Earth Day Thoughts

Cross-Posted from Coyote Blog

Happy Birthday Vladimer Lenin Earth Day.  I have a few thoughts for the day:

Sucking the Oxygen Out of the Environmental Movement

Observe today how little of the discussion is about anything other than climate.  There are still many environmental issues in the world that can be improved by the application of man’s effort and technology — unfortunately, climate is the least of these but the issue getting the most attention.  Consider how the global warming panic has sucked the oxygen out of the environmental movement.  Ten years from now, I predict that true environmentalists will be looking back on the hysteria over trace amounts of CO2 in the atmosphere as a huge setback for real environmental progress.

Environmentalism and Socialism

If you attend any Earth Day events today, notice how many of the speeches and presentations and such are anti-corporate, anti-trade, anti-capitalist, anti-wealth screeds, and have little to do with the environment.  If you actually go to a live Earth Day event, you will see why the selection of Lenin’s birthday was no accident.  You will not see this on the network news, because the media is sympathetic to the environmental movement and tends to edit the socialist rants out as PR protection for the environmentalists, knowing that American audiences would lose sympathy for them if they listened to the whole package. (This is mostly an American phenomenon – I have found from my brief travels in Europe that the media there does less such editing, perhaps because they know their audience is more comfortable with socialism).

The Climate Denier Trick

There are a lot of reasons not to be worried about "inaction" on global warming.  To justify the enormously expensive cuts in CO2 productions, on the order of 80% as supported by Obama and Clinton, one has to believe every element of a five-step logic chain:

  1. Mankind is increasing CO2 concentrations in the atmosphere
  2. Increased atmospheric CO2 causes the world to warm (by some amount, large or small)
  3. The increases in CO2 from man will cause substantial warming, large enough to be detectable above natural climate variations
  4. The increases in world temperatures due to man’s CO2 will have catastrophic impacts on civilization
  5. These catastrophic impacts and their costs are larger than the enormous costs, in terms of poverty and lost wealth, from reducing CO2 with current technologies.

Climate alarmists have adopted a rhetorical trick that no one in the media seems willing to call them on.   They like to wage the debate over global warming policy on points one and two only, skipping over the rest.  Why?  Because the science behind numbers one and two are pretty strong.  Yes, there are a few folks who will battle them on these points, but even very strong skeptics like myself accept points one and two as proved. 

Here are some examples of how this trick works.  If, like me, you do not accept steps 3-4-5 in the above logic chain, you will be called a "denier."  When asked what a denier means, a climate alarmist will often position this denial as somehow disputing #1 and #2.  On the other hand, if one publicly accepts #1 and #2, the alarmist will shout "QED" and then proceed to say that strong action on CO2 is now justified.  When an alarmist says that the a consensus exists, he is probably correct on points 1 and 2.  But he is absolutely incorrect that a consensus exists on 3-4-5.

Don’t believe me?  Think back to the early Republican debate, where the moderator asked for a show of hands whether [I can’t remember the exact question] man was causing global warming.  The implication is that you either have to accept this whole logic chain or not.  One can see why Fred Thompson begged to have 90 seconds to explain his position, and why the moderator, presumably in the alarmist camp, denied it to him. 

Over the last year or two, skeptics have gotten a lot better at making their argument.  Most all of them, like I do, begin their arguments by laying out a logic chain like this and explaining why one can believe that man-made greenhouse gases cause warming without accepting the need for drastic climate action.  The result?  Alarmists have stopped debating, and/or have declared that the debate is "over."  Remember that last great Al Gore climate debate?  Neither do I.

The Single Best Reason Not To Be Worried About Climate

I could, and have, in my books and videos, made arguments on many points in 3-4-5 (links at the bottom of the post).  In four, no one ever considers the good effects of warming (e.g. on growing seasons and crop yields) and most every other problem is greatly exaggerated, from hurricane formation to sea level rises.  And in five, every time someone has tried to put a price on even small reductions in CO2, the numbers are so enormous that they are quickly suppressed by a environmentalist-sympathetic media.  Suffice it to say that even the climate-sanctimonious Europeans have not been willing to pay the price for even slowing down their CO2 growth (which has risen faster than in the US), much less reducing it.

