Learning of Sea Surface Height Interpolation from Multi-variate Simulated Satellite Observations

TL;DR

This work tackles the problem of interpolating Sea Surface Height (SSH) maps from sparse satellite altimeter measurements by fusing SSH with Sea Surface Temperature (SST) through a data-driven framework. It introduces a 20-year Observing System Simulation Experiment (OSSE) to generate realistic SSH and SST observations and trains an Attention-Based Encoder-Decoder (ABED) network under supervised, unsupervised, and SST-enhanced losses, with a hybrid scheme that pre-trains on OSSE data and fine-tunes on real observations. Results show that incorporating SST substantially improves SSH reconstructions and the fidelity of derived geostrophic currents and mesoscale eddies, with supervised learning generally outperforming unsupervised approaches and SST-augmented losses achieving the strongest gains. A transfer-learning pathway—pre-training on OSSE and unsupervised fine-tuning on real data—yields state-of-the-art performance on the Ocean Data Challenge 2021, evidencing the approach’s practical impact for real-world SSH gridding and eddy analysis, and offering a route toward near-real-time SSH products and global interpolation in the future; the method leverages the geostrophic connections expressed by $u_{geo} = -\frac{g}{f} \frac{\partial h}{\partial y}$ and $v_{geo} = \frac{g}{f} \frac{\partial h}{\partial x}$ to constrain the SSH–SST relationship.

Abstract

Satellite-based remote sensing missions have revolutionized our understanding of the Ocean state and dynamics. Among them, space-borne altimetry provides valuable Sea Surface Height (SSH) measurements, used to estimate surface geostrophic currents. Due to the sensor technology employed, important gaps occur in SSH observations. Complete SSH maps are produced using linear Optimal Interpolations (OI) such as the widely-used Data Unification and Altimeter Combination System (DUACS). On the other hand, Sea Surface Temperature (SST) products have much higher data coverage and SST is physically linked to geostrophic currents through advection. We propose a new multi-variate Observing System Simulation Experiment (OSSE) emulating 20 years of SSH and SST satellite observations. We train an Attention-Based Encoder-Decoder deep learning network (\textsc{abed}) on this data, comparing two settings: one with access to ground truth during training and one without. On our OSSE, we compare ABED reconstructions when trained using either supervised or unsupervised loss functions, with or without SST information. We evaluate the SSH interpolations in terms of eddy detection. We also introduce a new way to transfer the learning from simulation to observations: supervised pre-training on our OSSE followed by unsupervised fine-tuning on satellite data. Based on real SSH observations from the Ocean Data Challenge 2021, we find that this learning strategy, combined with the use of SST, decreases the root mean squared error by 24% compared to OI.

Figures (11)

• Figure 1: Images of the ground truth SSH from GLORYS12, the simulated along-track measurements, and the difference.
• Figure 2: Images of our cloud cover, the ground truth SST from GLORYS12, the noised SST, and the difference.
• Figure 3: Images of satellite observations of the SSH and the SST, respectively.
• Figure 4: The architecture of the proposed Attention-Based Encoder Decoder (abed) neural network. It is designed to take a time series of 21 images of SSH, with or without a time series of SST. The encoder divides the spatial dimensions of the images by 4 through 2 "down-block". Then, a 3D attention layer block is used to highlight relevant information in the images, followed by a residual connection. Finally, a decoding block upsamples the images, and attention and decoding blocks are repeated to get back to the initial image size.
• Figure 5: Computational graph of the proposed unsupervised interpolation method. The neural network input is a 21-day time series of SSH satellite observations, excluding data from a single satellite, and optionally includes SST measurements. The network estimates a time series of SSH field states, upon which the observation operator is subsequently applied in order to deduce $\mathbf{\hat{Y}} \IfNoValueF{-NoValue-}{_{-NoValue-}} \IfNoValueF{ssh}{^{ssh}}$. Finally, the Mean Squared Error between the $\mathbf{\hat{Y}} \IfNoValueF{-NoValue-}{_{-NoValue-}} \IfNoValueF{ssh}{^{ssh}}$ and $\mathbf{Y} \IfNoValueF{-NoValue-}{_{-NoValue-}} \IfNoValueF{ssh}{^{ssh}}$ is used to control the network.