ICTS

Research Interests:

Three distinct themes of research in the group are (i) data assimilation problems, (ii) Hamiltonian dynamics, and most recently, (iii) dynamics of the Indian monsoon. In each of these themes, techniques from dynamical systems, statistics, and probability are used to elucidate physical phenomena, particularly in earth sciences.

Data assimilation (DA) refers to the powerful and versatile methodology for combining partial, noisy observational data of a nonlinear, chaotic, complex systems with its dynamical model, which is generally imperfect and incomplete, to generate estimates of the state of the system and also estimates of the associated uncertainty. Our work on DA is in the following themes: (i) to understand the mathematical and statistical foundations, and the consequent limitations and strengths, of various data assimilation methods; (ii) to search for new methods to overcome these limitations. We have worked extensively with the problem of Lagrangian data assimilation (LaDA). The focus is on using tools from dynamical systems theory to gain insights that help address the core issues in DA.

Another emerging theme is the work on developing basic dynamical system models as well as data based stochastic models of the Indian summer monsoon, in order to provide mathematical and theoretical underpinning to the description of the monsoon dynamics.

Earlier research on Hamiltonian system focused on nontwist maps, which are area-preserving maps that violate the twist condition. We studied the reconnection-bifurcation phenomena and also developed a renormalization group framework to describe the breakup of invariant circles