism which tells your accelerator that you are below your set point so more power is applied by the engine until your speed reaches its set point. If your speed goes over the reverse happens. Some people call this positive and negative feedback but it just plain feedback i.e. you set speed as your requirement and the speed indicator is the controlling feedback this has nothing to do with what caused the speed to fluctuate.

Barry Moore
November 30, 2010 8:13 pm

Curt
Looking at the big picture your assessment is valid, a system has to be designed to cope with all the external forces placed upon it but in the case of a car this is just the power of the engine and variations in wind strength, direction etc or incline or road surface is not part of the control system which controls the speed of the car, agreed the car must be designed to combat all these factors on instructions from the cruise control but there is no feedback here just a response to an external force.
Now when we consider feed forward (I know I am causing confusion here) in a boiler system someone opens a valve and the demand goes up, the level in the boiler drum drops so the boiler water feed pump responds to the drop in level and supplies more water, this increase in water flow tells the burner system to ramp up because more cold water is coming that is before the steam pressure drops, so the person who opened the valve was not a part of the feed forward system although he caused it to operate.

Dave F
November 30, 2010 11:18 pm

Did no one else notice that Figure 3 shows the models on the upswing while nature actually loses 20/WM^2 from ’93-’94? If models show that sensitivity is 0.265C/WM^2, then a cooling of 5.3C is in order from ’93-’94. That is clearly not what actually happened. Model sensitivity is clearly out of line by an order of magnitude, since Hansen claims a 0.5C cooling.

Curt
November 30, 2010 11:47 pm

kse: Are you seriously unfamiliar with the term “governor”? It’s the original term for an engineered feedback control system. Look up James Watt’s “flyball governor”, which was the key control mechanism for steam engines, basically enabling the industrial revolution.
The flyball governor employed heavy metal balls at the “elbows” of two-link mechanisms that rotated on the shaft of steam engines. The higher the angular velocity of the shaft, the more the balls were pushed outward, pulling up the ends of the arms, which served to choke off the supply to the steam engine. This was the negative feedback that stabilized the steam engine, and the key to its operation. (Great trivia fact: if the setpoint were set to full throttle, the engine was said to be running “balls out”, or because this mechanism had to be enclosed for safety, “balls to the wall”. Few people realize that these are engineering, not biological, metaphors, and therefore “polite”.)
George: Are you seriously claiming that a system must have a conscious setpoint to have feedbacks? By your logic, the climate system can have no feedbacks, because there is no conscious setpoint for temperature. The feedback from wind resistance is to the net force on the car. This can be compared to a correctional force from an active control system, or not, but it is always there. Willis’ argument is that the climatic response is more like there is an active control system, and presents evidence for that argument. (As I said, I am not yet convinced that he is correct, but he does present evidence in his favor.)
By the way, you say, “So if you guys still want to call wind resistance and friction negative feedback; that’s fine with me; but I’ll take a pass on buying any car with control systems that you designed into it.” You may not realize it, but your safety already depends on control systems designed by me, and by people who would agree with me. Get used to it… If you fly in any commercial aircraft, the autopilot system uses system models that take air resistance as a negative feedback in the physical system of the plane.
Barry: I’m not sure what your point is. A key function of a control system is “disturbance rejection”. In the case of a cruise-control system, it must maintain speed well in the presence of disturbances such as changes in air resistance due to wind changes and changes in incline. Feedforward can do nothing for this. I have been a key proponent of the use of feedforward in my field in tracking control, but it helps not at all in disturbance rejection. Willis’ analysis is looking at the climate system’s ability to reject the disturbance of a major volcanic eruption, as it affects both incoming and outgoing radiative power. His argument is that the climate behaves more like an engineered system with a temperature setpoint than a passive system.

Dave F
December 1, 2010 12:20 am

Also, since I didn’t account for the log effect, the cooling should be higher.

