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Chaos theory and global warming: can climate be predicted?

What the science says...

Select a level... Basic Intermediate
Weather is chaotic because air is light, it has low friction and viscosity, it expands strongly when in contact with hot surfaces and it conducts heat poorly. Therefore weather is never in equilibrium and the wind always blows. The climate is mostly explained by equilibrium radiation physics, which puts the brakes on variations in global temperatures. Effects from weather, the Sun, volcanoes etc. currently only causes a small amount of chaotic behavior compared to the deterministic, predictable greenhouse gas forcing for the next 100 years"

Climate Myth...

Climate is chaotic and cannot be predicted
'Lorenz (1963), in the landmark paper that founded chaos theory, said that because the climate is a mathematically-chaotic object (a point which the UN's climate panel admits), accurate long-term prediction of the future evolution of the climate is not possible "by any method". At present, climate forecasts even as little as six weeks ahead can be diametrically the opposite of what actually occurs, even if the forecasts are limited to a small region of the planet.' (Christopher Monckton)

One skeptic claim is that if weather is chaotic, then surely the climate must also be chaotic because "climate, of course, is very-long-range weather". This view seems to logically render all skeptic non-human-causes of global warming worthless, since all predictions would be equally futile. As everybody knows, weather is both chaotic and strongly seasonal. Air temperatures undergo significant daily variations, at times varying unpredictably by more than 20°C in a given location within a few days. Climate indeed varies non-linearly, but this has not prevented scientists from making good predictions. Here, we peek into chaos and why climate is rather predictable over both decades and centuries

In 1963 Edward Lorenz was studying the patterns of rising warm air in the atmosphere. It was known at the time that air could start to move if it came into contact with a warm object. The properties of air are such that it expands a lot when heated, it is a good insulator and it flows with relative ease - technically speaking, it has a high Rayleigh number. Think of a large hot air mass in the atmosphere as rising like a hot air balloon in the shape of a mushroom cloud (!). Based on known hydrodynamics Lorenz derived a set of simplified equations for this movement and found something amazing. For certain values of the parameters, the overall movement of the atmospheric air was oscillating unpredictably (Lorenz 1963):

Lorenz equations, oscillation air patterns
Figure 1: The simplified Lorenz phase space equations of air convection (top) and some numerical solutions (below, separated for clarity).

A major concern was that for small changes in starting conditions the system would always have an unpredictable outcome. This was the discovery of deterministic chaos and we knew there and then that we would never know the weather more than 10 days ahead without using disproportionate computing power with very little pay-off. Naturally, scientists knew about chaos from studying turbulence, which is not both smooth (deterministic) and unpredictable.

When Lorenz looked closer at his graphs, something exciting happened. A peculiar regularity emerged when he plotted the curves against each other: they were attracted to something never leaving a boxed volume. It was strange, because it was not a simple shape, but rather an entire subspace of points strangely smeared into three dimensions.

Strange Attractor
Figure 2: The numerical solutions of Lorenz' equations plotted in the same coordinate system. The curves are functions of time, so imagine them as a roller coaster tracing an invisible object called a strange attractor.

Even stranger, the structure is occupying not just a two dimensional surface but something which is more than two dimensional and less than three dimensional: it is two-dimensional plus a fraction. It exists in a so called fractal dimension. It never truly intersects itself thus committing every trajectory to infinite solitude. The object was therefore aptly dubbed a strange attractor.

A closer look reveals where the unpredictability arises. The blue and the magenta curves are closely following each other for a time. Suddenly the magenta curve takes a wild hike and quickly finds itself far away from its companion curve. This is known as sensitivity to initial conditions, which is seen in everyday weather.

Demonstration of chaotic effect
Figure 3: Illustration of deterministic chaos. Imagine two systems started at slightly different initial conditions. They will follow each other closely for some time, but within a short time our ability to predict them breaks down (front and side view of the Lorenz attractor).

This is what skeptics claim must happen in climate as well. Beyond variations in the solar cycles, airborne particle numbers and volcanic eruptions, most variability in the climate is due to changes in heat transfer between the atmosphere and the oceans. Water has a smaller Rayleigh number than air making it hard to obtain fully developed chaos in ocean currents. However, oceanic climate indices (the heat transfer) can exhibit small-scale chaos as we shall see below.

Ocean cycles. North Atlantic Oscillation, East Atlantic pattern, West Pacific pattern
Figure 4: Ocean cycles. North Atlantic Oscillation (blue), East Atlantic pattern (green), West Pacific pattern (red) (NOAA)

Looking at three of the leading climate indices we recognize the same problem that Lorenz faced. Actually proving that these indices are chaotic is exceedingly difficult, but Tziperman et al. (1994) showed in a simple model how El Niño is likely a seasonally induced chaotic resonance between the ocean and the atmosphere. Therefore, the climate system as a whole does exhibit some inherent minor unpredictability (Hansen et al. 2007). However, even though the El Niño of 1998 was a whopping 10% of the total heat content anomaly since 1950, it passed quickly. The greenhouse effect, on the other hand, works throughout the period.

Returning to the temperature record (normalized to the period 1950-1980) we can now put names on things. Chaotic influences from oceans and volcanoes etc. makes both weather more unpredictable and creates the unpredictable part of the 'wiggles' around the average trend in climate. The climate is definitely non-linear, but also not chaotic in this plot.

GHCN & HADISST1 global temperature record + moving average performed with lowess filter
Figure 5: GHCN & HADISST1 global temperature record. The moving average is performed with a lowess filter.

