SWOT Research - Spatiotemporal Inpainting

Introduction

5/30/2026. This project revolves around the Surface Water and Ocean Topography (SWOT) satellite, which collects unprecedented high resolution ocean data. However, as it is a single satellite it is only guaranteed to go over every swath of ocean once every 21 days, providing us with high spatial resolution but very low temporal resolution. In this project, I aim to increase this temporal resolution through spatiotemporal inpainting of the data, estimating the state of the ocean on the intervening days between satellite passes. This project focuses on SSH data, and started with LLC4320 simulation data before being verified using SWOT data.

💻 View Source on GitHub

LLC4320 Data Exploration

The project started with LLC4320 data exploration. Going into the project it was thought that we could use a diffusion model to inpaint SSH data directly, but we quickly realized this was a much harder task than previously thought. Through data exploration we discovered that the SSH means vary significantly with the tides.

Thus we decided to look at approaching the problem with a 2-phase approach: first using a fourier-based model to isolate and subtract tides from the data, and then using a generative diffusion model to inpaint the anomalies, which would include submesoscale and mesoscale events.

The 2-Phase Physics-Informed Approach

The initial approach was to sample the data in sync with the peak of the dominant K2 lunar tide. This gave better results by interpolating SSH data in sync with this tide rather than interpolating every 24 hours, but was still very clearly missing lots of tidal variation. Thus, we tested using a dynamic fourier decomposition on the means of our ocean regions, fitting the variation on these means with sinusoids, but through testing realized that this would perform better by using known tidal constituent frequencies to avoid overfitting the model and ensure the frequencies of the tides are correct.

Thus the model was formed by using 8 known tidal constituent frequencies, and fitting magnitudes for a given ocean region by using previous and subsequent data within the region. Then, these 8 fitted sinusoids would predict the variation in the mean at any given point in time, allowing our model to isolate the mean variation and simply linearly interpolate the anomalies (the remaining SSH after subtracting the means from the data). A comparison of our model to the ground truth with a 21 day gap of time omitted from the model is pictured below.

Real SWOT data

This success on simulation data needed to be verified using real SWOT data so we recreated the model to work for the real SWOT data. Initial testing was done on the CalVAL phase, which was a calibration period for the satellite in which it covered a limited swath of the ocean once every day. Using this real world data we were able to optimize the number of tidal constituents to use, the optimal window size for averaging spatially to predict tidal magnitudes, and the method of inpainting the ocean spatially. The results of this approach on a real region (this region was located off the coast of California) are given below:

Challenges

The challenges we faced mostly centered around the need to further understand the data to know how to best inpaint it. Initially, we thought there was no need for any further data processing and that deploying a large nueral network at the problem would be able to easily solve it, but this proved to be far from the case. We had to look in depth at how we could explain different changes in the data, and ultimately settled on our 2-phase physics-informed approach to predicting the SSH means.

The use of a mentor (Ryley McConkley) was great for helping to guide this data exploration, guiding me to a preprocessing stage that was as simple as possible to facilitate a model that works and can be easily deployed.

Next Steps

The logical next step to this project is to train a generative model on the anomalies to better predict the anomaly variation now that we have accounted for tidal variation. This is necessitated by the linear interpolation clearly not being a sufficient approach to this problem, with large error in the data further from the input data. This problem will be easier to solve now that the tides are removed because the generative model will not have to account for the tides but rather can solve the easier problem of simply inpainting anomalies.

The model also will need to be further tested, with the real-world SWOT model only being tested on a single ocean region, and thus not necessarily representative of the entire ocean. However, this success on a single region at the very least highlights the utility of the model on some regions of the ocean, even if some regions with more complicated dynamics can't be explained by the model.

Poster

Here is a poster I presented summarizing the simulation-data side of the project: