Related papers: Variational Data Assimilation for Optimizing Bound…
Ensemble data assimilation techniques form an indispensable part of numerical weather prediction. As the ensemble size grows and model resolution increases, the amount of required storage becomes a major issue. Data compression schemes may…
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…
Every day, weather forecasting centres around the world make use of noisy, incomplete observations of the atmosphere to update their weather forecasts. This process is known as data assimilation, data fusion or state estimation and is best…
Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational…
We mathematically derive the sensitivity of data assimilation results for tsunami modelling, to perturbations in the observation operator. We consider results of variational data assimilation schemes on the one dimensional shallow water…
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…
We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…
Data Assimilation is a cornerstone of atmospheric system modeling, tasked with reconstructing system states by integrating sparse, noisy observations with prior estimation. While traditional approaches like variational and ensemble Kalman…
In this study, we conduct parameter estimation analysis on a data assimilation algorithm for two turbulence models: the simplified Bardina model and the Navier-Stokes-{\alpha} model. Our approach involves creating an approximate solution…
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…
The weather and climate domains are undergoing a significant transformation thanks to advances in AI-based foundation models such as FourCastNet, GraphCast, ClimaX and Pangu-Weather. While these models show considerable potential, they are…
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…
Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…
Using a dynamical model to make predictions about a system has many sources of error. These can include errors in how the model was initialised but also errors in the dynamics of the model itself. For many applications in data assimilation,…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
It is well understood that dynamic instability is among the primary drivers of forecast uncertainty in chaotic, physical systems. Data assimilation techniques have been designed to exploit this phenomena, reducing the effective dimension of…
In data assimilation, the model may be subject to uncertainties and errors. The weak-constraint data assimilation framework enables incorporating model uncertainty in the dynamics of the governing equations. We propose a new framework for…
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…
Data assimilation involves estimating the state of a system by combining observations from various sources with a background estimate of the state. The weights given to the observations and background state depend on their specified error…