Information Theory in Earth Science: Been there, done that

Following up from this post, there is a recent sequence of articles in an AGU journal on Water Resources Research under the heading: “Debates: Does Information Theory Provide a New Paradigm for Earth Science?”

By anticipating all these ideas, you can find plenty of examples and derivations (with many centered on the ideas of Maximum Entropy) in our book Mathematical Geoenergy.

Here is an excerpt from the “Emerging concepts” entry, which indirectly addresses negative entropy:

“While dynamical system theories have a long history in mathematics and physics and diverse applications to the hydrological sciences (e.g., Sangoyomi et al., 1996; Sivakumar, 2000; Rodriguez-Iturbe et al., 1989, 1991), their treatment of information has remained probabilistic akin to what is done in classical thermodynamics and statistics. In fact, the dynamical system theories treated entropy production as exponential uncertainty growth associated with stochastic perturbation of a deterministic system along unstable directions (where neighboring states grow exponentially apart), a notion linked to deterministic chaos. Therefore, while the kinematic geometry of a system was deemed deterministic, entropy (and information) remained inherently probabilistic. This led to the misconception that entropy could only exist in stochastically perturbed systems but not in deterministic systems without such perturbations, thereby violating the physical thermodynamic fact that entropy is being produced in nature irrespective of how we model it.

In that sense, classical dynamical system theories and their treatments of entropy and information were essentially the same as those in classical statistical mechanics. Therefore, the vast literature on dynamical systems, including applications to the Earth sciences, was never able to address information in ways going beyond the classical probabilistic paradigm.”

That is, there are likely many earth system behaviors that are highly ordered, but the complexity and non-linearity of their mechanisms makes them appear stochastic or chaotic (high positive entropy) yet the reality is that they are just a complicated deterministic model (negative entropy). We just aren’t looking hard enough to discover the underlying patterns on most of this stuff.

An excerpt from the Occam’s Razor entry, lifts from my cite of Gell-Mann

“Science and data compression have the same objective: discovery of patterns in (observed) data, in order to describe them in a compact form. In the case of science, we call this process of compression “explaining observed data.” The proposed or resulting compact form is often referred to as “hypothesis,” “theory,” or “law,” which can then be used to predict new observations. There is a strong parallel between the scientific method and the theory behind data compression. The field of algorithmic information theory (AIT) defines the complexity of data as its information content. This is formalized as the size (file length in bits) of its minimal description in the form of the shortest computer program that can produce the data. Although complexity can have many different meanings in different contexts (Gell-Mann, 1995), the AIT definition is particularly useful for quantifying parsimony of models and its role in science. “

Parsimony of models is a measure of negative entropy

9 thoughts on “Information Theory in Earth Science: Been there, done that

  1. From the intro paper, 4 points to consider

    — While the “laws of physics” successfully help us to understand elementary behavior, they have not been as successful in explaining the expressions of “complexity,” that is, the emergent patterns of form and function that we see in nature.
    — “Information” enters the discourse about nature from 2 perspectives—that information is “physical” and that all physical understanding is rooted in info; i.e, “laws of physics”. This duality can be exploited to develop a better understanding of Earth system processes.
    — “Information” can be rigorously quantified in terms of “bits,” which characterize the number of binary
    (“yes‐no”) questions that must be answered in order to unambiguously characterize any state of affairs
    –The works of Shannon, Jaynes, and many others provide the firm philosophical and mathematical foundations (i.e. MaxEnt) needed for the use of information‐theoretic metrics in the characterization of scientific knowledge

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  2. So what is Entropy? Long ago it was described as the tendency for all things to return to rest. There were two types of entropy, total entropy Q and specific entropy q. Both of which needed to be considered when solving energy production problems and system efficiency.
    The new definition:
    1.
    PHYSICS
    a thermodynamic quantity representing the unavailability of a system’s thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.
    “the second law of thermodynamics says that entropy always increases with time”
    2.
    lack of order or predictability; gradual decline into disorder.
    “a marketplace where entropy reigns supreme”
    Q and q can be solved there is nothing random about it, nor is it chaotic. The only thing that is required is a complete understanding of the system.

