Comparison of Calibration Methods for Gravity Wave Parameterization

This work was led by Rob King, a grad student at Stanford University. We compare two calibration methods in the context of calibrating a gravity wave parameterization in an intermediate complexity climate model, to obtain statistics of the Quasi-Biennial Oscillation (QBO) consistent with observations. It is a continuation of my previous work that used Ensemble Kalman Inversion (EKI) to calibrate gravity wave parameters. Rob has explored the use of history matching for the same task, to calibrate the half-width of the distribution of phase speeds in the tropics ($c_w$) and the total gravity wave stress at the source level at the equator ($Bt_{eq}$). We consider two observables of the QBO: the period and amplitude at 10 hPa. Both methods are iterative techniques, where we start with an ensemble of parameters sampled from a prior and at each iteration, we run an ensemble of climate model simulations to estimate the QBO period and amplitude. This is used to generate a new ensemble of parameters for the next iteration. In EKI, the ensemble at the next iteration is created by updating the parameter values for each ensemble member to minimize a loss function. However, in history matching, we rule out areas of the parameter space that are deemed implausible and sample new parameters from a sub-space which we call the “Not Yet Ruled Out” space. The animation below shows how the ensemble members change at each iteration. Importantly, history matching has a slightly different goal, where it aims to learn a set of plausible parameters that could be consistent with observation. This is in contrast to EKI which is an optimization method and converges upon a single point estimate of parameters. You can see this in the animation below, where history matching samples converge upon an subspace of plausible parameters, while EKI samples converge upon a single point estimate.

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Both methods have their merits: EKI converges more rapidly upon the optimal parameters. However, we find it can become stuck in local minima. In contrast, history matching may more suitable for obtaining a range of plausible parameters. We hope to extend this work to consider the behavior of both methods in higher dimensional spaces.