Abstract: Lagrangian tracers are drifters or floaters that follow a parcel of fluid’s movement. These Lagrangian trajectories are widely used as observations, combined with dynamical or statistical models, to recover the underlying flow field. This is known as Lagrangian data assimilation. In the first part of this talk, I will discuss the general methodology for Lagrangian data assimilation. In addition to the ensemble data assimilation, I will present a mathematical framework that allows analytically solvable Lagrangian data assimilation solutions. I will also show a multiscale data assimilation method combining Lagrangian trajectories with the induced Eulerian measurements. In the second part of the talk, I will discuss a few topics focusing on the uncertainty resulting from the solution of Lagrangian data assimilation. They include quantifying the information gain in the state estimation as a number of tracers, eddy identification in the presence of uncertainty, and optimal design of the locations to deploy additional tracers for uncertainty reduction.

Biography: Nan Chen is an Assistant Professor at the Department of Mathematics, University of Wisconsin-Madison. He is also a faculty affiliate of the Institute for Foundations of Data Science. Dr. Chen received his Ph.D. from the Courant Institute of Mathematical Sciences and the Center of Atmosphere and Ocean Science, New York University (NYU), in 2016. He worked as a postdoc research associate at NYU for two years before joining UW-Madison. Dr. Chen’s research interests lie in applied mathematics, geophysics, complex dynamical systems, stochastic methods, numerical algorithms, and general data science. He is also active in developing dynamical and stochastic models and using these models to analyze and predict real-world phenomena related to atmosphere-ocean science, climate, and other complex systems with the help of real observational data.  He is a member of the U.S. CLIVAR Working Group on ENSO Conceptual Models. He has received several awards, including the Kurt O. Friedrichs Prize for an outstanding dissertation in mathematics and the Young Investigator Award from the Office of Naval Research.

The Bay of Bengal (BoB) exhibits a distinctive pattern of surface freshening primarily resulting from runoff originating from several major rivers and the monsoon precipitation. This freshening significantly modulates the spatial and temporal variations in the thermohaline structure, ultimately shaping the sound speed structure within this region. This study investigates the seasonal impact of river input on the sound speed structure of the BoB through two numerical simulations with and without river input using the Regional Ocean Modeling System (ROMS). The findings indicate that river inputs consistently reduce the surface sound speed across the domain throughout the year, with the most noticeable effect occurring in the northern part of BoB during the post-monsoon months of October and November. During this period, the surface variability is predominately driven by salinity variations induced by river inputs. In contrast, in the subsurface layers, the influence of reduced salinity becomes less pronounced with increasing depth, and the temperature modulations brought about by river inputs play a more important role. Freshening in the surface layers leads to the creation of a stratified barrier layer just below the mixed layer. Consequently, this results in the formation of warm temperature inversions in the subsurface layers, with cooling occurring beneath them. These phenomena contribute to variations in the sound speed, causing it to increase within the inversion layer and decrease below it. Notably, the sonic layer depth (SLD) is found to become shallower in the presence of river inputs during the post-monsoon and winter seasons in the northern BoB. The combination of enhanced vertical salinity gradients and subsurface temperature inversions significantly amplifies the vertical gradient of sound speed above the SLD. This, in turn, may lead to the development of more robust surface ducts and the expansion of shadow zones beneath the SLD.