Theoretical tools for understanding the climate crisis from Hasselmann’s programme and beyond

Lucarini, Valerio; Chekroun, Mickaël D.

doi:10.1038/s42254-023-00650-8

Cited by 12 publications

(7 citation statements)

References 274 publications

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“…This implies that convection and cloud parameterizations, for example, must be explicitly time dependent (i.e., have memory) and cannot be assumed to be in instantaneous equilibrium with the environment. Homogenization theories such as those of Mori and Zwanzig (Zwanzig, 2001), which employ averaging but also shows how fluctuations about averages arise on the macroscale, support the inclusion of these features (Majda et al, 2003;Wouters and Lu-carini, 2013;Lucarini et al, 2014;Wouters et al, 2016;Lucarini and Chekroun, 2023).…”

Section: Process-based Parameterizationsmentioning

confidence: 98%

Opinion: Optimizing climate models with process knowledge, resolution, and artificial intelligence

Schneider,

Leung,

Wills

2024

Atmos. Chem. Phys.

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Abstract. Accelerated progress in climate modeling is urgently needed for proactive and effective climate change adaptation. The central challenge lies in accurately representing processes that are small in scale yet climatically important, such as turbulence and cloud formation. These processes will not be explicitly resolvable for the foreseeable future, necessitating the use of parameterizations. We propose a balanced approach that leverages the strengths of traditional process-based parameterizations and contemporary artificial intelligence (AI)-based methods to model subgrid-scale processes. This strategy employs AI to derive data-driven closure functions from both observational and simulated data, integrated within parameterizations that encode system knowledge and conservation laws. In addition, increasing the resolution to resolve a larger fraction of small-scale processes can aid progress toward improved and interpretable climate predictions outside the observed climate distribution. However, currently feasible horizontal resolutions are limited to O(10 km) because higher resolutions would impede the creation of the ensembles that are needed for model calibration and uncertainty quantification, for sampling atmospheric and oceanic internal variability, and for broadly exploring and quantifying climate risks. By synergizing decades of scientific development with advanced AI techniques, our approach aims to significantly boost the accuracy, interpretability, and trustworthiness of climate predictions.

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Section: Process-based Parameterizationsmentioning

confidence: 98%

Opinion: Optimizing climate models with process knowledge, resolution, and artificial intelligence

Schneider,

Leung,

Wills

2024

Atmos. Chem. Phys.

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“…The aforementioned results show indeed that data-driven formulas of such parameterizations are accessible for much lower and computationally relevant cutoffs within the inertial range for 2D turbulence. However, note that lowering the cutoff scale is inevitably prone to the emergence of memory and/or stochastic terms at some point (Lucarini & Chekroun, 2023).…”

Section: Theoretical Consequences and Toward Interpretabilitymentioning

confidence: 99%

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

Srinivasan,

Chekroun,

McWilliams

2024

J Adv Model Earth Syst

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We parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.

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“…[49][50][51]). This success can be attributed to theoretical underpinnings from dynamical systems theory (Takens' delay embedding theorem [52]) and statistical mechanics (Mori-Zwanzig formulation [22,[53][54][55][56]). Additionally, we mention recent approaches combining Takens' embedding with Koopman operator theory and sparse regression to obtain linear representations of nonlinear dynamics [57].…”

Section: The High-frequency Barrier To Neural Closurementioning

confidence: 99%

“…Additionally, we mention recent approaches combining Takens' embedding with Koopman operator theory and sparse regression to obtain linear representations of nonlinear dynamics [57]. However, as highlighted in [22], memory effects might not be crucial for achieving effcient closure of solutions in the HLF regime. Studies have shown that using the BE manifold for capturing the geostrophic motion and a network of stochastic oscillators for IGWs can achieve high accuracy without recurrent architectures like LSTMs [26].…”

Section: The High-frequency Barrier To Neural Closurementioning

confidence: 99%

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The high-frequency and rare events barriers to neural closures of atmospheric dynamics

Chekroun,

Liu,

Srinivasan

et al. 2024

J. Phys. Complex.

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Recent years have seen a surge in interest for leveraging neural networks to parameterize small-scale or fast processes in climate and turbulence models. In this short paper, we point out two fundamental issues in this endeavor. The first concerns the difficulties neural networks may experience in capturing rare events due to limitations in how data is sampled. The second arises from the inherent multiscale nature of these systems. They combine high-frequency components (like inertia-gravity waves) with slower, evolving processes (geostrophic motion). This multiscale nature creates a significant hurdle for neural network closures. To illustrate these challenges, we focus on the atmospheric 1980 Lorenz model, a simplified version of the Primitive Equations that drive climate models. This model serves as a compelling example because it captures the essence of these difficulties.

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Theoretical tools for understanding the climate crisis from Hasselmann’s programme and beyond

Cited by 12 publications

References 274 publications

Opinion: Optimizing climate models with process knowledge, resolution, and artificial intelligence

Opinion: Optimizing climate models with process knowledge, resolution, and artificial intelligence

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

The high-frequency and rare events barriers to neural closures of atmospheric dynamics

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