TOPEX/POSEIDON tides estimated using a global inverse model

Abstract

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics of errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low‐dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open‐ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M2, S2, K1, and O1. The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the “default” tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (≈20–30%), even though only a small number of free parameters (≈1000) are actually fit to the crossover data.

The influence of the Plata River discharge on the western South Atlantic shelf

“…The inflows and outflows of the Malvinas (Falkland) and Brazil Currents were obtained from the Parallel Ocean Climate Model (experiment 4C [Tokmakian and Challenor, 1999]). The amplitude and phase of the principal tidal constituents are from the Oregon State University TPXO.5 tidal model [Egbert et al, 1994]. The model was spun-up for an initial 3-year period followed by an additional 1-year run for analysis.…”

Evaluation of a near-global eddy-resolving ocean model

“…This results in stronger mixing in regions of large-amplitude tides, such as the north-west of Australia. The tidal mixing coefficients depend on spatially resolved, but time invariant estimates of tidal amplitudes that are obtained from a global inverse model (Egbert et al, 1994). A convective adjustment is applied every time step using fully explicit mixing when the water column becomes unstable.…”

Altimeter‐derived variability of surface velocities in the California Current System: 1. Evaluation of TOPEX altimeter velocity resolution

“…The sea surface height, mean sea surface, dry troposphere, solid earth and pole fides are interpolated to the Zlotnicki-Fu along-track grid with 6.2-km spacing, and the corrections are then subtracted from the sea surface height. The ocean tide is calculated at the grid points and subtracted from the s6a surface height using the tide model of Egbert et al [1994]. The resulting signal is the dynamically important variable and is referred to as the "corrected sea surface height."…”