Articles | Volume 26, issue 2
https://doi.org/10.5194/npg-26-73-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-26-73-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
07 May 2019
Research article |
| 07 May 2019
| 07 May 2019
Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model
Mallory Carlu
CORRESPONDING AUTHOR
SUPA, Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, UK
Francesco Ginelli
SUPA, Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, UK
Valerio Lucarini
Department of Mathematics and Statistics, University of Reading, Reading, UK
Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
CEN, University of Hamburg, Hamburg, Germany
Antonio Politi
SUPA, Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, UK
Related authors
No articles found.
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
Short summary
Short summary
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
Short summary
Short summary
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.
Valerio Lucarini, Larissa Serdukova, and Georgios Margazoglou
Nonlin. Processes Geophys., 29, 183–205, https://doi.org/10.5194/npg-29-183-2022, https://doi.org/10.5194/npg-29-183-2022, 2022
Short summary
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.
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
Short summary
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).
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: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
Dynamically optimal models of atmospheric motion
A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations
Energy transfer from internal solitary waves to turbulence via high-frequency internal waves: seismic observations in the northern South China Sea
The role of time-varying external factors in the intensification of tropical cyclones
Solving a North-type energy balance model using boundary integral methods
Transformation of internal solitary waves at the edge of ice cover
Review article: Interdisciplinary perspectives on climate sciences – highlighting past and current scientific achievements
Variational techniques for a one-dimensional energy balance model
A new approach to understanding fluid mixing in process-study models of stratified fluids
Sensitivity of the polar boundary layer to transient phenomena
Aggregation of slightly buoyant microplastics in 3D vortex flows
Existence and influence of mixed states in a model of vegetation patterns
Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
Review article: Dynamical systems, algebraic topology and the climate sciences
An approach for projecting the timing of abrupt winter Arctic sea ice loss
An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling
Review article: Large fluctuations in non-equilibrium physics
On the interaction of stochastic forcing and regime dynamics
Applying dynamical systems techniques to real ocean drifters
Observations of shoaling internal wave transformation over a gentle slope in the South China Sea
Climate bifurcations in a Schwarzschild equation model of the Arctic atmosphere
Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation
Estimate of energy loss from internal solitary waves breaking on slopes
Regional study of mode-2 internal solitary waves at the Pacific coast of Central America using marine seismic survey data
The effect of strong shear on internal solitary-like waves
Enhanced diapycnal mixing with polarity-reversing internal solitary waves revealed by seismic reflection data
Enhanced internal tidal mixing in the Philippine Sea mesoscale environment
Detecting flow features in scarce trajectory data using networks derived from symbolic itineraries: an application to surface drifters in the North Atlantic
Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later
Anthropocene climate bifurcation
Effects of upwelling duration and phytoplankton growth regime on dissolved-oxygen levels in an idealized Iberian Peninsula upwelling system
Baroclinic and barotropic instabilities in planetary atmospheres: energetics, equilibration and adjustment
Numerical bifurcation methods applied to climate models: analysis beyond simulation
Competition between chaotic advection and diffusion: stirring and mixing in a 3-D eddy model
Climatic responses to systematic time variations of parameters: a dynamical approach
Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance
Wave propagation in the Lorenz-96 model
Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years
On the CCN (de)activation nonlinearities
Detecting changes in forced climate attractors with Wasserstein distance
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
Subvisible cirrus clouds – a dynamical system approach
Influence of finite-time Lyapunov exponents on winter precipitation over the Iberian Peninsula
Dynamics of the Hadley circulation in an axisymmetric model undergoing stratification periodic forcing
Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity
Oscillations in a simple climate–vegetation model
A novel method for analyzing the process of abrupt climate change
Equilibrium temperature distribution and Hadley circulation in an axisymmetric model
Alexander G. Voronovich
Nonlin. Processes Geophys., 31, 559–569, https://doi.org/10.5194/npg-31-559-2024, https://doi.org/10.5194/npg-31-559-2024, 2024
Short summary
Short summary
A derivation of discrete dynamical equations for the dry atmosphere without dissipative processes based on the least action principle is presented. For a given set of generally irregularly spaced grid points and a given mode of interpolation, through the minimization of action, the algorithm ensures maximal closeness of the evolution of the discrete system to the motion of the continuous atmosphere. The spatial resolution can be adjusted while executing calculations.
