that are arbitrarily close together in the system’s state space. The connection to climate modeling is straightforward. Given the difficulty--if not impossibility--of measuring the current (not to mention the past) state of the climate with anything even approaching precision, it’s hard to see how we’re justified in endorsing the predictions made by models which are initialized using such error-ridden measurements for their initial conditions. If we want to make accurate predictions about where a chaotic system is going, it seems like we need better measurements--or a better way to generate initial conditions[1].
This is where the discussion of the “predictive horizon” from Section 5.1.3 becomes salient. 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.
This foundational observation is implemented in the practice of ensemble modeling. Climatologists don’t examine the predictions generated by computational models in isolation--no single “run” of the model is treated as giving accurate (or even meaningful) output. Rather, model outputs are evaluated as ensembles: collections of dozens (or more) of runs taken as a single unit, and interpreted as defining a range of possible paths that the system might take over the specified time range.
Climate modelers’ focus is so heavily on the creation and interpretation of ensembles that the
- ↑ This problem is compounded by the fact that we often want to initialize climate models to begin simulating the behavior of the climate at times far before comprehensive measurements of any kind--let alone reliable measurements--are available. While we can get some limited information about the climate of the past through certain “proxy indicators” (see Michael Mann’s work with glacial air bubbles, for instance), these proxy indicators are blunt tools at best, and are not available at all for some time periods.
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