Data Assimilation Fundamentals

Geir Evensen gained his PhD in Mathematics at the University of Bergen, Norway. His extensive experiences include data assimilation in ocean and weather models, as well as ensemble-based history matching within petroleum-reservoir models. He has initiated and led several international research projects from an initial idea to operational implementation in various disciplines. Since 2016, he has worked as a Chief scientist at the International Research Institute of Stavanger (IRIS), which from 2018, merged into NORCE. He teaches data assimilation and its applications in various courses and summer schools. He also holds a secondary position at the Nansen Environmental and Remote Sensing Center in Bergen, Norway.Femke Vossepoel gained her PhD in Aerospace Engineering at Delft University of Technology, The Netherlands. Her research focuses on the use of data assimilation in numerical models of subsurface flow and mechanics to estimate the effects of subsurface activities and their uncertainties and associated risks. Applications of her current research include subsidence and induced seismicity, slope stability, and flooding risk. She works as an Associate Professor, Department of Geoscience and Engineering, Delft University of Technology, The Netherlands. She teaches on statistics and data assimilation in various international summer schools and courses. Peter Jan van Leeuwen gained his PhD from the Delft University of Technology, The Netherlands. His research focuses on the development of advanced data-assimilation methods and causal discovery methods for high-dimensional highly nonlinear systems, and applying these methods for a better understanding of geophysical fluids, especially atmosphere and ocean. He joined the University of Reading,UK, as Professor in Data Assimilation in 2009, and is also a Professor in Data Assimilation and Oceanography at Colorado State University, USA, since 2018. In 2016 we won the prestigious Advanced Investigator grant from the European Research Council, the largest personal award in the EU. The teaches many courses at universities and summerschools on Data Assimilation, Causal Discovery, Physical Oceanography, Statistical mechanics for the Geosciences, and Remote Sensing.

• Introduction.- Part I Mathematical Formulation: Problem formulation.- Maximum a posteriori solution.- Strong-constraint 4DVar.- Weak constraint 4DVar.- Kalman filters and 3DVar.- Randomized-maximum-likelihood sampling.- Low-rank ensemble methods.- Fully nonlinear data assimilation.- Localization and inflation.- Methods’ summary.- Part II Examples and Applications:  A Kalman filter with the Roessler model.- Linear EnKF update.- EnKF for an advection equation.- EnKF with the Lorenz equations.- 3Dvar and SC-4DVar for the Lorenz 63 model.- Representer method with an Ekman-flow model.- Comparison of methods on a scalar model.- Particle filter for seismic-cycle estimation.- Particle flow for a quasi-geostrophic model.- EnRML for history matching petroleum models.- ESMDA with a SARS-COV-2 pandemic model.- Final summary.- References.- Index.