Monday, September 23, 2013

Chaos theory explains why weather & climate cannot be predicted beyond 3 weeks

According to the originator of chaos theory, Edward Lorenz, you must know all the current conditions of the atmosphere, everywhere within it, to predict what the atmosphere will be doing in the distant future. In addition, one must know all the current conditions throughout the oceans as well, since the oceans control the atmosphere. “In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long-range forecasting would seem to be nonexistent,” Lorenz concluded. So even if the molecules in the air all interacted nonrandomly, in a totally cause-and-effect (deterministic) manner, you still couldn’t predict with certainty what they would do or what the weather would be."

Lorenz "was studying the equations that describe the atmosphere, trying to figure out how well math could be used to forecast the weather. He found that even if you had all the right equations for describing changes in the atmosphere, you couldn’t predict the weather very far into the future."

"When Lorenz ran [a crude weather model] using the rounded numbers, he found dramatic differences from the forecast using the full six-digit data. He had discovered the key concept behind chaos: sensitive dependence on initial conditions."

"In the years that followed, Lorenz worked out the implications for the weather. In the 1963 paper, he had not been able to calculate just how far the limit to accurate long-range forecasting would be. “Conceivably it could be a few days or a few centuries,” he wrote. But by 1969 he had pinned down the limit to something like three weeks. Of course, reaching even that theoretical limit would require readings from stations placed much too close together to be feasible."


Kevin Trenberth agrees with Lorenz that the initial starting conditions are unknown because "the observing system is inadequate," ergo the climate model projections are indeed a "travesty":
"The fact is that we can’t account for the lack of warming at the moment and it is a travesty that we can’t. The CERES data published in the August BAMS 09 supplement on 2008 shows there should be even more warming: but the data are surely wrong. [not the models, of course] Our observing system is inadequate. - Kevin Trenberth, Climategate I email
Related: New paper finds the same climate model produces different results when run on different computers

Born half a century ago, chaos theory languished for years before taking the sciences by storm
Predicting the impact of a scientific discovery is a lot like predicting the weather. You never know what obscure paper in the scientific literature (or small disturbance in the atmosphere) will eventually produce a deluge of new research (or rain).
One such paper appeared 50 years ago in the Journal of the Atmospheric Sciences. Its title, “Deterministic Nonperiodic Flow,” did not excite anybody. And its author, Edward Lorenz, was shy and not predisposed to seeking publicity. But in the decades that followed, that paper spawned a cyclone of scientific activity impacting fields ranging from meteorology and mathematics to astronomy, geology, neuroscience and medicine.
In short, that paper created chaos.
Actually, Lorenz did not use the term chaos in his 1963 paper, but he captured the idea that now goes by that name. He was studying the equations that describe the atmosphere, trying to figure out how well math could be used to forecast the weather. He found that even if you had all the right equations for describing changes in the atmosphere, you couldn’t predict the weather very far into the future.
“Two states differing by imperceptible amounts may eventually evolve into two considerably different states,” he wrote. “If, then, there is any error whatever in observing the present state — and in any real system such errors seem inevitable — an acceptable prediction of an instantaneous state in the distant future may well be impossible.”
In other words, you have to know all the current conditions of the atmosphere, everywhere within it, to predict what the atmosphere will be doing in the distant future. “In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long-range forecasting would seem to be nonexistent,” Lorenz concluded. So even if the molecules in the air all interacted nonrandomly, in a totally cause-and-effect (deterministic) manner, you still couldn’t predict with certainty what they would do or what the weather would be.
This insight into the weather came to be known as the “butterfly effect,” the suggestion that flapping wings in one locale can cause an atmospheric calamity far away. Originally, Lorenz attributed such flapping power to seagulls. “One meteorologist remarked that if the theory were correct, one flap of a seagull’s wings would be enough to alter the course of the weather forever,” Lorenz said when lecturing on his new paper in 1963.
Butterflies became the protagonists of chaos theory only much later. That switch came from the title given to a lecture Lorenz delivered in 1972: "Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?
In the beginning, the flapping of wings was actually just the rounding of numbers. Lorenz, a meteorology professor at MIT, had been entering atmospheric readings by hand into a computer to run some forecasting programs. He was using a printout of the data on which numbers had been truncated from their original accuracy (.506127, for instance, had been rounded to .506). When Lorenz ran the program using the rounded numbers, he found dramatic differences from the forecast using the full six-digit data. He had discovered the key concept behind chaos: sensitive dependence on initial conditions.
In the years that followed, Lorenz worked out the implications for the weather. In the 1963 paper, he had not been able to calculate just how far the limit to accurate long-range forecasting would be. “Conceivably it could be a few days or a few centuries,” he wrote. But by 1969 he had pinned down the limit to something like three weeks. Of course, reaching even that theoretical limit would require readings from stations placed much too close together to be feasible.
In the years following his 1972 talk (at a meeting of the American Association for the Advancement of Science), the butterfly effect idea seeped into both scientific and popular culture. By the mid-1970s the term chaos was adopted to signify the effects of sensitive dependence on starting conditions. Chaos was found in everything from the forces generating earthquakes to the time interval between heartbeats. Astronomers detected evidence that planetary orbits embody chaos, rendering the far future of the solar system unpredictable. Neuroscientists implicated chaos (or lack thereof) in problems afflicting signaling among brain cells.
As for butterflies in Brazil causing tornadoes in Texas, Lorenz did not actually answer the question posed in the title of his 1972 talk.
He did point out that if a butterfly could cause a tornado, it’s also possible that the right flapping could also prevent a tornado. Shortly before his death in 2008, Lorenz still said he didn’t really know whether a butterfly’s disturbance of the air could be magnified into a tornado.
Nevertheless the idea that small differences today can make big differences tomorrow is sound and is now well-established in science and widely recognized by the public. And that 1963 paper, referenced only three times in the following 10 years outside of the island of meteorology, has now been cited more than 11,000 times, by researchers on every scientific continent.
E.N. Lorenz. Deterministic Nonperiodic Flow. J. Atmos. Sci. Vol. 20, March 1963, p. 130. doi: 10.1175/1520-0469(1963)0202.0.CO;2. [Go to]
E.N. Lorenz. Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas. American Association for the Advancement of Science Meeting, Washington D.C., December 29, 1972. Available online: [Go to]
B. Bower. Ratio for a good life exposed as 'nonsense'. Science News. Vol. 184, September 7, 2013. p. 5. [Go to]

