Inference of global atmospheric states from sparse observations

Mentors:
Lead: Mohammad Farazmand (Mathematics, NCSU) Collaborator: Arvind Saibaba (Mathematics, NCSU)

Outline:
Numerical simulations of atmospheric dynamics, ocean currents, and the climate are carried out with ever-growing spatial resolution, but observational data are limited to relatively coarse sensor measurements. This dichotomy inhibits efficient integration of experimental data with high-fidelity computational methods for detailed and accurate flow analysis or prediction [1]. We will investigate the application of Direct Empirical Interpolation Method (DEIM) to assimilating observational data into high- fidelity computational models. Given the low computational cost of DEIM [2], we expect to achieve significant speed-up compared to existing methods, such as ensemble Kalman filters and variational data assimilation [3].

Objectives:
Implementing the DEIM-based data assimilation method in the context of a two-layer quasi- geostrophic model of the atmosphere. We will also compare our method’s computational cost and accuracy against ensemble Kalman filtering.

Outcomes:
A comprehensive framework for DEIM-based data assimilation, which can be easily extended to high-fidelity weather prediction models.

References:
1. Farazmand M, Sapsis T. Extreme events: Mechanisms and prediction. Appl Mech Rev. 2019;71:050801.
2. Farazmand M, Saibaba A. Tensor-based flow reconstruction from optimally located sensor measurements, J. Fluid Mech. 962, A27, 2023.
3. Law K, Stuart A, Zygalakis K. Data Assimilation: A Mathematical Introduction. Cham. Switzerland:Springer; 2015.