Abstract
Conventional tidal prediction models typically combine constituent
lunisolar forcing factors harmonically fit to sets of collected tidal
gauge data. A harmonics analysis is favored over a precise orbital
ephemeris-based gravitational forcing model, as tides are localized in
scope and sensitive to a particular volume geometry. But what happens
when the dynamic behavior is much larger in scale? As we have
demonstrated previously [1], lunisolar tidal constituents forced by
a strong biennial-modulated annual signal will provide a high-quality
fit to ENSO – albeit subject to over-fitting of the numerous
constituent factors available. Yet as ENSO is a large-scale phenomenon,
it should be more amenable to applying a precise set of ephemeris data
as the forcing to a Laplace’s tidal equation formulation. This should
reflect the underlying physics governing the dynamics more
realistically, while severely constraining the degrees of freedom (DOF)
in factors which lead to the possibility of over-fitting. We used the
NASA JPL Horizons (https://ssd.jpl.nasa.gov/horizons.cgi) ephemeris data
for the Sun and Moon as a parametric input to the well-known 1/R^3
gravitational forcing function and verify as good a quality fit as that
available from a high-DOF harmonics approach. This extends over the
modern-day instrumental record of ENSO but also covers the coral proxy
records that span the years from 1650 to 1880. The approach works
effectively because the extra DOF (including phases and elliptical
nonlinearities in the orbits) needed to precisely define the
gravitational forcing are accurately tracked by the Horizons ephemeris
algorithm. Importantly, the results are highly sensitive to the relative
forcing amplitudes, which is not surprising, since the fast lunisolar
cycles are projected over spans of hundreds of years. The challenge is
equivalent to attempting to perform a conventional tidal analysis over a
similarly lengthy time span, while also dealing with noise and a limited
resolution time-series. [1] Pukite, P.R. “Biennial-Aligned
Lunisolar-Forcing of ENSO: Implications for Simplified Climate Models.”
AGU Fall Meeting, 2017.