Articles | Volume 29, issue 2
https://doi.org/10.5194/npg-29-183-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/npg-29-183-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Lévy noise versus Gaussian-noise-induced transitions in the Ghil–Sellers energy balance model
Valerio Lucarini
CORRESPONDING AUTHOR
Department of Mathematics and Statistics, University of Reading, Reading, UK
Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
Invited contribution by Valerio Lucarini, recipient of the EGU Lewis Fry Richardson Medal 2020.
Larissa Serdukova
Department of Mathematics and Statistics, University of Reading, Reading, UK
Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
Georgios Margazoglou
Department of Mathematics and Statistics, University of Reading, Reading, UK
Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
Related authors
Lucy G. Recchia and Valerio Lucarini
Earth Syst. Dynam., 14, 697–722, https://doi.org/10.5194/esd-14-697-2023, https://doi.org/10.5194/esd-14-697-2023, 2023
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Simulations are performed with an intermediate-complexity climate model, PLASIM, to assess the future response of monsoons to changing concentrations of aerosols and greenhouse gases. The aerosol loading is applied to India, Southeast Asia, and eastern China, both concurrently and independently, to assess linearity. The primary effect of increased aerosol loading is a decrease in summer precipitation in the vicinity of the applied forcing, although the regional response varies significantly.
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Eddies in mid-latitudes characterize the exchange of heat between the tropics and the poles. This exchange is largely uneven, with a few extreme events bearing most of the heat transported across latitudes in a season. It is thus important to understand what the dynamical mechanisms are behind these events. Here, we identify recurrent weather regime patterns associated with extreme transports, and we identify scales of mid-latitudinal eddies that are mostly responsible for the transport.
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Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial conditions. However, obtaining the instability properties is burdensome for complex problems, both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.
Veronika Eyring, Lisa Bock, Axel Lauer, Mattia Righi, Manuel Schlund, Bouwe Andela, Enrico Arnone, Omar Bellprat, Björn Brötz, Louis-Philippe Caron, Nuno Carvalhais, Irene Cionni, Nicola Cortesi, Bas Crezee, Edouard L. Davin, Paolo Davini, Kevin Debeire, Lee de Mora, Clara Deser, David Docquier, Paul Earnshaw, Carsten Ehbrecht, Bettina K. Gier, Nube Gonzalez-Reviriego, Paul Goodman, Stefan Hagemann, Steven Hardiman, Birgit Hassler, Alasdair Hunter, Christopher Kadow, Stephan Kindermann, Sujan Koirala, Nikolay Koldunov, Quentin Lejeune, Valerio Lembo, Tomas Lovato, Valerio Lucarini, François Massonnet, Benjamin Müller, Amarjiit Pandde, Núria Pérez-Zanón, Adam Phillips, Valeriu Predoi, Joellen Russell, Alistair Sellar, Federico Serva, Tobias Stacke, Ranjini Swaminathan, Verónica Torralba, Javier Vegas-Regidor, Jost von Hardenberg, Katja Weigel, and Klaus Zimmermann
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The Earth System Model Evaluation Tool (ESMValTool) is a community diagnostics and performance metrics tool designed to improve comprehensive and routine evaluation of earth system models (ESMs) participating in the Coupled Model Intercomparison Project (CMIP). It has undergone rapid development since the first release in 2016 and is now a well-tested tool that provides end-to-end provenance tracking to ensure reproducibility.
Valerio Lembo, Frank Lunkeit, and Valerio Lucarini
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The Thermodynamic Diagnostic Tool (TheDiaTo v1.0) is a collection of diagnostics for the study of the thermodynamics of the climate system in climate models. This is fundamental in order to understand where the imbalances affecting climate projections come from and also to allow for easy comparison of different scenarios and atmospheric regimes. The tool is currently being developed for the assessment of models that are part of the next phase of the Coupled Model Intercomparison Project (CMIP).
