Excerpts from Evidence for Negative Water Feedback
by Clive Best
Abstract: Positive linear climate feedback for combined water effects is shown to be incompatible with the Faint Sun Paradox. In particular, feedback values of ~2.0 W/m2K-1 favored by current GCM models lead to non physical results at solar radiation levels present one billion years ago. A simple model is described whereby Earth like planets with large liquid water surfaces can self-regulate temperature for small changes in incident solar radiation. The model assumes that reflective cloud cover increases while normalized greenhouse effects decrease as the sun brightens. Net water feedback of the model is strongly negative. Direct evidence for negative water feedback is found in CRUTEM4 station data by comparing temperature anomalies for arid regions (deserts and polar regions) with those for humid regions (mainly saturated tropics). All 5600 weather stations were classified according to the Köppen-Geiger climatology [9]. Two separate temperature anomaly series from 1900 to 2011 were calculated for each region. A clear difference in temperature response is observed. Assuming the difference is due to atmospheric water content, a water feedback value of -1.5 +/- 0.8 W/m2K-1 can be derived.
I. INTRODUCTION
The Faint Sun Paradox was first proposed by Carl Sagan [1] who pointed out that the geological evidence that liquid oceans existed on Earth 4 billion years ago appears incompatible with a solar output 30% dimmer than today.
The sun is a main sequence star whose output is known to increase slowly with age. The total change in solar radiation over this long period turns out to be huge ~ 87 W/m2. It has been argued that an enhanced greenhouse effect due to very high CO2 and/or CH4 concentrations could resolve this paradox [2]. However, recent geological evidence does not support CO2 as being responsible but instead the authors propose a greater ocean surface leading lower albedo as a likely solution [3]. Others have suggested that high cirrus clouds effectively warmed the Earth [4]. Although the atmosphere must have been very different before photosynthesis began, the presence of large liquid oceans still implies that clouds and water vapor played a similar role in the Earth’s energy balance then, as they do today.
…
Figure 1: Past temperatures extrapolating backwards from today (T=288ºK) assuming different linear feedback values.
It is apparent that a simple linear positive feedback of +2 leads to unphysical results. The basic problem is that if the temperature falls sufficiently so that 4σT3= F then a singularity occurs ~1.5 billion years ago. Instead a negative feedback value of -2 W/m2K-1 is more compatible both with current temperatures and with the Faint Sun Paradox..
…
IV. CRUTEM4 ANALYSIS
Water vapor feedback in recent climate data have been investigated by studying differences between regions with very low atmospheric water vapor (Deserts and Polar) and those regions with very large water vapor content (Tropical Wet regions). The latest CRUTEM4 data [8] consisting of 5500 individual station data covering global land areas has been studied. Each station was classified by indexing its geographic location against the Köppen-Geiger climate classification [9].
“ARID” stations are defined as those with precipitation values ‘W’ or with climate ‘E’ in [9]. These are situated either in deserts or in polar areas having the lowest atmospheric water column on Earth [10]. “WET” stations are defined as those within fully humid Tropical areas – Climate ‘A’ and precipitation ‘f’ in [9]. These are situated in tropical rain forests or year-round humid climates having the highest atmospheric water column on Earth [10]. Global anomalies have been calculated for both stations ARID and WET stations independently using the same algorithm as used for CRUTEM4. The results are shown in Figure 4.
Figure 4: Temperature anomalies for ARID(DRY) stations in red and WET stations in blue. The smooth curves are FFT smoothed curves. The black dashed curve is an FFT smooth to the full CRUTEM4 global temperature anomalies.
There is a clear trend in the data that ARID stations warm faster and cool faster than WET stations. They respond stronger to changes in external forcing. The WET humid stations respond less than both the ARID stations and the global average.
Climate change is complex and global so it is reasonable to assume that both anthropogenic and natural forcing are reflected in the temperature anomaly data. For a given forcing DS the consequent change in temperature anomaly is gDT where g is a gain factor. The period between 1900 and 2005 is used to measure the temperature rise for each region DT1 and DT2 as given in Table 1. DS is assumed to be global in extent.
