Stochastic superparameterization and multiscale ensemble Kalman filters for geophysical turbulence.
Date and time:
Tuesday, November 11, 2014 - 11:30am
Modeling the effects of unresolved turbulent dynamics is a crucial and challenging prerequisite for providing the accurate simulations of global weather and climate needed to understand the present and predict the future. Stochastic superparameterization is a framework for multiscale modeling and simulation of turbulent fluid dynamics that has recently been developed by the author and collaborators. This talk describes the general framework, and uses a relatively simple, one-dimensional scalar PDE (the MMT equations) with turbulent dynamics, coherent structures, and dispersive waves as an example. Results in more complex, and more realistic problems are reviewed, and ongoing extensions to realistic global ocean models are described.
Filtering is the process of combining simulations and observations to estimate and predict the state of dynamical systems. Computational models of the global climate system are and will remain unable to resolve all of the dynamically active scales in the system, but observations include contributions from all scales. The contributions from unresolved scales are treated as a form of observation error (called "representation error"), and are typically incorporated into filtering algorithms using time-independent estimates of their variance. Stochastic superparameterization (and many other methods already in use in global models) come with built-in time- and state-dependent estimates of the variance of unresolved scales, and we show how these estimates can be incorporated into an ensemble Kalman filter framework. A key observation is that although the large and small scales are not independent, they can be consistently modeled as uncorrelated, which allows them to be incorporated efficiently into a Kalman filtering framework. The approach is demonstrated using the one-dimensional turbulent test problem with superparameterization.