Mallory Carlu, Francesco Ginelli, Valerio Lucarini, and Antonio Politi
Nonlin. Processes Geophys., 26, 73–89, https://doi.org/10.5194/npg-26-73-2019, https://doi.org/10.5194/npg-26-73-2019, 2019
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We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96, to unravel key mechanisms of interaction between scales of different resolutions and time scales. To do so, we use a mathematical machinery known as Lyapunov analysis, allowing us to capture the degrees of chaoticity associated with fundamental directions of instability. We find a non-trivial group of such directions projecting significantly on slow variables, associated with long term dynamics.
Gabriele Vissio and Valerio Lucarini
Nonlin. Processes Geophys., 25, 413–427, https://doi.org/10.5194/npg-25-413-2018, https://doi.org/10.5194/npg-25-413-2018, 2018
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Constructing good parametrizations is key when studying multi-scale systems. We consider a low-order model and derive a parametrization via a recently developed statistical mechanical approach. We show how the method allows for seamlessly treating the case when the unresolved dynamics is both faster and slower than the resolved one. We test the skill of the parametrization by using the formalism of the Wasserstein distance, which allows for measuring how different two probability measures are.
Lesley De Cruz, Sebastian Schubert, Jonathan Demaeyer, Valerio Lucarini, and Stéphane Vannitsem
Nonlin. Processes Geophys., 25, 387–412, https://doi.org/10.5194/npg-25-387-2018, https://doi.org/10.5194/npg-25-387-2018, 2018
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The predictability of weather models is limited largely by the initial state error growth or decay rates. We have computed these rates for PUMA, a global model for the atmosphere, and MAOOAM, a more simplified, coupled model which includes the ocean. MAOOAM has processes at distinct timescales, whereas PUMA surprisingly does not. We propose a new programme to compute the natural directions along the flow that correspond to the growth or decay rates, to learn which components play a role.
Tamás Bódai, Valerio Lucarini, and Frank Lunkeit
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2018-30, https://doi.org/10.5194/esd-2018-30, 2018
Revised manuscript not accepted
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We establish a framework to conduct a scenario analysis of the best possible outcomes under geoengineering. The scenarios may consist of scenarios of greenhouse gas emission the choice of the quantity that we want to keep under control. The motivation is the desire of an efficient way of assessing the side-effects of geoengineering, concerning the unwanted and uncontrolled changes. Countering CO2 emission by modulating insolation, we find considerable changes in local temperatures or rainfall.
S. Hasson, V. Lucarini, M. R. Khan, M. Petitta, T. Bolch, and G. Gioli
Hydrol. Earth Syst. Sci., 18, 4077–4100, https://doi.org/10.5194/hess-18-4077-2014, https://doi.org/10.5194/hess-18-4077-2014, 2014
S. Hasson, V. Lucarini, S. Pascale, and J. Böhner
Earth Syst. Dynam., 5, 67–87, https://doi.org/10.5194/esd-5-67-2014, https://doi.org/10.5194/esd-5-67-2014, 2014
R. Deidda, M. Marrocu, G. Caroletti, G. Pusceddu, A. Langousis, V. Lucarini, M. Puliga, and A. Speranza
Hydrol. Earth Syst. Sci., 17, 5041–5059, https://doi.org/10.5194/hess-17-5041-2013, https://doi.org/10.5194/hess-17-5041-2013, 2013
S. Hasson, V. Lucarini, and S. Pascale
Earth Syst. Dynam., 4, 199–217, https://doi.org/10.5194/esd-4-199-2013, https://doi.org/10.5194/esd-4-199-2013, 2013
Lucy G. Recchia and Valerio Lucarini
Earth Syst. Dynam., 14, 697–722, https://doi.org/10.5194/esd-14-697-2023, https://doi.org/10.5194/esd-14-697-2023, 2023
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Simulations are performed with an intermediate-complexity climate model, PLASIM, to assess the future response of monsoons to changing concentrations of aerosols and greenhouse gases. The aerosol loading is applied to India, Southeast Asia, and eastern China, both concurrently and independently, to assess linearity. The primary effect of increased aerosol loading is a decrease in summer precipitation in the vicinity of the applied forcing, although the regional response varies significantly.