NovaReason
December 1, 2010 4:46 am

Found a very interesting comparison for you.
http://www.mrothery.co.uk/module4/webnotes/Mod4Notes2ndhalf.htm
Natural body systems usually rely on negative feedbacks to maintain balance. As such, they exhibit the same kind of behavior you stated, Willis, like having a governor.
the link above goes into detail on it, but a great graph to look at is the effect of insulin and glucose on the bodies serum glucose levels.
http://www.mrothery.co.uk/module4/webnotes/Image14.gif
I can almost see the transposed long term temperature graphs on there… /sarc off

George E. Smith
December 1, 2010 12:20 pm

“”””” Curt says:
November 30, 2010 at 11:47 pm
……………………………………..
George: Are you seriously claiming that a system must have a conscious setpoint to have feedbacks? By your logic, the climate system can have no feedbacks, because there is no conscious setpoint for temperature. The feedback from wind resistance is to the net force on the car. This can be compared to a correctional force from an active control system, or not, but it is always there. Willis’ argument is that the climatic response is more like there is an active control system, and presents evidence for that argument. (As I said, I am not yet convinced that he is correct, but he does present evidence in his favor.)
No I am NOT seriously claiming that; in fact I NEVER claimed that. The “Feedback control system” that we were discussing happened to be an auto cruise control; and that IS a system wherein the “input signal” just happens to be a fixed set point. If you like, we could put a knob on the front panel, that sets the speed, and you could sit there and run it back and forth and see how well the car speed follows the knob.
In that sense the cruise ssytem , is much lke an auto pilot (but much simpler) or say a chemical processing plant wherein maybe hundreds of process variables are each under closed loop feedback control to fixed set points.
But NO a fixed set point does not define a feedback system; and of course in the case of electronic feedback amplifier or perhaps active filter systems, the input would be a potentially rapidly varying input signal.
I once designed a very high gain bandwidth product photo-detector integrated (CMOS) amplifier, that could respond to femptoWatt light signals at a one megaHertz bandwidth. The design used a feedback Current gain architecture rather than a transimpedance amplifier architecture, so the input and out put signals were both currents, and the current gain was set by the ratio of two resistors rather than the absolute value of one very large (several megohm) resistor. So those resistors were implemented as P-channel MOSFETs, which were somewhat non linear; but they were designed so that they both had the same signal Voltage across them at all times, and they both had the same non-linearity curve so the gain was linear, even theough the feedback elements weren’t. That architecture is also faster, and more stable than the much overused Transimpedance photo-detector amplifier architecture. Oddly, I used exactly the same current gain architecture with the very first transistor circuit I ever designed; which was back in 1959. It was an amplifier for a photomultiplier tube that was part of a scintillation type “Tissue equivalent” neutron monitor. The linear (sub critical Geiger tube) proportional counter , used a tube; actually an FN2/3/NF1830, which contained organic lining materials and gases, such that the current pulse amlitude versus Neutron energy matched the expected tissue damage in the human body; over the neutron energy range from thermal neutrons up to at least 14 MEV neutrons, which are released in collisions of accelerated Deuterons onto heavy ice targets. Well I have the schematic over my desk, so I could read the tube type off that. Thermal neutrons are not at all nice to be around (ask Anna); they are radioactive (unstable) and have a half life of the order of 11 or 12 minutes; and if they happen to go off inside of you, then you have a high energy proton blowing holes in your flesh.
Well enough digression; no a fixed set point is NOT the definer of a feedback system; but a signal that is SOME FUNCTION of the OUTPUT, that is COMBINED with the original INPUT signal, IS a requirement of a feedback system; and frictional or other loading of the output energy providing system is none of those things.
As to the question of feedbacks in the climate system; the MMGWDCC folks claim that CO2 IS a GHG “forcing” and H2O IS NOT; while H2O IS a “Feedback” while CO2 IS NOT.
