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stochastic parameterization of shallow cumulus convection estimated from high-resolution model data

THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS 2013年第1-2期27卷 133-148页

作者： Dorrestijn, Jesse Crommelin, Daan T. Siebesma, A. Pier Jonker, Harm J. J. CWI NL-1090 GB Amsterdam Netherlands Delft Univ Technol NL-2600 GA Delft Netherlands Royal Netherlands Meteorol Inst KNMI De Bilt Netherlands

In this paper, we report on the development of a methodology for stochastic parameterization of convective transport by shallow cumulus convection in weather and climate models. We construct a parameterization based on Large-Eddy Simulation (LES) data. These simulations resolve the turbulent fluxes of heat and moisture and are based on a typical case of non-precipitating shallow cumulus convection above sea in the trade-wind region. Using clustering, we determine a finite number of turbulent flux pairs for heat and moisture that are representative for the pairs of flux profiles observed in these simulations. In the stochastic parameterization scheme proposed here, the convection scheme jumps randomly between these pre-computed pairs of turbulent flux profiles. The transition probabilities are estimated from the LES data, and they are conditioned on the resolved-scale state in the model column. Hence, the stochastic parameterization is formulated as a data-inferred conditional Markov chain (CMC), where each state of the Markov chain corresponds to a pair of turbulent heat and moisture fluxes. The CMC parameterization is designed to emulate, in a statistical sense, the convective behaviour observed in the LES data. The CMC is tested in single-column model (SCM) experiments. The SCM is able to reproduce the ensemble spread of the temperature and humidity that was observed in the LES data. Furthermore, there is a good similarity between time series of the fractions of the discretized fluxes produced by SCM and observed in LES.

关键词： stochastic parameterization Atmospheric convection Large-Eddy Simulation Markov chain Clustering Grey zone

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stochastic parameterization identification using ensemble Kalman filtering combined with maximum likelihood methods

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TELLUS SERIES A-DYNAMIC METEOROLOGY AND OCEANOGRAPHY 2018年第1期70卷 1-17页

作者： Pulido, Manuel Tandeo, Pierre Bocquet, Marc Carrassi, Alberto Lucini, Magdalena Univ Nacl Nordeste Dept Phys FaCENA Corrientes Argentina CNRS CONICET IFAECI IMIT Buenos Aires DF Argentina IMT Atlantique UBL Lab STICC Brest France Univ Paris Est Joint Lab Ecole Ponts ParisTech & EDF R&D CEREA Champs Sur Marne France Nansen Environm & Remote Sensing Ctr Bergen Norway Univ Nacl Nordeste FaCENA Dept Math Corrientes Argentina Consejo Nacl Invest Cient & Tecn Corrientes Argentina

For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the best possible stochastic parameterization from noisy data. State-of-the-art sequential estimation methods such as Kalman and particle filters do not achieve this goal successfully because both suffer from the collapse of the posterior distribution of the parameters. To overcome this intrinsic limitation, we propose two statistical learning methods. They are based on the combination of the ensemble Kalman filter (EnKF) with either the expectation-maximization (EM) or the Newton-Raphson (NR) used to maximize a likelihood associated to the parameters to be estimated. The EM and NR are applied primarily in the statistics and machine learning communities and are brought here in the context of data assimilation for the geosciences. The methods are derived using a Bayesian approach for a hidden Markov model and they are applied to infer deterministic and stochastic physical parameters from noisy observations in coarse-grained dynamical models. Numerical experiments are conducted using the Lorenz-96 dynamical system with one and two scales as a proof of concept. The imperfect coarse-grained model is modelled through a one-scale Lorenz-96 system in which a stochastic parameterization is incorporated to represent the small-scale dynamics. The algorithms are able to identify the optimal stochastic parameterization with good accuracy under moderate observational noise. The proposed EnKF-EM and EnKF-NR are promising efficient statistical learning methods for developing stochastic parameterizations in high-dimensional geophysical models.

