Uncertainty Quantification of Ocean Parameterizations: Application to the K‐Profile‐Parameterization for Penetrative Convection

Souza, Andre N.; Wagner, Gregory LeClaire; Ramadhan, Ali; Allen, Benjamin D.; Churavy, Valentin; Schloss, Jennifer; Campin, Jean‐Michel; Hill, Christopher N.; Edelman, Alan; Marshall, John; Flierl, Glenn R.; Ferrari, Raffaele

doi:10.1029/2020ms002108

Cited by 18 publications

(14 citation statements)

References 68 publications

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Section: Introductionmentioning

confidence: 99%

“…Traditional Bayesian inference techniques, like random walk Metropolis (Metropolis et al, 1953) or sequential Monte Carlo (Moral et al, 2006), can be used in this context if the number of parameters is small and the model to be trained is cheap to evaluate. Such methods additionally provide uncertainty quantification, but they become intractable for expensive models with many parameters (Cotter et al, 2013;Souza et al, 2020). Model-agnostic tools that enable fast calibration of subgrid-scale closures from diverse data are a necessary step toward the development of hybrid closures that leverage the strengths of all modeling approaches.…”

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confidence: 99%

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Training Physics‐Based Machine‐Learning Parameterizations With Gradient‐Free Ensemble Kalman Methods

Lopez‐Gomez

Christopoulos

Ervik

et al. 2022

J Adv Model Earth Syst

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Most machine learning applications in Earth system modeling currently rely on gradientbased supervised learning. This imposes stringent constraints on the nature of the data used for training (typically, residual time tendencies are needed), and it complicates learning about the interactions between machine-learned parameterizations and other components of an Earth system model. Approaching learning about process-based parameterizations as an inverse problem resolves many of these issues, since it allows parameterizations to be trained with partial observations or statistics that directly relate to quantities of interest in long-term climate projections. Here we demonstrate the effectiveness of Kalman inversion methods in treating learning about parameterizations as an inverse problem. We consider two different algorithms: unscented and ensemble Kalman inversion. Both methods involve highly parallelizable forward model evaluations, converge exponentially fast, and do not require gradient computations. In addition, unscented Kalman inversion provides a measure of parameter uncertainty. We illustrate how training parameterizations can be posed as a regularized inverse problem and solved by ensemble Kalman methods through the calibration of an eddy-diffusivity mass-flux scheme for subgrid-scale turbulence and convection, using data generated by large-eddy simulations. We find the algorithms amenable to batching strategies, robust to noise and model failures, and efficient in the calibration of hybrid parameterizations that can include empirical closures and neural networks.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Training Physics‐Based Machine‐Learning Parameterizations With Gradient‐Free Ensemble Kalman Methods

Lopez‐Gomez

Christopoulos

Ervik

et al. 2022

J Adv Model Earth Syst

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show abstract

“…There is, however, often a natural variation of the key parameters required for accurate modelling which presents a challenge in many fields of research (e.g. boundary layer physics (Souza et al, 2020), pulmonary circulation (Păun et al, 2018), groundwater flow (Ghouili et al, 2017), population spread (Soubeyrand & Roques, 2014), and sediment transport (Manning & Schoellhamer, 2013;Valipour et al, 2017). Measurements can provide insight into these complex processes, but in many cases the parameter of interest is difficult to observe directly (e.g.…”

Section: Introductionmentioning

confidence: 99%

In-situ estimation of erosion model parameters using an advection-diffusion model and Bayesian inversion

Edge

Rayson

Jones

et al. 2022

Preprint

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We describe a framework for the simultaneous estimation of model parameters in a partial differential equation using sparse observations. Monte Carlo Markov Chain (MCMC) sampling is used in a Bayesian framework to estimate posterior probability distributions for each parameter. We describe the necessary components of this approach and its broad potential for application in models of unsteady processes. The framework is applied to three case studies, of increasing complexity, from the field of cohesive sediment transport. We demonstrate that the framework can be used to recover posterior distributions for all parameters of interest and the results agree well with independent estimates (where available). We also demonstrate how the framework can be used to compare different model parameterizations and provide information on the covariance between model parameters.

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“…High-resolution simulations have been used to calibrate climate model parameterizations at selected sites, primarily in low latitudes [50,84,89,85,31,102,21,71,91,86,19,32]. Similarly, limited-area high-resolution simulations e.g., [96,26] have been used to calibrate subgrid-scale parameterizations of upper-ocean turbulence [87,48,94,70,49,11,69].…”

Section: Introductionmentioning

confidence: 99%

“…Distribution information is beneficial, for example, because it enables model-based predictions of rare events with quantified uncertainties [22]. Analysis of the posterior distribution also may focus scientific development (e.g., improvement of parameterization schemes, [87]) 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.…”

Section: Introductionmentioning

confidence: 99%

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

Dunbar,

Howland,

Schneider

et al. 2022

Preprint

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Targeted high-resolution simulations driven by a general circulation model (GCM) can be used to calibrate GCM parameterizations of processes that are globally unresolvable but can be resolved in limited-area simulations. This raises the question of where to place high-resolution simulations to be maximally informative about the uncertain parameterizations in the global model. Here we construct an ensemble-based parallel algorithm to locate regions that maximize the uncertainty reduction, or information gain, in the uncertainty quantification of GCM parameters with regional data. The algorithm is based on a Bayesian framework that exploits a quantified posterior distribution on GCM parameters as a measure of uncertainty. The algorithm is embedded in the recently developed calibrateemulate-sample (CES) framework, which performs efficient model calibration and uncertainty quantification with only O(10 2 ) forward model evaluations, compared with O(10 5 ) forward model evaluations typically needed for traditional approaches to Bayesian calibration. We demonstrate the algorithm with an idealized GCM, with which we generate surrogates of high-resolution data. In this setting, we calibrate parameters and quantify uncertainties in a quasi-equilibrium convection scheme. We consider (i) localization in space for a statistically stationary problem, and (ii) localization in space and time for a seasonally varying problem. In these proof-of-concept applications, the calculated information gain reflects the reduction in parametric uncertainty obtained from Bayesian inference when harnessing a targeted sample of data. The largest information gain results from regions near the intertropical convergence zone (ITCZ) and indeed the algorithm automatically targets these regions for data collection.

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Uncertainty Quantification of Ocean Parameterizations: Application to the K‐Profile‐Parameterization for Penetrative Convection

Abstract: ter understand their biases and uncertainties. • Parameterization parameter distributions, learned using high-resolution simulations, should be used as prior distributions for climate modeling studies.

Cited by 18 publications

References 68 publications

Training Physics‐Based Machine‐Learning Parameterizations With Gradient‐Free Ensemble Kalman Methods

Training Physics‐Based Machine‐Learning Parameterizations With Gradient‐Free Ensemble Kalman Methods

In-situ estimation of erosion model parameters using an advection-diffusion model and Bayesian inversion

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

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