Branicki M., Chen N., Majda A.J.,   Non-Gaussian Test Models for Prediction and State Estimation with Model Errors, Chinese Ann. Math. (special issue in honor of Jacques-Louis Lions) 34B(1), 29–64 (2013)
Branicki M., Majda A.J.,   Dynamic Stochastic Superresolution of sparsely observed  turbulent systems, J. Comp. Phys. 241, 333-363,  (2013)
Majda, A.J., Branicki M., Lessons in Uncertainty Quantification for Turbulent Dynamical Systems, Discrete Contin. Dynam. Systems  32(9), 3133-3231, (2012)
Majda, A.J., Branicki, M., Frenkel, Y.,  Improving Complex Models Through Stochastic Parameterization and Information Theory,  ECMWF Proceedings, Representing Model Uncertainty and Error in Numerical Weather and Climate Prediction Models, 121-136(2011)
Branicki, M., Gershgorin, B., Majda, A.J., Filtering skill for turbulent signals for a suite of Nonlinear and Linear Extended Kalman Filters, J. Comp. Phys. 231(4), 1462--1498,(2012)
Majda A.J., Branicki M., Turbulent Dynamical Systems in Climate Science
Branicki M., Majda, A.J., Quantifying Filter Performance for Turbulent Dynamical  Systems through Information Theory

Many topical problems in science require making real-time predictions of nonlinear  spatially extended systems with  physical instabilities across a wide range of scales based on partial observations and an imperfect knowledge of the true dynamics with many degrees of freedom. In such cases data assimilation is usually necessary for mitigating the model error and constraining the unresolved turbulent fluxes  in order to improve the stability and skill of the imperfect predictions. However, various data assimilation/filtering strategies developed recently for these applications are also imperfect and not optimal due to the formidably complex nature of the problem.

The lack of  resolution in  the noisy observations  is  particularly severe in turbulent geophysical systems with an enormous range of interacting spatio-temporal scales  and  rough  energy  spectra near  the mesh  scale of the discretized  imperfect models.

Consequently, the lack of statistical accuracy in estimating the unresolved turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction exploiting discretized PDE models. In a series of joint papers with Andrew Majda, I have studied the stability and accuracy of imperfect Kalman filters with model error for estimating the multi-scale turbulent dynamics. This ongoing research benefits greatly from identifying and exploiting connections between the stochastic filtering, uncertainty quantification and information theory.