Global climate models represent small-scale processes such as clouds and convection using quasi-empirical models known as parameterizations, and these parameterizations are a leading cause of uncertainty in climate projections. A promising alternative approach is to use machine learning to build new parameterizations directly from high-resolution model output. However, parameterizations learned from three-dimensional model output have not yet been successfully used for simulations of climate. Here we use a random forest to learn a parameterization of subgrid processes from output of a three-dimensional high-resolution atmospheric model. Integrating this parameterization into the atmospheric model leads to stable simulations at coarse resolution that replicate the climate of the high-resolution simulation. The parameterization obeys physical constraints and captures important statistics such as precipitation extremes. The ability to learn from a fully three-dimensional simulation presents an opportunity for learning parameterizations from the wide range of global high-resolution simulations that are now emerging.
This document provides a detailed overview of the CLUBB-SILHS cloud and turbulence parameterization, including theoretical background, model equations, closure assumptions, simulation results, comparison with other parameterization methods, FAQs, and source code documentation.
Subgrid processes in global climate models are represented by parameterizations which are a major source of uncertainties in simulations of climate. In recent years, it has been suggested that machine-learning (ML) parameterizations based on high-resolution model output data could be superior to traditional parameterizations. Currently, both traditional and ML parameterizations of subgrid processes in the atmosphere are based on a single-column approach, which only use information from single atmospheric columns. However, single-column parameterizations might not be ideal since certain atmosph…
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 coarse graining the model equations and output. The NN parameterization has a structure that ensures physical constraints are respected, and it leads to stable simulations that …
We review some recent methods of subgrid-scale parameterization used in the context of climate modeling. These methods are developed to take into account (subgrid) processes playing an important role in the correct representation of the atmospheric and climate variability. We illustrate these methods on a simple stochastic triad system relevant for the atmospheric and climate dynamics, and we show in particular that the stability properties of the underlying dynamics of the subgrid processes has a considerable impact on their performances.
A stochastic subgrid-scale parameterization based on the Ruelle's response theory and proposed in Wouters and Lucarini [2012] is tested in the context of a low-order coupled ocean-atmosphere model for which a part of the atmospheric modes are considered as unresolved. A natural separation of the phase-space into an invariant set and its complement allows for an analytical derivation of the different terms involved in the parameterization, namely the average, the fluctuation and the long memory terms. In this case, the fluctuation term is an additive stochastic noise. Its application to the low…
The parameterization of moist convection contributes to uncertainty in climate modeling and numerical weather prediction. Machine learning (ML) can be used to learn new parameterizations directly from high-resolution model output, but it remains poorly understood how such parameterizations behave when fully coupled in a general circulation model (GCM) and whether they are useful for simulations of climate change or extreme events. Here, we focus on these issues using idealized tests in which an ML-based parameterization is trained on output from a conventional parameterization and its performa…
An unresolved problem of present generation coupled climate models is the realistic distribution of rainfall over Indian monsoon region, which is also related to the persistent dry bias over Indian land mass. Therefore, quantitative prediction of the intensity of rainfall events has remained a challenge for the state-of-the-art global coupled models. Guided by the observation, it is hypothesized that insufficient growth of cloud droplets and processes responsible for the cloud to rain water conversion are key components to distinguish between shallow to convective clouds. The new diffusional g…