On the timescale of decades, every planetary object has a mean temperature mainly given by the power of its star according to Stefan- Boltzmann’s law combined with the greenhouse effect. If the sources and sinks of CO2 were chaotic and could quickly release and sequester large fractions of gas perhaps the climate could be chaotic. If the Earth's orbit was affected by a moon of comparable mass to the planet itself, then the orbit and thus the Solar forcing could cause some amount of chaos in the climate. As it turns out the Moon is relatively small and actually stabilizes the rotation axis, which is considered a favorable condition for life on Earth.

To sum up, the weather is chaotic because it can run free, climate is on a leash. Pull the leash hard enough and the climate responds.

11-year moving average of global temperature with Lorenz attractor superimposed
Figure 6: Artistic rendering of the rising global temperatures carrying a small, slightly growing Lorenz attractor up along with it.

Guest post by Jacob Bock Axelsen
Jacob Bock Axelsen is MSc in biophysics and PhD in complexity studies, both from the Niels Bohr Institute, Copenhagen. He has worked twice as a visiting scientist in USA and subsequently as a postdoctoral fellow at the Weizmann Institute of Science. He is a contracted physicist at Centro de Astrobiologia in Madrid. His interest in climate science is purely non-professional.

Last updated on 9 July 2010 by Jacob Bock Axelsen.

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Comments

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Comments 1 to 50 out of 63:

  1. I suspect you have largely ignored variations in solar cycles on the earth's climate, whilst focussing on internal effects/variations of the earth's climate (El Nino, volcanoes etc).

    Increase radiation from the sun and you get non-linear chaotic effects on earth (references needed). The earth does not respond in a linear fashion to changes in the sun's output (references needed). You have assumed the sun/solar variations have a more or less peripheral/minor effect. They don't; any solar variation is hugely amplified on earth, and also, importantly, chaotically amplified (non linear response).

    Isn't it a bit like droppping a pebble into an already turbulent stream; the external influence is not only amplified, it creates even more chaos?.
  2. I concede that climate is not long term weather. However, I find it hard to believe that the forcing functions of climate are not non-linear feedback systems themselves. If they aren’t, they would be a rarity among naturally occurring phenomenon. I’ve seen temperature plots over millions of year in Jim Hansen’s book “Storms of My Grandchildren” and other sources that look very chaotic to me.

    The trend behavior shown in "Figure 5: GHCN & HADISST1 global temperature record" is unconvincing since a 130 year record is simply inadequate in the scheme of things. I could replicate this chart easily with a two function chaotic attractor.

    Trends often turn out to be oscillations on a different scale. Any practitioner of finance can attest to that. Chaotic behavior is independent of scale. Plots of stock prices taken every 5 minutes for a day, taken every hour for 12 days, taken every week for 2 years or taken every month for 8 years, each having roughly 100 data points, will all look similar.

    Could it be that the “leash”s pull on the climate is chaotic on a much large time scale.
  3. Dave, put a large pot on the stove and heat it from bottom. The surface temperatures and convection that result will be very complex - but the overall, over time, the pot heats up. Whatever games you play in maths have to be consistent with physics.

    Thingadonta - explain to me why if the forcing is solar, then why isnt the pattern of observations (esp. upper stratospheric cooling) consistent with solar?
  4. DaveU wrote "The trend behavior...is unconvincing since a 130 year record is simply inadequate in the scheme of things. I could replicate this chart easily with a two function chaotic attractor."

    DaveU, you are leaving out the physical, causal mechanisms, and the empirical support for them. Anthropogenic global warming predictions most certainly are not based only on statistics of temperature observations. The theory and its predictions date back to the 19th century before there there even was a set of global temperature observations in which to look for patterns. The observations came later, supporting the predictions and the underlying physical theory. Both the initial simple models and the subsequent general circulation models (GCMs) are physical models, not statistical ones. Statistics are used to validate and improve the physical models.

    I suggest you get an overview from cce's The Global Warming Debate.

    With regard to chaos, see RealClimate's Chaos Theory and Global Warming, and Butterflies, Tornadoes, and Climate Modelling.
  5. Whilst weather is not climate is an oft repeated phrase, I'm not certain that we can dismiss it so readily.
    The bottom line is that whatever the global climate is today, or what it may be at any point in the future, it can only be quantified by the weather conditions that exist at that point.
    What is global climate? There is not such thing, we have a vast collection of geographical diverse areas all with a completely different range of conditions that are both related to, and independent of the adjoining regions.
    When we describe the climate for each region we are actually typifying the range of weather conditions that exist for that region.
    Does this make climate a proxy for the weather, or is the weather a proxy for the climate?
    If "climate change" occurs then the only way the changes can be expressed in how those changes are exhibited in the weather for each region.
    So the process is to firstly quantify the typical weather, then classify that as a certain climate, add in the climate change factor, then convert new climate to typical weather conditions.
  6. scaddenp at 08:57 AM, your example assumes that the heat input exceeds the heat loss, but as many campers will tell you, that is not always a given.
    Apart from math games having to be consistent with physics, they also have to consistent with the physical world.
    Would the pot theory hold if it became numerous pots of various sizes placed at random on individual burners? All connected to a single fuel source but each fuel line controlled by a thermostat that may be at times be in close proximity to the pot or could be remote, perhaps in closer proximity to a larger, or smaller pot.
  7. Tom Dayton at 09:10 AM, re "Anthropogenic global warming predictions most certainly are not based only on statistics of temperature observations."

    Given most models can only be validated by backcasting, what else is there other than statistics of recently observed, but more so, reconstructed temperatures?
    Even though CO2 concentrations can be measured from ice cores, these still have to relate to reconstructed temperature statistics.

