3.2. Brief Typology of Simulation & Modeling Systems “I wanted to explain why observing the ocean was so difficult, and why it is so tricky to predict with any degree of confidence such important climate elements as its heat and carbon storage and transports in 10 or 100 years. I am distrustful of prediction scenarios for details of the ocean circulation that rely on extremely complicated coupled models that run out for decades to thousands of years. The science is not sufficiently mature to say which of the many complex elements of such forecasts are skillful” Carl Wunsh278 We’re going to try to provide some schematics to the situations one may encounter saying that there exists formal, convergent, divergent and totally chaotic systems. In fact with the same underlying theory (e.g. Kepler’s laws) you can sometimes face one or the other of these situations. For example, you can compute the orbit of a double star (i.e. a solution to the differential equation the system obeys to) and have a quick convergent way to compute the orbit, say some tens or hundreds of iterations like in the spreadsheet provided here (Poyet, 2017c) and given the trigonometric parallax, one can immediately compute the sum of the masses for the binary system by using the third Kepler’s law (the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit). Then you can miss one important parameter (e.g. the trigonometric parallax) but overcome the situation by means of an approximate relation, e.g. between the mass and luminosity (MLR) of main-sequence stars, which was predicted by Eddington (1924) and leads to the calculation of dynamic parallaxes (Russell, 1928), (Kuiper, 1938), (Baize, 1943), (Baize and Romani, 1946), (Baize, 1947), (Couteau, 1971), enabling the knowledge of each individual mass of the binary system. Using this method and coupling it to simple iterative calculations in a spreadsheet enables to derive in less than ten iterations stable absolute bolometric magnitudes for each star A and B, individual masses for A and B, the dynamic parallax and the sum of masses to serve as a crosscheck. Thus, one has both a formal and convergent means to compute the values he / she is interested in, this is the best situation. But at the same time, when one faces a n-body problem (e.g. solar system), the same theory does not provide any longer for a formal solution and by numerical integration, with billions of small steps (i.e. iterations) you know that the system will unfortunately be divergent over the very long run. This situation still enables to make very reliable solar system ephemeris over decades but totally prevent from knowing where the planets will be, say in 100 million years “The motion of the Solar System is thus shown to be chaotic, not quasi-periodic. In particular, predictability of the orbits of the inner planets, including the Earth, is lost within a few tens of millions of years ” (Laskar, 1990). This hints to the limits of the theory and of the knowledge available (as you miss of a formal solution to a n-body problem) as well as of the frontier introduced by the technology used, as billions of small increments required over a 100 million years simulation will erase any reliable accuracy due to minimal rounding over such a very long term. Then you have chaotic systems, like in meteorology or worse climate (the same but over longer timescales) and the situation gets a lot more desperate, this is the Lorentz effect and designates the instability of the solutions of certain systems of equations (non-linear) compared to the initial conditions; it can mean that the system that the equations want to describe is actually "chaotic" or that the equations used do not correctly describe the system. This instability of the discretization programs of the fluid equations limits to a few days the quality of the forecasts of meteorology… which are inapplicable in climatology. As reported by Snider (2016) «It's the proverbial butterfly effect said Clara Deser, a senior climate scientist at the National Center for Atmospheric Research (NCAR). Could a butterfly flapping its wings in Mexico set off these little motions in the atmosphere that cascade into large-scale changes to atmospheric circulation?». It is also the CACE syndrome, Change Anything Changes Everything. Believing that by averaging n runs, here n=30, provides for a « mean » having some significance is total delusion, it is like thinking that by throwing 30 times 2 (or more) dices and by averaging the results of the draws would give any insight into what will come out next ! Here we have left science and delved into beliefs, illusions when one think that because the map was calculated by a supercomputer it bears some meaning, it contains information. When one faces the wall of reality, like with meteorological forecasts, scientists know that they deal with a totally chaotic system that gives them no chance to make any meaningful prevision beyond 2 weeks, but when they are climate tinkerers they delude themselves thinking that extending the timescales to decades and furthermore adding complexity, would enable them to produce some reliable result, by wizardry. As reminded by Hansen (2016), «Averaging 30 results produced by the mathematical 278http://www.realclimate.org/index.php/archives/2007/03/swindled-carl-wunsch-responds/
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