New paper finds the same climate model produces different results when run on different computers

13 comments:

  1. https://pantherfile.uwm.edu/kswanson/www/publications/tsonis_GRL07.pdf

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  2. A little bit of disingenuity? Just because we cannot predict a specific state of a chaotic system, does not mean that we cannot look at overall properties of that system. Indeed, Lorenz never mentions in the interview that we cannot make predictions about climate, only that WEATHER can only be predicted within a maximum range of about 2 weeks.

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    1. Sure, we can look at the overall properties and sure, we can say based upon past knowledge of climate that it is likely temperatures will change by little over the next century.

      However, the specific projections made by the IPCC for the globe and specific regions are absurd given the implications of chaos theory. The uncertainties propagate and increase exponentially with time, rendering climate projections useless.

      A simple "no change" model outperforms IPCC GCMs by factor of 7:

      http://hockeyschtick.blogspot.com/2010/03/paper-no-change-climate-model-is-7_02.html


      as does a simple harmonic model

      http://hockeyschtick.blogspot.com/2013/08/simple-climate-model-outperforms-ipcc.html

      see also

      http://hockeyschtick.blogspot.com/2013/10/father-of-chaos-theory-explains-why-it.html

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  3. RalphieFairfield, Ct

    I'm not a climate scientist but hold a Ph.D. in a statistics and research heavy discipline. So...

    How many variables influence climate? How many are included in the computer models (I'm sure it depends on the model) -- what is typical. How correlated are predictors? How are interactions among predictors accounted for in the models?

    Climate must be a very complex system with several reasonably independent variables influencing change. Are there five? Ten? Any way you slice it, the more variables you invite into your model, the more complex things become, particularly the interactions. Assuming you have three independent variables -- A, B, C. Then you also have the A x B, A x C. B x C and A x B x C interactions -- if you add a fourth variable, D, then you also add the terms A x D, B x D, C x D, A x B x D, A x C x D, B x C x D and A x B x C x D.

    And if you add a fifth variable, the number of new terms is 16 I believe. I'm not going to figure this out out to ten variables, and of course many interaction terms are irrelevant or statistically redundant. And if there is multicollinearity among predictors, that may further complicates things.

    I don't know if climate models reflect that level of complexity, but I would not be surprised if real world climate is very complex and can become so if only a handful of variables impact climate.
    Nov. 1, 2013 at 11:36 a.m.

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  4. Article in Nature laments inability of climate models to project climate even 5 years in advance

    http://hockeyschtick.blogspot.com/2013/07/new-article-in-nature-laments-dismal.html

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  5. http://icecap.us/images/uploads/Oped_Gray_10_13_Long_range_forecasting.pdf

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  6. Many aspects of climate cannot be predicted beyond 2-3 weeks due to chaos:

    http://m.iopscience.iop.org/1748-9326/7/1/015602/pdf/1748-9326_7_1_015602.pdf

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  7. The all important Navier-Stokes equations can't even be solved for turbulence in a 4 inch pipe:

    http://www.energyadvocate.com/phystoda.pdf

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  8. http://www.sciencedaily.com/releases/2013/11/131117155613.htm

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  9. Paper by Lorenz

    http://eaps4.mit.edu/research/Lorenz/Index_Cycle_Alive_Well_85q.pdf

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  10. Must read related post by Dr. Robert Brown:

    http://wattsupwiththat.com/2014/10/06/real-science-debates-are-not-rare

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  11. http://www.climatemonitor.it/?p=36447

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  12. New paper finds, due to chaos, the weather and climate is "not what you expect" and climate shifts/variability/change are expected & normal

    http://link.springer.com/article/10.1007%2Fs00382-014-2324-0

    ReplyDelete