Analytical Formulation of Equatorial Standing Wave Phenomena: Application to QBO and ENSO
Abstract
Key equatorial climate phenomena such as QBO and ENSO have never been adequately explained as deterministic processes. This in spite of recent research showing growing evidence of predictable behavior. This study applies the fundamental Laplace tidal equations with simplifying assumptions along the equator — i.e. no Coriolis force and a small angle approximation. To connect the analytical Sturm-Liouville results to observations, a first-order forcing consistent with a seasonally aliased Draconic or nodal lunar period (27.21d aliased into 2.36y) is applied. This has a plausible rationale as it ties a latitudinal forcing cycle via a cross-product to the longitudinal terms in the Laplace formulation. The fitted results match the features of QBO both qualitatively and quantitatively; adding second-order terms due to other seasonally aliased lunar periods provides finer detail while remaining consistent with the physical model. Further, running symbolic regression machine learning experiments on the data provided a validation to the approach, as it discovered the same analytical form and fitted values as the first principles Laplace model. These results conflict with Lindzen's QBO model, in that his original formulation fell short of making the lunar connection, even though Lindzen himself asserted "it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential".By applying a similar analytical approach to ENSO, we find that the tidal equations need to be replaced with a Mathieu-equation formulation consistent with describing a sloshing process in the thermocline depth. Adapting the hydrodynamic math of sloshing, we find a biennial modulation coupled with angular momentum forcing variations matching the Chandler wobble gives an impressive match over the measured ENSO range of 1880 until the present. Lunar tidal periods and an additional triaxial nutation of 14 year period provide additional fidelity. The caveat is a phase inversion of the biennial mode lasting from 1980 to 1996. The parsimony of these analytical models arises from applying only known cyclic forcing terms to fundamental wave equation formulations. This raises the possibility that both QBO and ENSO can be predicted years in advance, apart from a metastable biennial phase inversion in ENSO.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFMOS11B..04P
- Keywords:
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- 4215 Climate and interannual variability;
- OCEANOGRAPHY: GENERALDE: 4522 ENSO;
- OCEANOGRAPHY: PHYSICALDE: 4532 General circulation;
- OCEANOGRAPHY: PHYSICALDE: 4556 Sea level: variations and mean;
- OCEANOGRAPHY: PHYSICAL