Pierre Lloret, Peter J. Diamessis, Marek Stastna, and Greg N. Thomsen
Nonlin. Processes Geophys., 31, 515–533, https://doi.org/10.5194/npg-31-515-2024, https://doi.org/10.5194/npg-31-515-2024, 2024
Short summary
Short summary
This study presents a new approach to simulating large ocean density waves that travel long distances without breaking down. This new approach ensures that these waves are depicted more accurately and realistically in our models. This is particularly useful for understanding wave behavior in lakes with distinct water layers, which can help predict natural phenomena and their effects on environments like swash zones, where waves meet the shore.
Linghan Meng, Haibin Song, Yongxian Guan, Shun Yang, Kun Zhang, and Mengli Liu
Nonlin. Processes Geophys., 31, 477–495, https://doi.org/10.5194/npg-31-477-2024, https://doi.org/10.5194/npg-31-477-2024, 2024
Short summary
Short summary
With seismic data, we observed high-frequency internal waves (HIWs) with amplitudes of around 10 m. A shoaling thermocline and gentle slope suggest that HIWs result from fission. Remote sensing data support this. Strong shear caused Ri below 0.25 over 20–30 km, indicating instability. HIWs enhance mixing, averaging 10-4 m2s-1, revealing a new energy cascade from shoaling waves to turbulence, and enhancing our understanding of energy dissipation and mixing in the northern South China Sea.
Samuel Watson and Courtney Quinn
Nonlin. Processes Geophys., 31, 381–394, https://doi.org/10.5194/npg-31-381-2024, https://doi.org/10.5194/npg-31-381-2024, 2024
Short summary
Short summary
The intensification of tropical cyclones (TCs) is explored through a conceptual model derived from geophysical principals. Focus is put on the behaviour of the model with parameters which change in time. The rates of change cause the model to either tip to an alternative stable state or recover the original state. This represents intensification, dissipation, or eyewall replacement cycles (ERCs). A case study which emulates the rapid intensification events of Hurricane Irma (2017) is explored.
Aksel Samuelsberg and Per Kristen Jakobsen
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-11, https://doi.org/10.5194/npg-2024-11, 2024
Revised manuscript accepted for NPG
Short summary
Short summary
We explored a simplified climate model based on Earth's energy budget. One advantage of such models is that they are easier to study mathematically. Using a mathematical technique known as boundary integral methods, we have found a new way to solve these climate models. This method is particularly useful for modeling climates very different from Earth's current state, such as those on other planets or during past ice ages.
Kateryna Terletska, Vladimir Maderich, and Elena Tobisch
Nonlin. Processes Geophys., 31, 207–217, https://doi.org/10.5194/npg-31-207-2024, https://doi.org/10.5194/npg-31-207-2024, 2024
Short summary
Short summary
The transformation of internal waves at the edge of ice cover can enhance the turbulent mixing and melting of ice in the Arctic Ocean and Antarctica. We studied numerically the transformation of internal solitary waves of depression under smooth ice surfaces compared with the processes beneath the ridged underside of the ice. For large keels, more than 40% of wave energy is lost on the first keel, while for relatively small keels energy losses on the first keel are less than 6%.
Vera Melinda Galfi, Tommaso Alberti, Lesley De Cruz, Christian L. E. Franzke, and Valerio Lembo
Nonlin. Processes Geophys., 31, 185–193, https://doi.org/10.5194/npg-31-185-2024, https://doi.org/10.5194/npg-31-185-2024, 2024
Short summary
Short summary
In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.
