Calibration and Uncertainty Quantification of a Gravity Wave Parameterization: A Case Study of the Quasi‐Biennial Oscillation in an Intermediate Complexity Climate Model

Abstract

The drag due to breaking atmospheric gravity waves plays a leading order role in driving the middle atmosphere circulation, but as their horizontal wavelength range from tens to thousands of kilometers, part of their spectrum must be parameterized in climate models. Gravity wave parameterizations prescribe a source spectrum of waves in the lower atmosphere and allow these to propagate upwards until they either dissipate or break, where they deposit drag on the large‐scale flow. These parameterizations are a source of uncertainty in climate modeling which is generally not quantified. Here, we explore the uncertainty associated with a non‐orographic gravity wave parameterization given an assumed parameterization structure within a global climate model of intermediate complexity, using the Calibrate, Emulate and Sample (CES) method. We first calibrate the uncertain parameters that define the gravity wave source spectrum in the tropics, to obtain climate model settings that are consistent with properties of the primary mode of tropical stratospheric variability, the Quasi‐Biennial Oscillation (QBO). Then we use a Gaussian process emulator to sample the calibrated distribution of parameters and quantify the uncertainty of these parameter choices. We find that the resulting parametric uncertainties on the QBO period and amplitude are of a similar magnitude to the internal variability under a 2xCO2 forcing.

Bayesian History Matching Applied to the Calibration of a Gravity Wave Parameterization

“…Both these features are useful to explain the structure of the implausibility in Figure 3, where we see that the gradients in the implausibility space are substantially greater along the B t axis than the c w axis, forming a "banana" shaped region. The form of this space resembles that obtained by Mansfield and Sheshadri (2022) when an uncertainty quantification analysis was performed on AD99 using EKI.…”

“…An alternate calibration method known as Ensemble Kalman Inversion (EKI) was investigated on AD99 in a previous study (Mansfield & Sheshadri, 2022); and has also been utilized in the calibration of other parameterization schemes, for example, Dunbar et al (2021). EKI is a gradient free optimization method, which converges upon a singular point that minimizes a loss function (Iglesias et al, 2013;Kovachki & Stuart, 2019).…”

“…In this paper, we present the results of applying an implementation of history matching for calibrating the AD99 parameterization and a comparison to the EKI calibration method (Mansfield & Sheshadri, 2022). The method and theory of this technique in addition to the emulator development are described in Section 2.…”

Parameterizing Vertical Mixing Coefficients in the Ocean Surface Boundary Layer Using Neural Networks

“…The random forest algorithm has been used to parameterize moist convection (O'Gorman & Dwyer, 2018) and to learn small-scale processes from a high resolution atmospheric model (Yuval & O'Gorman, 2020). Mansfield and Sheshadri (2022) used Gaussian Process emulator to tune gravity wave parameterization in The aforementioned examples show the potential of enhancing conventional physics-based schemes using machine learning techniques. This article draws inspiration from these demonstrations, recognizing the promise of machine learning in advancing ocean model parameterizations and prompting further investigation in this area.…”

“…The random forest algorithm has been used to parameterize moist convection (O'Gorman & Dwyer, 2018) and to learn small‐scale processes from a high resolution atmospheric model (Yuval & O'Gorman, 2020). Mansfield and Sheshadri (2022) used Gaussian Process emulator to tune gravity wave parameterization in an intermediate complexity atmospheric GCM. Souza et al.…”