But in this logic chain, there is little need to argue about four and five if #3 is wrong.  And it is.

The effects of CO2 acting alone on temperatures are quite small — And everyone, even the alarmists, agree!  A doubling of CO2 concentrations, without other effects that we will discuss in a moment, will heat the earth no more than about 1 degree Celsius (though several studies recently have argued the number is much less).  This is not some skeptic’s hallucination — this is straight out of the IPCC third and fourth assessments [IPCC text quoted here].  In fact, the IPCC in their reports has steadily reduced their estimate of the direct contribution of CO2 on temperatures.  CO2, acting alone, warms the Earth only slowly, and at this rate we would see less than a degree of warming over the next century, more of a nuisance than a catastrophe.

But some scientists do come up with catastrophic warming forecasts.  They do so by assuming that our Earth’s climate is dominated by positive feedbacks that multiply the initial warming from CO2 by a factor of three, four, five or more.  This is a key point — the catastrophe does not come from the science of greenhouse gases, but from separate hypotheses that the earth’s climate is dominated by positive feedback. This is why saying that greenhouse gas theory is "settled" is irrelevant to the argument about catastrophic forecasts.  Because these positive feedbacks are NOT settled science.

In fact, the IPCC admits it does not even know the sign of the most important effect (water vapor), much less its magnitude.  They assume that the net effect is positive, and in fact strongly so – on the order of 60-80% feedback or more, nearly unprecedented numbers for a long-term stable physical system [more on feedback and its math here].  This is particularly ironic because alarmist Michael Mann, with his hockey stick, famously posited that temperatures over the last 1000 years were incredibly flat and stable until man started burning fossil fuels, a proposition that is hard to believe if the climate is dominated by strong positive feedback.   Note that when people like Al Gore say things like "tipping point," they are in effect hypothesizing that feedback is greater than 100%, meaning that climate can be a runaway process, like nuclear fission.

In fact, with the 100 or so years of measurements we have for temperature and CO2, empirical evidence does not support these high positive feedbacks. Even if we assign all the 20th century warming to CO2, which is unlikely, our current warming rates imply close to zero feedback.  If there are other causes for measured 20th century warming other than CO2, thereby reducing the warming we blame on CO2, then the last century’s experience implies negative rather than positive feedback in the system.  As a result, it should not be surprising that high feedback-driven forecasts from the 1990 IPCC reports have proven to be way too high vs. actual experience (something the IPCC has since admitted).

However, climate scientists are unwilling to back down from the thin branch they have crawled out on.  Rather than reduce their feedback assumptions to non-catastrophic levels, they currently hypothesize a second man-made cooling effect that is masking all this feedback-driven warming.  They claim now that man-made sulfate aerosols and black carbon are cooling the earth, and when some day these pollutants are reduced, we will see huge catch-up warming.  If anything, this cooling effect is even less understood than feedback.  What we do know is that, unlike CO2, the effects of these aerosols are short-lived and therefore localized, making it unlikely they are providing sufficient masking to make catastrophic forecasts viable.  I go into several reality checks in my videos, but here is a quick one:  Nearly all the man-made cooling aerosols are in the northern hemisphere, meaning that most all the cooling effect should be there — but the northern hemisphere has actually exhibited most of the world’s warming over the past 30 years, while the south has hardly warmed at all.

In sum, to believe catastrophic warming forecasts, one has to believe both of the following:

  1. The climate is dominated by strong positive feedback, despite our experience with other stable systems that says this is unlikely and despite our measurements over the last 100 years that have seen no such feedback levels.
  2. Substantial warming, of 1C or more, is being masked by aerosols, despite the fact that aerosols really only have strong presence over 5-10% of the globe and despite the fact that the cooler part of the world has been the one without the aerosols.