Gianmarco Del Sarto, Jochen Bröcker, Franco Flandoli, and Tobias Kuna
Nonlin. Processes Geophys., 31, 137–150, https://doi.org/10.5194/npg-31-137-2024, https://doi.org/10.5194/npg-31-137-2024, 2024
Short summary
Short summary
We consider a one-dimensional model for the Earth's temperature. We give sufficient conditions to admit three asymptotic solutions. We connect the value function (minimum value of an objective function depending on the greenhouse gas (GHG) concentration) to the global mean temperature. Then, we show that the global mean temperature is the derivative of the value function and that it is non-decreasing with respect to GHG concentration.
Samuel George Hartharn-Evans, Marek Stastna, and Magda Carr
Nonlin. Processes Geophys., 31, 61–74, https://doi.org/10.5194/npg-31-61-2024, https://doi.org/10.5194/npg-31-61-2024, 2024
Short summary
Short summary
Across much of the ocean, and the world's lakes, less dense water (either because it is warm or fresh) overlays denser water, forming stratification. The mixing of these layers affects the distribution of heat, nutrients, plankton, sediment, and buoyancy, so it is crucial to understand. We use small-scale numerical experiments to better understand these processes, and here we propose a new analysis tool for understanding mixing within those models, looking at where two variables intersect.
Amandine Kaiser, Nikki Vercauteren, and Sebastian Krumscheid
Nonlin. Processes Geophys., 31, 45–60, https://doi.org/10.5194/npg-31-45-2024, https://doi.org/10.5194/npg-31-45-2024, 2024
Short summary
Short summary
Current numerical weather prediction models encounter challenges in accurately representing regimes in the stably stratified atmospheric boundary layer (SBL) and the transitions between them. Stochastic modeling approaches are a promising framework to analyze when transient small-scale phenomena can trigger regime transitions. Therefore, we conducted a sensitivity analysis of the SBL to transient phenomena by augmenting a surface energy balance model with meaningful randomizations.
Irina I. Rypina, Lawrence J. Pratt, and Michael Dotzel
Nonlin. Processes Geophys., 31, 25–44, https://doi.org/10.5194/npg-31-25-2024, https://doi.org/10.5194/npg-31-25-2024, 2024
Short summary
Short summary
This paper investigates the aggregation of small, spherical, slightly buoyant, rigid particles in a simple 3D vortex flow. Our goal was to gain insights into the behaviour of slightly buoyant marine microplastics in a flow that qualitatively resembles ocean eddies. Attractors are mapped out for the steady, axisymmetric; steady, asymmetric; and nonsteady, asymmetric vortices over a range of flow and particle parameters. Simple theoretical arguments are used to interpret the results.
Lilian Vanderveken, Marina Martínez Montero, and Michel Crucifix
Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, https://doi.org/10.5194/npg-30-585-2023, 2023
Short summary
Short summary
In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation patterns develop and effectively allow for vegetation to persist under low water input. The formation of patterns and the transition between patterns can be studied with small models taking the form of dynamical systems. Our study produces a full map of stable and unstable solutions in a canonical vegetation model and shows how they determine the transitions between different patterns.
Ulrike Feudel
Nonlin. Processes Geophys., 30, 481–502, https://doi.org/10.5194/npg-30-481-2023, https://doi.org/10.5194/npg-30-481-2023, 2023
Short summary
Short summary
Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science, ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing and predicting them.
Michael Ghil and Denisse Sciamarella
Nonlin. Processes Geophys., 30, 399–434, https://doi.org/10.5194/npg-30-399-2023, https://doi.org/10.5194/npg-30-399-2023, 2023
Short summary
Short summary
The problem of climate change is that of a chaotic system subject to time-dependent forcing, such as anthropogenic greenhouse gases and natural volcanism. To solve this problem, we describe the mathematics of dynamical systems with explicit time dependence and those of studying their behavior through topological methods. Here, we show how they are being applied to climate change and its predictability.