    Take away temperature statistics as a means of validation and what is left?
  8. johnd > Take away temperature statistics as a means of validation and what is left?
    Tom's post specifically pointed out that statistics are used to validate the output of the models. What he is saying is that the output itself is not generated from pure statistics, it comes from simulations of the underlying physics. As such, you cannot analyze the significance of the results using pure statistics (by which I do not mean comparison to observations, just statistical analysis all by itself). Some good discussion of the topic here.
  9. Johnd - while you are right, the pot will not heat if input exceeds loss, but once an equilibrium has been established, then increasing the heat (in our gas add GHG) will definitely raise the temp. As to how we know that heat loss does not equal heat gain - well the TOA energy imbalance persists no matter how how complex the energy exchanges below it.
  10. I'm particularly taken with DaveU (2) and his mention of share prices. Share price movement is quite unpredictable for an individual share over days. Indeed, even over long periods an individual company might go broke. However, when you take the whole share market, and look at it over any 30 year period, it goes up. It goes up because there is an underlying driver (productivity growth) always pushing in one direction - up.

    So yes, the share price index bounces around, sometimes making no gains over a 10 year period (just like global temps?), but in the long term it goes up and up and up..... Chaotic, but predictable.
  11. John Brookes at 18:35 PM, productivity growth is only an indirect driver.
    The direct driver is the overall consensus of the market sentiment which in turn is driven not what any individual component is valued at today, but what it is likely to be valued at at some point in the future, ie the anticipation that positive growth will continue unabated.
    Of course overall consensus can create a situation that often results in the market diverging from the underlying fundamental drivers until a correction takes place that catches by surprise all those who were of consensus, but not those who had been examining those relevant indicators that had been ignored by all bar a few.
    Generally it is those few who accumulate a disproportionate amount of the wealth over time.
  12. I should add to my post that the same principle applies when the anticipation is that negative growth will continue unabated as does also occur from time to time.
    OT a bit, but those who do accumulate the wealth transferred from others generally consider that it is made at the time the shares are bought, not at the time of selling.
  13. Responding to Norman from another thread. Read the above.

    WHAT have you read that says climate is chaotic? This is an open research question with likelihood that it is not.
  14. #13 scaddenp

    I will link you to a Scientific American article (1995). It is titled "Chaotic Climate" and to my surprise it had information that might be of great interest to you. "Cores drilled through several parts of the Greenland ice cap show a series of cold snaps and warm spells, each lasting 1,000 years or more-that raised or lowered the average winter temperature in northern Europe by as much as 10 degrees Celsius over the course of as little as a decade." Talk about Climate Change!

    Is Climate chaotic? This author believes it is.
  15. #14: "It is titled "Chaotic Climate""

    Wallace Broecker's work. Perhaps you might be interested in learning that in 1997 he was deeply concerned that atmospheric CO2 was the key trigger of these events:

    Might the ongoing buildup of greenhouse gases in our atmosphere trigger yet another reorganization of the climate system? Were this to happen a century from now, at a time when we struggle to produce enough food to nourish the projected population of 11 to 16 billion, the consequences could be devastating. ... Clearly, if we are to prepare properly for the consequences of the buildup of CO2 and other greenhouse gases in the atmosphere, we must greatly improve our knowledge of the deep water formation process. To me, it is the Achilles heel of the climate system. ... Everyone would agree that the smaller the CO2 buildup the less the likelihood of dire impacts.

    But this is old news. In 2008, Broecker was so concerned about increasing atmospheric CO2 as the primary driver of climate change, he was writing extensively about developing CO2 sequestration technologies (see 'Fixing Climate'). A big-scale technological fix for a complex system? Sounds like its not all that chaotic after all.
  16. "Chaos" has a formal definition, and this doesnt meet it. Non-linear and sometimes highly sensitive to changes in forcing, but its not showing signs of developing in highly different directions for slight changes in conditions. You dont get an iceage because there is a volcano erupting.

    It is well worth reading Broecker - another one in works - but his work on the sudden hemispheric climate reversal's doesnt give you any reason for thinking the current warming is related to causes of these events. And no reason for thinking these events dont have specific causes. Catch up on some recent literature.
  17. I dont have access to my paper lists (nor to my knowledgeable colleague) at home but if you look at Chp6 IPCC WG1 and look at section on "Abrupt climate changes in the glacial-interglacial record". Note that these are not necessarily global events - indeed some types are hemispherically anti- phased. Look at cites for main review papers. Note that this is very active field with interesting papers in the pipeline.
  18. #16 scaddenp

    ""Chaos" has a formal definition, and this doesnt meet it. Non-linear and sometimes highly sensitive to changes in forcing, but its not showing signs of developing in highly different directions for slight changes in conditions. You dont get an iceage because there is a volcano erupting."

    I guess that would depend on what you define as "slight". I am not the Master of Choao theory on the detailed definition.

    Here is a model of Earth's temp (simple model). It calculates Earth temp based on only solar energy and Albedo. This would be Earth without any GHG warming. But it is useful in demonstrating that Climate is indeed chaotic. Primarily with the Albedo (the Solar energy will not change much). They have lists of Albedo's to put into the calculator. I noticed that if the Earth were mostly forest the albedo would be much lower (oceans would be the same at there low albedo). Put in a lower albedo and see what happens to the Earth's temp even with no GHG effect. And you claim this is not a chaotic system? If the land is grass, desert, snow or forest it makes a huge difference in albedo and the overall temp. Try it and see and if I am wrong explain what is the flaw in my thinking. Thanks.

    Albedo Earth Temp calculator.
  19. #18: "Here is a model of Earth's temp (simple model). It calculates Earth temp"

    There's nothing at all chaotic about this model; its just a demonstration of two straightforward equations. One of them just happens to have T4, which makes it sensitive -- not chaotic.

