# Surrogate-based variational data assimilation for tidal modelling

arXiv: https://arxiv.org/abs/2106.11926 · HTML: https://mlsanity.com/paper/2106.11926/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 70 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Tackling Climate Change with Machine Learning](https://mlsanity.com/paper/1906.05433/) (2019)
- [Machine Learning for the Geosciences: Challenges and Opportunities](https://mlsanity.com/paper/1711.04708/) (2017)
- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [Background Error Covariance Iterative Updating with Invariant Observation Measures for Data Assimilation](https://mlsanity.com/paper/1910.09408/) (2019)
- [Physically interpretable machine learning algorithm on multidimensional non-linear fields](https://mlsanity.com/paper/2005.13912/) (2020)
- [A Review of Innovation-Based Methods to Jointly Estimate Model and Observation Error Covariance Matrices in Ensemble Data Assimilation](https://mlsanity.com/paper/1807.11221/) (2018)

## Abstract (arXiv)

Data assimilation (DA) is widely used to combine physical knowledge and observations. It is nowadays commonly used in geosciences to perform parametric calibration. In a context of climate change, old calibrations can not necessarily be used for new scenarios. This raises the question of DA computational cost, as costly physics-based numerical models need to be reanalyzed. Reduction and metamodelling represent therefore interesting perspectives, for example proposed in recent contributions as hybridization between ensemble and variational methods, to combine their advantages (efficiency, non-linear framework). They are however often based on Monte Carlo (MC) type sampling, which often requires considerable increase of the ensemble size for better efficiency, therefore representing a computational burden in ensemble-based methods as well. To address these issues, two methods to replace the complex model by a surrogate are proposed and confronted : (i) PODEn3DVAR directly inspired from PODEn4DVAR, relies on an ensemble-based joint parameter-state Proper Orthogonal Decomposition (POD), which provides a linear metamodel ; (ii) POD-PCE-3DVAR, where the model states are POD reduced then learned using Polynomial Chaos Expansion (PCE), resulting in a non-linear metamodel. Both metamodels allow to write an approximate cost function whose minimum can be analytically computed, or deduced by a gradient descent at negligible cost. Furthermore, adapted metamodelling error covariance matrix is given for POD-PCE-3DVAR, allowing to substantially improve the metamodel-based DA analysis. Proposed methods are confronted on a twin experiment, and compared to classical 3DVAR on a measurement-based problem. Results are promising, in particular superior with POD-PCE-3DVAR, showing good convergence to classical 3DVAR and robustness to noise.