Camille Hankel and Eli Tziperman
Nonlin. Processes Geophys., 30, 299–309, https://doi.org/10.5194/npg-30-299-2023, https://doi.org/10.5194/npg-30-299-2023, 2023
Short summary
Short summary
We present a novel, efficient method for identifying climate
tipping pointthreshold values of CO2 beyond which rapid and irreversible changes occur. We use a simple model of Arctic sea ice to demonstrate the method’s efficacy and its potential for use in state-of-the-art global climate models that are too expensive to run for this purpose using current methods. The ability to detect tipping points will improve our preparedness for rapid changes that may occur under future climate change.
Bin Shi and Guodong Sun
Nonlin. Processes Geophys., 30, 263–276, https://doi.org/10.5194/npg-30-263-2023, https://doi.org/10.5194/npg-30-263-2023, 2023
Short summary
Short summary
We introduce a sample-based algorithm to obtain the conditional nonlinear optimal perturbations. Compared with the classical adjoint-based method, it is easier to implement and reduces the required storage for the basic state. When we reduce the number of samples to some extent, it reduces the computation markedly more when using the sample-based method, which can guarantee that the CNOP obtained is nearly consistent with some minor fluctuating errors oscillating in spatial distribution.
Giovanni Jona-Lasinio
Nonlin. Processes Geophys., 30, 253–262, https://doi.org/10.5194/npg-30-253-2023, https://doi.org/10.5194/npg-30-253-2023, 2023
Short summary
Short summary
Non-equilibrium is dominant in geophysical and climate phenomena. Most of the processes that characterize energy flow occur far from equilibrium. These range from very large systems, such as weather patterns or ocean currents that remain far from equilibrium, owing to an influx of energy, to biological structures. In the last decades, progress in non-equilibrium physics has come from the study of very rare fluctuations, and this paper provides an introduction to these theoretical developments.
Joshua Dorrington and Tim Palmer
Nonlin. Processes Geophys., 30, 49–62, https://doi.org/10.5194/npg-30-49-2023, https://doi.org/10.5194/npg-30-49-2023, 2023
Short summary
Short summary
Atmospheric models often include random forcings, which aim to replicate the impact of processes too small to be resolved. Recent results in simple atmospheric models suggest that this random forcing can actually stabilise certain slow-varying aspects of the system, which could provide a path for resolving known errors in our models. We use randomly forced simulations of a
toychaotic system and theoretical arguments to explain why this strange effect occurs – at least in simple models.
Irina I. Rypina, Timothy Getscher, Lawrence J. Pratt, and Tamay Ozgokmen
Nonlin. Processes Geophys., 29, 345–361, https://doi.org/10.5194/npg-29-345-2022, https://doi.org/10.5194/npg-29-345-2022, 2022
Short summary
Short summary
Techniques from dynamical systems theory have been widely used to study transport in ocean flows. However, they have been typically applied to numerically simulated trajectories of water parcels. This paper applies different dynamical systems techniques to real ocean drifter trajectories from the massive release in the Gulf of Mexico. To our knowledge, this is the first comprehensive comparison of the performance of different dynamical systems techniques with application to real drifters.
Steven R. Ramp, Yiing Jang Yang, Ching-Sang Chiu, D. Benjamin Reeder, and Frederick L. Bahr
Nonlin. Processes Geophys., 29, 279–299, https://doi.org/10.5194/npg-29-279-2022, https://doi.org/10.5194/npg-29-279-2022, 2022
Short summary
Short summary
Earlier work in the vicinity of the shelf and slope in the northeastern South China Sea serendipitously revealed the presence of large, stunning bed forms (sand dunes) whose height (>15 m) and length (>350 m) are quite unique and unusual. We hypothesize that the dunes formed due to shoaling very large-amplitude nonlinear internal waves that scour the bottom and resuspend and redistribute the sediments. As a first step, the wave characteristics are observed and described in detail.