Well: #1/ BOTH CO2 and H2O ARE GHGs; they BOTH capture some part of the LWIR thermal spectrum.
#2/ BOTH CO2 and H2O DO transfer some of their exxcitation energy to the ordinary atmospehric gases in molecular collisions.
#3/ In BOTH cases, such collisions lead to WARMING of the ATMOSPHERE.
#4/ The Atmospheric gases cannot keep track of where their extra energy came from; it’s irrelevent.
#5/ Thermal continuum LWIR radiation from the (warmed) atmospheric gases does radiate isotropically, so about half of it escapes to space, and about half of it returns towards the surface.
#6/ Some of that downward LWIR (most of it) strikes the ocean or other water surface; and gets absorbed in the top 50 microns of water (99% or five absoprion lengths)
#7/ The rest of that LWIR strikes the ground; and some will be reflected, and some will be absorbed, so it LOWERS the net output LWIR rate.
#8/ The LWIR that hits the ocean will partly conduct to cooler deeper waters; but it will also tend to promote PROMPT evaporation from the surface, since it is absorbed in such a thin surface layer. That returns a lot of latent heat and water vapor to the atmosphere, therby cooling the ocean surface, and increasing the atmospheric water vapor.
#9/ The warmer surface water layer, cannot hold as much CO2 as cooler water can; so the LWIR heating of the surface also results in a Henry’s law emission of CO2 from the ocean along with the H2O evaporated; and also a slower CO2 uptake in the warmer water.
#10/ The water vapor in the atmosphere; including the now augmented water vapor fromt he LWIR warming also happens to absorb INCOMING SOLAR SPECTRUM ENERGY in the 0.75 micron to 4.0 micron range; which can be as much as 20% of the total solar energy captured by H2O. As in #3 and #4 that captured SOLAR energy is also transferred to the ordinary atmosphere gases, and they can’t distinguish that from GHG energy; and that too is eventually re-radiated as thermal LWIR in an isotropic distribution; half going up, and half going down.
So bottom line. both H2O and CO2 are GHGs and both absorb LWIR and both heat the atmosphere, and part of that energy is returned to the surface and the oceanic part of it results in the emission of both H2O and CO2 from the ocean, so that is arguably a positive feedback for both H2o AND CO2. SoBOTH are forcings, and both are POSITIVE feedbacks.
BUT H2O also captures incoming soalr energy, and only half of that energy eventually can reach the ground as atmospheric LWIR thermal radiation; so that is A NET LOSS of solar energy from the surface; and that is a negative feedback for H2O since more H2O vapor means less sunlight on the ground; so water VAPOR has BOTH positive and negative feedback components.
BUT ONLY H2O condenses to form water or ice clouds; and ANY sort of cloud ANYWHERE on earth reduces the amount of incoming solar energy that reaches the surface; some is lost from the cloud tops in diffuse reflection contributing to the albedo; and more is lost to refractive scattering from water droplets in the cloud or absorption in ice crystals, further lowering the amount of input solar energy that reaches the gorund.
So ANY WATER ANYWHERE IN ANY PHASE in the atmosphere REDUCES the ground level solar insolation; no matter what and that is a purely NEGATIVE FEEDBACK effect from clouds.
Now clouds can also scatter and absorb and reflect ground level LWIR radiation, and some of that will then be lost upwards to space, and some will be returned to the surface. The optical losses go as cloud height^4 power, and there also is a cosine^8 of slant angle, as far as returning that LWIR to the surface origin point. But a lot more can hit other surface places, some of which may not be under that cloud. In any case, more clouds over the climate time unit of 30 years means less solar energy reaching the earth surface; and that is pretty much the only significant energy input to the earth; so that means the earth must cool down.
So it is simply political climatism that insists that CO2 is aGHG positive feedback forcing, while H2O is just a positive feedback “amplification” of CO2 and NOT a forcing; and low clouds ar enegative feedback while high clouds are positive feedback warming adn the higher the cloud, the more warming, so there is a neutral zone where clouds neigher warm nor cool according to climatism 101 mantra; so that means that the ultra-high noctilucent clouds are the biggest cloud contributors to global warming; well BS !