    Here's a definition of 'chaotic behavior'; note that it mentions 'weather,' not climate. You may be mistaking 'chaotic' with 'sensitive to change.'

    For example, in this image of a chaotic system, the position of the swinging pendulum (ie, the weather) depends on where it is when the machine starts. However, the envelope of possible positions (ie, the climate) is entirely predictable.
  20. Norman, a "chaotic system" is characterized by non-linear dynamics (yep, lots of those in climate change) and by extreme sensitivity to initial conditions (nope, not the case with climate). The behavior of a chaotic system is very predictable - it will vary around it's attractor.

    Weather is chaotic, in that it varies hugely around the climate means due to the initial conditions - hence the ever changing state of sun, wind, rain, clouds, etc. The strange attractor for weather provides variability, and the extreme sensitivity to initial conditions (temps, humidity, clouds, etc., which we known only to a certain degree of accuracy) prevents accurate weather forecasts weeks in advance.

    But climate, as defined as long term averages, is not chaotic. If top of atmosphere IR decreases, there is an energy imbalance, the climate will warm. If the sun decreases it's output, there is an energy imbalance, and the climate will cool.

    The very nature of a running 20-30 average smooths the chaotic weather effects - and the "climate", although non-linear, is predictable to some degree of accuracy. It's not chaotic.
  21. #20 KR

    "But climate, as defined as long term averages, is not chaotic. If top of atmosphere IR decreases, there is an energy imbalance, the climate will warm. If the sun decreases it's output, there is an energy imbalance, and the climate will cool."

    The purpose of posting the calculator was so scaddenp could play with various albedos to see how these cause change in Global temps. There is a nice list of various albedo numbers to try. Global temp can effect these albedo numbers on both land and water. Water can range from a super low albedo in liquid form to a very high albedo in ice and snow form. You can put the albedo number in the calcuator and leave the solar radiation alone. The effect on global temps are far more significant than the 1 to 2 degree range given for CO2 doubling (in absence of feedbacks, justs its own contribution). Global temp can also detemine the types of plants that grow on land. Forests have very low albedo, desert fairly high and grass in the middle. Combinations of temperature, long term wind patterns, evaporation rate and all go into determining what type of land coverage will take place. The albedo effects the Global Temp in a major way and the Global temp can effect various albedo numbers in a major way. This in itself creates and unpredictable loop...What type of land form will favor a warming Earth? If it is desert than the sand will actually reflect a lot more solar radiation than forest and work to cool the Earth (Sahara desert acts in this fashion...learned that when taking a Meteorology course in College). Forests absorb a lot more solar energy but they also pull water up from the ground and cause evaporation which cools the local environment but can cause heating in the upper atmposphere when the humid air condenses back into water.
  22. #19 muoncounter

    If you read my response to KR...You say "For example, in this image of a chaotic system, the position of the swinging pendulum (ie, the weather) depends on where it is when the machine starts. However, the envelope of possible positions (ie, the climate) is entirely predictable."

    Use the calculator and move the albedo bar from one extreme to the other (both albedo ranges are possible on Earth, from a water world to an ice and snow world). With our current level of solar insolation the low albeo point would have a globe at 35F At the high albedo side the Earth woud be -138F. That is a 173 difference in Global temp based upon albedo. Now tell me how do you predict what the albedo will be if the Earth warms 10F? Will there be more relflective clouds? Of the 30% of the Earth that is Land what type of albedo will there be? If it becomes a desert that will shift it from the current estimate of 0.3 albedo to 0.37 and will cool the Earth more than it is currently being cooled. On the calculator if you slide the albeo bar to 0.37 it creates a cooling factor 0f
    -12F compared to 0.3 abledo. It means a warming climate in this case would end up cooling the Earth.

    If you can explain to me how this is not chaotic and how you can predict it then I am all ears. I can't see how anyone could predict what type of albedo will take place with a warming Earth, and if you can't predict that major factor, how can you predict a future trend?
  23. Norman, fail to see how this demonstrates any chaotic behaviour at all - a no-atmosphere earth has fast extremes so dont get fooled.

    You are entertaining this idea because you wish demonstrate the climate cannot be predicted despite the success of models in doing just this. I dont need a calculator to know the effect of a fourth power on sensitivity. This demonstrates nothing about supposed chaos.

    Furthermore, you would wish to hypothesize that current warming is a dynamical effect - an internal heat movement that is part of a larger cycle. I am still waiting for you tell me where this heat is being moved from that is causing the heating. Chaotic system still have to obey the laws of physics. Will your alternative model explain all the other observed features (which happen to fit our existing climate model).

    Lets suppose that climate IS chaotic. Now what is the time scale for predictions to fail for imprecisely known systems? For weather, its about 4 days. For the solar system?? Successful model predictions would suggest that it is not chaotic on scales so far worked on.

    Do you seriously think that your questions about albedo etc. are not built into the climate models? Could be time to study them.
  24. #22: "move the albedo bar from one extreme to the other"

    The earth's average albedo is given here as 0.30 or 30%. We do not go 'from one extreme to the other'.

    Here is a prior SkS article on the question of albedo.

    Look at the graph (figures 2 and 3) of measured albedo anomalies in that article; a big anomaly is on the order of 1%. That limits the plausible range of your slider bar considerably. We do not live in a world that is all desert one day, all ice the next, all forest the day after that.

    Look at the graph in figure 1; as scadden points out, albedo variation is already taken into account in the models.

    Sorry, this dog won't hunt.
  25. Norman, you still have not understood that there is a formal definition of "chaos" that is not the same as the normal English meaning. You have been pointed to the definition by other commenters. You should have read the Intermediate version of the post at the top of this page. Until you understand what "chaos" means, neither you nor anyone else will benefit from discussions with you on this topic.
  26. Norman, you do not appear to have looked at the definition of a chaotic system.

