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1. Memory-based parameterization with differentiable solver: Application to Lorenz ’96

   https://doi.org/10.1063/5.0131929  

   Bhouri, Mohamed Aziz; Gentine, Pierre (July 2023, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   Physical parameterizations (or closures) are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These parameterizations are typically grounded on physically based, yet empirical, representations of the underlying small-scale processes. Machine learning-based parameterizations have recently been proposed as an alternative solution and have shown great promise to reduce uncertainties associated with the parameterization of small-scale processes. Yet, those approaches still show some important mismatches that are often attributed to the stochasticity of the considered process. This stochasticity can be due to coarse temporal resolution, unresolved variables, or simply to the inherent chaotic nature of the process. To address these issues, we propose a new type of parameterization (closure), which is built using memory-based neural networks, to account for the non-instantaneous response of the closure and to enhance its stability and prediction accuracy. We apply the proposed memory-based parameterization, with differentiable solver, to the Lorenz ’96 model in the presence of a coarse temporal resolution and show its capacity to predict skillful forecasts over a long time horizon of the resolved variables compared to instantaneous parameterizations. This approach paves the way for the use of memory-based parameterizations for closure problems. 

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2. Data Imbalance, Uncertainty Quantification, and Transfer Learning in Data‐Driven Parameterizations: Lessons From the Emulation of Gravity Wave Momentum Transport in WACCM

   https://doi.org/10.1029/2023MS004145  

   Sun, Y_Qiang; Pahlavan, Hamid_A; Chattopadhyay, Ashesh; Hassanzadeh, Pedram; Lubis, Sandro_W; Alexander, M_Joan; Gerber, Edwin_P; Sheshadri, Aditi; Guan, Yifei (July 2024, Journal of Advances in Modeling Earth Systems)

   Abstract Neural networks (NNs) are increasingly used for data‐driven subgrid‐scale parameterizations in weather and climate models. While NNs are powerful tools for learning complex non‐linear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are (a) data imbalance related to learning rare, often large‐amplitude, samples; (b) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and (c) generalization to other climates, for example, those with different radiative forcings. Here, we examine the performance of methods for addressing these challenges using NN‐based emulators of the Whole Atmosphere Community Climate Model (WACCM) physics‐based gravity wave (GW) parameterizations as a test case. WACCM has complex, state‐of‐the‐art parameterizations for orography‐, convection‐, and front‐driven GWs. Convection‐ and orography‐driven GWs have significant data imbalance due to the absence of convection or orography in most grid points. We address data imbalance using resampling and/or weighted loss functions, enabling the successful emulation of parameterizations for all three sources. We demonstrate that three UQ methods (Bayesian NNs, variational auto‐encoders, and dropouts) provide ensemble spreads that correspond to accuracy during testing, offering criteria for identifying when an NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4 × CO₂). However, their performance is significantly improved by applying transfer learning, for example, re‐training only one layer using ∼1% new data from the warmer climate. The findings of this study offer insights for developing reliable and generalizable data‐driven parameterizations for various processes, including (but not limited to) GWs. 

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3. Uncertainty Quantification of a Machine Learning Subgrid‐Scale Parameterization for Atmospheric Gravity Waves

   https://doi.org/10.1029/2024MS004292  

   Mansfield, L_A; Sheshadri, A. (July 2024, Journal of Advances in Modeling Earth Systems)

   Abstract Subgrid‐scale processes, such as atmospheric gravity waves (GWs), play a pivotal role in shaping the Earth's climate but cannot be explicitly resolved in climate models due to limitations on resolution. Instead, subgrid‐scale parameterizations are used to capture their effects. Recently, machine learning (ML) has emerged as a promising approach to learn parameterizations. In this study, we explore uncertainties associated with a ML parameterization for atmospheric GWs. Focusing on the uncertainties in the training process (parametric uncertainty), we use an ensemble of neural networks to emulate an existing GW parameterization. We estimate both offline uncertainties in raw NN output and online uncertainties in climate model output, after the neural networks are coupled. We find that online parametric uncertainty contributes a significant source of uncertainty in climate model output that must be considered when introducing NN parameterizations. This uncertainty quantification provides valuable insights into the reliability and robustness of ML‐based GW parameterizations, thus advancing our understanding of their potential applications in climate modeling. 

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4. Explainable Offline‐Online Training of Neural Networks for Parameterizations: A 1D Gravity Wave‐QBO Testbed in the Small‐Data Regime

   https://doi.org/10.1029/2023GL106324  

   Pahlavan, Hamid A; Hassanzadeh, Pedram; Alexander, M Joan (January 2024, Geophysical Research Letters)

   Abstract There are different strategies for training neural networks (NNs) as subgrid‐scale parameterizations. Here, we use a 1D model of the quasi‐biennial oscillation (QBO) and gravity wave (GW) parameterizations as testbeds. A 12‐layer convolutional NN that predicts GW forcings for given wind profiles, when trained offline in abig‐dataregime (100‐year), produces realistic QBOs once coupled to the 1D model. In contrast, offline training of this NN in asmall‐dataregime (18‐month) yields unrealistic QBOs. However, online re‐training of just two layers of this NN using ensemble Kalman inversion and only time‐averaged QBO statistics leads to parameterizations that yield realistic QBOs. Fourier analysis of these three NNs' kernels suggests why/how re‐training works and reveals that these NNs primarily learn low‐pass, high‐pass, and a combination of band‐pass filters, potentially related to the local and non‐local dynamics in GW propagation and dissipation. These findings/strategies generally apply to data‐driven parameterizations of other climate processes. 

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5. Use of Neural Networks for Stable, Accurate and Physically Consistent Parameterization of Subgrid Atmospheric Processes With Good Performance at Reduced Precision

   https://doi.org/10.1029/2020GL091363  

   Yuval, Janni; O'Gorman, Paul_A; Hill, Chris_N (March 2021, Geophysical Research Letters)

   Abstract A promising approach to improve climate‐model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data‐driven. However, neural networks (NNs) often lead to instabilities and climate drift when coupled to an atmospheric model. Here, we learn an NN parameterization from a high‐resolution atmospheric simulation in an idealized domain by accurately calculating subgrid terms through coarse graining. The NN parameterization has a structure that ensures physical constraints are respected, such as by predicting subgrid fluxes instead of tendencies. The NN parameterization leads to stable simulations that replicate the climate of the high‐resolution simulation with similar accuracy to a successful random‐forest parameterization while needing far less memory. We find that the simulations are stable for different horizontal resolutions and a variety of NN architectures, and that an NN with substantially reduced numerical precision could decrease computational costs without affecting the quality of simulations. 

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