Here’s what this means:  Man will cause, at most, about a degree of warming over the next century.  Most of this warming will be concentrated in raising minimum temperatures at night rather than maximum daytime temperatures  (this is why, despite some measured average warming, the US has not seen an increase of late in maximum temperature records set).  There are many reasons to believe that man’s actual effect will be less than 1 degree, and that whatever effect we do have will be lost in the natural cyclical variations the climate experiences, but we are only just now starting to understand.

To keep this relatively short, I have left out all the numbers and such.  To see the graphs and numbers and sources, check out my new climate video, or my longer original video, or download my book for free.

Update: Very relevant article by Roy Spencer on the over-estimation of feedback in climate models.

Many of us, especially those who were trained as meteorologists, have long questioned the climate research community’s reliance on computerized climate models for global warming projections.  In contrast to our perception that the real climate system is constantly readjusting to internal fluctuations in ways that stabilize the system, climate models built upon measured climate behavior invariably suggest a climate system that is quite sensitive – sometimes catastrophically sensitive — to perturbations such as those from anthropogenic greenhouse gas emissions.  Unfortunately, it has been difficult to articulate our ‘hand-waving’ concerns in ways that the modelers would appreciate, i.e., through equations.   

After years of pondering this issue, and after working on our two latest papers on feedbacks (Spencer et al., 2007; Spencer and Braswell, 2008, hereafter SB08), I believe that I can now explain the main reason for this dichotomy.   Taking the example of clouds in the climate system, the issue can be introduced in the form of a question:

To what extent are climatic variations in clouds caused by temperature change (feedback), versus temperature change being the result of cloud variations? 

  • Scientist

    the northern hemisphere has actually exhibited most of the world’s warming over the past 30 years, while the south has hardly warmed at all. – yes, this is because the southern hemisphere is dominated by oceans and has far greater thermal inertia.

    The climate is dominated by strong positive feedback… – you always use this terminology. What on earth do you mean by ‘dominated’? All you really need to say about the climate system is that feedbacks exist and will magnify the effect of any initial perturbation. Your use of the word ‘dominated’ is scientifically meaningless.

    …despite our experience with other stable systems that says this is unlikely… – nonsense.

    …and despite our measurements over the last 100 years that have seen no such feedback levels. – our measurements over the last 100 years clearly show that the most rapid warming is occurring at high northern latitudes. This is because of the ice-albedo feedback.

    As always, you don’t even really try to hide your real motivation for disbelieving the science of global warming. For you, it’s obviously purely about politics.

  • In the Iowa debate you mentioned Fred Thompson’s legitimate request to be heard instead of manipulated into confirming her political agenda…she tried to pull that on presidential candidates by the way, and would have gotten away with it if Thompson wouldn’t have declined to answer.

    THAT is exactly the strength and honesty in a leader the environmentalists absolutely need to get the ball rolling. If they know they’ll tell you straight out what’s going on and if they don’t they’ll tell you that as well.

    Poor excuses for human beings like Gore, Clinton and naive clowns such as Obama are exactly who we DON’T need.

    Is anyone catching on here??

  • Hey “Scientist”,

    While you’re feeling chatty, rummage through this for us;

    U.S. Senate Report: Over 400 Prominent Scientists Disputed Man-Made Global Warming Claims in 2007
    Senate Report Debunks “Consensus” Report Released on December 20, 2007
    http://epw.senate.gov/public/index.cfm?FuseAction=Minority.SenateReport

    Now, where exactly does your nonsense stop and reality begin?

  • coveman

    If anyone out there needs any more proof of the folly of environmentalists trying to save us all from ourselves, just stay tuned to the developing food crisis and riots stemming from the biofuels business. This is serious, folks. This disaster is REAL and it is happening NOW, not fifty years from now.

    Like something out of a Shyamalan film, rich people’s fear of a mythical disaster called “Global Warming” has taken food from the mouths of the poor.

    And now that we have thoroughly entangled our infrastructure with these biofuels, the earth has stopped cooperating with the Alarmists and is defying all of their predictions. It seems the good earth is doing what it wants to do, regardless of what clowns dressed up in polar bear suits say. How about that?

