Breaking atmospheric gravity waves in the tropical stratosphere are essential in driving the roughly two year oscillation of zonal winds in this region known as the Quasi-Biennial Oscillation (QBO). As Global Climate Models (GCM)s are not typically able to directly resolve the spectrum of waves required to drive the QBO, parameterizations are necessary. Such parameterizations often require knowledge of poorly constrained physical parameters. In the case of the spectral gravity parameterization used in this work, these parameters are the total equatorial gravity wave stress and the half width of phase speed distribution. Radiosonde observations are used to obtain the period and amplitude of the QBO, which are compared against values obtained from a GCM. We utilize two established calibration techniques to obtain estimates of the range of plausible parameter values: History Matching & Ensemble Kalman Inversion (EKI). History Matching is found to reduce the size of the initial range of plausible parameters by a factor of 98%, requiring only 60 model integrations. EKI cannot natively provide any uncertainty quantification but is able to produce a single best estimate of the calibrated values in 25 integrations. When directly comparing the approaches using the Calibrate, Emulate, Sample method to produce a posterior estimate from EKI, History Matching produces more compact posteriors with fewer model integrations at lower ensemble sizes compared to EKI; however, these differences become less apparent at higher ensemble sizes.

Subgrid-scale processes, such as atmospheric gravity waves, play a pivotal role in shaping the Earth’s climate but cannot be explicitly resolved in climate models due to limitations on resolution. Instead, subgrid-scale parameterizations are used to capture their effects. Recently, machine learning has emerged as a promising approach to learn parameterizations. In this study, we explore uncertainties associated with a machine learning parameterization for atmospheric gravity waves. Focusing on the uncertainties in the training process (parametric uncertainty), we use an ensemble of neural networks to emulate an existing gravity wave parameterization. We estimate both offline uncertainties in raw neural network output and online uncertainties in climate model output, after the neural networks are coupled. We find that online parametric uncertainty contributes a significant source of uncertainty in climate model output that must be considered when introducing neural network parameterizations. This uncertainty quantification provides valuable insights into the reliability and robustness of machine learning-based gravity wave parameterizations, thus advancing our understanding of their potential applications in climate modeling.