Explore dynamical information with Pseudo-orbit Data Assimilation

Durham University
Seminar Date: 
13. June 2019 - 11:00 - 12:00
Lecture room, Ground Floor, NERSC

Physical processes such as the weather are usually modeled using nonlinear dynamical systems. Traditional statistical approaches are found to be difficult to draw dynamical information from the nonlinear dynamics. This talk is focusing on exploring dynamical information with Pseduo-orbit data assimilation to address various problems encountered in analyzing and modeling nonlinear dynamical systems. The talk will start with solving an “impossible” challenge pointed out by Berliner (1991) when applying the Bayesian paradigm to state estimation in chaotic systems. Even when the equations of the system are given, he demonstrated “chaotic likelihood functions” of initial conditions in the 1-D Logistic Map. Chaotic likelihood functions, while ultimately smooth, have such complicated small scale structure as to cast doubt on the possibility of identifying high likelihood estimates in practice. An importance sampling approach is introduced, where Pseudo-orbit Data Assimilation is employed in the sequence-space in order first to identify relevant pseudo-orbits and then relevant trajectories. Estimates are identified with likelihoods comparable to the Truth, thereby Berliner’s “impossible” challenge is solved. The Pseudo-orbit Data Assimilation is then shown to outperform the Ensemble Kalman Filter and variational approach in the context of Lorenz96 and Ikeda map in terms of nowcast. The idea of exploring dynamical information led to the creation of a novel methodology for multi-model ensemble scheme, named Multi-model Cross Pollination in Time, where data assimilation is used to improve model forecasts at future time. The proposed approach generates model states in time via applying data assimilation scheme(s) to yield truly “multi-model trajectories”. It is demonstrated to outperform traditional statistical post-processing in the 40-dimensional Lorenz96 flow.