Prof. Pierre Lermusiaux is presenting a talk on Monday July 8 at the 2013 SIAM annual meeting, entitled “Uncertainty Predictions, Non-Gaussian Data Assimilation and Bayesian Inference of Dynamical Model Equations”. This talk is being given in the session on “Uncertainty Quantification in Climate Modeling and Prediction”.

Uncertainty quantification (UQ) of climate system forecasts presents challenges in mathematics, intertwined with limitations in observations and understanding of the system. Our goal is to provide a forum for this diverse community to discuss ideas for advancing the science of UQ in climate modeling and many of its components. Topics of interest include UQ in a hierarchical set of climate models, representing uncertainties in coupled climate system models, risk assessment strategies, use of new approaches such as information theoretic metrics/simplified stochastic models for UQ, assimilation and calibration for UQ of initial and forcing fields.

A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and 0(105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and 0(105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed.

A new paper by Ueckermann et al. has been published in the Journal of Computational Physics. The paper derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. A pdf of the paper can be found here.