Jonathan Lawhead

“ As we saw in Section 6.3.2, the question of whether or not a non-chaotic approximation of our solar system’s behavior is a “good” approximation is purpose-relative. There’s no interesting way in which one or another model of the solar system’s long-term behavior is “good” without reference to our predictive goals. Pragmatic idealization lets us start with a goal--a particular prediction, explanation, or decision--and construct models that help us reach that goal. ”

“ I argued that chaotic dynamics don’t prevent us from making meaningful predictions in general; rather, they force us to make a choice between precision and time. If we’re willing to accept a certain error range in our predictions, we can make meaningful predictions about the behavior of a system with even a very high maximal Lyapunov exponent out to any arbitrary time. ”

“ We saw how the more specialized EMIC-family of models can help ameliorate the shortcomings of the simplest models, and while the breadth and power of EMICs is impressive, there is surely a niche left to be filled in our modeling ecosystem: the comprehensive, high-fidelity, as-close-to-complete-as-we-can-get class of climate models. Coupled global circulation models [1] (CGCMs) fill that niche, and strive for as much verisimilitude as possible given the technological constraints. ”

“ On this view, one major role for CGCMs’ in the context of climate science (and climate science policy) as a whole is to proscribe the field of investigation and focus our attention on proposals worthy of deeper consideration. Knowledge of the avenues we can safely ignore is just as important to our decision making as knowledge of the details of any particular avenue, after all.
I should emphasize again that this perspective also explains the tendency, discussed in Chapter Four, of progress in climatology to involve increasing model pluralism rather than convergence on any specific model. ”

“ Once the model has converged on this equilibrium state, modelers can feed in hypothetical parameters and observe the impact. They can change the concentration of greenhouse gases in the atmosphere, for instance, and see what new equilibrium the system moves to (as well as what path it takes to get there) . By tinkering with the initial equations of motion (and doing another spin up) , the length of the spin-up, and the values of parameters fed in after the spin up, modelers can investigate a variety of different scenarios, time-periods, and assumptions. ”

“ Given the dynamics describing how the positions of the planets evolves, two trajectories through the solar system’s state space that begin arbitrarily close together will diverge exponentially over time. However, as we noted before, just noting that a system’s behavior is chaotic leaves open a number of related questions about how well we can predict its long-term behavior. Among other things, we should also pay attention to the spatio-temporal scales over which we’re trying to generate interesting predictions, as well as our tolerance for certain kinds of error in those predictions. ”

“ The size of the cells is constrained by a few factors, most significantly the computational resources available and the desired length of the time-step when the model is running. The first condition is fairly intuitive: smaller grids require both more computation (because the computer is forced to simulate the dynamics at a larger number of points) and more precise data in order to generate reliable predictions (there’s no use in computing the behavior of grid cells that are one meter to a side if we can only resolve/specify real-world states using a grid 1,000 meters to a side) . ”

“ The spin up approach has a number of advantages; in addition to freeing climate modelers from the impossible task of empirically determining the values of all the parameters needed to run the model, the spin up also serves as a kind of rough test of the proposed dynamics of the model before it’s employed for prediction and ensures that parameter values are tailored for the grid-scale of the individual model. ”

“ That is, while the parameters for (say) cloud cover, greenhouse gas concentration, and insolation correspond rather straightforwardly to real aspects of the global climate, the action of the flux adjustment seems more like an ad hoc “fudge factor” with no physical correspondence. The most forceful way of phrasing the concern suggests that by manipulating the parameterization of a flux adjustment, a disingenuous climate modeler might easily craft the output of the model to suit his biases or political agenda. ”

“ After all, our entire discussion of dynamical complexity has been predicated on the notion that fundamental physics deserves neither ontological nor methodological primacy over the special sciences. How can we justify this sort of implied primacy for the physics-based patterns of the global climate system? ”

“ The climate modelers then input relevant insolation parameters--they flip on the sun. This (unsurprisingly) causes a cascade of changes in the previously dark Earth. The model is allowed to run for (in general) a few hundred thousand years of “model time” until it settles down into a relatively stable equilibrium with temperatures, cloud cover, and air circulation patterns that resemble the real climate’s state at the start of the time period under investigation. The fact that the model does settle into such a state is at least a prima facie proof that it’s gotten things relatively right ”