Kolja L. Kypke, William F. Langford, Gregory M. Lewis, and Allan R. Willms
Nonlin. Processes Geophys., 29, 219–239, https://doi.org/10.5194/npg-29-219-2022, https://doi.org/10.5194/npg-29-219-2022, 2022
Short summary
Short summary
Climate change is causing rapid temperature increases in the polar regions. A fundamental question is whether these temperature increases are reversible. If we control carbon dioxide emissions, will the temperatures revert or will we have passed a tipping point beyond which return to the present state is impossible? Our mathematical model of the Arctic climate indicates that under present emissions the Arctic climate will change irreversibly to a warm climate before the end of the century.
Karl R. Helfrich and Lev Ostrovsky
Nonlin. Processes Geophys., 29, 207–218, https://doi.org/10.5194/npg-29-207-2022, https://doi.org/10.5194/npg-29-207-2022, 2022
Short summary
Short summary
Internal solitons are an important class of nonlinear waves commonly observed in coastal oceans. Their propagation is affected by the Earth's rotation and the variation in the water depth. We consider an interplay of these factors using the corresponding extension of the Gardner equation. This model allows a limiting soliton amplitude and the corresponding increase in wavelength, making the effects of rotation and topography on a shoaling wave especially significant.
Kateryna Terletska and Vladimir Maderich
Nonlin. Processes Geophys., 29, 161–170, https://doi.org/10.5194/npg-29-161-2022, https://doi.org/10.5194/npg-29-161-2022, 2022
Short summary
Short summary
Internal solitary waves (ISWs) emerge in the ocean and seas in various forms and break on the shelf zones in a variety of ways. This results in intensive mixing that affects processes such as biological productivity and sediment transport. Mechanisms of wave interaction with slopes are related to breaking and changing polarity. Our study focuses on wave transformation over idealized shelf-slope topography using a two-layer stratification. Four types of ISW transformation over slopes are shown.
Wenhao Fan, Haibin Song, Yi Gong, Shun Yang, and Kun Zhang
Nonlin. Processes Geophys., 29, 141–160, https://doi.org/10.5194/npg-29-141-2022, https://doi.org/10.5194/npg-29-141-2022, 2022
Short summary
Short summary
Compared with mode-1 internal solitary waves (ISWs), mode-2 ISWs in the ocean require further study. A mass of mode-2 ISWs developing at the Pacific coast of Central America have been imaged using seismic reflection data. We find that the relationship between the mode-2 ISW propagation speed and amplitude is diverse. It is affected by seawater depth, pycnocline depth, and pycnocline thickness. The ISW vertical amplitude structure is affected by the ISW nonlinearity and the pycnocline deviation.
Marek Stastna, Aaron Coutino, and Ryan K. Walter
Nonlin. Processes Geophys., 28, 585–598, https://doi.org/10.5194/npg-28-585-2021, https://doi.org/10.5194/npg-28-585-2021, 2021
Short summary
Short summary
Large-amplitude waves in the interior of the ocean-internal waves in the ocean propagate in a dynamic, highly variable environment with changes in background current, local depth, and stratification. These waves have a well-known mathematical theory that, despite considerable progress, has some gaps. In particular, waves have been observed in situations that preclude an application of the mathematical theory. We present numerical simulations of the spontaneous generation of such waves.
Yi Gong, Haibin Song, Zhongxiang Zhao, Yongxian Guan, Kun Zhang, Yunyan Kuang, and Wenhao Fan
Nonlin. Processes Geophys., 28, 445–465, https://doi.org/10.5194/npg-28-445-2021, https://doi.org/10.5194/npg-28-445-2021, 2021
Short summary
Short summary
When the internal solitary wave propagates to the continental shelf and slope, the polarity reverses due to the shallower water depth. In this process, the internal solitary wave dissipates energy and enhances diapycnal mixing, thus affecting the local oceanic environment. In this study, we used reflection seismic data to evaluate the spatial distribution of the diapycnal mixing around the polarity-reversing internal solitary waves.
