Dynamical Parameter Estimation for LES Closure Models

We present an algorithm for dynamically estimating the parameters of chaotic systems. The algorithm uses partial observations of a system of dissipative differential equations to estimate the state of the system and relevant physical parameters simultaneously. The algorithm was first applied to the Lorenz system, and then to Rayleigh Benard convection to estimate the Rayleigh and Prandtl numbers. In both cases, convergence of parameter estimation was established both numerically and analytically. We first review the implementation and results of parameter recovery in these two settings to illustrate the general approach, and then move to applying this algorithm to estimating parameters for turbulence closure models for ocean large eddy simulations (LES). This problem requires a new approach both in the numerics and the theory as the desired parameter doesn't have a 'unique true' value. Rather than converging to the true value, the parameter estimation algorithm instead converges to the optimal approximate one.