Spatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition

Abstract Stochastic parameterizations are increasingly being used in climate modeling to represent subgrid‐scale processes. While different parameterizations are being developed considering different aspects of the physical phenomena, less attention is given to technical and numerical aspects. In pa...

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Autores principales:	Federica Gugole, Christian L. E. Franzke
Formato:	article
Lenguaje:	EN
Publicado:	American Geophysical Union (AGU) 2020
Materias:	Koopman operator dynamic mode decomposition empirical orthogonal functions stochastic parameterizations dynamically adapted noise covariance Physical geography GB3-5030 Oceanography GC1-1581
Acceso en línea:	https://doaj.org/article/73fa82f776994ed5b2375a08d1d3e839
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id	oai:doaj.org-article:73fa82f776994ed5b2375a08d1d3e839
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spelling	oai:doaj.org-article:73fa82f776994ed5b2375a08d1d3e8392021-11-15T14:20:26ZSpatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition1942-246610.1029/2020MS002115https://doaj.org/article/73fa82f776994ed5b2375a08d1d3e8392020-08-01T00:00:00Zhttps://doi.org/10.1029/2020MS002115https://doaj.org/toc/1942-2466Abstract Stochastic parameterizations are increasingly being used in climate modeling to represent subgrid‐scale processes. While different parameterizations are being developed considering different aspects of the physical phenomena, less attention is given to technical and numerical aspects. In particular, empirical orthogonal functions (EOFs) are employed when a spatial structure is required. Here, we provide evidence they might not be the most suitable choice. By applying an energy‐consistent parameterization to the two‐layer quasi‐geostrophic (QG) model, we investigate the model sensitivity to a priori assumptions made on the parameterization. In particular, we consider here two methods to prescribe the spatial covariance of the noise: first, by using climatological variability patterns provided by EOFs, and second, by using time‐varying dynamics‐adapted Koopman modes, approximated by dynamic mode decomposition (DMD). The performance of the two methods are analyzed through numerical simulations of the stochastic system on a coarse spatial resolution and the outcomes compared to a high‐resolution simulation of the original deterministic system. The comparison reveals that the DMD‐based noise covariance scheme outperforms the EOF‐based one. The use of EOFs leads to a significant increase of the ensemble spread and to a meridional misplacement of the bimodal eddy kinetic energy (EKE) distribution. Conversely, using DMDs, the ensemble spread is confined, the meridional propagation of the zonal jet stream is accurately captured, and the total variance of the system is improved. Our results highlight the importance of the systematic design of stochastic parameterizations with dynamically adapted spatial correlations, rather than relying on statistical spatial patterns.Federica GugoleChristian L. E. FranzkeAmerican Geophysical Union (AGU)articleKoopman operatordynamic mode decompositionempirical orthogonal functionsstochastic parameterizationsdynamically adapted noise covariancePhysical geographyGB3-5030OceanographyGC1-1581ENJournal of Advances in Modeling Earth Systems, Vol 12, Iss 8, Pp n/a-n/a (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Koopman operator dynamic mode decomposition empirical orthogonal functions stochastic parameterizations dynamically adapted noise covariance Physical geography GB3-5030 Oceanography GC1-1581
spellingShingle	Koopman operator dynamic mode decomposition empirical orthogonal functions stochastic parameterizations dynamically adapted noise covariance Physical geography GB3-5030 Oceanography GC1-1581 Federica Gugole Christian L. E. Franzke Spatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition
description	Abstract Stochastic parameterizations are increasingly being used in climate modeling to represent subgrid‐scale processes. While different parameterizations are being developed considering different aspects of the physical phenomena, less attention is given to technical and numerical aspects. In particular, empirical orthogonal functions (EOFs) are employed when a spatial structure is required. Here, we provide evidence they might not be the most suitable choice. By applying an energy‐consistent parameterization to the two‐layer quasi‐geostrophic (QG) model, we investigate the model sensitivity to a priori assumptions made on the parameterization. In particular, we consider here two methods to prescribe the spatial covariance of the noise: first, by using climatological variability patterns provided by EOFs, and second, by using time‐varying dynamics‐adapted Koopman modes, approximated by dynamic mode decomposition (DMD). The performance of the two methods are analyzed through numerical simulations of the stochastic system on a coarse spatial resolution and the outcomes compared to a high‐resolution simulation of the original deterministic system. The comparison reveals that the DMD‐based noise covariance scheme outperforms the EOF‐based one. The use of EOFs leads to a significant increase of the ensemble spread and to a meridional misplacement of the bimodal eddy kinetic energy (EKE) distribution. Conversely, using DMDs, the ensemble spread is confined, the meridional propagation of the zonal jet stream is accurately captured, and the total variance of the system is improved. Our results highlight the importance of the systematic design of stochastic parameterizations with dynamically adapted spatial correlations, rather than relying on statistical spatial patterns.
format	article
author	Federica Gugole Christian L. E. Franzke
author_facet	Federica Gugole Christian L. E. Franzke
author_sort	Federica Gugole
title	Spatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition
title_short	Spatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition
title_full	Spatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition
title_fullStr	Spatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition
title_full_unstemmed	Spatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition
title_sort	spatial covariance modeling for stochastic subgrid‐scale parameterizations using dynamic mode decomposition
publisher	American Geophysical Union (AGU)
publishDate	2020
url	https://doaj.org/article/73fa82f776994ed5b2375a08d1d3e839
work_keys_str_mv	AT federicagugole spatialcovariancemodelingforstochasticsubgridscaleparameterizationsusingdynamicmodedecomposition AT christianlefranzke spatialcovariancemodelingforstochasticsubgridscaleparameterizationsusingdynamicmodedecomposition
_version_	1718428382134272000

Spatial Covariance Modeling for Stochastic Subgrid‐Scale Parameterizations Using Dynamic Mode Decomposition

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