Frank
December 1, 2010 12:49 pm

Willis: Your cumulative energy deficit analysis is probably misleading. Your analysis is totally dependent on the accuracy with which the zero point of the anomaly is set. Both the observed and GCM zero anomaly point are set by averaging a pre-Pinatubo period. If the averages that determine zero anomaly disagree by 1 W/m^2, the disagreement in cumulative energy deficit over the 50 months on your graph will be 50 W-months/m^2. The absolute magnitude of SW and LW radiation being measured is hundreds of W/m^2, so a 1 W/m^2 error in defining zero on the anomaly scale is only =<1% error.
Your own analysis shows how sensitive the results can be to precisely where the zero anomaly is set. For the GCM results, there does not appear any significant area above the zero anomaly line, however your graph shows that about half of the cumulative energy deficit has been eliminated over the years 1993-1995. This problem could arise because of errors in digitizing the data in Soden Figure 1. The 9 W-month/m^2 recovery you show over about 30 months could be due to a miniscule 0.3 W/m^2 error in identifying the zero anomaly point on the graph.
Under these circumstances, any analysis based on cumulative energy deficits appears meaningless.
Your post does illuminate the major weakness of Soden's work (which was actually published in '02 rather than '08): The positive SW anomaly in 1994-1996, which is about half the size of that associated with Mt. Pinatubo. This can only be due to a reduction in albedo and therefore presumably to changes in clouds. Soden02 completely ignores the role clouds play in the response to Pinatubo. The aerosols released by Pinatubo certainly could have a direct impact on cloud formation and rainfall, and therefore the extent of drying. Soden's analysis assumes that all changes in water vapor (which he presumably can only measure the changing locations where the sky is clear) are due to classical water vapor feedback responding only to changes in temperature. The idea that the response to Pinatubo can be analyzed in a meaningful way without mentioning changes in clouds appears totally absurd.

George E. Smith
December 1, 2010 3:19 pm

“”””” Curt says:
November 30, 2010 at 11:47 pm
……………………
By the way, you say, “So if you guys still want to call wind resistance and friction negative feedback; that’s fine with me; but I’ll take a pass on buying any car with control systems that you designed into it.” You may not realize it, but your safety already depends on control systems designed by me, and by people who would agree with me. Get used to it… If you fly in any commercial aircraft, the autopilot system uses system models that take air resistance as a negative feedback in the physical system of the plane. “””””
Curt, I don’t have a problem with your comment about taking air resistance as a negative feedback; presuming that your planes have a sensor that actually measures the air resistance, as an output separate from the plane’s speed; and produces some feedback signal to the input (maybe fuel adjustment, or attitude change) based on that measurement, via some control algorithm (feedback network). Onec ould make the argument that such control is actually a feed forward, in the sense that if you can sense the air resistance BEFORE it acts to decelerate the plane, and apply a compensating thrust; however jet engines do that.
Air resistance and friction are variables that create decelerating forces; but they don’t produce instantaneous speed change (I hope not); since the inertial mass of the plane prevents that; so feed forward is possible.
Way back in the Plasticine era, of feedback, some designers used to apply positive feedback (regeneration) with the idea of increasing the forward gain; and then they would add some overall negative feedback; in the belief that the higher forward gain would reduce the offset error. Of course the positive feedback amplifies any perturbations; so you don’t really gain anything; except a system that is more likely to go unstable.
Some of the worst (dynamic) feedback systems, are made with “op-amps” with forward gains of 10 million, and tons of feedback to get a gain of ten or something, and they think they have a signal bandwidth of 100 kHz or even 1 mHz; because that may be where there closed loop -3dB point is.
Well the problem is that their forward gain started dropping way back at 0.1 or maybe 1 Hz, so they may have DC precision, and distortion; but at higher frequencies the amplifier sucks.
I would rather have an open loop bandwidth that was as great as my required closed loop signal frequency response range, so that I had the same degree of feedback over my whole signal bandwidth range. Well I suppose within a factor of two or so, that would put any high frequency second harmonic distortion component beyond my signal band.
That will mean a lower open loop gain, so maybe the DC error is larger; but there are other ways to compensate for that.
Op-amp circuits make some of the worst feedback amplifiers if very low noise is required, because the two resistors to set the gain also form a forward attenuator, that attenuates the actual input signal power before it ever gets to any amplifier; not to mention the thermal noise of the ressitors themselves.
I want ALL of the available signal power to go right into the base or gate of an input transistor, so it has a chance of being heard above the input noise. But of course you can’t do that with the climate system.
I think feedback is a bad way to look at climate; because if you try to determine what the actual “forward gain” is you find there really isn’t much of any such thing.
You just have a lot of wildly interrelated variables, and there is some possible equilibrium or steady state solution for that set of variables and relations; but even that is useless, because the system is NEVER in equilibrium or anything like a steady state; because the earth rotates, and the sun only shines on half of it.
But there simply is NO defensible argument for saying Co2 is a GHG but H2O isn’t and H2O is a feedback but CO2 isn’t. Both of them directly affect themselves as well as everything else; but only H2o produces clopuds; and nobody ever observed it to get colder in the shadow zone when a cloud passes in front of the sun; it ALWAYS gets colder, because the amount of sunlight reaching the ground ALWAYS goes down with MORE H2O in any form anywhere in the atmosphere; and anywhere on earth.
And as to Barry Moore’s comment; I’m not as good as some at producing succinct rigorous scientific proofs; such as this for example:-
“””””“”””” Dinostratus says:
November 30, 2010 at 2:21 pm
George, you just missed the ball. That’s okay, we all do from time to time. I will say, most of us have done it enough such that we learn to adjust our internal transfer functions to require a minimum of negative feedback for a positive gain, just one person’s feedback.
Now that is right up there with “E = m.c^2 ” for brevity and rigor.
I have learned over the last 50 years on the job, that every time I write something brief; thinking the reader can fill in the details, I always get “feedback” from somebody, who says:- “well you forgot about such and such ?”; or “what about so and so?”, when in fact I didn’t forget a thing; I just didn’t think it needed to be spelled out in words of one syllable.
But here at WUWT we have a whole range of backgrounds and knowledge, and I would rather try and assist those who maybe don’t have a scientific background; but are still interested or concerned about this problem; if somebody can explain it in some way they can get their teeth into. If that raises the ire of all of the PhDs; most of whom know a hell of a lot more than I do, then that is better than leaving someone else unanswered; and if I get too far out on the thin ice; there’s always someone who can toss me a rope; like Phil has done from time to time.
I’m having to hit the books to bone up on some of this stuff myself; I only have a Bachelor of Science degree; and from some far flung University in the South Pacific; rather than from MIT or Stanford. so I’m doing the best I can.
I work in a sea of PhD physicists, and mathematicians, and materials scientists; and yesterday, I asked every one of them what they knew about the quantum theory of “thermal radiation” (BB-like); or for that matter any classical theory of thermal radiation. Not a one of them knows anything about either subject; including my immediate boss who has a list of degrees as long as your arm. So most of what I know; or think I know comes from 50 years in industry; I got out of Academia in 1960 because it was clear that it was going to be too confining.
And nobody snarfs up new information as eagerly as I do, so I am not at all bashful about learning from anyone who comes to WUWT to spread some real knowledge.

