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Mathematics of Climate and Weather Forecasting

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Numerical Development and Evaluation of an Energy Conserving Conceptual Stochastic Climate Model

Federica Gugole
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  • Meteorological Institute and Center for Earth System Research and Sustainability, University of Hamburg, Hamburg, Germany
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/ Christian L. E. Franzke
  • Meteorological Institute and Center for Earth System Research and Sustainability, University of Hamburg, Hamburg, Germany
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Published Online: 2019-05-24 | DOI: https://doi.org/10.1515/mcwf-2019-0004


In this study we aim to present the successful development of an energy conserving conceptual stochastic climate model based on the inviscid 2-layer Quasi-Geostrophic (QG) equations. The stochastic terms have been systematically derived and introduced in such away that the total energy is conserved. In this proof of concept studywe give particular emphasis to the numerical aspects of energy conservation in a highdimensional complex stochastic system andwe analyzewhat kind of assumptions regarding the noise should be considered in order to obtain physical meaningful results. Our results show that the stochastic model conserves energy to an accuracy of about 0.5% of the total energy; this level of accuracy is not affected by the introduction of the noise, but is mainly due to the level of accuracy of the deterministic discretization of the QG model. Furthermore, our results demonstrate that spatially correlated noise is necessary for the conservation of energy and the preservation of important statistical properties, while using spatially uncorrelated noise violates energy conservation and gives unphysical results. A dynamically consistent spatial covariance structure is determined through Empirical Orthogonal Functions (EOFs). We find that only a small number of EOFs is needed to get good results with respect to energy conservation, autocorrelation functions, PDFs and eddy length scale when comparing a deterministic control simulation on a 512 × 512 grid to a stochastic simulation on a 128 × 128 grid. Our stochastic approach has the potential to seamlessly be implemented in comprehensive weather and climate prediction models.

Keywords: stochastic parameterization; energy conservation; projection operator; spatial noise structure; Empirical Orthogonal Functions

MSC 2010: 65C20; 68U20


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About the article

Received: 2018-11-08

Accepted: 2019-04-18

Published Online: 2019-05-24

Published in Print: 2019-02-01

Citation Information: Mathematics of Climate and Weather Forecasting, Volume 5, Issue 1, Pages 45–64, ISSN (Online) 2353-6438, DOI: https://doi.org/10.1515/mcwf-2019-0004.

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© 2019 Federica Gugole et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. BY 4.0

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