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Machine learning models have shown great success in predicting weather up to two weeks ahead, outperforming process-based benchmarks. However, existing approaches mostly focus on the prediction task, and do not incorporate the necessary…
This chapter provides various perspective on an important challenge in data assimilation: model error. While the overall goal is to understand the implication of model error of any type in data assimilation, we emphasize on the effect of…
While machine learning-based weather prediction (MLWP) has achieved significant advancements, research on assimilating real observations or ensemble forecasts within MLWP models remains limited. We introduce ClimaX-LETKF, the first purely…
Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses continuous data assimilation for a model arising as a…
This work integrates ensemble-based data assimilation (DA) with the energy-aware hybrid modeling approach, applied to a three-layer quasi-geostrophic (QG) model of the Gulf Stream flow. Building on prior DA success in the QG channel regime,…
Weather prediction is a critical task for human society, where impressive progress has been made by training artificial intelligence weather prediction (AIWP) methods with reanalysis data. However, reliance on reanalysis data limits the…
We show how the 3DVAR data assimilation methodology can be used in the astrophysical context of a two-dimensional convection flow. We study the way this variational approach finds best estimates of the current state of the flow from a…
As artificial intelligence (AI) continues to rapidly evolve, the realm of Earth and atmospheric sciences is increasingly adopting data-driven models, powered by progressive developments in deep learning (DL). Specifically, DL techniques are…
Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range…
A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…
Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…
The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use…
Accurate estimation of error covariances (both background and observation) is crucial for efficient observation compression approaches in data assimilation of large-scale dynamical problems. We propose a new combination of a covariance…
In three-dimensional variational data assimilation (3DVar) for numerical weather prediction (NWP), the observation operator $\mathcal{H}$ plays a central role by mapping model state variables to an observation equivalent. For weather radar,…
We formulate a strong equivalence between machine learning, artificial intelligence methods and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in…
The hybrid model combines the physics-based primitive-equations model SPEEDY with a machine learning-based (ML-based) model component, while ERA5 reanalyses provide the presumed true states of the atmosphere. Six-hourly simulated noisy…
Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of…
In the past couple of years, there is a proliferation in the use of machine learning approaches to represent subgrid scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical…
Accurate forecasting in the e-commerce finance domain is particularly challenging due to irregular invoice schedules, payment deferrals, and user-specific behavioral variability. These factors, combined with sparse datasets and short…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…