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.

A framework for evaluating ocean mixed layer depth evolution

“…Future work could use the parameter space for comparing the behaviors of different vertical mixing schemes (KPP, TKE, GLS) and for comparing coupled and forced models. The information of the joint PDF of the three 2D projections of the 3D parameter space, given in Appendix B could also be used for choosing relevant values of forcing and preconditioning conditions (u * , B 0 , N h ) in the context of parameter tuning (Souza et al, 2020;Wagner et al, 2023). Beyond these direct applications, an interesting extension of the approach would be to evaluate the performance of the parameter space with LES data and observations.…”

“…Additionally, for informative purposes, the density maps and associated joint Probability Density Functions (PDF) showing the density distribution of the values of λ s , R h , and f /N h in the three 2D projections of the 3D parameter space are given in Appendix B. This information can be useful when selecting relevant values of forcing and preconditioning conditions (u * , B 0 , N h ) in the context of parameter tuning (Souza et al, 2020;Wagner et al, 2023).…”

A generic framework for evaluating the oceanic mixed layer depth dynamics

“…Additionally, for informative purposes, the density maps and associated joint Probability Density Functions (PDF) showing the density distribution of the values of λ s , R h , and f /N h in the three 2D projections of the 3D parameter space are given in Appendix B. This information can be useful when selecting relevant values of forcing and preconditioning conditions (u * , B 0 , N h ) in the context of parameter tuning (Souza et al, 2020;Wagner et al, 2023).…”

“…Kraus & Turner, 1967;Pollard et al, 1973;Price et al, 1986;Gaspar, 1988). These models have been used to derive theoretical scalings for the evolution of the MLD, such as the wind-driven deepening h ∝ u * N −1/2 t 1/2 (Pollard et al, 1973), observed empirically by Price (1979), and the free convection scal- (Turner, 1973;Van Roekel et al, 2018) measured empirically by Souza et al (2020) (h being the MLD, u * the surface friction velocity, t the time, Q the net surface heat flux and N the Brunt Väisälä frequency).…”

“…Nev-ertheless, KPP remains one of the most widely used parameterizations of convection in ocean models (Van Roekel et al, 2018;Q. Li et al, 2019;Souza et al, 2020).…”