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  3. Mod: I have no idea what this guy is ranting about. He says “Anyway. To an uneducated individual these all kind of seem linked to me”, so perhaps he should just shut up

    Look, those graphs correlate. No matter what you say they correlate. Quite incredibly closely for those things to be unrelated.

    Now I cannot provide a theory on this clearly as what you are describing is quite true. It’s clearly chaos maths that would determine the action of liquid water as it runs over a surface. The corse it takes and any effect that would then have on its surroundings. Those graphs correlate though. So I will just give my observations and leave it there for now. We are due an excitement event at some point so hopefully considering how many things are now monitored compared to the 1930’s era then it may be nailed down.

    Now I know that if I drive in a car at 70 mph with this cart wheels on then the car will be unstable. This is because the wheels would bounce around easier which would be translated through to the axel which would then affect the whole car. I know if you have large heavy modern alloy wheels then the wheels themselves will roll smoother which I turn would keep the whole car smoother through the axel being stable.

    The earth now has cart wheels on its axis of spin where as before it had alloys.

    Now the graphs align. One thing every scientist I’ve spoken to on this agree is that the wobble cannot affect arctic temperatures therefore cannot be the cause of the shrinking ice mass. So the moon does not affect temperature so cannot affect the ice mass and because the wobble and the ice mass are so clearly linked cannot be the cause of the excitement events. It could exaggerate an excitement over a thirty to forty year period dragging it outwards until something causes the ice mass to reform. (The graphs are clearly correlated so these things have to be linked). It on its own cannot be the cause of the excitement though as the wobble doesn’t affect ice mass but ice mass clearly affects wobble.

    Now further to this I observer that there was a previous low point which was the 1920-1940 period. We are in 2021 basically exactly 100 years on. Now this is a coincidence I understand yet through my research I found an article called historic arctic temperature anomalies part 1 and 2. Now these both describe ice mass loss at the same period.

    Further to this I had a similar discussion with a climatologist on flooding as weather data seems to be the only data that was recorded prior to 1880 ish. Now the UK does have an extensive weather record going back. Now I put this in a graph and although it doesn’t align with these observations as well as the other three graphs do you will see that for the twenty year period roughly around the 20’s to the 40’s the temperature is higher than during the 60’s. Like I say it’s not perfect as many things effect temperatures but it is there.

    Anyway. To an uneducated individual these all kind of seem linked to me.

    Personally as we are talking about excitement events well these in nature would seem chaotic but what is chaos math is it not the attempt to understand randomness. This is not random, this repeats, or at least I really feel it does based on the recordings we have. In history the largest floods do seem to occur close to the thirtieth year in a century (google massive historic floods and see what comes up).

    You see chaos in a hydrodynamic system. I see structure and although seemingly chaotic it cannot be. The ice mass has melted giving the poles the ability to move around easier. There is far more liquid water moving around creating a much larger system with greater effect. Are these enough on there own to create an excitement, clearly not but they are clearly needed.

    Before the last excitement desalination had been recorded, higher pressure at ocean depth, more floods (although not currently being linked) giving an impression that there was more liquid water and less fresh water locked in the poles ice mass.

    These are my observations, I know we will detect the next excitement but what ever people believe actually caused it. It couldn’t happen unless the earth was in the state it is in now, like observably it was in the 1930’s prior to the last excitement. Hopefully we will have an answer more definitively by the end of the next 20 years or so as it does look like an excitement event is due.

    The graphs definitely correlate though. That needs some attention as I do believe the answer lies in the correlation.

