4D-variational data assimilation is applied to the Lorenz '63 model to introduce a new method for parameter estimation in chaotic climate models. The approach aims to optimise an Earth system model (ESM), for which no adjoint exists, by utilising the adjoint of a different, potentially simpler ESM. This relies on the synchronisation of the model to observed data. Dynamical state and parameter estimation (DSPE) is used to stabilise the tangent linear system by reducing all positive Lyapunov exponents to negative values, thereby improving parameter estimation by enabling long assimilation windows. The method introduces a second layer of synchronisation between the two models, with and without an adjoint, to facilitate linearisation around the trajectory of the model for which no adjoint exists. This is achieved by synchronising two Lorenz '63 systems, one with and the other without an adjoint model. Results are presented for an idealised case of identical, perfect models and for a more realistic case in which they differ from one another. If employed on a high-resolution ESM for which a coarse resolution adjoint exists, the method will save computational resources as only one forward run with the full high-resolution ESM per iteration is needed. It is demonstrated that there is negligible error and uncertainty change compared to the traditional optimisation of a full ESM with an adjoint. Stemming from this approach, it is shown that the synchronisation between two identical models can be used to filter noisy data in a dynamical way which reduces the parametric uncertainty of the optimised model by approximately one third. Such a precision gain could prove valuable for seasonal, annual, and decadal predictions.
Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model
Sorbonne University（索邦大学）；University of Reading（雷丁大学）；University of Utrecht（乌得勒支大学）；École des Ponts ParisTech（巴黎高科路桥学院）；EDF R&D（法国电力集团研发部）；Université Paris-Est（巴黎东大学）
Enabling High-Accuracy Data Assimilation with Limited Ensembles via Machine Learning-Based Covariance Correction
University of Macau（澳门大学）；Macau Millennium College（澳门千禧学院）；Huazhong University of Science and Technology（华中科技大学）；Ningbo Institute of Dalian University of Technology（大连理工大学宁波研究院）；Hongik University（弘益大学）；Zhuhai UM Science and Technology Research Institute（珠海中大（或澳门大学）科学与技术研究院）
A score-based particle flow filter for non-Gaussian data assimilation in high-dimensional chaotic systems
Hohai University（河海大学）；University of Northern British Columbia（北不列颠哥伦比亚大学）；Second Institute of Oceanography, Ministry of Natural Resources（自然资源部第二海洋研究所）
Online machine-learning forecast uncertainty estimation for sequential data assimilation
Servicio Meteorológico Nacional（国家气象局）；Universidad de Buenos Aires（布宜诺斯艾利斯大学）；Instituto Franco-Argentino para el Estudio del Clima y sus Impactos (IRL 3351 IFAECI)（法阿气候及其影响研究所（IRL 3351 IFAECI））；Universidad Nacional del Nordeste（东北国立大学）；Centro de Investigaciones del Mar y la Atmósfera（海洋与大气研究中心）；IMT Atlantique（大西洋国立高等工业技术学院）；Inria（法国国家信息与自动化研究所）