关键词： parameter estimation model error estimation stochastic parameterization expectation-maximization algorithm

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Machine Learning for stochastic parameterization: Generative Adversarial Networks in the Lorenz '96 Model

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JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS 2020年第3期12卷 e2019MS001896-e2019MS001896页

作者： Gagne, David John, II Christensen, Hannah M. Subramanian, Aneesh C. Monahan, Adam H. Natl Ctr Atmospher Res POB 3000 Boulder CO 80307 USA Univ Oxford Atmospher Ocean & Planetary Phys Oxford England Univ Colorado Dept Atmospher & Ocean Sci Boulder CO 80309 USA Univ Victoria Sch Earth & Ocean Sci Victoria BC Canada

stochastic parameterizations account for uncertainty in the representation of unresolved subgrid processes by sampling from the distribution of possible subgrid 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 subgrid forcings. Recent research on machine learning parameterizations has focused only on deterministic parameterizations. In this study, we develop a stochastic parameterization using the generative adversarial network (GAN) machine learning framework. The GAN stochastic parameterization is trained and evaluated on output from the Lorenz '96 model, which is a common baseline model for evaluating both parameterization and data assimilation techniques. We evaluate different ways of characterizing the input noise for the model and perform model runs with the GAN parameterization at weather and climate time scales. Some of the GAN configurations perform better than a baseline bespoke parameterization at both time scales, and the networks closely reproduce the spatiotemporal correlations and regimes of the Lorenz '96 system. We also find that, in general, those models which produce skillful forecasts are also associated with the best climate simulations. Plain Language Summary Simulations of the atmosphere must approximate the effects of small-scale processes with simplified functions called parameterizations. Standard parameterizations only predict one output for a given input, but stochastic parameterizations can sample from all the possible outcomes that can occur under certain conditions. We have developed and evaluated a machine learning stochastic parameterization, which builds a mapping between large-scale current conditions and

关键词： machine learning stochastic parameterization generative adversarial networks lorenz climate weather

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A note on 'Toward a stochastic parameterization of ocean mesoscale eddies'

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OCEAN MODELLING 2017年 113卷 30-33页

作者： Grooms, Ian Zanna, Laure Univ Colorado Dept Appl Math Boulder CO 80309 USA Univ Oxford Dept Phys Atmospher Ocean & Planetary Phys Oxford OX1 3PU England

Porta Mana and Zanna (2014) recently proposed a subgrid-scale parameterization for eddy-permitting quasigeostrophic models. In this model the large-scale fluid is represented as a non-Newtonian viscoelastic medium, with a subgrid-stress closure that involves the Lagrangian derivative of large-scale quantities. This note derives this parameterization, including the nondimensional proportionality coefficient, using only two statistical assumptions: that the subgrid-scale term is locally homogeneous and decorrelates rapidly in space. The parameterization is then verified by comparing against eddy-resolving quasigeostrophic simulations, independently reproducing the results of Porta Mana and Zanna in a simpler model. (C) 2017 The Authors. Published by Elsevier Ltd.

关键词： Mesoscale eddies stochastic parameterization Eddy backscatter

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A data-conditioned stochastic parameterization of temporal plant trait variability in an ecohydrological model and the potential for plasticity

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AGRICULTURAL AND FOREST METEOROLOGY 2019年 274卷 184-194页

作者： Liu, Shaoqing Ng, Gene-Hua Crystal Univ Minnesota Twin Cities Dept Earth Sci Minneapolis MN 55455 USA Univ Minnesota Twin Cities St Anthony Falls Lab Minneapolis MN USA

Recent studies have begun to incorporate spatially variable plant traits into ecohydrological models, but temporal trait variability remains under-studied. Because of its potential to influence ecosystem function, representing stress-induced temporal trait variability into models should be a research priority. We present a new data-model integration approach to identify temporal variability in plant traits and generate stochastic-in-time model parameterizations. The data-conditioned stochastic parameterization was developed within the CLM 4.5 model utilizing global trait data as prior information and tested for a desert shrubland site. A synthetic experiment demonstrated that the framework successfully uncovered time-varying trait values. Using in-situ ecohydrological observations, we found the specific leaf area (SLA) for a common broadleaf-evergreen-shrub to be temporally dynamic and significantly correlated with seasonal water availability. We constructed a regression model based on the data-conditioned SLA estimates and soil wetness and used it to generate stochastic SLA parameters for a 40-year hindcast simulation. The stochastic-in-time SLA parameters resulted in greater productivity and water use efficiency than a standard static parameter. Our stochastic-in-time method can help evaluate stress-induced trait plasticity that extends our understanding beyond sparse spatial plant trait database and improve our ability to simulate carbon and water fluxes under global change.

