# Data-Driven Reconstruction of Sea Surface Turbidity Dynamics with 4dVarNet Neural Scheme Applied To Gappy Satellite Images

Clément Dorffer, F. Jourdin, D. Mouillot, Rodolphe Devillers, Ronan Fablet, Quentin Febvre

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► To cite this version:

Clément Dorffer, F. Jourdin, D. Mouillot, Rodolphe Devillers, Ronan Fablet, et al. Data-Driven Reconstruction of Sea Surface Turbidity Dynamics with 4dVarNet Neural Scheme Applied To Gappy Satellite Images. IGARSS 2023: IEEE International Geoscience and Remote Sensing Symposium, Jul 2023, Pasadena, CA, United States. IEEE, pp.4025-4027, 2023, IGARSS 2023 - 2023 IEEE International Geoscience and Remote Sensing Symposium. 10.1109/IGARSS52108.2023.10281712. [https://hal.science/hal-04363492](https://hal.science/hal-04363492)

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Submitted on 15 Mar 2024

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Distributed under a Creative Commons Attribution 4.0 International License
# DATA-DRIVEN RECONSTRUCTION OF SEA SURFACE TURBIDITY DYNAMICS WITH 4DVARNET NEURAL SCHEME APPLIED TO GAPPY SATELLITE IMAGES

Clément DORFFER¹, Frédéric JOURDIN², David MOUILLOT³, Rodolphe DEVILLERS⁴, Ronan FABLET¹, and Quentin FEBVRE¹

¹IMT Atlantique, UMR CNRS Lab-STICC, INRIA team Odyssey, Brest, France
²MARBEC, University of Montpellier, CNRS, IFREMER, IRD, Montpellier, France

³Service Hydrographique et Océanographique de la Marine (SHOM), 29603 Brest, France

⁴Espace-Dev (IRD-UM-UG-UR-UA-UNC), Station SEAS-OI, 97410 Saint-Pierre, La Réunion, France

## 1. Objective

**Turbidity:** the measurement of the amount of suspended matter in a liquid or solution.
⇒ **A Key parameter that influences coastal and marine ecosystems.**

**How to get turbidity values?**

► In-situ measurement techniques:

<figure><img src="image_3.png" /><figcaption>Figure: Secchi Disk</figcaption></figure>

► Remote sensing measurements:

<figure><img src="image_4.png" /><figcaption>Figure: Satellite multispectral imaging.</figcaption></figure>

→ **Good data reliability, but poor time and/or space coverage.**

→ **Perennial but missing values may occur due to e.g., a cloud coverage.**

► **Our objective:** fill in the missing data of satellite images and provide complete turbidity maps.

## 2. Proposed approach

**Data assimilation problem to be solve**

$$ \tilde{x} = \arg \min_{x} U(x, y, \Omega) = \arg \min_{x} \lambda_1 \underbrace{\|x - y\|^2}_{\text{data fidelity term}} + \lambda_2 \underbrace{\|x - \phi(x)\|^2}_{\text{dynamical prior}}, \quad \text{with} \quad x \text{ the completed field,} \\ y \text{ the observations (uncomplete),} \\ \Omega \text{ the observation mask,} \\ \phi(\cdot) \text{ the dynamical model.} \tag{1} $$

Problem (1) solved by gradient descent, i.e., by successive updates:

$$ x^{k+1} = x^k - \alpha \nabla_x U(x^k, y, \Omega). \tag{2} $$

**4DVarNet-architecture**

Sat. Obs.

<figure><img src="image_5.png" /><figcaption>Figure: Graphical representation of 4DVarNet algorithm. Parameters to be trained appear in red.</figcaption></figure>

Produces a smoothed gradient descent of (1).

**4DVarNet training step:**

<figure><img src="image_6.png" /></figure>

► Minimizes defined training loss *i.e.*, the reconstruction error.

► Adjusts both "model" and solver parameters.

## 3. Considered Data

**Mediterranean Sea** with focus along the French coast:

<figure><img src="image_7.png" /></figure>

**CMEMS product:**
**OCEANCOLOUR_MED_BGC_L3_MY_009_143**

► Multi-sensor product.

► L3 data (preprocessed data).

► Daily mean turbidity values.

► **Problem: No ground truth available for training.**

**Idea: No gap-free GT? → Data subsampling for artificial obs. generation!**

**Reconstruction results**

<table><thead><tr><th></th><th>Patch-based</th><th>Sat.-masks</th><th>Comp.-Sat.-mask</th></tr></thead><tbody><tr><th>Patch-based</th><td>0.044</td><td>0.088</td><td>0.085</td></tr><tr><th>Satellite-masks</th><td>0.084</td><td>0.09</td><td>0.098</td></tr><tr><th>Comp.-satellite-masks</th><td>0.08</td><td>0.093</td><td>0.087</td></tr><tr><th>DInEOF</th><td>0.081</td><td>0.12</td><td>0.095</td></tr><tr><th>eDInEOF</th><td>0.078</td><td>0.098</td><td>0.085</td></tr></tbody></table>

Table: RMSLE reached w.r.t. the subsampling strategies used for learning (lines) and testing (columns).

The lower the better: **4DVarNet provides up to 43% of relative gain compare to eDInEOF.**

**Reconstruction examples (log10 bbp443 the particulate backscattering coefficient at 443nm)**

<figure><img src="image_8.png" /></figure>

**Acknowledgements**

This work was funded by the french ANR, as part of the AI-biodiv Challenge: fish-predict.

This work was performed using HPC resources from GENCI-IDRIS.

This study has been conducted using E.U. Copernicus Marine Service Information: https://doi.org/10.48670/moi-00299

<footnote>[1] Fablet, R., et al. "Learning variational data assimilation models and solvers." Journal of Advances in Modeling Earth Systems 13.10 (2021).</footnote>

<footnote>[2] Beckers, J.-M., et al. "EOF calculations and data filling from incomplete oceanographic datasets." Journal of Atmospheric and oceanic technology 20.12 (2003).</footnote>