Table 1 : Temperature changes for ARID and WET regions and their ratio. Errors on DT are derived from differences between the FFT smooth and a linear fit.
| Period | DT1(DRY) | DT2(WET) | DT1/DT2 |
| 1900-2005 | 1.1 +/-0.1 ºK | 0.8+/- 0.1 ºK | 1.4 +/- 0.2 |
Heat inertia effects due to nearby oceans may cause tropical climates to react slower than desert regions, but not over such long periods. If positive feedbacks from increased water evaporation lead to enhance warming then this should be apparent in the tropics, and this is not observed. In fact the opposite is the case implying a negative feedback. Under the assumption that net water feedback F is present only for the WET stations (taking F=0 for ARID stations) then F can be measured from the data:
DT1/DT2 = 1 – G0F , where DT1 = G0DS and DT2 = G0 (DS+FDT2)
For G0-1 = 3.75W/m2K gives Water Feedback F = – 1.5 +/- 0.8 W/m2K-1
This is compatible with the value needed to resolve the Faint Sun Paradox. As has been pointed out by Lindzen [11] and others, much of the Earth’s heat is transported bodily through evaporation and convection to the upper atmosphere where IR opacity is low and can then escape to space. Therefore water feedback effects depend mostly on the water vapor content of the upper atmosphere. Increased evaporation, convection and consequent rain out could then result in lower humidity in the upper atmosphere. This is a possible mechanism for negative feedbacks in the tropics. Such effects would be largely absent in ARID areas, which have no local sources of evaporation.
Read the entire analysis here, it is well worth your time, well written, and easy to comprehend.
h/t to Scott Gates
From Leif Svalgaard on May 28, 2012 at 12:28 am:
Just plain kelvins, the unit. It’s been awhile, but that was drummed into me long before I got my physics bachelor’s degree, there are no degrees Kelvin. So I know you should be well aware of the distinction. You ever do a paper with “degrees Kelvin”?
There was also the inconsistency of using “K⁻¹” without the degree symbol (see Abstract and elsewhere), or simply “K” (the equation before the Conclusion), and also the lack of the symbol in the title of Figure 1 and elsewhere when “288K” was used, that indicates he should have known better.
Actually, when I think about it, the mix of notations gives the appearance of more than one mind working on it. Perhaps there was another author involved, or there was some amount of cut-and-paste, whatever it was. Good proofreading by a knowledgeable person should have caught it, at least made the usage consistent.
The use of °C for Figure 4 is allowable, as that’s what CRUTEM4 uses. But how can the rest of the paper use Kelvin otherwise, except for the Conclusion which is suddenly in °C? How could a single author do that?
This was submitted to the “prestigious” Geophysics Research Letters, which gets lots of more-polished submissions thus would have no reason to bother with it further. If I was an editor at a much-smaller journal, and considered the content interesting and I could simply remove the erroneous “degrees” from the text, I might do so, consider unifying to only kelvins as possible, and send it through the review process.
Yet the graphs also need correcting, there are the attribution questions, etc. Don’t get me wrong, it’s a great blog post, very informative. But as an editor, I would at least want this to look more professional before putting in the effort of getting it reviewed and maybe published. As professional as it should have been when it was sent to me in the first place.
To anyone reading this, feel free to continue talking about the publishing embargo against climate skepticism, which is real enough. What I’m pointing out is for this paper there are valid reasons to reject it regardless of content. Discussing the often-blatant discrimination against skepticism seems pointless to me with regards to this paper, when it is currently unpublishable anyway due to its amateurish style and presentation problems.
LS;
It’s improper use of the term “kelvin”.
1. In the International System of Units, the base unit of thermodynamic temperature; 1/273.16 of the thermodynamic temperature of the triple point of water. Shown as “K”.
