Data Assimilation with Pseudo-orbits
Dr. Hailiang Du
Durham University, UK
邀请人 ： 王斌 研究员
Data assimilation for nonlinear models is a challenging task mathematically. Performing this task in real time is even more challenging as the models are imperfect: the mathematical system that generated the observations (if such a thing exists) is not a member of the available model class (i.e. the set of mathematical structures admitted as potential models). To the extent that traditional approaches address structural model error at all, most fail to produce consistent treatments. This results in questionable estimates both of the model state and of its uncertainty. A promising alternative approach, Pseudo-orbit based data assimilation (PDA), is proposed to produce more consistent estimates of the model state and to estimate the (state-dependent) model error simultaneously. The PDA approach improves data assimilation by allowing an enhanced balance between the information derived from the dynamic equations and the information derived from the observations. As a data assimilation approach, PDA is shown to outperform variational approach (4DVAR) and sequential approach (Ensemble Kalman filter) in the context of the 18-dimensional Lorenz96 flow and the 2-dimensional Ikeda map in terms of nowcast. For hindcast, PDA can be applied to produce useful reanalysis (for example) especially when the system is partially observed. For forecast, PDA can be adopted in a multi-model cross pollination scheme to significantly improve the multi-model forecast performance by integrating the dynamical information from each individual model operationally in time. It is suggested that this is a general result and the proposed approach can be immediately deployed in operational models.
Hailiang Du is an Associate Professor in the Department of Mathematical Sciences at Durham University, where he has been since 2017. He received his PhD in statistics from the London School of Economics and Political Science (LSE) in 2009. After his PhD, he worked in the Centre for the Analysis of Time Series at LSE for 4 years and in the Center for Robust Decision making on Climate and Energy Policy at the University of Chicago for 3 years as a research scientist. His research interests and work cover a variety of research topics including data assimilation, uncertainty quantification, theory of nonlinear dynamics, machine learning, optimization, multi-model forecasting, Bayesian linear analysis, weather and climate modelling, forecast interpretation and evaluation.