Background-error correlation model based on the implicit solution of a diffusion equation

TL;DR: The NCOM-4DVAR as mentioned in this paper is a new tool for data analysis, formulated for weak-constraint data assimilation based on the indirect representer method.

TL;DR: In this article, satellite wind data were used to correct the bias of wind originating from a global atmospheric model, while satellite sea level data are used to improve the initial conditions of the model simulations.

TL;DR: In this paper, a method for representing spatially correlated observation errors in variational data assimilation is proposed, which is based on the numerical solution of a diffusion equation, a technique commonly used for representing spatial correlated background errors and discretizing the pseudo-time derivative of the diffusion equation implicitly using a backward Euler scheme.

TL;DR: New approaches for defining correlation operators based on diffusion operators are described and an iterative algorithm based on the Chebyshev iteration, which uses a fixed number of iterations and pre‐computed eigenvalue bounds, is shown to be particularly promising.

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 the 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 or 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, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). 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 (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

TL;DR: In this article, a fully three-dimensional, multivariate, optimum interpolation ocean data assimilation system has been developed that produces simultaneous analyses of temperature, salinity, geopotential and vector velocity.

TL;DR: In this paper, a global three-dimensional variational analysis system is formulated in model grid space, where the horizontal scales of variables are obtained through the variances of the variables and of their Laplacian.

TL;DR: Underwater gliders are autonomous vehicles that profile vertically by buoyancy control and move horizontally on wings as mentioned in this paper, and are among the best approaches to achieving subsurface spatial resolution necessary for ocean research.