Valerio Lembo, Federico Fabiano, Vera Melinda Galfi, Rune Grand Graversen, Valerio Lucarini, and Gabriele Messori
Weather Clim. Dynam., 3, 1037–1062, https://doi.org/10.5194/wcd-3-1037-2022, https://doi.org/10.5194/wcd-3-1037-2022, 2022
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Eddies in mid-latitudes characterize the exchange of heat between the tropics and the poles. This exchange is largely uneven, with a few extreme events bearing most of the heat transported across latitudes in a season. It is thus important to understand what the dynamical mechanisms are behind these events. Here, we identify recurrent weather regime patterns associated with extreme transports, and we identify scales of mid-latitudinal eddies that are mostly responsible for the transport.
Yumeng Chen, Alberto Carrassi, and Valerio Lucarini
Nonlin. Processes Geophys., 28, 633–649, https://doi.org/10.5194/npg-28-633-2021, https://doi.org/10.5194/npg-28-633-2021, 2021
Short summary
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Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial conditions. However, obtaining the instability properties is burdensome for complex problems, both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.
Veronika Eyring, Lisa Bock, Axel Lauer, Mattia Righi, Manuel Schlund, Bouwe Andela, Enrico Arnone, Omar Bellprat, Björn Brötz, Louis-Philippe Caron, Nuno Carvalhais, Irene Cionni, Nicola Cortesi, Bas Crezee, Edouard L. Davin, Paolo Davini, Kevin Debeire, Lee de Mora, Clara Deser, David Docquier, Paul Earnshaw, Carsten Ehbrecht, Bettina K. Gier, Nube Gonzalez-Reviriego, Paul Goodman, Stefan Hagemann, Steven Hardiman, Birgit Hassler, Alasdair Hunter, Christopher Kadow, Stephan Kindermann, Sujan Koirala, Nikolay Koldunov, Quentin Lejeune, Valerio Lembo, Tomas Lovato, Valerio Lucarini, François Massonnet, Benjamin Müller, Amarjiit Pandde, Núria Pérez-Zanón, Adam Phillips, Valeriu Predoi, Joellen Russell, Alistair Sellar, Federico Serva, Tobias Stacke, Ranjini Swaminathan, Verónica Torralba, Javier Vegas-Regidor, Jost von Hardenberg, Katja Weigel, and Klaus Zimmermann
Geosci. Model Dev., 13, 3383–3438, https://doi.org/10.5194/gmd-13-3383-2020, https://doi.org/10.5194/gmd-13-3383-2020, 2020
Short summary
Short summary
The Earth System Model Evaluation Tool (ESMValTool) is a community diagnostics and performance metrics tool designed to improve comprehensive and routine evaluation of earth system models (ESMs) participating in the Coupled Model Intercomparison Project (CMIP). It has undergone rapid development since the first release in 2016 and is now a well-tested tool that provides end-to-end provenance tracking to ensure reproducibility.
Valerio Lembo, Frank Lunkeit, and Valerio Lucarini
Geosci. Model Dev., 12, 3805–3834, https://doi.org/10.5194/gmd-12-3805-2019, https://doi.org/10.5194/gmd-12-3805-2019, 2019
Short summary
Short summary
The Thermodynamic Diagnostic Tool (TheDiaTo v1.0) is a collection of diagnostics for the study of the thermodynamics of the climate system in climate models. This is fundamental in order to understand where the imbalances affecting climate projections come from and also to allow for easy comparison of different scenarios and atmospheric regimes. The tool is currently being developed for the assessment of models that are part of the next phase of the Coupled Model Intercomparison Project (CMIP).