Jia You, Zhenhua Xu, Qun Li, Robin Robertson, Peiwen Zhang, and Baoshu Yin
Nonlin. Processes Geophys., 28, 271–284, https://doi.org/10.5194/npg-28-271-2021, https://doi.org/10.5194/npg-28-271-2021, 2021
Short summary
Short summary
Turbulent mixing in the ocean is mainly attributed to internal wave breaking, but the modulation of the mesoscale environment is unclear. The spatially inhomogeneous and seasonally variable diapycnal diffusivities in the upper Philippine Sea were estimated from Argo float data using a strain-based, fine-scale parameterization. Internal tides contributed significant diapycnal mixing here, with the mesoscale environment greatly regulating the intensity and spatial inhomogeneity of tidal mixing.
David Wichmann, Christian Kehl, Henk A. Dijkstra, and Erik van Sebille
Nonlin. Processes Geophys., 27, 501–518, https://doi.org/10.5194/npg-27-501-2020, https://doi.org/10.5194/npg-27-501-2020, 2020
Short summary
Short summary
The surface transport of heat, nutrients and plastic in the North Atlantic Ocean is organized into large-scale flow structures. We propose a new and simple method to detect such features in ocean drifter data sets by identifying groups of trajectories with similar dynamical behaviour using network theory. We successfully detect well-known regions such as the Subpolar and Subtropical gyres, the Western Boundary Current region and the Caribbean Sea.
Michael Ghil
Nonlin. Processes Geophys., 27, 429–451, https://doi.org/10.5194/npg-27-429-2020, https://doi.org/10.5194/npg-27-429-2020, 2020
Short summary
Short summary
The scientific questions posed by the climate sciences are central to socioeconomic concerns today. This paper revisits several crucial questions, starting with
What can we predict beyond 1 week, for how long, and by what methods?, and ending with
Can we achieve enlightened climate control of our planet by the end of the century?We review the progress in dealing with the nonlinearity and stochasticity of the Earth system and emphasize major strides in coupled climate–economy modeling.
Kolja Leon Kypke, William Finlay Langford, and Allan Richard Willms
Nonlin. Processes Geophys., 27, 391–409, https://doi.org/10.5194/npg-27-391-2020, https://doi.org/10.5194/npg-27-391-2020, 2020
Short summary
Short summary
The climate of Earth is governed by nonlinear processes of geophysics. This paper presents energy balance models (EBMs) embracing these nonlinear processes which lead to positive feedback, amplifying the effects of anthropogenic forcing and leading to bifurcations. We define bifurcation as a change in the topological equivalence class of the system. We initiate a bifurcation analysis of EBMs of Anthropocene climate, which shows that a catastrophic climate change may occur in the next century.
João H. Bettencourt, Vincent Rossi, Lionel Renault, Peter Haynes, Yves Morel, and Véronique Garçon
Nonlin. Processes Geophys., 27, 277–294, https://doi.org/10.5194/npg-27-277-2020, https://doi.org/10.5194/npg-27-277-2020, 2020
Short summary
Short summary
The oceans are losing oxygen, and future changes may worsen this problem. We performed computer simulations of an idealized Iberian Peninsula upwelling system to identify the main fine-scale processes driving dissolved oxygen variability as well as study the response of oxygen levels to changes in wind patterns and phytoplankton species. Our results suggest that oxygen levels would decrease if the wind blows for long periods of time or if phytoplankton is dominated by species that grow slowly.
Peter Read, Daniel Kennedy, Neil Lewis, Hélène Scolan, Fachreddin Tabataba-Vakili, Yixiong Wang, Susie Wright, and Roland Young
Nonlin. Processes Geophys., 27, 147–173, https://doi.org/10.5194/npg-27-147-2020, https://doi.org/10.5194/npg-27-147-2020, 2020
Short summary
Short summary
Baroclinic and barotropic instabilities are well known as the processes responsible for the production of the most important energy-containing eddies in the atmospheres and oceans of Earth and other planets. Linear and nonlinear instability theories provide insights into when such instabilities may occur, grow to a large amplitude and saturate, with examples from the laboratory, simplified numerical models and planetary atmospheres. We conclude with a number of open issues for future research.