    A chaotic system shows extreme sensitivity to initial conditions. Weather does exhibit this behavior (the "butterfly effect"), but climate, as defined by long term averages, does not.

    A small variation in cloud cover doesn't affect global temperatures 20 years out by +/- 5 degrees. The albedo changes of parking lots in Europe don't determine whether we're heading into meltdown or an ice age. The climate simply doesn't have divergent behavior based upon small condition changes - rather, it has a straightforward (albeit non-linear) predictable response to changes in conditions.

    As Tom Dayton stated, until you understand the definition of a "chaotic system" your statements will not be relevant to this topic.
  27. #23 scaddenp

    Your questions: "Lets suppose that climate IS chaotic. Now what is the time scale for predictions to fail for imprecisely known systems? For weather, its about 4 days. For the solar system?? Successful model predictions would suggest that it is not chaotic on scales so far worked on.

    Do you seriously think that your questions about albedo etc. are not built into the climate models? Could be time to study them"

    The last question is not part of this current point. I do not know what exactly are in climate models but the point of discussion is not about models, it is about the potential for climate to be chaotic (as defined in the mathematical view).

    I am not sure, by the definition of chaos on the links above, that chaos is a time dependent phenomena. Because of the size and momentum of the Earth's system the chaotic changes are slow and won't show up in 30 year study but do seem to show up when the time frame is extended.

    All of you have looked at these graphs. If you plot a chaotic system point would not it look similar? Forget the time scale and look at the system itself as a whole.

    Look at the many fluctuations in Global temps in 400,000 years.

    5 million years of Global Temp with many unpatterned fluctations but not random which is a sign of chaos.
  28. #26 KR

    "A chaotic system shows extreme sensitivity to initial conditions. Weather does exhibit this behavior (the "butterfly effect"), but climate, as defined by long term averages, does not"

    Are you sure about this statement? You can look at the links I posted for scaddenp and explain why the high degree (10 C temp cycle)and relative numerous Global temp cycles are taking place. The graph is jagged with little uniform behavior.

    Check out this on rapid climate change in the Sahara. Things totally changed in that area the last 100,000 years.

    Sahara desert climate change.

    Quote from the above article: "The climate of the Sahara has undergone enormous variation between wet and dry over the last few hundred thousand years."

    And your proof for this statement is? "A small variation in cloud cover doesn't affect global temperatures 20 years out by +/- 5 degrees. The albedo changes of parking lots in Europe don't determine whether we're heading into meltdown or an ice age. The climate simply doesn't have divergent behavior based upon small condition changes - rather, it has a straightforward (albeit non-linear) predictable response to changes in conditions."

    You seem stuck on rate of the change to dispel what the longer term clearly demonstrates. A volcano may indeed cause a drastic change in climate but just not on the short time scale of 20 or even 100 years. It may take thousands of years for the intitial effects to demonstrate the chaotic nature of the climate system with all its complex feedbacks.
  29. #24 muoncounter

    I am still looking for a way to demonstrate my point...

    You state: "The earth's average albedo is given here as 0.30 or 30%. We do not go 'from one extreme to the other'.

    Here is a prior SkS article on the question of albedo.

    Look at the graph (figures 2 and 3) of measured albedo anomalies in that article; a big anomaly is on the order of 1%. That limits the plausible range of your slider bar considerably. We do not live in a world that is all desert one day, all ice the next, all forest the day after that."

    You, like the others, seem to think a chaotic system must happen really fast or the system is not chaotic. Why do you think this? I thought a chaotic system was a particular characteristic and I was not aware it was time dependent.

    I am looking for changes in Earth's Albedo. Primarily during known ice ages. The articles I looked at only stated the Earth's Albedo went up during ice ages but they never seem to give an estimated amount.

    On Science of Doom I found a blogger who gave a number...not sure where he got it from but it may show that albedo is far from constant or stable in the longer time scale of Earth time (not our time).

    Science of Doom page with post I refer to, name is Bill Illis.

    Bill's post: "Earth’s Albedo has varied throughout the last 650 million years between 25% to 50% (29.83% today) depending on the continental arrangements and the amount of ice that builds up and spreads out from the poles. That is a big range and the values are capable of explaining the majority of the temperature changes over the period."

    Thats the best I could do for now. Put 0.25 in the calculator and 0.50 for albedo and see how this variation effects Global Temp.
    Response: Norman, it sounds like you still have not read the Intermediate version of this post. You should read it carefully, because it describes chaos and explains why climate is not chaotic. If you are not really trying to assert that climate is chaotic, but only that climate cannot be predicted, then you should read the different post Models are unreliable--both the Basic and Intermediate versions--and you should comment on that post rather than this one that is devoted to the technically defined "chaos."
  30. Norman, "I am looking for changes in Earth's Albedo. Primarily during known ice ages."

    You can save yourself a lot of time trying to find things about climate science but just going to the ipcc WG1 report. (Why dont you just read it). Radiative forcing estimated at -3.2W/m2 for effects of ice and lowered sealevel. Vegetation change estimated at -1W/m2. GHG changes are estimated to contribute -2.8W/m2 for comparison purposes. See the report for references (many) on which these numbers are based.

    However, this has nothing to do with chaos. Albedo is straightforward and well-behaved.

    Also, remember your calculator is for airless earth.

    "It may take thousands of years for the intitial effects to demonstrate the chaotic nature of the climate system with all its complex feedbacks. "

    What is lacking is any evidence for your assertion. On the contrary, climate seems to behave instead as function of net forcings. If you are waiting for some effect in from say pinatoba to influence climate, then you are in for a very long wait.
  31. Also, just noticed your earlier point. "It looks like the output of a chaotic system". If you look at the instruments for just about any component of a power plant then they "look" chaotic too. You cant tell chaos by just looking at the graph. One feature of chaos is quasiperiod cycles, but milankovitch cycles are not quasiperiodic as analysis would show you.