2. A unit interval on the Kelvin scale.
3. The interval between the freezing and boiling points of water is 100 kelvins.
(usually as postpositioned adjective) A unit for a specific temperature on the Kelvin scale.
a) Ice melts above 273.16 kelvin.
b) Water boils above 373.16 kelvin.
The word “degrees” is redundant with kelvins; one may say 100 degrees Fahrenheit, or 100 degrees Celsius, but 100 kelvin.
OK agreed it should really be K and NOT deg.K. However the paper must use both deg.C and K because all calculations using Stefan Boltzman are in K, while all CRUTEM4 data is in deg.C. Since 273.15K = 0 deg.C , the rounding error converting K to deg.C by approximating 273K to be 0 deg.C is minuscule compared to measurement errors.
Sorry, reproduced the numbering above incorrectly:
1. In the International System of Units, the base unit of thermodynamic temperature; 1/273.16 of the thermodynamic temperature of the triple point of water. Shown as “K”.
2. A unit interval on the Kelvin scale.
——The interval between the freezing and boiling points of water is 100 kelvins.
3. (usually as postpositioned adjective) A unit for a specific temperature on the Kelvin scale.
a) Ice melts above 273.16 kelvin.
b) Water boils above 373.16 kelvin.
GES;
Kinda pit-nicky today! You’re too hard on Robert; the best analogy for the GE is DC positive feedback. Close enough for government work, which it is.
Oh, by the way, could you explificate a bit more about these very intriguing radios using “positie” feedback? Sounds downright cutsie!
And I didn’t realize you were so religious!
Are you conflating Christ and Ra?
kadaka (KD Knoebel) says:
May 28, 2012 at 2:48 am
“What should he have used? Fahrenheit?”
Just plain kelvins, the unit
Being picky today eh? We used ‘degrees Kelvin’ up to about 1968. After it is ‘kelvin’ without the ‘s’..
But even so, the ‘degrees Kelvin’ is still around, e.g. in: http://csep10.phys.utk.edu/astr162/lect/cosmology/cbr.html
http://eesc.columbia.edu/courses/ees/climate/lectures/radiation/
http://www.sciencedaily.com/releases/2006/03/060308212104.htm
It seems overly pedantic to disallow ‘degrees’. Even the well-known text books http://www.amazon.com/Essentials-Meteorology-Invitation-Atmosphere-CD-ROM/dp/0534372007
uses ‘degrees Kelvin’.
kadaka (KD Knoebel) says:
May 27, 2012 at 10:25 pm
As to the rejection of Clive Best’s paper, could it be because he used degrees Kelvin?
Leif Svalgaard says: May 28, 2012 at 12:28 am
What should he have used? Fahrenheit?
_______________
Good question Leif – I too was wondering about this.
I had forgotten about degrees Rankine.
Apparently there are also degrees
Delisle
[°De] = (100 − [°C]) × 3⁄2
Newton
[°N] = [°C] × 33⁄100
Réaumur
[°Ré] = [°C] × 4⁄5
Rømer
[°Rø] = [°C] × 21⁄40 + 7.5
Not to mention Goode Olde Englishe units – how about something involving hogsheads or firkins?
Not to forget the gill, drachm, minim, spoon, pin, peck, kilderkin, barrel, puncheon, tun, butt, cord, rick, fathom, and my personal favorite, the Hoppus foot.
Apparently, in Scotland, 2 mutchkins = 1 chopin. Who knew?
Can anyone tell me if the faint sun paradox takes into consideration the initial specific heat of the earth, it’s initial temp, the fluid dynamics of a mostly molten ball of iron and rock, and given the much higher density atmosphere (and our complete ignorance of same), how much such a system would cool in a billion years with no solar insolation whatsoever ?
Mike Wryley says:
May 28, 2012 at 6:50 am
Can anyone tell me if the faint sun paradox takes into consideration the initial specific heat of the earth, it’s initial temp, the fluid dynamics of a mostly molten ball of iron and rock, etc…
Yes, scientists are not morons and the review I linked to goes through the various factors.