Curt
December 1, 2010 11:06 pm

George — You mistake my (and others’) point about air resistance as a feedback, which is that its effect on the dynamics of the system is every bit as real as if it were an engineered feedback effort. In the cruise control system, it is no less real because the engineered feedback system does not sense it directly.
I think your confusion stems from not understanding where in the block diagram the air resistance force gets fed back to. It is not to the summing node with the commanded velocity setpoint. Instead, it is to the summing node of forces on the car, of which the output of the engine governed by the cruise control system is one of the force inputs.
If I had a way of easily posting a block diagram, my point would be obvious. I will try to explain the block diagram in words, using the traditional orientation of these diagrams:
Into the top left is a signal representing the commanded velocity (the setpoint). It goes into a “summing node” where it is compared to a signal representing the measured velocity, coming from below and the right. The output of the node going to the right is the velocity error. This enters the transfer function for the “control law”, most likely with a proportional and integral term. The output of this block, continuing to the right, is the resulting motive force on the car. (If you want to get more detailed this would go through another block representing the dynamics of the engine and drive train that produce the force.)
This “control force” is an input to another summing node, this one combining all of the forward and reverse forces on the car, including gravity (if there is an incline) and air resistance. The output of this summing node, again going to the right, is the net forward/reverse force on the car. This enters the transfer function for the car’s physical “plant”, which is basically a 1/[M*s] integrator from force (through acceleration) to actual velocity, which is output to the right.
This actual velocity value “goes” two places in this simple model. First, it goes through a transfer function block that produces the retarding air resistance force as a function of the velocity. This force is one of the inputs into the force summing node mentioned above. Second, it goes through a sensor block to the velocity summing node first mentioned, where it is subtracted from the setpoint velocity value.
The fact that the first feedback is inherent in the physics of the plant, and the second feedback is an engineered effect does not matter — both are feedbacks.

