The Fallacy of Steady-State

The central idea of The Fluid Catastrophe (henceforth TFC) is that, in all but a few special cases, deterministic models do not provide a realistic picture of reality; stochastic models are more powerful. Determinism works well for the motions of the planets but not for fluid dynamics

A closely related idea is the idea of the steady-state whereby the equations describing quantities are assumed to be independent of time. The more sophisticated idea is that of stationarity whereby the statistics of a system are assumed independent of time; values of measured quantities may vary over time and it is only the statistics and model parameters which are assumed to be static. This is one step removed from steady-state; it is a higher level of abstraction.

We assume steady-state in order to come to grips with reality, in order to make reality conceivable and manageable. It is only ever a working hypothesis. We can never be sure that a system is steady-state but we can be sure when it isn’t. There is a natural tendency to assume that those processes which are long compared with a human lifetime are steady-state: wilderness, undisturbed ecosystems, ocean circulation. Events which disturb such systems are then sufficiently rare to be regarded as accidents or aberrations, outside the cosy delusion we have constructed for ourselves. It then follows that someone or something must be to blame: the gods, God, capitalism, humanity. Non-indigenous Australians seem to believe this of bushfires and talk of the “devastation” wrought by bushfires in wilderness areas. We could equally well talk of “renewal” or “regeneration” following such fires. Even qualified ecologists go along with this hand-wringing, while well aware that numerous native species could only have evolved in a regime of regular burning. This is the human lifetime fallacy.

Most people have an intuitive grasp of the Law of Large Numbers: that the average of a sample gets closer and closer to the true value as the sample size gets bigger.

But this is only true of the average! It is not true of the sum! 

The average converges only because the sum is divided by the number in the sample, N. The sum of a number of zero mean, random fluctuations becomes larger as N becomes larger. Its standard deviation is the the square root of N even though the mean tends to zero. The belief that the variance of the sum of random quantities tends to zero is the Law of Large Numbers fallacy.

For a physical system in which a large number of small rapid fluctuations are added, the outcome will not be a steady state, it will be a variation which is both larger and slower than that of the input fluctuations. This sort of slow variation is called red noise because there is more variance at lower frequencies compared to white noise. An example is the temperature of a body of water heated and cooled by radiation and evaporation in the course of a year (TFC pp 64-65).

Another example is ocean circulation. At short time scales we see the surface currents driven by wind and tides. At longer time scales we see the big warm core eddies which spin off promontories like the Cape of Good Hope and Cape Horn. At even longer time scales we see the great ocean gyres and ocean currents such as the Gulf Stream, the Kurashio and the Aghulas. It would be comforting to assume, because these large gyres are the sum of component smaller currents and eddies, that they are steady-state and not subject to variation over time. This would be wrong. It is an example of the human lifetime fallacy and the law of large numbers fallacy. Large scale ocean currents are not the average of smaller variations, they are more like their sum and most likely have a red-noise frequency spectrum with significant variability at low frequencies.

Ocean currents are not steady-state. Concerns about variations in the Gulf Stream are unwarranted.

 

4 Replies to “The Fallacy of Steady-State”

  1. Like the storm on Jupiter. A fascinating time lapse on https://en.m.wikipedia.org/wiki/Great_Red_Spot Seems it’s been going for hundreds of years but it is larger than earths diameter.
    It is all too easy to see patterns and expect a steady state, such that things will always be the same. They never do stay the same over an extended time frame.

  2. I thought of the fluid catastrophy when reading this article:
    https://m.techxplore.com/news/2019-05-aims-capturing-power-energy-production.html
    It relates;
    “Results from the project, called “Perdigão,” which included a major field experiment in Vale do Cobrão, a valley in eastern Portugal, show that the speed and direction of wind over complex terrain at the height of wind turbine hubs differ significantly from standard weather forecasts, according to the report published in the Bulletin of the American Meteorological Society.

    Those forecasts, which wind turbine operators rely on to bring facilities online and supply wind power to the grid, are only 40 to 50 percent accurate in regard to the annual energy production—creating a challenge for the industry.

    “A major focus of Perdigão project is to improve forecasting and planning horizons for wind turbine facilities, both in terms of turbine siting and operations,” said Harindra Joseph Fernando, lead principal investigator of the study for the U.S. group and Wayne and Diana Murdy Endowed Professor in the Department of Civil and Environmental Engineering and Earth Sciences and the Department of Aerospace and Mechanical Engineering at the University of Notre Dame. “Wind flows are steered sensitively by topography. Mountains, vegetation, rivers and streams shape the speed and direction of wind, so what happens at the site of the turbine is very different from macroscale meteorological forecasts.”

    To be useful, wind power forecasts need to be made at least six hours in advance so that electric grid operators can balance the loads effectively. The project aims to improve such forecasts using a combination of techniques, in particular by improving the so-called microscale models. These models capture the details of flow surrounding a wind turbine with fine accuracy, and provide winds at points separated by 100 meters or so horizontally (compared to tens of kilometers in weather predictions models).

    The study’s location was chosen specifically for its all-encompassing terrain of ridges, slopes, farmland, vegetation, canyons and river flow. Complex terrain accounts for the majority of all land surface on Earth—one reason why scientists want to better understand how to maximize wind capture for turbine facilities.

    Both the United States and the European Union (EU) are working to increase wind energy shares of their respective total energy consumption. In 2017, 6.3 percent of the total electricity produced in the U.S. was from wind turbines whereas the share in the EU was 11.6 percent. According to the Department of Energy, utility-scale wind power facilities have been installed in 41 states, with smaller-scale systems distributing wind power in all 50 states as well as Puerto Rico, Guam and the U.S. Virgin Islands.

    “The Perdigão project represented a true international collaboration, culminating in a project with an unprecedented number of instruments,” said Nick Anderson, program director with the National Science Foundation’s Division of Atmospheric and Geospace Sciences, which funded the research. “The data from the field campaign will be used by researchers for decades, and will improve forecasts of local wind conditions that impact wind energy, firefighting, air pollution and warfare applications.””
    I’m guessing that these people will be at it for sometime in order to find a pattern, test it, only to find that ever so often it doesn’t work.

  3. I downloaded a satellite map of Vale do Cobrao. It is situated between two long thin ridges. These ridges would need to be smoothed out in any numerical meteorological model of the region because, otherwise, they would generate instabilities that would “blow up” the model as discussed on page 26 of TFC. Hence such a numerical model will be unable to adequately predict local winds in this region.

  4. “The data from the field campaign will be used by researchers for decades, and will improve forecasts of local wind conditions that impact wind energy, firefighting, air pollution and warfare applications.” A failure for Science, a triumph for ongoing Funding.

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