Data assimilation works for unstable systems

What is it about?

Data assimilation (DA) is the merging of observations about a phenomenon with the equations that describe its evolution. DA started in numerical weather prediction, where observations about the current state of the atmosphere are incomplete and inaccurate, while the equations are known but still subject to imperfections. The improvement of DA methodology for properly merging observational and theoretical knowledge has greatly contributed to the increasing range and accuracy of numerical weather forecasts over several decades. Theoretically, such improvements are only warranted if the equations that describe the evolution of the weather were stable. But these equations are nonlinear and chaotic, i.e., very unstable. This paper shows, for the first time, that this instability is not an obstacle to DA methodology working as well as it does. These results are particularly important at a time when DA methodology is spreading across the physical and life sciences, to areas where much less is known about the nature of the governing equations.

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Why is it important?

The paper shows, for the first time, in rigorous mathematical language that unstable dynamics does not prevent data assimilation (DA) from improving the simulation and prediction of a system's highly nonlinear behavior. The proofs also suggest improvements in DA methodology for incomplete observations.

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