Supervised Calibration and Uncertainty Quantification of Subgrid Closure Parameters using Ensemble Kalman Inversion

Abstract

Data-driven approaches are increasingly being used to identify and remove structural biases in dynamical models for real-world systems. However, because model updates alter the dependency of a model on its free parameters, evidence about structural biases is often muddied by the variable influences of inadequately-tuned parameters on the model solution. We elaborate a framework for model development that combines calibration, sensitivity analysis, and uncertainty quantification of free parameters to shed light on where structural biases are likely to exist in a model, and where the model may be unnecessarily complex. The approach is useful for general applications because it is easy to implement, derivative-free, robust against model instabilities, and computationally inexpensive, requiring a modest number of model evaluations. A diffusive closure for turbulence penetrated by air-sea fluxes of the ocean surface, presently called the “Convective Turbulent Kinetic Parameterization," is developed as a testbed for and proof-of-concept for the approach. Modifications to the traditional Ensemble Kalman Inversion [1] algorithm are devised to improve convergence during the calibration phase of this process. Further, the Calibrate Emulate Sample [2] framework for uncertainty quantification is validated with modifications.