George E. Smith
December 2, 2010 10:34 am

Well Curt, my intent was not to make you jump through hoops; and actually your word description of the system gave me a crystal clear picture of the block diagram. And I’m impressed that people do design such elaborate control loops, and I can see how many of your factors would become applicable to controlling a plane flight.
Where I differ in use of the term “feedback”, is that to me feedback comes directly from the controlled out put variable that the loop is supposed to be controlling, by adjusting the input signal (or set point) using whatever processing algorithm one may choose; such as three mode controllers would do.
I agree completely that other parameters or variables may exist that affect the desired output, such as wind resistance, friction, gravity, power supply noise or changes; water in the gasoline; etc. And it is clear to me that any of those things which can change the desired output, could if they can be “sensed” be used to create what I believe are properly “feedforward” terms; well I would call them “guesser circuits”, in that they anticipate things before they happen.
A change in headwind for example, is going to place an increased drag on an aeroplane, and absent a control mechanism, that would eventually slow the plane through F= ma. Now the velocity feedback will correct for this but only after the change has already started to happen. Directly sensing the perturbing force, such as an increased wind resistance allows one to deduce that the plane will be slowing; and the controller can figure out that relationship, to apply a corrective (engine thrust) to immediately oppose the grag increase, and actually stop the speed decline from even starting. Those sort of pre-emptive strikes are in my view feed forward examples; not feedbacks; they react to something that is expected to change the controlled variable (output) eventually.
And note that I said if you can “Sense” the perturbing influence such as wind resistance. That is not the same as calculating some presumed change in wind resistance that would accompany a change in speed, and using that as an input control signal, because that can’t pre-empt the ouput velocity change.
One of the best ways in chemical processing control loops to make a bomb, is to sense something other than the specific variable you want to control, and then generate a control feedback command that is based on some theoretical presumption of a specific relationship between the sensed variable, and the desired controlled variable. If any other perturbing influences can change that assumed relationship, then you don’t really have control of the process at all.
Having designed and built reactors, and process controllers for growing crystals and epitaxial layers in materials like Gallium Arsenide, and Gallium Arsenide Phosphide, involving quantities of Arsenic sufficient to poison all life in the universe; with lots of Hydogen carrier gas flowing around; I’ve had plenty of opportunity so contemplate what could happen if a loop got out of control.
Through about 12 years of operating such environments; we never once had a single employee ever test positive on a monthly Arsenic test. That is not the same as saying we never had any Hydrogen escape incidents. Well hydrogen being super light quickly floats up, and can form pockets in ceiling cavities, which can make for some interesting sparkles; but those are a lot more spectacle, than danger.
But honestly; if in your field it is the practice to consider these output perturbing variables as feedbacks and refer to them as such; then I certainly wouldn’t want to create confusions.
As it relates to the climate situation, thermal re-radiation from a warmed atmosphere back to the surface; which can release more CO2, AND more H2O into the atmosphere; i s absolutely independent of how that atmospheric warming occurred; so whether it resulted from H2O GHG effect, or CO2 GHG effect, of from H2O solar energy capture; the re-emision from the atmosphere is totally oblivious to what caused the atmospheric heating; and it is disingenuous for climatists to say that one (CO2) is a GHG “forcing”, but the other (H2O) is merely a “feedback amplification”. That is just plain silly.