    Who will save us from the saviors?

  • For you, it’s obviously purely about politics.

    Oh, that’s rich. You probably would have ridiculed Galileo for getting involved in politics, too. The difference is that this time, it’s the so-called “scientists” playing the role of the church.

  • Stevo

    “our measurements over the last 100 years clearly show that the most rapid warming is occurring at high northern latitudes. This is because of the ice-albedo feedback.”

    How can a feedback cause warming? Surely it only amplifies change?

    Ice cover feedback works both ways. If it warms, ice retreats causing more warming. If it cools, ice extends causing more cooling. So if the aerosol effect was causing net cooling in the Northern hemisphere, the ice albedo feedback would magnify this and make it cool even more. Yes?

    And if the aerosols were providing a cooling roughly three quarters the magnitude of the total warming (1.2 W/m^2 vs 1.6 W/m^2), but concentrated into five or ten percent of the Earth’s surface (or indeed, anything less than about half the Earth), shouldn’t that show up as a rapidly cooling patch over India and China? Can you show me that?

  • Scientist

    How can a feedback cause warming? Surely it only amplifies change? – your questions don’t really make sense. A feedback causes warming because it amplifies change. In the same way, if you turn up the gain on an amplifier, that causes more noise.

    if the aerosol effect was causing net cooling in the Northern hemisphere, the ice albedo feedback would magnify this and make it cool even more. Yes? – yes.

    concentrated into five or ten percent of the Earth’s surface – what makes you think aerosols should be concentrated like this?

  • TCO

    Another butt ugly post by SM on calibration formologies. I completely think that this is an area where SM could have made some interesting and easily explored discussion. But instead we have meanderings and half explanations. He is such a Monica pole smoker.

  • Doug Foss

    The central point of this post seems to be the proportion of projected warming arising from direct CO2 forcing versus amplification from feedback(s). Is there any data, as opposed to theories (read “models”), that supports (1) positive feedback and (2) relative contributions of (i) direct greenhouse gas forcing and (ii) feedback. I generally am aware that, over time, IPCC has taken different positions on the extent of direct forcing and relative contributions of direct forcing and feedback, but I would appreciate it if anyone could point to published research and archived data addressing this question. Also, if there is no such data, then how do programmers properly code GCMs?

  • Scientist

    Doug Foss – here’s a link to a great website that’s got an extensive summary of all the scientific work on this: http://www.ipcc.ch.

  • Doug Foss

    Scientist – Thanks for your link. Your reference was to both the Working Group I and Working Group II reports, and from what I could ascertain, you likely were pointing to the chapter 2 discussion in the Working Group I Report. On page 215 of that discussion I found the following comment concerning forcing by CO2: “The [Anthropogenic Global Warming Potential] of CO2 again depends on the radiative efficiency for a small perturbation of CO2 from the current level of about 380 ppm. The radiative efficiency per kilogram of CO2 has been calculated using the same expression as for the CO2 RF in Section 2.3.1, with an updated background CO2 mixing ratio of 378 ppm. For a small perturbation from 378 ppm, the RF is 0.01413 W m–2 ppm–1 (8.7% lower than the TAR value).” There were similar discussions of implications for other greenhouse gases – halocarbons, carbon monoxide, methane and so forth. The portion I looked at referred back to Part 2.3.1, which had lengthy discussion concerning intensifying levels of CO2 over time and Ramaswamy (2001) calculations resulting in +3.7 W m-2 in radiative forcing. It adds in this respect: “These formulae are based on global RF calculations where clouds, stratospheric adjustment and solar absorption are included, and give an RF of +3.7 W m–2 for a doubling in the CO2 mixing ratio.”