“ The project of modeling the global climate in general, then, is a project of pragmatic idealization. The sense of ‘idealization’ here is perhaps somewhere between Weisberg’s and Norton’s. It differs most strongly from Norton’s in the sense that the values of parameters in a pragmatic idealization need not approximate values in the “target system” of the global climate at all. Some apsects of even the best models, in fact, will have explicitly non-physical parameters ”

“ Even a fairly low-power computer can render the output of a small grid / short time step model given enough time to run. At a certain point, the model output becomes useless; a perfect simulation of the next decade of the global climate isn’t much use if it takes several centuries to output. ”

“ We might worry even in standard cases, that is, that committed scientists might appropriately take falsifying observations not as evidence that a particular model ought to be abandoned, but just that it ought to be refined. ”

“ Weather prediction must be far more precise than climate prediction in order to be interesting. However, it also need only apply to a timeframe that is many, many order of magnitude shorter than climate predictions. Meteorologists are interested in predicting with relatively high accuracy whether or not it will rain on the day after tomorrow. Climatologists are interested in predicting--with roughly the same degree of accuracy--whether or not average precipitation will have increased in 100 years. ”

“ It’s often non-trivial to decide whether, in light of some new evidence, we ought to discard or merely refine a given model. Oreskes’ discussion cites the problem of the observable parallax for Copernican cosmology and Lord Kelvin’s proposed refutation of old-earth gradualism in geology and biology--which was developed in ignorance of radioactivity as a source of heat energy--as leading cases, but we need not reach so far back in history to see the point. ”

“ The solar system, while chaotic, is a system of relatively low dynamical complexity. The advantages of pragmatic MMI-style accounts of idealization over Norton-style hard-nosed realist accounts of idealization become increasingly salient as we consider more dynamically complex systems. ”

“ The fact that we can’t give a reliable prediction about where Mercury will be in its orbit at around the time Sol ceases to be a main-sequence star--or similarly that we can’t give a prediction about Mercury’s position in its orbit in five years that gets things right down to the centimeter--doesn’t really trouble us most of the time. ”

“ Contemporary computational climate modeling has evolved from the combined insights of Bjerknes and Richardson. Designers of high-level Coupled General Circulation Models (CGCMs) build on developments in atmospheric physics and fluid dynamics. In atmospheric circulation models, the primitive equations track six basic variables across three dimensions [6] : surface pressure, horizontal wind components (in the x and y directions) , temperature, moisture, and geopotential height. ”

“ The use of spin up and ensemble modeling is designed to smooth over the roughness and error that results from the demonstrably tricky business of simulating the long-term behavior of a large, complex, chaotic system ”

“ After all, the grid must be designed such that during the span between one time-step and the next, no relevant information about the state of the world inside one grid cell could have been communicated to another grid cell. ”

“ The legitimacy of CGCMs, from this perspective, stands or falls with the legitimacy of models in the rest of science. Sociological worries about theory-dependence in model design are, while not trivial, at least well-explored in the philosophy of science. There’s no sense in holding computational models to a higher standard than other scientific models. ”

“ Despite superficial similarities in the primitive equations underlying both atmospheric and oceanic models--both are based heavily on fluid dynamics--differences in surface area, mass, specific heat, density, and a myriad of other factors lead to very different responses to environmental inputs. Perhaps most importantly, the ocean and atmosphere have temperature response and equilibrium times that differ by several orders of magnitude. ”

“ A myriad computers [2] are at work upon the weather of the part of the map where each sits, but each computer attends only to one equation or one part of an equation. The work of each region is coordinated by an official of higher rank. ”

“ In a neighboring building there is a research department, where they invent improvements. But there is much experimenting on a small scale before any change is made in the complex routine of the computing theatre. In a basement an enthusiast is observing eddies in the liquid lining of a huge spinning bowl, but so far the arithmetic proves the better way. ”

“ Alan Turing’s seminar 1950 paper on artificial intelligence made a similar observation when considering popular objections to the notion of thinking machines: it is unreasonable to hold a novel proposal to higher standards than already accepted proposals are held to. ”

“ They can’t be falsified, as by the time evidence proves them inadequate, they’ll be rendered irrelevant in any case. The kind of parameterization and spin up procedure discussed above can be seen, in this more critical light, as a pernicious practice of curve-fitting: the CGCMs are designed to generate the predictions that they do, as model builders simply adjust them until they give the desired outputs. ”

“ For most cases, it’s clear that the sine-wave shape is: if the pencil has to move in such a way that it follows the shape of the sine-wave on the middle sheet, there are vast swaths of area in the other two sheets that it just can’t access, no matter whether there’s a cut-out there or not. ”