Impact of Data-Driven Eddy Parameterization on Climate State in an Idealized Coupled CESM Model
Courant Institute School of Mathematics, Computing, and Data Science, New York University（纽约大学柯朗数学科学研究所）；Atmospheric and Oceanic Sciences Program, Princeton University（普林斯顿大学大气与海洋科学项目）
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the limitations of traditional neural networks (NNs) in fluid dynamical applications in that they can readily incorporate conservation laws and boundary conditions and are stable when integrated over time. We advocate a method that employs a 'residual' approach, in which the NN is used to improve upon an existing parameterization through the representation of resi…
Stable Machine-Learning Parameterization of Subgrid Processes in a Comprehensive Atmospheric Model Learned From Embedded Convection-Permitting Simulations
In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a coarse-grained field on a grid cannot properly resolve regions of saturation---in which condensation occurs---that are smaller than the grid boxes. Thus, in the absence of a parameterization scheme, either the grid box must become saturated or condensation will be underestimated. On the other hand, in a stochastic Lagrangian model of moisture transport, trajector…
Data Imbalance, Uncertainty Quantification, and Generalization via Transfer Learning in Data-driven Parameterizations: Lessons from the Emulation of Gravity Wave Momentum Transport in WACCM
Beyond the Training Data: Confidence-Guided Mixing of Parameterizations in a Hybrid AI-Climate Model
Deutsches Zentrum für Luft- und Raumfahrt（德国航空航天中心）；Faculty of Geosciences and Environment, University of Lausanne（洛桑大学地球科学与环境学院）；Expertise Center for Climate Extremes, University of Lausanne（洛桑大学气候极端研究中心）；University of Bremen, Institute of Environmental Physics (IUP)（不来梅大学环境物理研究所）
From stable online coupling to decade-long climate simulations: A machine learning parameterization for cloud microphysics in ICON
Deutsches Zentrum für Luft- und Raumfahrt e.V.（德国航空航天中心）；University of Oxford（牛津大学）；European Centre for Medium-Range Weather Forecasts（欧洲中期天气预报中心）；University of Bremen（不来梅大学）
The quantitative prediction of the intensity of rainfall events (light or heavy) has remained a challenge in Numerical Weather Prediction (NWP) models. For the first time the mean coefficient of diffusional growth rates are calculated using an Eulerian-Lagrangian particle-based small-scale model on in situ airborne measurement data of Cloud Aerosol Interaction and Precipitation Enhancement Experiment (CAIPEEX) during monsoon over Indian sub-continent. The results show that diffusional growth rates varies in the range of 0.00025 - 0.0015(cm/s). The generic problem of the overestimation of light…
Argonne National Laboratory（阿贡国家实验室）；Virginia Tech（弗吉尼亚理工学院）
Machine learning models have been employed to perform either physics-free data-driven or hybrid dynamical downscaling of climate data. Most of these implementations operate over relatively small downscaling factors because of the challenge of recovering fine-scale information from coarse data. This limits their compatibility with many global climate model outputs, often available between $\sim$50--100 km resolution, to scales of interest such as cloud resolving or urban scales. This study systematically examines the capability of convolutional neural networks (CNNs) to downscale surface wind s…
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy and improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing longstanding climate biases and relevant for determining the climate response to external forcing. This a…
Cloud microphysical parameterizations in atmospheric models describe the formation and evolution of clouds and precipitation, a central weather and climate process. Cloud-associated latent heating is a primary driver of large and small-scale circulations throughout the global atmosphere, and clouds have important interactions with atmospheric radiation. Clouds are ubiquitous, diverse, and can change rapidly. In this work, we build the first emulator of an entire cloud microphysical parameterization, including fast phase changes. The emulator performs well in offline and online (i.e. when coupl…
Stochastic subgrid-scale parametrizations aim to incorporate effects of unresolved processes in an effective model by sampling from a distribution usually described in terms of resolved modes. This is an active research area in climate, weather and ocean science where processes evolved in a wide range of spatial and temporal scales. In this study, we evaluate the performance of conditional generative adversarial network (GAN) in parametrizing subgrid-scale effects in a finite-difference discretization of stochastically forced Burgers equation. We define resolved modes as local spatial averages…