Stephen Wilde says:
May 26, 2012 at 11:42 pm
Liquid oceans for 4 billion years despite huge volcanic outbreaks, asteroid strikes, changed atmospheric density and composition and a substantial change in the output of the sun.
The only solution is a strongly negative water cycle response to ANY disruption to the system.
I agree, only a strong negative feedback really holds water in resolving the dim sun paradox. CO2 is a non-starter as it has fluctuated wildly with no credible relationship with temperature, e.g. snow-ball earth ice-ages during CO2 concs >10k ppm. (While very loosely one can say CO2 has declined over the earth’s history, there have been periods of hundreds of millions of years where temperatures and CO2 levels were moving in opposite directions, e.g. around the Silurian-Carboniferous.) Other factors such as ocean cover, volcanism, require a gradual change precisely calibrated by pure chance to exactly counter the increasing insolation. Not credible.
As other posters have pointed out, the major point here is that AGW needs a positive water feedback which can be shown not to be credible. CAGW was formulated with a narrow, blinkered focus on the second half 20th century, ignoring any previous climate history. Their palaeoclimate defences have been awkwardly bolted on later.
Water vapour in the atmosphere is acknowledged by most to be dominant in the atmosphere’s thermal dynamics. If this dominant component were characterised by positive feedbacks, then the whole climate system would be hugely unstable – and it is not. So the formulation of the AGW theory has been not only in willful ignorance of palaeoclimate history, but also sterile of any appreciation whatsoever of nonlinear system dynamics. They just dont understand the consequences of their assertion of dominant positive feedback.
In a non-equilibrium/nonlinear quasi-chaotic system such as the earth’s atmosphere-oceanic climate, if positive feedbacks are dominant then they suppress complex emergent structure (nonlinear pattern formation) and impose monotonic oscillation. (The heart-beat is an example of this.) Since climate does not oscillate monotonically – but in a complex and modulating way – then it is clear that positive feedbacks are not dominant. Negative feedback, otherwise called damping or dissipation, lead to the emergence of complex fractal structure. So the fleeting appearance of oscillations in an overall complex jumble with fractal characteristics point to a tension between positive and negative feedbacks.
In short, its impossible for the earth’s stable and robust – while at the same time complex and fractal – climate system NOT to be damped. And the evidence is strong that atmospheric water is doing the damping (negative feedback).
Crispin in Waterloo says:
May 27, 2012 at 12:56 pm
@Larry Plume P.
“The Mantle of the Earth is said to contain about twice as much water as the oceans. Could it be that it simply sunk into the mantle over time until it was ‘balanced’? It is very possible that we were ‘Water World’ in the early days.”
Crispin, Pope and colleagues – in the article that I linked – found out that the isotope ratio of deuterium to normal hydrogen changed during the ages and this ratio change can be explained through methanogenesis (two-stage process, water and carbon dioxide react to form methane, and subsequently hydrogen – see above link) which favours hydrogen to deuterium.
In this explanation doesn’t matter how much water did flow in the mantle it does not explain the ratio change. It does not exclude the water flow into the mantle but is an indicator of very probable water decomposition and hydrogen flow into space.
Probably the oxygen has been then bounded to other minerals and in my view may also explain why oxygen appeared relative early in the history, but this is only speculation on my side.
“”””” In a non-equilibrium/nonlinear quasi-chaotic system such as the earth’s atmosphere-oceanic climate, if positive feedbacks are dominant then they suppress complex emergent structure (nonlinear pattern formation) and impose monotonic oscillation. (The heart-beat is an example of this.) Since climate does not oscillate monotonically – but in a complex and modulating way – then it is clear that positive feedbacks are not dominant. Negative feedback, otherwise called damping or dissipation, lead to the emergence of complex fractal structure. So the fleeting appearance of oscillations in an overall complex jumble with fractal characteristics point to a tension between positive and negative feedbacks. “””””
Sorry; negative feedback doesn’t have a thing to do with damping or dissipation; they are totally different and unrelated subjects. You can demonstrate the effect of damping or the lack thereof, in a complete absence of ANY feedback; whether positive or negative. I will grant you that “dissipation” is a rather imprecise colloquialism for damping.
