# Graduate Student / Postdoc Seminar

#### Rigorous statistical bounds in uncertainty quantification for turbulent geophysical flows

**Speaker:**
Di Qi, Courant Institute of Mathematical Sciences

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, October 19, 2018, 1 p.m.

**Synopsis:**

Statistical bounds controlling the total fluctuations in mean and variance about a basic steady state solution are developed for the

truncated barotropic flows over topography. Statistical ensemble prediction is an important topic in weather and climate research. Here the evolution of an ensemble of trajectories is considered in the statistical instability analysis and is compared and contrasted with the classical deterministic instability for the growth of perturbations in one pointwise trajectory. The maximum growth of the total statistics in fluctuations is derived relying on the statistical conservation principle of the pseudo-energy. The saturation of the statistical mean fluctuation and variance in the unstable regimes with non-positive-definite pseudo-energy is achieved by linking with a class of stable reference states and minimizing the stable statistical energy bounds. Two cases with dependence on initial statistical uncertainty and on external forcing and dissipation are compared and unified with a consistent statistical stability framework.