The Global S $$_1$$ 1 Tide in Earth’s Nutation

Abstract

Diurnal S tidal oscillations in the coupled atmosphere–ocean system induce small perturbations of Earth’s prograde annual nutation, but matching geophysical model estimates of this Sun-synchronous rotation signal with the observed effect in geodetic Very Long Baseline Interferometry (VLBI) data has thus far been elusive. The present study assesses the problem from a geophysical model perspective, using four modern-day atmospheric assimilation systems and a consistently forced barotropic ocean model that dissipates its energy excess in the global abyssal ocean through a parameterized tidal conversion scheme. The use of contemporary meteorological data does, however, not guarantee accurate nutation estimates per se; two of the probed datasets produce atmosphere–ocean-driven S terms that deviate by more than 30 as (microarcseconds) from the VLBI-observed harmonic of as. Partial deficiencies of these models in the diurnal band are also borne out by a validation of the air pressure tide against barometric in situ estimates as well as comparisons of simulated sea surface elevations with a global network of S tide gauge determinations. Credence is lent to the global S tide derived from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) and the operational model of the European Centre for Medium-Range Weather Forecasts (ECMWF). When averaged over a temporal range of 2004 to 2013, their nutation contributions are estimated to be as (MERRA) and as (ECMWF operational), thus being virtually equivalent with the VLBI estimate. This remarkably close agreement will likely aid forthcoming nutation theories in their unambiguous a priori account of Earth’s prograde annual celestial motion.

Report of the IAU/IAG Joint Working Group on Theory of Earth Rotation and Validation

“…The S1 signal, considered anomalous for long, has been further explained. Schindelegger et al (2016Schindelegger et al ( , 2017 showed that the S1 LOD estimate (6 s) determined from VLBI is in agreement with atmosphere-ocean excitation estimates. 3.…”

The Tides They Are A‐Changin': A Comprehensive Review of Past and Future Nonastronomical Changes in Tides, Their Driving Mechanisms, and Future Implications

“…These meteorological forcings include diurnal variations in air pressure and also small‐scale contributions from land‐sea breezes (Ray & Egbert, ; Rosenfeld, ). Numerical modeling (e.g., Ray & Egbert, ; Schindelegger et al, ) shows that the radiational part of the S 1 ocean tide can have amplitudes of a few centimeters in some regions (Arabian Sea, eastern Indian Ocean, and Okhotsk Sea) and that it dominates the solar diurnal gravitational component by an approximate factor of 5 throughout the ocean. Pugh and Woodworth () also point to possible spurious manifestations of S 1 in tide gauge measurements, related, for example, to the daily heating and cooling of thermally sensitive instruments.…”

Can We Model the Effect of Observed Sea Level Rise on Tides?

“…Codes from Einšpigel and Martinec (; see also http://geo.mff.cuni.cz/~einspigel/debot.html, accessed 14 June 2017) were adopted as time domain solver of the nonlinear shallow water equations with forcing from individual partial tides. Following up on earlier experiments (Schindelegger et al, ), we have stripped down the model to its very core to prepare for inclusion of the full SAL machinery. Writing the undisturbed water depth as H , the tidal surface displacement with respect to the moving seafloor as ζ , and the corresponding velocity vector u as depth‐integrated volume transport U = u H , the one‐layer momentum and mass conservation equations read where f is the Coriolis vector orientated along the local vertical, ∇ is the spherical del operator, ⊗ is the outer product, g denotes gravitational acceleration, ζ EQ refers to the equilibrium tide (Hendershott, ), and ζ SAL is the SAL elevation.…”