We address the question of how to use a machine learned parameterization in a general circulation model, and assess its performance both computationally and physically. We take one particular machine learned parameterization \cite{Guillaumin1&Zanna-JAMES21} and evaluate the online performance in a different model from which it was previously tested. This parameterization is a deep convolutional network that predicts parameters for a stochastic model of subgrid momentum forcing by mesoscale eddies. We treat the parameterization as we would a conventional parameterization once implemented in the…
In this study, we have identified certain fundamental limitations of a mixing length parameterization used in a popular turbulent kinetic energy-based subgrid-scale model. Replacing this parameterization with a more physically realistic one significantly improves the overall quality of the large-eddy simulations (LESs) of stable boundary layers. For the range of grid sizes considered here (specifically, 1 m -- 12.5 m), the revision dramatically reduces the grid-size sensitivity of the simulations. Most importantly, the revised scheme allows us to reliably estimate the first- and second-order s…
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；IMT Atlantique（大西洋国立高等矿业电信学校）；INRIA（法国国家信息与自动化研究所）；Institut Pierre Simon Laplace（皮埃尔·西蒙·拉普拉斯研究所）；IRD（法国国家可持续发展研究所）；Sorbonne Université（索邦大学）；Institut Universitaire de France（法兰西大学研究院）
The use of machine learning to build subgrid parametrizations for climate models is receiving growing attention. State-of-the-art strategies address the problem as a supervised learning task and optimize algorithms that predict subgrid fluxes based on information from coarse resolution models. In practice, training data are generated from higher resolution numerical simulations transformed in order to mimic coarse resolution simulations. By essence, these strategies optimize subgrid parametrizations to meet so-called $\textit{a priori}$ criteria. But the actual purpose of a subgrid parametriza…
Paraformer: Parameterization of Sub-grid Scale Processes Using Transformers
Northeastern University（东北大学）；Microsoft Corporation（微软公司）；The Institute for Experiential AI（体验式人工智能研究所）；Roux Institute（鲁克斯研究所）；Zeus AI（宙斯人工智能公司）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
A new tuning-free subgrid-scale model, termed `locally-averaged scale-dependent dynamic' (LASDD) model, is developed and implemented in large-eddy simulations (LESs) of stable boundary layers. The new model dynamically computes the Smagorinsky coefficient and the subgrid-scale Prandtl number based on the local dynamics of the resolved velocity and temperature fields. Overall, the agreement between the statistics of the LES-generated turbulence and some well-established empirical formulations and theoretical predictions (e.g., Nieuwstadt's local scaling hypothesis) is remarkable. The results sh…
Moist convection plays a leading role in the dynamics and energy budget of Earth's tropics and influences the sensitivity of Earth's climate to greenhouse gas increases. Because individual convective cells are much smaller than the gridboxes of 3-dimensional global climate models (GCMs), these models parameterize the effects of an ensemble of moist convective updrafts and downdrafts on the environment. Cumulus parameterization has been a focus of the terrestrial meteorology community for half a century. Only in past decade, however, have GCMs with moist convective physics been applied to other…
The issue of the parameterization of small scale (``subgrid'') turbulence is addressed in the context of passive scalar transport. We focus on the Kraichnan advection model which lends itself to the analytical investigation of the closure problem. We derive systematically the dynamical equations which rule the evolution of the coarse-grained scalar field. At the lowest-order approximation in $l/r$, $l$ being the characteristic scale of the filter defining the coarse-grained scalar field and $r$ the inertial range separation, we recover the classical eddy-diffusivity parameterization of small s…
Multi-Scale Dynamics of the Interaction Between Waves and Mean Flows: From Nonlinear WKB Theory to Gravity-Wave Parameterizations in Weather and Climate Models