Mallory Carlu, Francesco Ginelli, Valerio Lucarini, and Antonio Politi
Nonlin. Processes Geophys., 26, 73–89, https://doi.org/10.5194/npg-26-73-2019, https://doi.org/10.5194/npg-26-73-2019, 2019
Short summary
Short summary
We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96, to unravel key mechanisms of interaction between scales of different resolutions and time scales. To do so, we use a mathematical machinery known as Lyapunov analysis, allowing us to capture the degrees of chaoticity associated with fundamental directions of instability. We find a non-trivial group of such directions projecting significantly on slow variables, associated with long term dynamics.
Gabriele Vissio and Valerio Lucarini
Nonlin. Processes Geophys., 25, 413–427, https://doi.org/10.5194/npg-25-413-2018, https://doi.org/10.5194/npg-25-413-2018, 2018
Short summary
Short summary
Constructing good parametrizations is key when studying multi-scale systems. We consider a low-order model and derive a parametrization via a recently developed statistical mechanical approach. We show how the method allows for seamlessly treating the case when the unresolved dynamics is both faster and slower than the resolved one. We test the skill of the parametrization by using the formalism of the Wasserstein distance, which allows for measuring how different two probability measures are.
Lesley De Cruz, Sebastian Schubert, Jonathan Demaeyer, Valerio Lucarini, and Stéphane Vannitsem
Nonlin. Processes Geophys., 25, 387–412, https://doi.org/10.5194/npg-25-387-2018, https://doi.org/10.5194/npg-25-387-2018, 2018
Short summary
Short summary
The predictability of weather models is limited largely by the initial state error growth or decay rates. We have computed these rates for PUMA, a global model for the atmosphere, and MAOOAM, a more simplified, coupled model which includes the ocean. MAOOAM has processes at distinct timescales, whereas PUMA surprisingly does not. We propose a new programme to compute the natural directions along the flow that correspond to the growth or decay rates, to learn which components play a role.
Tamás Bódai, Valerio Lucarini, and Frank Lunkeit
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2018-30, https://doi.org/10.5194/esd-2018-30, 2018
Revised manuscript not accepted
Short summary
Short summary
We establish a framework to conduct a scenario analysis of the best possible outcomes under geoengineering. The scenarios may consist of scenarios of greenhouse gas emission the choice of the quantity that we want to keep under control. The motivation is the desire of an efficient way of assessing the side-effects of geoengineering, concerning the unwanted and uncontrolled changes. Countering CO2 emission by modulating insolation, we find considerable changes in local temperatures or rainfall.
S. Hasson, V. Lucarini, M. R. Khan, M. Petitta, T. Bolch, and G. Gioli
Hydrol. Earth Syst. Sci., 18, 4077–4100, https://doi.org/10.5194/hess-18-4077-2014, https://doi.org/10.5194/hess-18-4077-2014, 2014
S. Hasson, V. Lucarini, S. Pascale, and J. Böhner
Earth Syst. Dynam., 5, 67–87, https://doi.org/10.5194/esd-5-67-2014, https://doi.org/10.5194/esd-5-67-2014, 2014
R. Deidda, M. Marrocu, G. Caroletti, G. Pusceddu, A. Langousis, V. Lucarini, M. Puliga, and A. Speranza
Hydrol. Earth Syst. Sci., 17, 5041–5059, https://doi.org/10.5194/hess-17-5041-2013, https://doi.org/10.5194/hess-17-5041-2013, 2013
S. Hasson, V. Lucarini, and S. Pascale
Earth Syst. Dynam., 4, 199–217, https://doi.org/10.5194/esd-4-199-2013, https://doi.org/10.5194/esd-4-199-2013, 2013
Related subject area
Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Simulation
Empirical adaptive wavelet decomposition (EAWD): an adaptive decomposition for the variability analysis of observation time series in atmospheric science
Direct Bayesian model reduction of smaller scale convective activity conditioned on large-scale dynamics
Improvements to the use of the Trajectory-Adaptive Multilevel Sampling algorithm for the study of rare events
Simulation-based comparison of multivariate ensemble post-processing methods
A prototype stochastic parameterization of regime behaviour in the stably stratified atmospheric boundary layer
Olivier Delage, Thierry Portafaix, Hassan Bencherif, Alain Bourdier, and Emma Lagracie
Nonlin. Processes Geophys., 29, 265–277, https://doi.org/10.5194/npg-29-265-2022, https://doi.org/10.5194/npg-29-265-2022, 2022
Short summary
Short summary
The complexity of geophysics systems results in time series with fluctuations at all timescales. The analysis of their variability then consists in decomposing them into a set of basis signals. We developed here a new adaptive filtering method called empirical adaptive wavelet decomposition that optimizes the empirical-mode decomposition existing technique, overcoming its drawbacks using the rigour of wavelets as defined in the recently published empirical wavelet transform method.