If you apply a step function from a zero source impedance source, to a series connected inductor, and capacitor combination; or their analogs in some other discipline, you WILL get an oscillation, which theoretically will persist forever (in classical Physics, anyway). Ther’s not a whit of feedback anywhere in that system, so one can’t even talk about positive or negative; it is zero.
But in practice; no source actually has zero source impedance, and no inductor or capacitor has zero resistance component; maybe at superconducting Temperatures, they can have zero R.
So the inclusion, accidently or deliberately of some resistance; which IS an energy dissipative element, will gradually dissipate some of the energy, which is being transferred back and forth between a Voltage across the capacitance, and a current through the inductance Ppower is lost at the rate of I^2.R.
When talking about climate elements, and feedbacks, it is wise and instructive, to consider the following simple fact.
There is NO SUCH THING as a an electronic amlifying system, which makes a practical usage of feedback; either positive or negative; where such amlifying system; prior to the connection of feedback networks, HAS A POWER GAIN OF LESS THAN UNITY. ALL such systems start with an input to output POWER GAIN, that is greater than 1, and usually VERY MUCH GREATER THAN ONE, before any feedback networks are added. Those feedback networks, will result in a reduction of the final system power gain. They do that without necessarily DISSIPATING any power in the process, although dissipation of small amounts of power is not prohibited.
So what about the climate system. Starting with an input signal from the sun, and for the moment excluding all GHGs from the atmosphere; just WHAT in the earth climate system has an input to output power gain, GREATER THAN ONE.
Well there is nowhere in the system where you ever see an “output” signal power, that is GREATER THAN TSI.
So talking about feedback in relation to climate, is total nonsense. There is no amlifying structure in in with a power gain in excess of one. One consequence of the absence of a positive power gain, anywhere in the climate system, is that there also cannot be any positive power gain involved in ANY feedback network; so both the forward, and feedback power gains for any feedback loop you want to create out of the climate system elements, are ALWAYS less than unity. Consequently the LOOP GAIN, which is the product of the forward, and feedback power transfer functions, can never reach; let alone exceed unity.
Ergo, it is inherently impossible; no matter what, for such a system to oscillate in any runaway mode.
Lief,
With all due respect, the incidence of morons within the scientific community is at least as high
as within the general population.
And your link does not work
4 billion years ago, the sun was heavier than it is today, which would have made the earth’s orbit smaller. Being closer to the sun would help to compensate for the sun being dimmer. Also the tidal affect between the earth and the sun would have added a few miles to the earth’s orbit over that time period.
As to the amount of water on the earth back then. The earth is still comets of varying sizes, from dinosaur killers to micro. I would assume that 4 billion years ago, the rate of impact would have been higher, gradually decreasing to today’s rate. Over 4 billion years, that’s a lot of water.
George E. Smith; says:
May 28, 2012 at 9:02 pm
“”””” In a non-equilibrium/nonlinear quasi-chaotic system such as the earth’s atmosphere-oceanic climate, if positive feedbacks are dominant then they suppress complex emergent structure (nonlinear pattern formation) and impose monotonic oscillation. (The heart-beat is an example of this.) Since climate does not oscillate monotonically – but in a complex and modulating way – then it is clear that positive feedbacks are not dominant. Negative feedback, otherwise called damping or dissipation, lead to the emergence of complex fractal structure. So the fleeting appearance of oscillations in an overall complex jumble with fractal characteristics point to a tension between positive and negative feedbacks. “””””
Sorry; negative feedback doesn’t have a thing to do with damping or dissipation; they are totally different and unrelated subjects. You can demonstrate the effect of damping or the lack thereof, in a complete absence of ANY feedback; whether positive or negative. I will grant you that “dissipation” is a rather imprecise colloquialism for damping.