关键词： Plant trait Data-model integration Ecohydrological models stochastic parameterization Temporal trait variability

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stochastic parameterization of column physics using generative adversarial networks

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ENVIRONMENTAL DATA SCIENCE 2022年 1卷 e22-e22页

作者： Nadiga, Balasubramanya T. Sun, Xiaoming Nash, Cody Los Alamos Natl Lab Los Alamos NM 87545 USA

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 previous similar but deterministic approaches that seek to alleviate both, shortcomings of human-designed physics parameterizations, and the computational demand of the "physics" step in climate models. Impact Statement Global climate models can now be used to produce realistic simulations of climate. However, large uncertainties remain: for example, the estimated change in globally-averaged surface-temperature to a doubling of atmospheric CO2 varies between 2 degrees and 6 degrees C across leading models. Uncertainty in representing cumulus convection (think thunderstorm) is a major contributor to this spread: Scales at which they occur, 100m-10 km, are too small to be resolved in global climate models, requiring their effects on larger scales to be approximated with simple models. Improving such approximations using new probabilistic machine-learning techniques, initial steps toward which are successfully demonstrated in this work will likely lead to improvements in the modeling of climate through improvements in the representation of cumulus convection.

关键词： Column physics generative adversarial network machine learning stochastic parameterization

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A stochastic parameterization of non-orographic gravity waves: Formalism and impact on the equatorial stratosphere

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GEOPHYSICAL RESEARCH LETTERS 2012年第6期39卷

作者： Lott, F. Guez, L. Maury, P. Ecole Normale Super Meteorol Dynam Lab F-75231 Paris 05 France

A formalism is proposed to represent a broadband spectrum of Gravity Waves (GWs) via the superposition of a large ensemble of statistically independent monochromatic ones. To produce this large ensemble at a reasonable numerical cost, we use the fact that the life cycles of the waves needed to be parameterized in General Circulation Models (GCMs) have time scales that largely exceed the time step of the model. We can therefore launch few waves with characteristics chosen randomly at each time step, and make them having an effect on a longer time scale by applying an AR1 relation between the gravity waves drag at a given time and that at the next time step. The stochastic GW parameterization is applied to a GCM in the tropics, and its additional drag causes a realistic Quasi-Biennial Oscillation (QBO). The more realistic wind structure also results in a better representation of the large scale equatorial waves, like the Rossby Gravity Waves (RGWs) with periods around 4-5 day. Citation: Lott, F., L. Guez, and P. Maury (2012), A stochastic parameterization of non-orographic gravity waves: Formalism and impact on the equatorial stratosphere, Geophys. Res. Lett., 39, L06807, doi: 10.1029/2012GL051001.

关键词： Quasi-Biennial Oscillation Rossby-gravity waves gravity waves stochastic parameterization stratospheric dynamics

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Resampling with neural networks for stochastic parameterization in multiscale systems

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PHYSICA D-NONLINEAR PHENOMENA 2021年 422卷 132894-132894页

作者： Crommelin, Daan Edeling, Wouter Ctr Wiskunde & Informat Sci Comp Grp Sci Pk 123 NL-1098 XG Amsterdam Netherlands Univ Amsterdam Korteweg de Vries Inst Math Sci Pk 105-107 NL-1098 XG Amsterdam Netherlands

In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for parameterizations. We present a machine-learning method, used for the conditional resampling of observations or reference data from a fully resolved simulation. It is based on the probabilistic classification of subsets of reference data, conditioned on macroscopic variables. This method is used to formulate a parameterization that is stochastic, taking the uncertainty of the unresolved scales into account. We validate our approach on the Lorenz 96 system, using two different parameter settings which are challenging for parameterization methods. (C) 2021 The Author(s). Published by Elsevier B.V.