    If this constitutes the AR4 discussion of effect with feedbacks, I could not find the reference to feedbacks other than the simple statement that “clouds, stratospheric adjustment and solar absorption are included”. Further, as evidenced by the quotes, the conclusions offered in chapter 2 all appear to be “calculated” without any reference to measured data. Nor did I find reference to measurement of feedback data in the list of references immediately following chapter 2. Maybe I looked in the wrong spot. Could you point me more specifically within the material to the references to any research results resting on data compilation? It appears that all conclusions in this area proceed by calculation and that the results change over time for reasons other than data analysis. Is this so?

  • Scientist

    Check the paleoclimate section. Plenty about feedbacks there.

  • morganovich

    once more “scientist”, you make lots of broad claims and provide zero evidence.

    go read the spencer pieces he cites. the NASA AQUA satellite is giving us some pretty clear data that the net feedback from water vapor is negative in direct contradiction to all the GCM’s.

    where is the evidence of all the feedback posited by the IPCC? where has it been measured and demonstrated? where is the data?

    the vast majority of the water vapor/cloud feedbacks in the GCMs are pure assumptions with little empirical basis.

    even the IPCC admits this.

    and the best data show that the assumptions are incorrect.

    the AQUA data was to be the proof that the AGW theorists needed to demonstrate they were correct. but instead, it has become the proof that they are wrong.

    of interest, it gels nicely with the work from miskolczi (formerly of NASA) and schwartz at brookhaven which seem to indicate that the approximations used to derive the forcing equations used in the GCM’s led to inaccurate representation of feedbacks (and that negative feedback dominates) and that co2 sensitivity is not as high as posited.

    so the evidence is starting to pile up that these models all need to be rethought and they are clearly not a source for policy.

  • morganovich

    doug-

    monkton takes an interesting look at a number of feedback assumptions in this piece:

    http://climatesci.org/2008/04/08/has-the-ipcc-inflated-the-feedback-factor-a-guest-weblog-by-christopher-monckton/

    i found figure 3 to be particularly interesting as it shows clearly that report to report, the IPCC has very significantly increased their CO2 driven forcing estimates (up from about 8 to around 10.5 w/m2) while simultaneously dropping the figure for the effect of CO2 itself (drops from 4.44 to 3.47). the increase all comes from greater assumptions of feedback.

    in 1995 feedback was less than 1/2 of modeled forcing, in 2007 it was greater than 2/3.

    you would think that such a shift would be meticulously supported by data, but it seems to be mostly just speculation. there is no real empiricism to support it.

  • “I predict that true environmentalists will be looking back on the hysteria over trace amounts of CO2 in the atmosphere as a huge setback for real environmental progress.”

    Here’s my prediction: In 10 years when the doomsday foercasts are clearly not coming true, the alarmists will all declare victory. “See, we took serious action and saved the planet,” they will cry. “Nobel Prizes all around!”

    I agree that global warming/climate change is sucking up all the attention and grant money while true environmental concerns are being ingnored.

    GlobalWarmingInsanity.com

  • Stevo

    Doug Foss,

    Try section 8.6 in Chapter 8. Particular 8.6.4 discussing how much confidence there is in the results which says there are a load of metrics you might try to apply to real data to test validity “but few of them have been applied to a majority of the models currently in use. Moreover, it is not yet clear which tests are critical for constraining future projections. Consequently, a set of model metrics that might be used to narrow the range of plausible climate change feedbacks and climate sensitivity has yet to be developed.”

    I.e. there is no experimental evidence.

    You will also see that the majority of numbers used by the IPCC come from Soden and Held. You will see that this is actually a survey of GCMs rather than observational data. It says “Although the analysis and validation of these feedbacks are crucial tasks in climate change research, there has never been a coordinated assessment of climate feedbacks in models used for global warming projections. As a result, the relative magnitude of different feedback processes and their contributions to the range of climate sensitivities remain uncertain.” and “As a result, the true contribution of various feedback processes to the range in climate model sensitivity remains uncertain, particularly for the current generation of models.” and “Our results further indicate that while the change in cloud forcing may not accurately represent the sign or magnitude of cloud feedback, it does provide a useful metric for assessing intermodel differences in cloud feedback.” and so on. Lots of uncertainty.