If you apply a step function from a zero source impedance source, to a series connected inductor, and capacitor combination; or their analogs in some other discipline, you WILL get an oscillation, which theoretically will persist forever (in classical Physics, anyway). Ther’s not a whit of feedback anywhere in that system, so one can’t even talk about positive or negative; it is zero.
Your definition of feedback may be a little restrictive – you are looking only at electrical circuits. Feedback can be meant more widely as anything which is a consequence of a forcing agent in a system which sets in motion processes which eventually act to either reinforce (positive feeback) or resist (negative feedback) the initial forcing agent. In this sense simple friction is a negative feedback – increasing road speed in a car results in increased friction both in air and at the road surface so that friction resistance increases with speed. Eventually friction equals accelerating force and the car reaches equilibrium speed.
So talking about feedback in relation to climate, is total nonsense.
This is quite a bold statement when the majority of climate scientists on both sides of the AGW fence repeatedly assert that the CENTRAL question in climate is the magnitude and sign of feedbacks. I think this is a question of terminology – different disciplines use the term feedback differently. “Climate science” as has been explained before, is not really a field in its own right, it lives parasitically off oceanography, radiative and optical physics, geology, solar physics, ecology, geosciences and several other disciplines.
I (unlike you) am no engineer. This means I am not best placed to really get to grips with these issues of nonlinear dynamics since it is within certain fields of engineering where understanding of nonlinear system dynamics is strongest and best developed – in my view chemical engineering is foremost among these.
Thus although trying to sound knowlegable in these things, I am discussing work and theory that I only partially understand at best. But I would still bet my house (flat) or car that I am right – in the general sense that the nonlinear / nonequilibrium system paradigm is the right one for climate. Why? Because it “feels” compelling and appropriate. That might sound crap, but sometimes in nonlinear chaos-like systems its the best you can hope for – until someone fully works out the science of it. The experimental system that I am thinking of primarily in relation to the role of feedbacks in nonlinear pattern formation is the one much used in this context, the platinum-catalysed oxidation of CO under the influence of chemical feedbacks regulated by gas pressures, and specifically the spatio-temporal patterns formed on the crystal surfaces. (This is what happens in your car’s catalytic converter.) Two papers describing it are (unfortunately paywalled):
Science 18 May 2001:
Vol. 292 no. 5520 pp. 1357-1360
Controlling Chemical Turbulence by Global Delayed Feedback: Pattern Formation in Catalytic CO Oxidation on Pt(110)
Minseok Kim, Matthias Bertram, Michael Pollmann, Alexander von Oertzen, Alexander S. Mikhailov, Harm Hinrich Rotermund* and Gerhard Ertl
http://www.sciencemag.org/content/292/5520/1357.short
APPLIED PHYSICS A: MATERIALS SCIENCE & PROCESSING
Volume 51, Number 2 (1990), 79-90,
Nonlinear dynamics in the CO-oxidation on Pt single crystal surfaces
Ralf Markus Eiswirth, Katharina Krischer and Gerhard Ertl
http://www.springerlink.com/content/j587322461531360/
One of these authors, Matthas Bertram, with whom I have corresponded on these issues, used to have his excellent PhD thesis online, which is a rich source of explanation and experiemental plus mathematical work on chaos, turbulence and spontaneous pattern formation, from the field of chemical engineering. Sadly he took it down. If you are interested I can upload a copy of it.
It is this Pt 110 crystal catalysed CO oxidation system that shows very clearly that (a) negative feedbacks in the system stimulate spontaneous pattern formation (all nonlinear pattern formation needs a dissipative element – here again I am loosely associating dissipation with negative feedback, but I’m not alone in doing so) and that (b) introducing positive feedback “kills” the more fecund and complex pattern formation and imposes more uniform and monotomic oscillation. What is most compelling from the climate perspective is that you get this scenario of tension between the positive and negative feedbacks resulting in complex nonperiodic pattern but with periodic uniform oscillation intermittently and partially manifesting in the system. This looks a lot like climate temperature series.