Curt
December 2, 2010 6:23 pm

George — I think we’re getting a little closer. I’ll flog this almost-dead horse one more time. It is common terminology in many fields to use “feedback” to refer to effects that feed back within the physical system, and not just to the engineered controller. Of course, there is no engineered controller (yet!) for the climate system.
As far as sensors are concerned, a very large fraction of modern control design practice concerns the decision as to what states of the system should be measured, and which should be estimated. In any real-world system, it would be cost-prohibitive to sense every state and possible input. I doubt that there is any cruise-control system on the market that directly senses windspeed or inclination. Could you get better control if you did? Sure. But would it be worth the extra cost? Very doubtful. People are willing to tolerate a temporary speed perturbation when the wind or inclination changes. But they do expect the cruise-control system to reasonably quickly return the car to the setpoint speed. (And to do this, the controller must temporarily “overshoot” its response, a key point of Willis’ post.)
The control system I described to you in my last post was a “toy” system, the simplest possible system I could think of that could make my point. Many real-world control systems are several orders of magnitude more complex. In modern “state-space” control practice, one of your first steps is to create a matrix of relationships between each degree of freedom (“state”) of the physical system and every other one. Most of these are “feedbacks” inherent in the physics of the system. Then you figure out which of these states you can/want to sense, and which you will estimate. Next you write your algorithms for estimating the unmeasured states (the “observer”), based on your model of the system. Finally, you design your controller to act on the measured and estimated states as compared with any desired values for the states (the setpoints), again based on your model of the dynamics of the system. As I said before, your life often depends on the success of these systems.
In this formal system analysis, you must define which effects on a state are internal to the system as you have defined it (including feedbacks), and which are external to the system (called “disturbances”). In my cruise-control model, air resistance due to ground speed is a feedback to the force node. Air resistance due to wind is an external disturbance to this node, as are gravitational effects due to inclination. This is completely standard terminology and practice.
With this in mind, I do not have trouble with climate scientists calling CO2 radiative effects (primarily) a forcing and H2O radiative effects (primarily) a feedback. I don’t see any evidence that any internal effect could cause the CO2 concentration changes we have seen in the last century. Yes, there is a feedback effect from temperature that increases CO2 as a function of warming, but that is too slow and weak to explain what we have seen. Conversely, I don’t see any way human activity (external to the climate “system” as usually defined) could directly change the global water vapor concentration to a significant degree, especially given the atmosphere’s capability to quickly “rain out” excess vapor.
By the way, for 3 years in the 1980s, my office was on the floor directly above a III/V GaAs etc. fab. I developed a healthy respect for the issues there. I also noticed that no one was lobbying for on-site daycare…

kse
December 3, 2010 5:55 pm

Sorry about the blowing the gasket and posting a rather stupid comment. And yes – I have checked the dictionary for the meaning of “governor” and now I believe that I understand what it means. It just does not happen to be a common definition in signal processing (or I just have forgot it). But try to bear with me – after all, English is something like 3rd language for me.
Anyhow, I still what to claim that Willis’ concept about differencies between “governor” and “feedback” systems are bogus – mainly because (as I now understand) governor is just one type of feedback system. Furthermore, I do not see any need for taking back my words about the true nature of the likely reason for Willis’ misconception in this topic – and besides that – well, all your lengthy speculations about cruise-control, boilers and so on are not exactly very helpful in making this issue more understandable.
So, lets’ get back to basics – first of all there are two types of feedback systems: positive and negative ones. The former tends to multiply the effect of the input signal and in this case we are quite clearly not interested in that case. In the latter case, the feedback system dampens the effect of the input signal and tries to direct the system response towards a certain system dependent “normal state”.
If we forgot the badly designed feedback systems (poles of the transfer function are in veeery bad places) that can have chaotic behavior, we have basically two possible basic behaviors in our negative feedback system: one system that tends to overdampen the input (that is there won’t be any overshot) and another a system that allows the system response to oscillate around the “normal state” (there will be some overshooting).
If we now look at the “Soden08 figure 1” in the Willis’ blog post, we can quite easily make a claim that the GCM response is overdampened while the observed system behavior is not, that is, there is some overshoot.
I assume that the latter alternative is the one that Willis and the most of you commenters understand as a “governor” system, right? But that is just one kind of a negative feedback system and you really cannot claim that “feedback” would be bogus because the system is clearly a “governor”. Such claim is just an oxymoron.
If that did not make my point clear, please, take “Signal processing 101” or “Control theory 101” – or ask anyone with signal processing masters.