fredag 6 november 2009

How Climate Alarmism Got Started: The Lorenz Equations

Climate change alarmism was initiated at the 1965 conference Causes of Climate Change in Boulder, when the mathematician and meteorologist Edward Lorenz presented a simple mathematical model with solutions being very sensitive to perturbations in e.g. initial values. The assembled scientists where shocked because Lorenz mathematical model, later referred to as the Lorenz equations, could be viewed as a simplified version of the Navier-Stokes equations of fluid dynamics and thus as a simple climate model. 

The shock came from the argument that since solutions of the Lorenz equation are so sensitive to perturbation, a flap of a butterfly in the Amazonas could very well set off a tornado in Texas. Truely shocking mathematics! As summarized after the conference by Roger Revelle, advisor of the young Harward student Al Gore. Climate alarmism was under way, although Revelle became a skeptic before passing away.

But let's take a step back from shock and see more precisely what the Lorenz equations as a simple climate model tell us. I have already done that in Chapter 13 my book with Johan Hoffman Computational Turbulent Incompressible Flow, where in the context of turbulent flow we exhibit the Lorenz equations as an example of a mathematical model with solutions being 
  • pointwise predictable over short-time
  • pointwise unpredictable over long-time
  • mean-value predictable over long-time
which also are characteristics of climate systems. This means that it is possible to predict the daily weather a couple of days ahead but not a year ahead, because the system is short-time exponentially unstable with positive feedback. However it is possible to predict the  monthly mean-value a year ahead, like tourist guide books do, because of cancellation with positive feedback compensated by negative feedback. 

For the Lorenz equations the butterfly pattern is stable and predictable, and as shown in the book the ratio of the number of trajectory revolutions in the two "wings" tends to 1.

In other words, it is impossible to say if it will rain 30 days ahead, but it is possible to predict the monthly mean precipitation one year ahead, simply because after rain comes sunshine.
Not because the weather is random, but because the dynamics of the system is such that if
goes up for a while it has to go down.

The waving flag is an example of such a system: after waving to one side the flag will wave to the other side: the mean direction over long-time can be predicted to be the wind direction, but to predict on what side the flag will be is possible only a very short time ahead. 

We conclude that the Lorenz system is not a sign of alarm. If anything, it can be taken as support of beliefs that mean-values will never change over long time, e.g. that the global mean temperature will never change. But doing so would not be correct from a scientific point of view, because systems like the Lorenz equations, or the Navier-Stokes equations for fluid flow, do not model non-linear effects which could cause a drift of mean-values over long time. We know that in the real climate the mean global temperature has changed and will continue to change, and climate models must capture this effect to be meaningful.

long-time mean-value accurate, and hence probably are meaningless. Compare Short-time vs Long-time Accuray 1 and 2.

Climate alarmism was thus born out of a misunderstanding of mathematics, as perfected by Einstein.

This is not good news for Australian Prime Minister Kevin Rudd who launched a spirited attack on climate skeptics on Friday, saying a vocal minority is powerful enough to threaten a global deal at next month's Copenhagen climate summit:
  • Climate skeptics, deniers and opponents of climate action are active in every country, have limited the ambition of national climate change commitments and slowed progress of carbon trade laws in the United States and Australia. They are a minority. They are powerful, and invariably they are driven by vested interests.
  • They are powerful enough to threaten a deal on global climate change both in Copenhagen and beyond.
Ban-Ki Moon joins with The Greatest Challenge og Our Time opening a new debate in SVD: Climate from different angles. Almost all 50 comments so far are negative to climate alarmism reflecting an increasing global apathy...  It will be interesting to see if SVD will invite skeptics with different angles... 

2 kommentarer:

  1. Mycket intressant bloggpostning. Tack för den utmärtka informationen och förklaringen. Att dom på 1960 talet arbetade med starka förenklingar är väl självklart då datorkraften var så klen. Men att dom hållit fast vid det är alarmerande ;)

  2. Man how you do this really hard, but you are too good.

    Term papers within deadlines.