Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

Abstract

Abstract. The diffusive back-and-forth nudging (DBFN)is an easy-to-implement iterative data assimilation method based on the well-known nudging method. It consists of a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore, in the DBFN, the nudging asymptotic behaviour is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability, the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system set-up are analysed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusioninduced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar.

Spurious Forces Can Dominate the Vorticity Budget of Ocean Gyres on the C‐Grid

“…The first experiment in this article is an idealized double gyre configuration based on the GYRE PISCES reference configuration in NEMO. The GYRE PISCES reference configuration has been used for a wide range of experiments (Lévy et al, 2010(Lévy et al, , 2015Perezhogin, 2019;Ruggiero et al, 2015). The domain is a closed rectangular basin which is 3,180 km long, 2,120 km wide, and is rotated at an angle of 45° relative to the zonal direction.…”

Global Observations of Fine-Scale Ocean Surface Topography With the Surface Water and Ocean Topography (SWOT) Mission

“…Another dynamical approach where the time interpolation relies upon quasi-geostrophic dynamics is also explored, where simulated SWOT observations are combined with the model through a back-and-forth nudging approach (Auroux and Blum, 2008;Ruggiero et al, 2015): the model is iteratively run forward and backward over a fixed time window, and gently nudged toward the observations at every time step with an elastic restoring force. Results indicate that this approach successfully reconstructs the SSH field in the full space and time domain considered.…”

Physics-Informed Deep Neural Network for Backward-in-Time Prediction: Application to Rayleigh–Bénard Convection

“…These models were used in a data assimilation setting with large-scale ocean and atmospheric models. For example, Ruggiero et al (2015) implemented a forward-backward nudging data assimilation algorithm using a negative diffusion coefficient to stabilize the Nucleus for European Modelling of the Ocean (NEMO) model over a short period of time. Forward-backward nudging algorithms were also examined to incorporate high-frequency remotely sensed observations of low-level wind into a high-resolution Meso-NH mesoscale model (Boilley and Mahfouf 2012), to analyze the Lorenz '05 (Osborne 2021) and the two-dimensional shallow-water model (Auroux et al 2016).…”

“…These efforts are hindered because the diffusion time scale limits the backward integration period, raising numerical difficulties in simulating the quantity and making the problem of obtaining accurate backward-in-time forecasts "uniquely challenging" (Clement 2010;Sun and Sun 2017). This problem was also explicitly noted by Ruggiero et al (2015) that the key limitation of their proposed nudging algorithm is the accuracy of the backward-in-time integration.…”