Henk A. Dijkstra
Nonlin. Processes Geophys., 26, 359–369, https://doi.org/10.5194/npg-26-359-2019, https://doi.org/10.5194/npg-26-359-2019, 2019
Short summary
Short summary
I provide a personal view on the role of bifurcation analysis of climate models in the development of a theory of variability in the climate system. By outlining the state of the art of the methodology and by discussing what has been done and what has been learned from a hierarchy of models, I will argue that there are low-order phenomena of climate variability, such as El Niño and the Atlantic Multidecadal Oscillation.
Genevieve Jay Brett, Larry Pratt, Irina Rypina, and Peng Wang
Nonlin. Processes Geophys., 26, 37–60, https://doi.org/10.5194/npg-26-37-2019, https://doi.org/10.5194/npg-26-37-2019, 2019
Short summary
Short summary
The relative importance of chaotic stirring and smaller-scale turbulent mixing for the distribution of dye in an idealized ocean flow feature is quantified using three different methods. We find that stirring is the dominant process in large areas with fast stirring, while mixing dominates in small fast-stirring regions and all slow-stirring regions. This quantification of process dominance can help oceanographers think about when to model stirring accurately, which can be costly.
Catherine Nicolis
Nonlin. Processes Geophys., 25, 649–658, https://doi.org/10.5194/npg-25-649-2018, https://doi.org/10.5194/npg-25-649-2018, 2018
Short summary
Short summary
Ordinarily the climatic impact of systematic variations of parameters arising from anthropogenic effects is addressed on the basis of large numerical models, where parameters are set to a prescribed level and the system is subsequently left to relax. We have revisited the problem from a nonlinear dynamics perspective in which the time variation of parameters is fully incorporated into the evolution laws. Some universal trends of the response have been identified.
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.
Dirk L. van Kekem and Alef E. Sterk
Nonlin. Processes Geophys., 25, 301–314, https://doi.org/10.5194/npg-25-301-2018, https://doi.org/10.5194/npg-25-301-2018, 2018
Short summary
Short summary
In this paper we investigate the spatiotemporal properties of waves in the Lorenz-96 model. In particular, we explain how these properties are related to the presence of Hopf and pitchfork bifurcations. We also explain bifurcation scenarios by which multiple stable waves can coexist for the same parameter values.
Davide Faranda, Gabriele Messori, M. Carmen Alvarez-Castro, and Pascal Yiou
Nonlin. Processes Geophys., 24, 713–725, https://doi.org/10.5194/npg-24-713-2017, https://doi.org/10.5194/npg-24-713-2017, 2017
Short summary
Short summary
We study the dynamical properties of the Northern Hemisphere atmospheric circulation by analysing the sea-level pressure, 2 m temperature, and precipitation frequency field over the period 1948–2013. The metrics are linked to the predictability and the persistence of the atmospheric flows. We study the dependence on the seasonal cycle and the fields corresponding to maxima and minima of the dynamical indicators.
Sylwester Arabas and Shin-ichiro Shima
Nonlin. Processes Geophys., 24, 535–542, https://doi.org/10.5194/npg-24-535-2017, https://doi.org/10.5194/npg-24-535-2017, 2017
Short summary
Short summary
The paper bridges cloud/aerosol modelling with bifurcation analysis. It identifies two nonlinear peculiarities in the differential equations describing formation of atmospheric clouds through vapour condensation on a population of aerosol particles. A key finding of the paper is an analytic estimate for the timescale of the process. The study emerged from discussions on the causes of hysteretic behaviour of the system that we observed in the results of numerical simulations.
