Uncertainty quantification of ocean parameterizations: application to the K-Profile-Parameterization for penetrative convection

Abstract

Parameterizations of unresolved turbulent processes often compromise the fidelity of large-scale ocean models. In this work, we argue for a Bayesian approach to the refinement and evaluation of turbulence parameterizations. Using an ensemble of large eddy simulations of turbulent penetrative convection in the surface boundary layer, we demonstrate the method by estimating the uncertainty of parameters in the convective limit of the popular "K-Profile Parameterization." We uncover structural deficiencies and propose an alternative scaling that overcomes them. Plain Language SummaryClimate projections are often compromised by significant uncertainties which stem from the representation of physical processes that cannot be resolved-such as clouds in the atmosphere and turbulent swirls in the ocean-but which have to be parameterized. We propose a methodology for improving parameterizations in which they are tested against, and tuned to, high-resolution numerical simulations of subdomains that represent them more completely. A Bayesian methodology is used to calibrate the parameterizations against the highly resolved model, to assess their fidelity and identify shortcomings. Most importantly, the approach provides estimates of parameter uncertainty. While the method is illustrated for a particular parameterization of boundary layer mixing, it can be applied to any parameterization.

Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning

“…In the past few years, there has been a rapidly growing interest in using ML methods to improve the modeling and analysis of chaotic systems and turbulent flows [e.g., 2,13,15,28,37,54,61,65,72,73,84,94,106,111]; also see the recent review papers on this topic [5,8,23,24,69]. Specific to SGS modeling (for LES or other approaches), a number of studies have aimed to obtain better estimates for the parameter(s) of physics-based SGS models, such as ν e , from high-fidelity data (e.g., DNS or observations) [22,57,89,91,96,112]. Alternatively, a growing number of recent papers have aimed to learn a data-driven SGS model from high-fidelity data, often in a non-parametric fashion, i.e., without any prior assumption about the model's structural/functional form [e.g., 28,29,36,50,70,74,82,88,101,107,108].…”

Capturing missing physics in climate model parameterizations using neural differential equations

“…Processes that control the depth of the mixed layer are important for climate because they mediate the exchange of heat, carbon and other soluble gases between the atmosphere and the ocean. Mixed layer depth biases are present in models especially in the Southern Ocean where existing boundary layer turbulence parameterizations fail to simulate deep wintertime mixed layers and ensuing restratification processes [Souza et al, 2020, Large et al, 2019, Marshall and Speer, 2012.…”

“…In this second NDE, the neural network is responsible for predicting the turbulent heat flux after convective adjustment has taken place. This concentrates the efforts of the NDE on to the entrainment layer at the base of the mixed layer which is the most challenging to predict accurately [Souza et al, 2020].…”

Ensemble-Based Experimental Design for Targeted High-Resolution Simulations to Inform Climate Models

“…Zhang et al, 2013;de Rooy et al, 2013;Romps, 2016;Tan et al, 2018;Smalley et al, 2019;Couvreux et al, 2021;Hourdin et al, 2021). Similarly, limited-area high-resolution simulations (e.g., Wang et al, 1996;Fox-Kemper & Menemenlis, 2013) have been used to calibrate subgrid-scale parameterizations of upper-ocean turbulence (Souza et al, 2020;Li & Fox-Kemper, 2017;Van Roekel et al, 2018;Reichl et al, 2016;Li et al, 2019;Campin et al, 2011;Reichl & Hallberg, 2018).…”

“…Distribution information is beneficial, for example, because it enables modelbased predictions of rare events with quantified uncertainties (Dunbar et al, 2021). Analysis of the posterior distribution also may focus scientific development (e.g., improvement of parameterization schemes, Souza et al (2020)) on areas where uncertainties can most effectively be minimized. In this paper, we use the posterior distribution to determine regions and times where local data (e.g., from high-resolution simulations) are maximally effective at reducing parameter uncertainties.…”