关键词： Machine learning Multiscale dynamical systems stochastic parameterization Conditional resampling

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stochastic convective parameterization improving the simulation of tropical precipitation variability in the NCAR CAM5

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GEOPHYSICAL RESEARCH LETTERS 2016年第12期43卷 6612-6619页

作者： Wang, Yong Zhang, Guang J. Craig, George C. Tsinghua Univ Ctr Earth Syst Sci Beijing Peoples R China Scripps Inst Oceanog Ctr Atmospher Sci La Jolla CA USA Univ Munich Inst Meteorol Munich Germany

The Plant-Craig (PC) stochastic convective parameterization scheme is implemented into the National Center for Atmospheric Research Community Atmosphere Model version 5 (CAM5) to couple with the Zhang-McFarlane deterministic convection scheme. To evaluate its impact on tropical precipitation simulation, two experiments are conducted: one with the standard CAM5 and the other with the stochastic scheme incorporated. Results show that the PC stochastic parameterization decreases the frequency of weak precipitation and increases the frequency of strong precipitation, resulting in better agreement with observations. The most striking improvement is in the probability distribution function (PDF) of precipitation intensity, with the well-known too-much-drizzle problem in CAM5 largely eliminated. In the global tropical belt, the precipitation intensity PDF from the simulation agrees remarkably well with that of Tropical Rainfall Measuring Mission observations. The stochastic scheme also yields a similar magnitude of intraseasonal variability of precipitation to observations and improves the simulation of the eastward propagating intraseasonal signals of precipitation and zonal wind.

关键词： stochastic parameterization convection tropical precipitation CAM5

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The stochastic GM + E Closure: A Framework for Coupling stochastic Backscatter With the Gent and McWilliams parameterization

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Journal of Advances in Modeling Earth Systems 2025年第5期17卷

作者： I. Grooms N. Agarwal G. Marques P. J. Pegion H. Yassin Department of Applied Mathematics University of Colorado Boulder CO USA Cooperative Institute for Research in Environmental Sciences University of Colorado Boulder Boulder CO USA NOAA Physics Sciences Lab Boulder CO USA Climate and Global Dynamics Laboratory National Center for Atmospheric Research Boulder CO USA

Ocean general circulation models (OGCMs) are often used at horizontal resolutions that preclude the appearance of mesoscale eddies. The ocean mesoscale constitutes a significant component of ocean variability, and OGCMs whose resolutions are too coarse to represent the mesoscale are necessarily lacking this variability. In addition to being variable, the ocean mesoscale also induces variability on larger scales that could be resolved on a coarse grid, but coarse OGCMs often lack this variability too. This paper develops a stochastic parameterization that adds small increments to an OGCM's lateral velocity field, which excites natural modes of variability in the model. The rate at which these velocity increments add energy to the flow is tied to the rate at which the Gent-McWilliams parameterization—a popular parameterization of the effect of mesoscale eddies on tracer transport—removes potential energy from the resolved scales. The stochastic parameterization is implemented in a non-eddying OGCM, where it is shown to increase the variability significantly. Mesoscale eddies backscatter kinetic energy to scales resolvable by non-eddying ocean models A stochastic kinetic energy backscatter parameterization is developed for non-eddying ocean models Models used to simulate global ocean currents often have horizontal resolutions that are too low to see ocean mesoscale eddies, which are to the ocean what weather systems are to the atmosphere. These ocean eddies jostle each other and the larger-scale currents in a chaotic manner, leading to variability on scales that could, in principle, be resolved by ocean models. But since the ocean models don't actually include the eddies themselves, the currents they resolve won't be jostled about realistically unless we enhance the models by adding a realistic description of the effects of the eddies that the models can't see. This paper develops such a description, called a stochastic parameterization. The eddies get their energy by

关键词： ocean modeling stochastic parameterization mesoscale backscatter

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