    You would get a better feel for cause by plotting global temperature against estimated net forcing through time.

    Please, please try reading and understanding the science rather than reading to try and find an excuse to reject the conclusions.
  32. Moderator

    I am still working on the possibility that Climate is indeed chaotic and the reasons I feel it may be so I think I am still on the correct thread. I have read your intermediate version of chaos and see you do not include albedo as a means to induce a chaotic climate. Here you state "If the sources and sinks of CO2 were chaotic and could quickly release and sequester large fractions of gas perhaps the climate could be chaotic."

    Forget about CO2, what about albedo? A change of 1% in the albedo is equal to the effect of CO2 doubling.

    The reason I still suggest climate may easily be chaotic is because the major climate variables (temperature and precipitation) will have an effect on albeo and albedo in turn can easily change these two variables so it makes for a very unstable situation.
  33. #30 scaddenp

    Your statement "However, this has nothing to do with chaos. Albedo is straightforward and well-behaved." Does not seem valid in the material I have looked into.

    Wonder why you believe this statement to be true. I have another calcualtor for you. It is on a site you probably do not like but the calcultor is still valid. It includes the atmosphere and the Greenhouse effect in the calculator. Small albedo changes can cause large climate changes. This seems to fit the concept of sensitivity into the climate system. Very sensitive to small changes and the changes to climate can then effect the albedo, very nonlinear effect.

    Global Temp calculator that includes atmophere for scaddenp.
  34. #33: "Small albedo changes can cause large climate changes."

    So can small GHG changes, as this calculator clearly demonstrates. And this calculator demonstrates that temperature response to albedo is nearly linear -- systems described by linear function are hardly chaotic.

    Do you have any idea what it would take to change the planet's average albedo by a few percent for a significant period of time? Even the Pinatubo eruption produced only a short term climate effect.

    While the global cooling after Pinatubo was not surprising, the observed winter warming over Northern Hemisphere continents in the two winters following the eruption is now understood as a dynamic response to volcanically produced temperature gradients in the lower stratosphere from aerosol heating and ozone depletion, and to reduced tropospheric storminess.

    To obtain the kind of albedo change you keep postulating, how many Pinatubos would you need?

    On the other hand, we have measured the increase in GHGs. The junksci calculator you reference shows how effective that is as a control know on global temperature, as do articles here. What part of this isn't clear?
  35. Interestingly, Norman points us to a website--junkscience.com--that was created by tobacco money to promote industry-friendly "science." At the same time, Frederick Seitz is under fire in another thread for his role in promoting the idea that tobacco use is healthy.
  36. #35 DSL

    I am not promoting the webpage. But the calculator is probably sound. It matches well with the one I linked to. I have that one for scaddenp because it includes atmopshere as well as GHG effects.
  37. Norman, see RealClimate's Chaos Theory and Global Warming, and Butterflies, Tornadoes, and Climate Modelling.
  38. #34 muoncounter

    I agree with your statement: "So can small GHG changes, as this calculator clearly demonstrates. And this calculator demonstrates that temperature response to albedo is nearly linear -- systems described by linear function are hardly chaotic."

    Temperature response to albedo is linear as is temperature response to GHG levels. Look at it the other way, that is where I see the nonlinear and chaotic response. How does temperature effect albedo? This is a harder question to answer. Cooler Northern climate generate the snowfall that is highly reflective and will drastically increase the local albedo in the local area. Globally it may decrease the albedo by 1%. However the bigger albedo effect would be with the clouds. If the climate cools in the Northern regions (higher albedo from increased snow) like during an ice age but the oceans are still fairly warm (from the previous warm cycle) you may get an increase of cloud formation all around (still plenty of water vapor from the warm oceans but now a lot colder air to lift the moisture up to form clouds as a cold front moves through). This increased cloud cover acts to cool the Earth more and the decline in temp becomes steep and drops several degrees in a relative short time frame. As the Earth's overall temperature goes down the oceans begin to cool. Due to the heat capacity of water, the time lag is long. Once the ocean's are cool enough, less water evaporates and cloud formation really becomes significantly less and the albedo drops to much lower levels allowing much more solar radiation in to be absorbed by oceans gradually warming them and ending the ice age. When the oceans get warm enough the cloud formation reaches levels we see today and the albedo averages out to around 0.3.

    I am not saying this is what happens or takes place, I am using the above scenerio to point out how temperatures could have a nonlinear and drastic effect on albedo, which then will feedback and greatly effect the temperature.
  39. #37 Tom Dayton

    I did look at the Real Climate explanation of chaos. They do not talk about how temperature can effect albedo. If the only effect on temperature where GHG then the point would be valid. Small changes in albedo (the sensitivity response to determine if a system is chaotic) also have a large effect on temperature. As far as I have read the effect of increasing temperature on albedo is not worked out. There will be more water vapor in the air...will this form more clouds and increase albedo a few % points driving temps down?
  40. muoncounter,

    Here is some reading to back up some of my thoughts.

    Clouds effect on Albedo.

    Selected quote from the above article link: "Clouds, therefore, are responsible for about 55% of the sunlight that is reflected into space without adding heat to the climate system. Clouds alone roughly double Earth's albedo, from 0.15 (no clouds) to 0.31 (including clouds). In short, clouds are the predominant means by which incoming sunlight is reflected back out into space."

    Put those albedo changes in the calculator and see what a difference it makes.

