Mapping Altimetry in the Forthcoming SWOT Era by Back-and-Forth Nudging a One-Layer Quasigeostrophic Model

Abstract

During the past 25 years, altimetric observations of the ocean surface from space have been mapped to provide two dimensional sea surface height (SSH) fields which are crucial for scientific research and operational applications. The SSH fields can be reconstructed from conventional altimetric data using temporal and spatial interpolation. For instance, the standardDUACS products are created with an optimal interpolation method which is effective for both low temporal and low spatial resolution. However, the upcoming next-generation SWOT mission will provide very high spatial resolution but with low temporal resolution.The present paper makes the case that this temporal-spatial discrepancy induces the need for new advanced mapping techniques involving information on the ocean dynamics. An algorithm is introduced, dubbed the BFN-QG, that uses a simple data assimilation method, the back-and-forth nudging, to interpolate altimetric data while respecting quasigeostrophic dynamics. The BFN-QG is tested in an observing system simulation experiments and compared to the DUACS products. The experiments consider as reference the high-resolution numerical model simulation NATL60 from which are produced realistic data: four conventional altimetric nadirs and SWOT data. In a combined nadirs and SWOT scenario, the BFN-QG substantially improves the mapping by reducing the root-mean-square errors and increasing the spectral effective resolution by 40km. Also, the BFN-QG method can be adapted to combine large-scale corrections from nadirs data and small-scale corrections from SWOT data so as to reduce the impact of SWOT correlated noises and still provide accurate SSH maps.

Joint Estimation of Balanced Motions and Internal Tides From Future Wide‐Swath Altimetry

“…The mapping technique for BMs is presented in detail in Le Guillou et al. (2021). It is based on a QG model and a data assimilation method called Back and Forth Nudging (Auroux & Blum, 2008), and referred to as BFN‐QG.…”

“…As explained in Le Guillou et al. (2021), the nudging term K ( q obs − q ) must exhibit smooth variations in time to avoid the emergence of numerical instabilities and enhance the constraint of the observations on the model dynamics. A Gaussian kernel is used for the nudging term: $$$K({q}_{\text{obs}}-q)[t]=\sum\limits _{{t}_{\text{obs}}}{K}_{0}{e}^{-{(\frac{t-{t}_{\text{obs}}}{\tau })}^{2}}({q}_{\text{obs}}[{t}_{\text{obs}}]-q[t])$$$ where K 0 and τ are the nudging parameters and t obs are the observation times.…”

“…Note that, similarly, spatial smoothing needs to be implemented in the case of irregular space distribution of observations, as discussed in Le Guillou et al. (2021).…”

“…For operational implementation, DUACS L4 product (or equivalent) could be used, as in Le Guillou et al. (2021). The length of the BFN time window T BFN is fixed to 15 days after a few trial and error experiments.…”

“…where K is a tunable coefficient controlling the strength of nudging. As explained in Le Guillou et al (2021), the nudging term K(q obs − q) must exhibit smooth variations in time to avoid the emergence of numerical instabilities and enhance the constraint of the observations on the model dynamics. A Gaussian kernel is used for the nudging term:…”