    Essentially, the bulk of the positive feedback comes from the common GCM assumption that relative humidity (RH) stays constant. The models disagree on how much it will increase, but much of the uncertainty is offset by an anti-correlated negative lapse rate feedback. There are a couple of other feedbacks covered in this paper, and if you do a search on ‘feedback’ in the other IPCC chapters you’ll find lots of instances, most of them caveated with major uncertainties.

    (Incidentally, the lapse rate feedback is the source of the tropical upper troposphere warming that all the GCMs predict and which Christy’s balloons failed to find. As this indicates the absence of a negative feedback that would mitigate global warming, it isn’t clear what this means for temperatures, other than that the GCMs don’t seem to be a good way to predict them.)

    As for the accuracy of the RH assumption, I’m aware of one experimental result of Minschwaner and Dessler where they look at the correlation of temperature and humidity in Fig 7. The dotted line is the GCM assumption of constant RH. The dashed line is their model. And the stars are the actual data. Judge for yourself.

  • Scientist

    Stevo – intelligent people don’t stop reading when they reach a paper they think supports their pre-conceived viewpoint. Check up on the citations to your Minschwaner and Dessler paper. Climate science is moving rapidly. I think you’ll find that in the five years since it was published, observations and models have both moved on quite significantly.

  • Stevo

    Really?

    Well, let me know when it stops moving and they come to a stable conclusion that we can rely on not to get overturned in a couple of years.

    The sound of “settled science”…!

  • Scientist

    You really have some problems with this science lark, don’t you. Do you wait for a final unchangeable answer on all scientific questions?

  • bud

    Let’s not get overboard on the emotional issues. I’ve got enough experience with computer modeling (in the electronics biz) to be very wary of making predictions based on something with as little demonstrative predictive ablilty, so I defer to no man in my contempt for the AGW con job, but…

    Yes, Earth Day happens to fall on Lenin’s birthday, but that is happenstance, not a plot by the usual claque of leftists that show up at the GW demonstrations. It is also the birthday of J. Sterling Morton, the originator of Arbor Day, which was proposed by him in 1872, when Vladimir was all of two years old. Earth Day is a lineal descendent of that tradition.

    The usual suspects may treat this as serendipity, but lets’s not go along with them.

  • Stevo

    “Do you wait for a final unchangeable answer on all scientific questions?”

    No, of course not. Only those questions where assorted persons are trying to claim “the debate is over”, “the science is settled”, “there is a scientific consensus”, “we’ve MovedOn from that paper and this time we’ve got all the right answers, honest”, “the conclusive evidence is already out there in the literature, … somewhere”, “we already know all the answers to this stuff, why are you still asking questions?”, “I think you’ll find that if you keep reading long enough you’ll find a rpaper that agrees with me and that’s when you should stop” and similar unscientific nonsense.

    You are so transparent. Everybody here can see what you’re doing. Why do you still persist? Do you really think you can still fool anybody?

  • Scientist

    So basically, if you think that people are saying things about science that you don’t think they should, you’ll behave like you are a bit retarded? Well, keep it up!

  • Alan D. McIntire

    Minschwaner indicated a measured warming factor of at most about 1.5 due to water vapor:

    http://www.nasa.gov/centers/goddard/news/topstory/2004/0315humidity.html

    and Roy Spencer points out problems in measuring actual cloud feedback, and overestimating climate sensitivity:

    http://climatesci.org/2008/04/22/internal-radiative-forcing-and-the-illusion-of-a-sensitive-climate-system-by-roy-spencer/

    – A. McIntire

  • Scientist

    Learn to make links, you lazy, stupid fool!

  • Rob

    Scientist,

    “…despite our experience with other stable systems that says this is unlikely… – nonsense.”

    What do you mean by nonsense? Obviously, you think there is positive feedback, but what is your counter evidence? It seems that the arguments posted on climate skeptic are pretty solid regarding positive feedback. Can you post a link to something?

