# A multi-model ensemble Kalman filter for data assimilation and forecasting

arXiv: https://arxiv.org/abs/2202.02272 · HTML: https://mlsanity.com/paper/2202.02272/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2022.

## Built on by (most cited first, 5 of 5)

- [Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems](https://mlsanity.com/paper/2206.04811/) (2022)
- [Deep Bayesian Filter for Bayes-faithful Data Assimilation](https://mlsanity.com/paper/2405.18674/) (2024)
- [4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models](https://mlsanity.com/paper/2408.02767/) (2024)
- [Data Assimilation in Chaotic Systems Using Deep Reinforcement Learning](https://mlsanity.com/paper/2401.00916/) (2024)
- [RL-DAUNCE: Reinforcement Learning-Driven Data Assimilation with Uncertainty-Aware Constrained Ensembles](https://mlsanity.com/paper/2505.05452/) (2025)

## Abstract (arXiv)

Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the minimum variance linear unbiased estimator. Here, we formulate and implement a multi-model ensemble Kalman filter (MM-EnKF) based on this framework. The MM-EnKF can combine multiple model ensembles for both DA and forecasting in a flow-dependent manner; it uses adaptive model error estimation to provide matrix-valued weights for the separate models and the observations. We apply this methodology to various situations using the Lorenz96 model for illustration purposes. Our numerical experiments include multiple models with parametric error, different resolved scales, and different fidelities. The MM-EnKF results in significant error reductions compared to the best model, as well as to an unweighted multi-model ensemble, with respect to both probabilistic and deterministic error metrics.