Facilitating Strongly Coupled Ocean–Atmosphere Data Assimilation with an Interface Solver

Abstract

In a strongly coupled data assimilation (DA), a cross-fluid covariance is specified that allows measurements from a coupled fluid (e.g., atmosphere) to directly impact analysis increments in a target fluid (e.g., ocean). The exhaustive solution to this coupled DA problem calls for a covariance where all available measurements can influence all grid points in all fluids. Solution of such a large algebraic problem is computationally expensive, often calls for a substantial rewrite of existing fluid-specific DA systems, and, as shown in this paper, can be avoided. The proposed interface solver assumes that covariances between coupled measurements and target fluid are often close to null (e.g., between stratospheric observations and the deep ocean within a 6-h forecast cycle). In the interface solver, two separate DA solvers are run in parallel: one that produces an analysis solution in the atmosphere, and one in the ocean. Each system uses a coupled observation vector where in addition to resident measurements in the target fluid it also includes nonresident measurements in the coupled fluid that are likely to have significant influence on the analysis in the target fluid (interface measurements). An ensemble-based method is employed and a localization function for coupled ensembles is proposed. Using a coupled model for the Mediterranean Sea (in a twin setting), it is demonstrated that (i) the solution of the interface solver converges to the exhaustive solution and (ii) that in presence of poorly known error covariances, the interface solver can be configured to produce a more accurate solution than an exhaustive solver.

Treating Sample Covariances for Use in Strongly Coupled Atmosphere‐Ocean Data Assimilation

“…For our model, the atmosphere ensemble error correlation length scales are approximately 2 orders of magnitude greater than those for the ocean over the time scales we consider; to ensure that the atmospheric variables do not have undue influence on the ocean beyond the near-surface boundary, we need to account for this disparity when we define the localization length scales for the subblock AO . Similarly to Frolov et al (2016), we found that this could be achieved by replacing (3) with the scaled distancê …”

“…The first method is based on forming a multivariate localization matrix from the univariate GC function. A similar approach is adopted by Frolov et al (2016) for localizing the coupled cross-domain ensemble covariances in their atmosphere-ocean interface solver. One potential flaw in this approach, noted by Roh et al (2015), is that a multivariate localization matrix constructed this way is not guaranteed to be positive definite; they propose fixing this by setting equal to the product of a univariate function and a symmetric, positive-definite matrix whose diagonal entries are one.…”

“…We have developed a vertical localization strategy built on similar ideas to those proposed by Roh et al (2015) and Frolov et al (2016). Our approach is the same on a broad level, but here we give specific consideration to the trade-off between filtering sampling noise and improving conditioning, and preserving the atmosphere-ocean error cross-correlation signals; this aspect of coupled model space localization is not addressed in previous studies.…”

“…For coupled atmosphere-ocean assimilation, the importance of intervariable error correlations is well acknowledged, especially in the lower atmosphere-upper ocean boundary layer; but these correlations may be small relative to single variable autocorrelations and to correlations between errors in variables within the same fluid; therefore, extra care must be taken to that ensure that the localization does not destroy the smaller, yet physical, atmosphere-ocean error cross correlations. We have developed a vertical localization strategy built on similar ideas to those proposed by Roh et al (2015) and Frolov et al (2016). Our approach is the same on a broad level, but here we give specific consideration to the trade-off between filtering sampling noise and improving conditioning, and preserving the atmosphere-ocean error cross-correlation signals; this aspect of coupled model space localization is not addressed in previous studies.…”

“…The ideal approach to coupled data assimilation is strongly (or fully) coupled in which components of the Earth system are analyzed within a single seamless assimilation framework: a single assimilation algorithm is used to combine the available observations from each subcomponent with a fully coupled model forecast state, producing a single fully coupled analysis. Despite recent advancements (e.g., Frolov et al, 2016;Laloyaux et al, 2016;Lea et al, 2015;Sluka et al, 2016) there are still a number of scientific challenges to solve before coupled assimilation can become the primary technique for weather and climate forecasting and reanalysis (Penny & Hamill, 2017). A particular challenge for strongly coupled data assimilation systems is modeling the cross covariances that characterize the relationship between errors in the atmosphere and ocean model forecasts (Smith et al, 2017).…”