    -Rob

    PS: Try not to post one of those links for “lazy stupid fools.” Ad hominem away!!! (i.e. Let’s not make personal attacks, it doesn’t progress the debate!)

  • Scientist

    Here’s a little thought experiment. Imagine yourself in an echo chamber. Imagine that each time a sound hits a wall, 90% of the energy is reflected. Imagine the air inside transmits sound perfectly. That is a system with positive feedback. Now, when you make a sound, how will the volume of that sound compare to what it would be if you were not in an echo chamber? Will that sound eventually die away, or will it become louder and louder and louder? Is the system stable or unstable?

    The arguments here consist basically of saying ‘but positive feedback = unstable!” despite it being pointed out time and time again that this is nonsense.

  • Stevo

    Rob,

    The problem is there are several definitions of what is meant by ‘positive’ feedback. Amplifying but stable processes may be considered positive under one definition while they are negative under another.

    A simple example: we suppose the behaviour is governed by an equation dX/dt = f(X), where X is our variable under study, dX/dt is the rate at which X changes over time, and f(X) is a known function of X that says how the changes in depend on its value. The current value is fed back into the calculation of future values.

    You can test to see if the process is stable by looking at df/dX, the rate at which the function changes when you vary X. If df/dX is positive, the process is unstable, and if it is negative, stable. The sign of df/dX is taken to be the sign of the feedback.

    But there is another way of looking at it, and I’m sorry to say this this is going to get very mathematical from here on.
    This way is to first rewrite the equation as Integral dX = Integral f(X)dt. (If you don’t know calculus, don’t worry about this. I’ve just ‘sort of’ multiplied through by the time step dt to get the X step dX that corresponds to it.) The left hand side is X(t2)-X(t1) (I’ve made X a function of time again since X changes with time), the right hand side is some function g(X(t2))-g(X(t1)) representing the cumulative change in feedback. So we can find the value at a future time X(t2) = X(t1) + g(X(t2))-g(X(t1)) which is approximately X(t1) + g'(X(t1))(t2-t1), taking a first order approximation. We can absorb the (x2-x1) into the function and rename it, so we have the form X(t2) = X(t1) + h(X(t1)) where h is some new function of X. This is essentially the form cited by our friend above, where the sound at the next time step is the sound at this time step plus the echo. It is a discrete-time version of the more correct continuous time differential equation.

    Now if you consider h(X) to be ‘the feedback’ the condition for stability is somewhat different. If the rate at which it varies as you change X, written dh/dX, is between -1 and 0, then the ‘echo’ cancels part of the signal and it is quieter than it would be without the feedback. If dh/dX is between 0 and 1, then the system is still stable, but the echo reinforces the sound and the eventual level is louder than it would otherwise be. Only if the dh/dX ‘feedback’ equals or exceeds 1 (or falls below -1) does it go unstable.

    It is in this second sense that you can get ‘positive’ feedback being stable.

    The second approach is used in a branch of mathematics called control theory, and is commonly used for designing electronic circuits. The climatologists have simply borrowed the language.

    The two forms of feedback are obviously related, and both are taught in different places as being ‘the feedback’, but they are distinct concepts. So people who remember being taught that positive feedback means instability are not misremembering, nor talking nonsense. But in this case the climatologists’ definition is also correct.

  • james griffin

    No global warming since 1998, oceans cooling for last five years.
    Temp measuring on ground stations has been seriously criticised, so much so that 1990’s has been downgraded as the warmest decade of the last century, this now reverts to the 1930’s.
    If that is not bad enough NASA re-instated the wrong data screen after the millenium bug scare and temps this century have been reduced as well.

    On top of this and most importantly the Aqua satellite has compromised the IPCC computer models with the negatives cancelling out the positives…as predicted by the “deniers”.
    Just how much longer are the media and politicians going to hide the truth from the public?
    It is one of the most shameful episodes in the history our our “democracy”.

  • Scientist

    No global warming since 1998 – you have to be really committed to being stupid to trot this one out. It’s nonsense, as even a couple of minutes of research would show you.