Berkeley Fluids Seminar

Data-driven modeling of geophysical turbulence using Koopman-based fluctuation-dissipation theorem

Monday, November 4, 2019

12:00-13:00, 3110 Etcheverry Hall

Prof. Pedram Hassanzadeh

(Department of Mechanical Engineering
Rice University)

Abstract: Data-driven modeling of geophysical turbulence, mainly motivated by problems in weather/climate prediction, has been of great interest at least since the 1970s. Fluctuation-dissipation theorem (FDT), a powerful tool from statistical physics, has been particularly pursued as a mean of finding linear response functions (LRFs) for atmospheric/oceanic turbulence. However, while the calculated LRFs are often found to be accurate for low-dimensional toy models, they are not accurate for higher dimensional systems such as two-layer quasi-geostrophic (QG) models or general circulation models (GCMs). In earlier work (Hassanzadeh & Kuang, 2016 J. Atmos. Sci.), Hassanzadeh and his colleagues showed that a major source of inaccuracy is a step aimed at regularizing ill-conditioned covariance matrices by truncating the data into the leading modes from proper orthogonal decomposition (POD), a.k.a empirical orthogonal functions (EOFs). They found that the error arises from using POD/EOF modes, which are orthonormal, for systems that have non-normal LRFs. Professor Hassanzadeh will present results from Khodkar & Hassanzadeh (2018 J. Fluid Mech.) and more recent work in which the advantage of truncating data onto modes that are obtained from data-driven approximations of the Koopman operator such as dynamic mode decomposition (DMD) and time-delayed DMD is shown. In this talk, Professor Hassanzadeh will also show how this approach substantially improves the accuracy of the computed LRFs for turbulent Rayleigh-Benard convection, QG, and an atmospheric GCM.

Bio: Dr. Hassanzadeh studies fluid dynamics and heat transfer in complex natural phenomena and engineering systems using numerical, mathematical, and statistical models, guided by observational and experimental data. The main theme of his work is understanding multi-scale processes at fundamental levels and then applying this knowledge to real-world and practical problems. He received his B.S. from the University of Tehran, M.S. from the University of Waterloo, and Ph.D. from UC Berkeley, all in Mechanical Engineering. He also holds a M.A. degree in Mathematics from UC Berkeley. He was a Ziff Environmental Fellow at the Harvard University Center for the Environment and a Postdoctoral Fellow at the Harvard University Department of Earth and Planetary Science. Dr. Hassanzadeh was also a Research Associate at the University of Waterloo, GFD Fellow at the Woods Hole Oceanographic Institution, and Associate at Harvard University. He joined the faculty at Rice in 2016.

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Acknowledgments

Prof. Eliot Quataert on behalf of The Theoretical Astrophysics Center and the Astronomy Department (UC Berkeley)

Prof. Philip S. Marcus on behalf of the Mechanical Engineering Department (UC Berkeley)

Prof. Michael Manga (Earth and Planetary Science, UC Berkeley)

Prof. Evan Variano (Civil and Environmental Engineering, UC Berkeley)