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 atmospheric phenomena, such as organized convective systems, can cross multiple grid boxes and involve slantwise circulations that are not purely vertical. Here we train neural networks (NNs) using non-local inputs spanning over 3$\times$3 columns of inputs. We find that including the non-local inputs improves the offline prediction of a range of subgrid processes. The improvement is especially notable for subgrid momentum transport and for atmospheric conditions associated with mid-latitude fronts and convective instability. Using an interpretability method, we find that the NN improvements partly rely on using the horizontal wind divergence, and we further show that including the divergence or vertical velocity as a separate input substantially improves offline performance. However, non-local winds continue to be useful inputs for parameterizating subgrid momentum transport even when the vertical velocity is included as an input. Overall, our results imply that the use of non-local variables and the vertical velocity as inputs could improve the performance of ML parameterizations, and the use of these inputs should be tested in online simulations in future work.
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.
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-di…
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…
In large-eddy simulations of atmospheric boundary layer turbulence, the lumped coefficient in the eddy-diffusion subgrid-scale (SGS) model is known to depend on scale for the case of inert scalars. This scale dependence is predominant near the surface. In this paper, a scale-dependent dynamic SGS model for the turbulent transport of reacting scalars is implemented in large-eddy simulations of a neutral boundary layer. Since the model coefficient is computed dynamically from the dynamics of the resolved scales, the simulations are free from any parameter tuning. A set of chemical cases represen…
A new scale-dependent dynamic subgrid-scale (SGS) model based on Kolmogorov's scaling hypothesis is presented. This SGS model is utilized in large-eddy simulation of a well-known case study on shear-driven neutral atmospheric boundary layer flows. The results are compared comprehensively with an alternate scale-dependent dynamic SGS model based on the popular Smagorinsky closure. Our results show that, in the context of this particular problem, the scale-dependent dynamic modeling approach is extremely useful, and reproduces several establised results (e.g., the surface layer similarity theory…
Stable Machine-Learning Parameterization of Subgrid Processes in a Comprehensive Atmospheric Model Learned From Embedded Convection-Permitting Simulations
In large-eddy simulations, subgrid-scale (SGS) processes are parameterized as a function of filtered grid-scale variables. First-order, algebraic SGS models are based on the eddy-viscosity assumption, which does not always hold for turbulence. Here we apply supervised deep neural networks (DNNs) to learn SGS stresses from a set of neighboring coarse-grained velocity from direct numerical simulations (DNSs) of the atmospheric boundary layer at friction Reynolds numbers Re_τ up to 1243 without invoking the eddy-viscosity assumption. The DNN model was found to produce higher correlation of SGS st…
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…
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…
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…
Growing set of optimization and regression techniques, based upon sparse representations of signals, to build models from data sets has received widespread attention recently with the advent of compressed sensing. This paper deals with the parameterization of the Lorenz-96 model with two time-scales that mimics mid-latitude atmospheric dynamics with microscopic convective processes. Compressed sensing is used to build models (vector fields) to emulate the behavior of the fine-scale process, so that explicit simulations become an online benchmark for parameterization. We apply compressed sensin…
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…
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）
climt-paraformer: Stable Emulation of Convective Parameterization using a Temporal Memory-aware Transformer
Sustainability and Data Sciences Laboratory, Northeastern University（可持续性与数据科学实验室，东北大学）；Microsoft（微软）；Indian Institute of Science Education and Research Pune（印度科学教育与研究中心普纳分校）；AI for Climate and Sustainability, The Institute for Experiential AI, Northeastern University（气候与可持续性人工智能，体验式人工智能研究所，东北大学）
The representation of cloud processes in weather and climate models is crucial for their feedback on atmospheric flows. Since there is no general macroscopic theory of clouds, the parameterization of clouds in corresponding simulation software depends crucially on the underlying modeling assumptions. In this study we present a new model of inter-mediate complexity (a one-and-a-half moment scheme) for warm clouds, which is derived from physical principles. Our model consists of a system of differential-algebraic equations which allows for supersaturation and comprises intrinsic automated drople…
We demonstrate the use of a probabilistic machine learning technique to develop stochastic parameterizations of atmospheric column-physics. After suitable preprocessing of NASA's Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA2) data to minimize the effects of high-frequency, high-wavenumber component of MERRA2 estimate of vertical velocity, we use generative adversarial networks to learn the probability distribution of vertical profiles of diabatic sources conditioned on vertical profiles of temperature and humidity. This may be viewed as an improvement over …
Physical parameterizations 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 and have shown great promises to reduce uncertainties associated with small-scale processes. Yet, those approaches still show some important mis…
Generating realistic global precipitation fields from modelled atmospheric circulation
Technical University of Munich（慕尼黑技术大学）；Munich Climate Center（慕尼黑气候中心）；TUM School of Engineering and Design（TUM工程与设计学院）；Department of Aerospace and Geodesy（航空航天与大地测量系）；Earth System Modelling Group（地球系统建模组）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Global Systems Institute（全球系统研究所）；Department of Mathematics（数学系）；University of Exeter（埃克塞特大学）
