Seminars at the Faculty of Informatics

The statistical dynamics of geophysical flows with application to ensemble prediction and data assimilation

The Faculty of Informatics is pleased to announce a seminar given by Terence O'Kane

DATE: Wednesday, October 02nd, 2013
PLACE: USI Lugano Campus, room SI-008, Informatics building (Via G. Buffi 13)
TIME: 16.30

We describe the development of an accurate yet computationally tractable statistical dynamical closure theory for general inhomogeneous turbulent flows, coined the quasi-diagonal direct interaction approximation closure (QDIA), and its application to problems in ensemble prediction and data assimilation.

The QDIA provides prognostic equations for evolving mean fields, covariances and higher-order non-Gaussian terms, all of which are also required in the formulation of data assimilation schemes for nonlinear geophysical flows. The QDIA is a generalization of the class of direct interaction approximation theories, initially developed by Kraichnan (1959 J. Fluid Mech. 5 497) for isotropic turbulence, to fully inhomogeneous flows and has been further generalized to allow for both inhomogeneous and non-Gaussian initial conditions and long integrations. A regularization procedure or empirical vertex renormalization that ensures correct inertial range spectra is also described.

Unlike previous approximations, such as those based on cumulant-discard (CD) and quasi-normal (QN) hypotheses (Epstein and Fleming), the QDIA closure is stable for long integration times and is valid for both strongly non-Gaussian and strongly inhomogeneous flows. The roles of non-Gaussian initial perturbations and small-scale noise in determining error growth are examined. The importance of the cumulative contribution of non-Gaussian terms to the evolved error tendency is demonstrated, as well as the role of the off-diagonal covariances in the growth of errors. Cumulative and instantaneous errors are quantified using kinetic energy spectra and a small-scale palinstrophy production measure, respectively. As a severe test of the methodology herein, synoptic situations during a rapid regime transition associated with the formation of a block over the Gulf of Alaska are considered.

Finally we present the statistical dynamical Kalman filter and compare its performance to deterministic ensemble square root and stochastic ensemble Kalman filters for error covariance modeling with applications to data assimilation. Our studies compare assimilation and error growth in barotropic flows during a period in 1979 in which several large scale atmospheric blocking regime transitions occurred in the Northern Hemisphere. We examine the role of sampling error and its effect on estimating the flow dependent growing error structures and the associated effects on the respective Kalman gains. We also introduce a Shannon entropy reduction measure and relate it to the spectra of the Kalman gain.In general, the full QDIA closure results compare well with the statistics of direct numerical simulations.

Dr O'Kane received his MSc in theoretical physics in 1999 (University of Melbourne) and PhD in applied mathematics in 2003 (Monash University). Between 2003 and 2007 he held postdoctoral and research fellow positions at CSIRO Atmospheric Research and the Antarctic Climate and Ecosystems CRC. From 2007-2009 he was ensemble prediction scientist at the Australian Bureau of Meteorology where he developed the Australian Global & Regional Ensemble Prediction System for operational weather forecasting. Since 2009 he has worked on atmospheric and ocean dynamics and predictability at CSIRO Marine Research in Hobart.
 In 2013 for his outstanding original contributions to difficult and important problems in applied mathematics he was awarded the prestigeous JH Michell Medal from ANZIAM and the Australian Mathematical Society.

HOST: Prof. Illia Horenko