A multifactor parameterization is described to permit the efficient calculation of collision efficiency (E) between electrically charged aerosol particles and neutral cloud droplets in numerical cloud and climate models. The four parameter representation summarizes the results obtained from a detailed microphysical model of collision efficiency, which accounts for the different forces acting on the aerosol in the path of falling cloud droplets. The parameterizations range of validity is for aerosol particle radius 0.4 to 10 micron, aerosol particle density 1 to 2.0 g.cm-3, aerosol particle cha…
The impact of gravity waves (GW) on diurnal tides and the global circulation in the middle/upper atmosphere of Mars is investigated using a General Circulation Model (GCM). We have implemented a stochastic parameterization of non-orographic GW into the Laboratoire de Météorologie Dynamique (LMD) Mars GCM (LMD-MGCM) following an innovative approach. The source is assumed to be located above typical convective cells ($\sim$ 250 Pa) and the effect of GW on the circulation and predicted thermal structure above 1 Pa ($\sim$ 50 km) is analyzed. We focus on the comparison between model simulations an…
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations as well as for model error representation, uncertainty quantification, data assimilation and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practica…
Allen Institute for Artificial Intelligence（艾伦人工智能研究所）；Geophysical Fluid Dynamics Laboratory, NOAA（美国国家海洋和大气管理局地球物理流体动力学实验室）；NVIDIA（英伟达）
Due to computational constraints, running global climate models (GCMs) for many years requires a lower spatial grid resolution (${\gtrsim}50$ km) than is optimal for accurately resolving important physical processes. Such processes are approximated in GCMs via subgrid parameterizations, which contribute significantly to the uncertainty in GCM predictions. One approach to improving the accuracy of a coarse-grid global climate model is to add machine-learned state-dependent corrections at each simulation timestep, such that the climate model evolves more like a high-resolution global storm-resol…
Ludwig-Maximilian-University（慕尼黑大学）；Columbia University（哥伦比亚大学）；University of California, Irvine（加州大学欧文分校）
The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but only for short-term simulations of at most a few years because of computational limitations. Here we demonstrate that deep learning can be used to capture many advantages of cloud-resolving modeling at a fraction of the computational cost. We train a deep neural network to represent all atmospheric sub-grid processes in a climate model by learning from a multi-…
Navigating the Noise: Bringing Clarity to ML Parameterization Design with O(100) Ensembles
Expertise Center for Climate Extremes, University of Lausanne（洛桑大学气候极端事件专业中心）；NVIDIA Research（英伟达研究院）；Department of Biomedical Data Science, Stanford University School of Medicine（斯坦福大学医学院生物医学数据科学系）；Department of Earth System Sciences, University of California at Irvine（加州大学欧文分校地球系统科学系）；Multimodal Cognitive AI, Intel Labs（英特尔实验室多模态认知人工智能部门）；Faculty of Geosciences and Environment, University of Lausanne（洛桑大学地球科学与环境学院）；Department of Statistics, University of California at Irvine（加州大学欧文分校统计系）；Department of Earth and Planetary Sciences, Harvard University（哈佛大学地球与行星科学系）；LEAP Science and Technology Center, School of Engineering and Applied Sciences, Climate School, Columbia University（哥伦比亚大学气候学院工程与应用科学学院LEAP科技中心）；Berkeley AI Research (BAIR), Department of Electrical Engineering and Computer Science, University of California at Berkeley（加州大学伯克利分校电气工程与计算机科学系伯克利人工智能研究中心）
National Center for Atmospheric Research（美国国家大气研究中心）；University of Colorado Boulder（科罗拉多大学博尔德分校）；University of Victoria（维多利亚大学）；University of Oxford（牛津大学）
Stochastic parameterizations account for uncertainty in the representation of unresolved sub-grid processes by sampling from the distribution of possible sub-grid forcings. Some existing stochastic parameterizations utilize data-driven approaches to characterize uncertainty, but these approaches require significant structural assumptions that can limit their scalability. Machine learning models, including neural networks, are able to represent a wide range of distributions and build optimized mappings between a large number of inputs and sub-grid forcings. Recent research on machine learning p…
Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizations
Technical University of Munich（慕尼黑技术大学）；Helmholtz Munich（海德堡-慕尼黑研究所）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；Centrum Wiskunde & Informatica (CWI)（荷兰代尔夫特数学与信息研究所）；Korteweg-de Vries Institute for Mathematics, University of Amsterdam（阿姆斯特丹大学克罗内克-德·维尔斯数学研究所）
