Systematic error correction in numerical ocean models with artificial neural networks

Systematic biases pose a significant challenge in ocean general circulation models, where numerical approximations, unresolved physical processes, and parameterization choices can lead to state-dependent errors. Addressing these biases is crucial for improving forecasts of the Earth’s climate system, yet remains nontrivial—particularly given the sparse nature of ocean observations, which complicates bias detection and correction.

One promising route is to harness analysis increments within a Machine Learning (ML) framework to learn state-dependent systematic errors from archived data assimilation corrections. For instance, neural networks can be used to train a model with the ocean state as input and the Data Assimilation corrections as output. By training on these increments, the ML model learns how errors systematically depend on the local physical state.

In our work, we use outputs from ocean reanalysis data using variational data assimilation and the NEMO ocean model. The ML-based correction is embedded in NEMO’s tendency equations as an additional forcing term, allowing the model to evolve more realistically by accounting for state-dependent systematic errors in temperature and salinity.

However, the sparsity of ocean observations can lead to “punctual” analysis increments that contain not only model biases but also noise from intermittent measurement coverage, errors, and initial-condition uncertainties. To mitigate this issue, we apply a two dimensional low-pass filter to remove high-frequency fluctuations in both the ocean fields and the analysis increments, preserving larger-scale patterns.

We adopt a feed-forward neural network (NN) that processes vertical profiles. By focusing on the ocean’s vertical stratification and processes, the network is trained on these filtered analysis increments and learns the non-linear relationships linking NEMO’s state variables (temperature, salinity) to the corrections identified by the variational scheme. Through this level-specific, column-oriented NN, the model more effectively adjusts for systematic errors.

In this poster, we present preliminary results on offline validation of the trained NN—predicting analysis increments on independent test data beyond the training period—without yet applying these corrections in a fully integrated forecast. Our preliminary findings show how well the NN reproduces systematic biases at various depths and in different oceanic regions, even under sparse data conditions and complex multi-scale dynamics. This demonstration highlights the potential of combining analysis increments with ML to systematically reduce model errors in next-generation ocean prediction systems, setting the stage for future work that integrates these learned corrections into an online, real-time workflow.