    Another quote that supports my current view that Climate is chaotic: "However, water vapor and clouds play numerous roles in the climate system, and the net affect of increased evaporation rates caused by global warming are difficult to predict"

    Another article that also talks about the albedo effect.

    MIT article about Cloud effects.

    Quote from this article stating how much clouds change Temperature. "Recent observational studies show that these effects almost balance, but that the cooling effect is somewhat more important. From the point of view of global change, however, it is crucial to note that this small difference is about five times larger than the radiative effect anticipated from a doubling of atmospheric carbon dioxide (CO2), and that the individual components of the difference are orders of magnitude larger. In existing climate models about one third of the predicted warming due to increasing CO2 arises because of the predicted cloud changes. These predictions, however, are highly speculative because none of the models include interactive cloud physics"

    Another quote suggesting the difficult nature in predicting future climate: "Clearly, without a proper treatment of both layer clouds and convection, model predictions of climate are uncertain. Cloud effects are so much larger than the anticipated effects of added greenhouse gases, that small changes in the cloud picture can easily alter predictions of global warming. In addition, existing methods of representing convection and clouds are crude, and, in some cases, can be shown even to be qualitatively incorrect"
  41. #38, #40:

    Norman,
    It sounds like you are trying to run a climate model without benefit of any computing. That's not particularly helpful, as complicated systems don't simplify so easily. Best left to the pros; we can then read their results and form our own picture with the benefit of educated input.

    What you describe sounds to me a bit like what happens every year, as we move from summer to winter. That alone is neither a net warming nor cooling.

    Here's one inconsistency in your scheme:
    "If the climate cools in the Northern regions (higher albedo from increased snow) like during an ice age but the oceans are still fairly warm (from the previous warm cycle) you may get an increase of cloud formation ... This increased cloud cover acts to cool the Earth more ..."

    Here's what Holland and Bitz 2003 found:
    ... clouds reduce the strength of the ice-albedo feedback by shielding the planetary albedo from the surface. Furthermore most models predict Arctic cloud cover increases with warming, which increases the planetary albedo

    Further, drawing comparisons to glacial stages is too tricky to do on the back of an envelope. Burt et al showed that the increased albedo due to glacial ice is moderated by the accompanying lowered sea level:

    Although the positive ice-albedo feedback acts to amplify the climate change ... , due to the melting of sea ice and ice sheets in the Northern Hemisphere, the ice-albedo feedback is actually negative over large regions of the high-latitude Northern Hemisphere, due to changes in the size of the Arctic Ocean basin.

    Both of those mechanisms do not enhance change, they moderate change: Cloud cover moderates the increased albedo of surface ice; warming air causes clouds which cool. These act to reduce the 'chaotic' nature that you seem to want to find. There are no sharp changes in temperature in this system.

    What is needed to explain sharply increasing or decreasing temps? Some other agent: We know its not the sun, as TSI is down while temperature is going up. We have a known warming agent in increasing atmospheric GHGs.

    Insisting that "Clouds alone roughly double Earth's albedo, from 0.15 (no clouds) to 0.31" is possible and should be put into the calculator makes no sense. We do not go from no clouds to heavy clouds. Look at satellite photos; there are always some clouds.

    Finally "the net affect of increased evaporation rates caused by global warming are difficult to predict" doesn't mean its chaotic. Repetition doesn't make it so.
  42. Norman - Have you read the intermediate version of this topic? Non-linear does not imply chaotic, although all chaotic systems are non-linear.

    Weather is highly dependent on initial conditions (you can't predict next July 17th's temperature). Climate, on the other hand, as described in the RealClimate links posted earlier, is a boundary condition issue - when does outgoing energy match incoming energy?

    Feedback, not incidentally, is a geometric relationship (Forcing / (1 - Feedback Gain)), which is linear. There are certainly non-linear transition points, such as vanishing ice in the Arctic, but it's still not a chaotic system.

    You've repeated your albedo feedback question, but have not established that there is chaos in long term climate. Unless you do, you have failed to raise an objection.
    Response: Norman, you should give up your assertion that climate is chaotic, and instead comment on a different thread to focus on what seems to be your real assertion that Climate Models are Unreliable.
  43. Moderator,

    Before I leave the topic I will post a link that has evidence of the chaotic nature of climate. Dust patterns in ice cores suggest sudden and dramic changes in Global atmopheric circulation patterns.

    Article suggest climate is chatotic.
  44. #41 muoncounter

    "Insisting that "Clouds alone roughly double Earth's albedo, from 0.15 (no clouds) to 0.31" is possible and should be put into the calculator makes no sense. We do not go from no clouds to heavy clouds. Look at satellite photos; there are always some clouds"

    But what is the percentage? Unfortunately we do not have satellite photos of the Earth during an ice age and cannot empirically determine the percentage of cloud cover during one of these periods.
  45. #43: "evidence of the chaotic nature of climate."

    OK, I'll see your evidence and raise you this bit:

    Even though climate is chaotic, with weather states impossible to predict in detail more than a few days ahead, there is a predictable impact of anthropogenic forcing on the probability of occurrence of the naturally-occurring climatic regimes.

    ... it is a false dichotomy to suppose that some recently-occurring drought or flood is either on the one hand caused by global warming, or on the other hand is merely due to natural climate variability.

    Rather, the correct way to address such an issue is to ask instead whether anthropogenic climate change will increase or decrease the probability of occurrence of the type of drought or flood

    -- emphasis added

    All that is similar to the comments here:

    Weather in a given region occurs in such a complex and unstable environment, driven by such a multitude of factors, that no single weather event can be pinned solely on climate change. In that sense, it's correct to say that the Moscow heat wave was not caused by climate change.