Robert Polzin, Annette Müller, Henning Rust, Peter Névir, and Péter Koltai
Nonlin. Processes Geophys., 29, 37–52, https://doi.org/10.5194/npg-29-37-2022, https://doi.org/10.5194/npg-29-37-2022, 2022
Short summary
Short summary
In this study, a recent algorithmic framework called Direct Bayesian Model Reduction (DBMR) is applied which provides a scalable probability-preserving identification of reduced models directly from data. The stochastic method is tested in a meteorological application towards a model reduction to latent states of smaller scale convective activity conditioned on large-scale atmospheric flow.
Pascal Wang, Daniele Castellana, and Henk A. Dijkstra
Nonlin. Processes Geophys., 28, 135–151, https://doi.org/10.5194/npg-28-135-2021, https://doi.org/10.5194/npg-28-135-2021, 2021
Short summary
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This paper proposes two improvements to the use of Trajectory-Adaptive Multilevel Sampling, a rare-event algorithm which computes noise-induced transition probabilities. The first improvement uses locally linearised dynamics in order to reduce the arbitrariness associated with defining what constitutes a transition. The second improvement uses empirical transition paths accumulated at high noise in order to formulate the score function which determines the performance of the algorithm.
Sebastian Lerch, Sándor Baran, Annette Möller, Jürgen Groß, Roman Schefzik, Stephan Hemri, and Maximiliane Graeter
Nonlin. Processes Geophys., 27, 349–371, https://doi.org/10.5194/npg-27-349-2020, https://doi.org/10.5194/npg-27-349-2020, 2020
Short summary
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Accurate models of spatial, temporal, and inter-variable dependencies are of crucial importance for many practical applications. We review and compare several methods for multivariate ensemble post-processing, where such dependencies are imposed via copula functions. Our investigations utilize simulation studies that mimic challenges occurring in practical applications and allow ready interpretation of the effects of different misspecifications of the numerical weather prediction ensemble.
Carsten Abraham, Amber M. Holdsworth, and Adam H. Monahan
Nonlin. Processes Geophys., 26, 401–427, https://doi.org/10.5194/npg-26-401-2019, https://doi.org/10.5194/npg-26-401-2019, 2019
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Atmospheric stably stratified boundary layers display transitions between regimes of sustained and intermittent turbulence. These transitions are not well represented in numerical weather prediction and climate models. A prototype explicitly stochastic turbulence parameterization simulating regime dynamics is presented and tested in an idealized model. Results demonstrate that the approach can improve the regime representation in models.
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Short summary
In most of the investigations on metastable systems, the stochastic forcing is modulated by Gaussian noise. Lévy noise laws, which describe jump processes, have recently received a lot of attention, but much less is known. We study stochastic versions of the Ghil–Sellers energy balance model, and we highlight the fundamental difference between how transitions are performed between the competing warm and snowball states, depending on whether Gaussian or Lévy noise acts as forcing.
In most of the investigations on metastable systems, the stochastic forcing is modulated by...