An Adaptive Optimal Interpolation Based on Analog Forecasting: Application to SSH in the Gulf of Mexico

Abstract

Because of the irregular sampling pattern of raw altimeter data, many oceanographic applications rely on information from sea surface height (SSH) products gridded on regular grids where gaps have been filled with interpolation. Today, the operational SSH products are created using the simple, but robust, optimal interpolation (OI) method. If well tuned, the OI becomes computationally cheap and provides accurate results at low resolution. However, OI is not adapted to produce high resolution and high frequency maps of SSH. To improve the interpolation of SSH satellite observations, a data-driven approach (i.e., constructing a dynamical forecast model from the data) was recently proposed: analog data assimilation (AnDA). AnDA adaptively chooses analog situations from a catalog of SSH scenes – originating from numerical simulations or a large database of observations – which allow the temporal propagation of physical features at different scales, while each observation is assimilated. In this article, we review the AnDA and OI algorithms and compare their skills in numerical experiments. The experiments are observing system simulation experiments (OSSE) on the Lorenz-63 system and on an SSH reconstruction problem in the Gulf of Mexico. The results show that AnDA, with no necessary tuning, produces comparable reconstructions as does OI with tuned parameters. Moreover, AnDA manages to reconstruct the signals at higher frequencies than OI. Finally, an important additional feature for any interpolation method is to be able to assess the quality of its reconstruction. This study shows that the standard deviation estimated by AnDA is flow-dependent, hence more informative on the reconstruction quality, than the one estimated by OI.

Data-Driven Interpolation of Sea Surface Suspended Concentrations Derived from Ocean Colour Remote Sensing Data

“…The common main reasons for this is that these methods exploit much more past observations for the present reconstruction. Indeed, when applying an OI in a multi-map context with a total absence of data, it is necessary to extend the spatial influence of the Gaussian kernel and obtain a covariance matrix that can provide results [46]. This extension of the neighborhood search to observations implies a more important smoothing of the map during the completed interpolation.…”

Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review

“…To mitigate this, in some cases, a purely data-driven interpolation (e.g., Kriging) can be performed in place of the first DA step to produce the first estimate of x 0:T . Another option is to emulate the dynamical system M t using analog forecasting methods, and plug it into an ensemble DA technique [263], [264]. In absence of any original physical-based model, the data-driven model can only reconstruct dynamics on variables of the system that are observed, even though the problem can be circumvented by using Takens's delay embedding theorem [265], [49] as it is detailed in Section IV-D .…”

Data-Driven Mapping With Prediction Neural Network for the Future Wide-Swath Satellite Altimetry

“…The theoretical expressions of COR, RMSE, and STD are detailed in Eqs. ( 21), ( 22), and (23) (Taylor and Karl, 2001;Beauchamp et al, 2020;Zhen et al, 2020), respectively.…”

“…The DI method has limitations on mapping the sea areas where the PV conservation fails (Roge et al, 2017;Ballarotta et al, 2020). Then, consequently, the "data-driven" mapping methods (Lguensat et al, 2017(Lguensat et al, , 2019bZhen et al, 2020) are proposed. Unlike the classical model-driven methods (Lguensat et al, 2017), the data-driven methods rely on the spatial-temporal relationship of the observations (Lguensat et al, 2019b).…”

“…Unlike the classical model-driven methods (Lguensat et al, 2017), the data-driven methods rely on the spatial-temporal relationship of the observations (Lguensat et al, 2019b). Lguensat et al (2017), who used machine learning (ML) methods in the Mediterranean, South China sea area (Lguensat et al, 2019b), and the Gulf of Mexico (Zhen et al, 2020) through principal component analysis (PCA), K nearest neighbor (KNN), and k-dimensional tree (KD-Tree) technologies, introduced a data-driven mapping method named AnDA (Lguensat et al, 2017). Furthermore, Lopez-Radcenco et al (2019) extended the AnDA method to the mapping for multi-satellitecombined observations, SWOT observing system simulation experiments (OSSEs)-simulated data, as well as the combination of observations of nadir altimeter satellites and SWOT, and then obtained higher-accuracy SSH grid data products than the result of the OI method (Lopez-Radcenco et al, 2019).…”