    However, if one frames the question slightly differently: "Would an event like the Moscow heat wave have occurred if carbon dioxide levels had remained at pre-industrial levels," the answer, Hansen asserts, is clear: "Almost certainly not."


    So even if we accept your premise that climate has chaotic behavior, that does not mean it is unpredictable. End of story.
  46. In another thread, fdijkstra writes:

    Scientists should not make any predictions about the climate. No cool predictions, no warm predictions, because the climate is unpredictable. It is a chaotic system with many unknown and ununderstood factors.

    That is silly, as a moment's reflection would have told you. Would you seriously object to any of the following predictions?

    (1) On average, in 2011, the Arctic and the Antarctic will be cooler than the tropics.

    (2) On average, in 2011, regions lying in the Intertropical Convergence Zone will have higher precipitation than regions lying at the poleward edge of the Hadley Cell.

    (3) On average, in 2011, the northern hemisphere will be warmer in July than in December, while the southern hemisphere will show the opposite seasonality.


    Those are all very specific, quantifiable predictions about the climate (well, #2 would require some complicated definitions to quantify...). I suspect that virtually everyone who understands the basics of the Earth's climate would agree that all three of those predictions are reasonable.

    OK, how about these predictions:

    (4) In the absence of any other countervailing forcings, an instantaneous 25% decrease in solar irradiance, sustained for a century, would cause the Earth's mean surface temperature to decrease and the extent of sea ice to increase.

    (5) A volcanic eruption or large asteroid impact that injected a large quantity of aerosols into the stratosphere would also cause the Earth's mean surface temperature to decrease.


    Those are slightly more complicated predictions, but still things that pretty much everyone would agree with. Again, they are based on conceptual or numerical models of the climate system.

    From here, one could move to more detailed and more complex predictions. Naturally, we will be less confident in our predictions as they get more specific in terms of time, place, and phenomena. That's OK, everyone understands that.

    The claim that somehow the climate is just too complicated to predict is just plain wrong. We can make simple predictions with a very high degree of confidence, and more specific predictions with correspondingly greater uncertainty.
  47. "It is a chaotic system with many unknown and ununderstood factors"

    It was the consensus (bad word) of this thread that weather is chaotic, while climate is not. In each of Ned's examples, there will be times and locations where the weather varies due to local conditions and is therefore difficult to predict. However, the overall pattern and trend is well-determined from the conditions in each case.

    See the wiki article on chaos theory for other examples and an explanation of the specific meaning of 'chaotic' in the scientific sense. In short, complicated does not equal chaotic.
  48. @scaddenp

    I don't doubt the utility of climate models. However here, and elsewhere you have said that the mathematical systems representing weather (in GCMs) formally display chaos, but that climate models are not chaotic.

    Since the mathematical system of equations in weather and climate models are practically identical, I don't see any reason why chaotic behaviour should be formally excluded from the latter. The only difference is the length of the integration. Perhaps you can explain what you mean.

    As a practical example, in the UVic Earth Systems Climate Model we can show sensitive dependence to initial conditions for the MOC strength in long equilibrium simulations (i.e. multiple equilibria in an intermediate complexity climate model in 3000 year long integrations).

    The MITgcm, set up as a fully coupled AO-GCM with simple geography, has also demonstrated multiple equilbria (
    see MITgcm website). There is also a Journal of Climate paper submitted on this.

    So, it seems to me that chaotic behaviour certainly is permitted by these mathematical systems (climate models). Whether this holds in the real climate system is another question.

    To me this does not imply that climate models are useless - rather that they warn us that abrupt climate change is a possibility (even if the chances are low).
  49. neil - The difference between a chaotic initial value system (weather) and a boundary limited system (climate) is the difference between trajectory details and trajectory averages.

    Weather is highly susceptible to initial conditions, and predicting weather and it's details (rain or not, where will the pressure systems go?) requires detailed information and a lot of computing power to predict even a few days out. This is a very hard problem, as even a small error or approximation of initial conditions will inevitably cause the prediction to deviate from reality a few days out.

    Climate, however, is a boundary condition system. We don't know what days in March 2012 it will rain, but we can predict even this far out what the average temperature is likely to be with high certainty. When a particular bit of weather departs from the averages, it will (statistically) return to the average, and spend some time on the other side as well.

    So why is climate a boundary limited system? It depends on total energies. If energy leaving the climate exceeds energy coming in, we'll get colder, and less heat will leave - back to the average as determined by the insolation and thermal radiation. If we have a hot season, the climate will radiate above the average, and we'll cool down. The weather will vary around those averages in a difficult to predict way, but it will vary around the averages determined by energy conservation! And those averages are what climate predictions are about.

    Boundary conditions drive any deviations back to the averages for that system. So while we cannot state whether it will be sunny on your birthday - we can still note that winters will be colder than summers, and that reducing the amount of energy leaving the climate at any temperature (with GHG's) will make the average temperatures higher.

    ---

    In terms of modeling - regardless of the initial conditions of a global climate model (GCM), it will move fairly quickly to the averages determined by energy flows and conservation. The further you have run a GCM, the less sensitive to initial conditions. This is the reverse of weather predictions, as your prediction of detailed weather, while still within a few standard deviations of the averages, may be anywhere around that average once you've run your prediction for a while.
  50. neil - In terms of multiple equilibria, when those have not been observed in nature, I would suspect that either there are some issues with the model, or that if accurate the climate may be moving to a transitional state, such as severe changes in the thermohaline circulation. I don't know the particular models you mentioned - I cannot opine as to which this might be. Although you seem to be stating that these are fairly simple models...

    If multiple models show several equilibria, given different modeling criteria, complexity, and assumptions, I would watch that particular aspect of climate rather carefully for change.

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