Improved Precipitation Variability in the Community Atmosphere Model through Implementation of a Neural-Network Deep Convection Scheme
Columbia University（哥伦比亚大学）；Massachusetts Institute of Technology（麻省理工学院）；U.S. National Science Foundation National Center for Atmospheric Research（美国国家科学基金会国家大气研究中心）；University of Cambridge（剑桥大学）；Stony Brook University（石溪大学）；Google Research（谷歌研究）
There has been a lot of recent interest in developing hybrid models that couple deterministic numerical model components to statistical model components derived using machine learning techniques. One approach that we follow in this pilot study is to replace an existing computationally expensive deterministic model component with its fast machine-learning-based emulator, leading to the model speed-up and/or improvement. We developed a shallow neural network-based emulator of a complete suite of atmospheric physics parameterizations in NCEP Global Forecast System (GFS) general circulation model …
General circulation models (GCMs) typically have a grid size of 25--200 km. Parametrizations are used to represent diabatic processes such as radiative transfer and cloud microphysics and account for sub-grid-scale motions and variability. Unlike traditional approaches, neural networks (NNs) can readily exploit recent observational datasets and global cloud-system resolving model (CRM) simulations to learn subgrid variability. This article describes an NN parametrization trained by coarse-graining a near-global CRM simulation with a 4~km horizontal grid spacing. The NN predicts the residual he…
Neural networks are a promising technique for parameterizing sub-grid-scale physics (e.g. moist atmospheric convection) in coarse-resolution climate models, but their lack of interpretability and reliability prevents widespread adoption. For instance, it is not fully understood why neural network parameterizations often cause dramatic instability when coupled to atmospheric fluid dynamics. This paper introduces tools for interpreting their behavior that are customized to the parameterization task. First, we assess the nonlinear sensitivity of a neural network to lower-tropospheric stability an…
University of Cambridge（剑桥大学）；British Antarctic Survey（英国南极调查局）；University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）
The modelling of small-scale processes is a major source of error in climate models, hindering the accuracy of low-cost models which must approximate such processes through parameterization. Red noise is essential to many operational parameterization schemes, helping model temporal correlations. We show how to build on the successes of red noise by combining the known benefits of stochasticity with machine learning. This is done using a physically-informed recurrent neural network within a probabilistic framework. Our model is competitive and often superior to both a bespoke baseline and an ex…
NORi: An ML-Augmented Ocean Boundary Layer Parameterization
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology（麻省理工学院地球、大气与行星科学系）；Center for Computational Science and Engineering, Massachusetts Institute of Technology（麻省理工学院计算科学与工程中心）；Department of Physics, Imperial College London（伦敦帝国学院物理系）；atdepth；Aeolus Labs（Aeolus实验室）；Department of Environment, Land and Infrastructure Engineering, Politecnico di Torino（托里诺理工学院环境、土地与基础设施工程系）
Assessing Emulator Design and Training for Modal Aerosol Microphysics Parameterizations in E3SMv2
Advanced Computing, Mathematics, and Data Division（先进计算、数学与数据部门）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；Earth and Biological Sciences Directorate（地球与生命科学 Directorate）；Lawrence Berkeley National Laboratory（伯克利国家实验室）
Wageningen University and Research（瓦赫宁根大学及研究中心）；Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder（科罗拉多大学博尔德分校环境科学合作研究所）；University of Colorado at Boulder（科罗拉多大学博尔德分校）；NOAA Physical Sciences Laboratory（美国国家海洋和大气管理局物理科学实验室）；SURFsara（SURFsara科研网络机构）
The radiative transfer equations are well-known, but radiation parametrizations in atmospheric models are computationally expensive. A promising tool for accelerating parametrizations is the use of machine learning techniques. In this study, we develop a machine learning-based parametrization for the gaseous optical properties by training neural networks to emulate a modern radiation parameterization (RRTMGP). To minimize computational costs, we reduce the range of atmospheric conditions for which the neural networks are applicable and use machine-specific optimised BLAS functions to accelerat…
Brazilian National Institute of Space Research（巴西国家空间研究院）
This paper presents an approach for employing artificial neural networks (NN) to emulate an ensemble Kalman filter (EnKF) as a method of data assimilation. The assimilation methods are tested in the Simplified Parameterizations PrimitivE-Equation Dynamics (SPEEDY) model, an atmospheric general circulation model (AGCM), using synthetic observational data simulating localization of balloon soundings. For the data assimilation scheme, the supervised NN, the multilayer perceptrons (MLP-NN), is applied. The MLP-NN are able to emulate the analysis from the local ensemble transform Kalman filter (LET…
While various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first-order closure schemes such as the K-Profile Parameterization (KPP) lack energetic constraints; two-equation models like $k-ε$ directly solve an equation for the turbulent kinetic energy but do not account for non-local fluxes, and high-order closures that include the non-local transport terms are computationally expensive. To address these, here we extend the Assumed-Distribution Higher-Order Closure (ADC) framework originall…
A new non-hydrostatic and cloud-resolving atmospheric model is developed for studying moist convection and cloud formation in planetary atmospheres. It is built on top of the Athena++ framework, utilizing its static/adaptive mesh-refinement, parallelization, curvilinear geometry, and dynamic task scheduling. We extend the original hydrodynamic solver to vapors, clouds, and precipitation. Microphysics is formulated generically so that it can be applied to both Earth and Jovian planets. We implemented the Low Mach number Approximate Riemann Solver (LMARS) for simulating low speed atmospheric flo…