    No one individual thing could ever move the earth or it would move around a lot more. You could say it was a once in a 100 year event (hydrodynamic engineers would have you believe this means something with a one in a hundred chance of happening Like a 100 year flood but I don’t agree with that. We have had more than 100, 100 year floods this year. The idea of that being down to probability is nonsense. So probability has no place in it. I bet the probability of there actually being a period of flooding once in 100 years and engineers got it wrong is lower then the probability of having 100, 100 year floods in one year) but that may not be correct as when the poles had weight on them the same event may not have caused an excitement.

    Time to wait for the next excitement event I think see what is recorded at the time. Whether the ice mass increases first or the wobble excites before the ice mass reforms.

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    • Commenting specifically on the unbalanced car tire model, the force that causes the instability is the road. With out the road the unbalanced wheel would not generate a harmonic pattern it would just maintain the same elliptical pattern provided no change in revolutions.

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  4. I think I’ve figured it out kind of.

    Look at the graphs. When the ice mass increases so does the wobble. When it reduces the wobble does too.

    Do you think the lunar effect you are looking at could actually be the moon pulling on ice rather than water. Or maybe more likely the sun. As the ice mass increases the gravitational pull does too.

    The wobble increases and decreases exactly with the ice mass. This must indicate the ice mass is the cause. Other things effect the ice mass. Clearly co2.

    So does this not indicate that something is pulling at the ice rather than the water because when the ice goes the wobble does too.

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    • Chicken v. Egg hypothesis, does artic ice sheet influence CW or does CW influence arctic ice sheet?
      So my questions are:
      what is the mass of the moon
      what is the velocity of the moon
      what is the mass of the arctic ice sheet at the peak
      what is the velocity of the artic ice sheet at the peak
      My hypothesis is that lunar forcing greatly affects oceanic currents (fluid flow) which affects ice formation and melting. Thus the basic gist of this conversation the greatest force is going to have the greatest influence, once the four questions above are answered you can apply some vectoral math (admittedly the most difficult math for me to comprehend so it is up to you to determine the force required to maintain a lunar orbit and the force required to maintain the arctic ice sheet on earth) and determine which is likely to have the greatest influence on CW. In the end you may defy credulity.

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      • This is all so ridiculous. Most people lack intuition based on technical experience. If I heard or measured a strong 60 Hz hum on an audio signal, I would guess it came from the AC power source and not intended as the audio. End of story. The Chandler wobble is the aliased frequency of the lunar nodal cycle. End of story.

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  5. Last post on it.

    I wouldn’t even know where to begin with the maths but could you consider the idea that the increasing mass alone with no external force causes the increase in the wobble.

    NO, BECAUSE THE IMPORTANT POINT IS EXPLAINING THE PERIODIC CYCLE OF THE WOBBLE

    When a spherical object spins perfectly it is in balance. If the spin was out slightly as it is with the earth the simply adding mass to the axis would pull it out via centrifugal force alone.

    The fact the ice mass and the wobble are perfectly aligned. The prior knowledge that the earth is already wobbling on its axis. It’s never straight. If all the ice mass melts it’ll be straight again but that doesn’t look likely to happen. What does happen is the ice increases and decreases in size and the wobble moves with it.

    This means co2 is the ultimate cause of the wobble variations and that the ice mass alone is responsible for the wobble.

    So, Co2 affects the temperature Temperature affects ice mass size The ice mass increasing on an already destabilised spin increases it. Or reducing ice mass reduces it.

    That’s it, no other planetary body or external source of gravity would be required at all so wouldn’t affect it. Simplest solutions are normally the right ones and this is really pretty simple and you know increasing mass on the pole whilst it spins the way the earth does would further increase the wobble and the graphs are just close they are exact.

    The increasing mass creates a further destabilisation of the rotation.

    It looks like if the winter ice mass is larger this year than last then the wobble increases but if it’s less it reduces. It’s like the wobble is the first sign of increasing or decreasing polar ice. (I know I have only put the northern ice sheet in but the Antarctic mirrors the arctic in ice mass.

    So, how would you work out the actual effect of the volumes of ice on the poles have on a destabilised spin during fluctuations in their mass.

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