Testing the Hypothesis that Atmospheric Blocking Follows the Nonlinear Schrödinger Equation

Atmospheric blocking (the stagnation of the weather systems) often causes weather extremes in the mid- to high-latitudes, yet its first-order dynamics are still not well understood. While synoptic weather systems typically last 3-5 days, atmospheric blocking can last 10-20 days. Despite rich literature, atmospheric blocking's first-order dynamics remain enigmatic.

Inspired by growing evidence of the propagating Rossby wave packets as a critical aspect in block life cycles, it becomes natural to connect such observations with the solution of a particular type of nonlinear equation - the Nonlinear Schrödinger (NLS) Equation. We assess a key and classical hypothesis that views atmospheric blocking as governed by the NLS Equation, which was first proposed by Benny (1979) and Yamagata (1980). Our goal is to fill the gap of the theory-driven approach and data-driven approach. Using a combination of a two-layer and a companion barotropic quasi-geostrophic model, we start from the same configuration of these classical papers, and follow a similar asymptotic approach to derive a NLS equation as its slow evolution of atmospheric pattern. Meanwhile, we utilize a data-driven approach by applying the recently developed local finite-amplitude wave activity diagnostics on a large number of blocks generated by the quasi-geostrophic model, and ultimately use machine learning approach to decipher the key equation, which can be compared against the theoretical derivations. By assessing this hypothesis, we will argue that the evolution of coherent and propagating Rossby wave packets is instrumental in block lifecycles. We will further discuss the significance of confirming this NLS equation's relation to atmospheric blocking and how it allows a physics-informed machine learning to further improve the predictability of blocking, and the implications of a new theory for predicting blocks in a warming climate.