Ian W says
“The paper should be assessing the heat content in kilojoules. Temperature alone is meaningless and the incorrect metric for heat content.”
You need to speak to the IPCC about that. In order to speak the same language as the IPCC and avoid comparing “apples to oranges,” we are forced to evaluate climate not only in terms of temperature but globally-averaged temperature.
“”””” re phlogiston Your definition of feedback may be a little restrictive – you are looking only at electrical circuits. “””””
No I am not looking only at electrical circuits; I simply gave an electrical analogy, which is among the easiest to understand for non experts. How many different examples of feedback would it take for you to see, my description is not at all restrictive. If I gave examples from 50 different classes of physical systems, would that be enough to show lack of restriction, or should I give perhaps 100 ?
By the way, virtually all physical systems are bidirectional; twoports being the simplest to understand. They have both forward, and backward transfer functions, and traditionally the forward direction is commonly regarded as the direction in which there is a net power gain.
The mathematics of feedback networks, is not at all restricted to any one physical implementation; they can be mechanical, hydraulic, optical, and on and on. What you are calling feedback is little more than the natural cause and effect relationship, including time delays.
When you toss a rock into a pond; lots of physical cause and effect relationships are activated. Waves spread out from the rock, the rock meanders down to the bottom, where it will collide with what is there which might happen to be a scuba diver. Eventually all those consequent effects will settle down. That is NOT feedback operating, it is simply the finite propagation delay of physical phenomena.
George E. Smith; says:
May 30, 2012 at 1:48 pm
I’ll keep an eye open above me for falling rocks next time I go scuba diving.
With so much talk of feedbacks it is indeed necessary to clarify definitions of what is feedback and what is not.
The PhD thesis of Matthias Bertram that I mentioned can be downloaded here.
Here is a quote from it [page 27, section on global feedback]. I boldened the word “information” since here Bertram brings in an interesting and important aspect of feedback (he is talking about delayed feedback) – that it is an information signal. So feedback is not just about power/energy, it is about information also.
3.2 Global feedback
3.2.1 Overview of feedback schemes
Feedback techniques differ from periodic forcing by the fact that the control signal is not fixed a priori, but an acting force is generated by the system itself. Feedback techniques were originally designed for the control of chaos in dynamical systems with only a few degrees of freedom [96–99], but were later extended for the application to high-dimensional systems governed by partial differential equations [36, 63–71].
In global feedback methods, information continuously gathered from all system elements is summed up and used to generate a control signal which acts back on a common parameter that affects the dynamics of the entire medium. Such a feedback loop can be easily implemented into many experimental systems, and does not require the knowledge of the governing equations. The action of global feedbacks on chaotic extended systems has been recently investigated experimentally for arrays of electrochemical oscillators [100], and theoretically for semiconductors [38] and surface chemical reactions [101, 102]; effects of global feedback also have been discussed in the general context of the complex Ginzburg-Landau equation [36, 37]. Furthermore, various forms of global feedback have been successfully applied to control pattern formation in non-chaotic oscillatory [41,103,104] and excitable [105–109] chemical systems.
Some climatic or oceanographic phenomena set in motion processes which take years to run their course. For instance, an El Nino event generates a pool of equatorial warm water which then migrates anticlockwise around the Pacific basin for several years, warming the Arctic up to a decade later. Changes induced in cold water downwelling – say at the Norwegian sea – could have effects on ThermoHaline Circulation at even longer times in the future. Could such delayed “signals” act as feedback signals in the sense that Bertram is describing in the various experimental systems?
OK so killing the bold killed the italics also. The Bertram quote extends to “and excitable [105-109] chemical systems”. After that it’s me again.