Yoann Robin, Pascal Yiou, and Philippe Naveau
Nonlin. Processes Geophys., 24, 393–405, https://doi.org/10.5194/npg-24-393-2017, https://doi.org/10.5194/npg-24-393-2017, 2017
Short summary
Short summary
If climate is viewed as a chaotic dynamical system, its trajectories yield on an object called an attractor. Being perturbed by an external forcing, this attractor could be modified. With Wasserstein distance, we estimate on a derived Lorenz model the impact of a forcing similar to climate change. Our approach appears to work with small data sizes. We have obtained a methodology quantifying the deformation of well-known attractors, coherent with the size of data available.
Jezabel Curbelo, Víctor José García-Garrido, Carlos Roberto Mechoso, Ana Maria Mancho, Stephen Wiggins, and Coumba Niang
Nonlin. Processes Geophys., 24, 379–392, https://doi.org/10.5194/npg-24-379-2017, https://doi.org/10.5194/npg-24-379-2017, 2017
Short summary
Short summary
Lagrangian coherent structures have supported the description of transport processes in fluid dynamics. In this work we use the M function to provide new insights into the 3-D Lagrangian structure of the southern stratosphere. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied to describe the vertical extension of the stratospheric polar vortex and its evolution.
Elisa Johanna Spreitzer, Manuel Patrik Marschalik, and Peter Spichtinger
Nonlin. Processes Geophys., 24, 307–328, https://doi.org/10.5194/npg-24-307-2017, https://doi.org/10.5194/npg-24-307-2017, 2017
Short summary
Short summary
We developed a simple analytical model for describing subvisible cirrus clouds qualitatively. Using theory of dynamical systems we found two different states for the long-term behaviour of subvisible cirrus clouds, i.e. an attractor case (stable equilibrium point) and a limit cycle scenario. The transition between the states constitutes a Hopf bifurcation and is determined by environmental conditions such as vertical updraughts and temperature.
Daniel Garaboa-Paz, Nieves Lorenzo, and Vicente Pérez-Muñuzuri
Nonlin. Processes Geophys., 24, 227–235, https://doi.org/10.5194/npg-24-227-2017, https://doi.org/10.5194/npg-24-227-2017, 2017
Short summary
Short summary
This paper evaluates the connection between winter precipitation over the Iberian Peninsula and the large-scale tropospheric mixing over the eastern Atlantic Ocean. Finite-time Lyapunov exponents (FTLEs) have been calculated from 1979 to 2008 to evaluate this mixing. Our study suggests that significant negative correlations exist between summer FTLE anomalies and winter precipitation over Portugal and Spain.
Nazario Tartaglione
Nonlin. Processes Geophys., 24, 167–178, https://doi.org/10.5194/npg-24-167-2017, https://doi.org/10.5194/npg-24-167-2017, 2017
Short summary
Short summary
This paper aims to show how the tropical circulation responds to changes of the vertical stratification of the imposed temperature that drives the model. These changes mimic the presence of water vapor cycles. Thus, for simplicity's sake we impose a periodic change of this stratification with variable periods of 10–90 days. The model responds with quasi-periodic oscillations having two or more dominant frequencies. After a long forcing time period, chaotic behavior starts to appear cyclically.
Rahel Vortmeyer-Kley, Ulf Gräwe, and Ulrike Feudel
Nonlin. Processes Geophys., 23, 159–173, https://doi.org/10.5194/npg-23-159-2016, https://doi.org/10.5194/npg-23-159-2016, 2016
Short summary
Short summary
Since eddies play a major role in the dynamics of oceanic flows, it is of great interest to gain information about their tracks, lifetimes and shapes. We develop an eddy tracking tool based on structures in the flow with collecting (attracting) or separating (repelling) properties. In test cases mimicking oceanic flows it yields eddy lifetimes close to the analytical ones. It even provides a detailed view of the dynamics that can be useful to gain more insight into eddy dynamics in oceanic flows.
J. Rombouts and M. Ghil
Nonlin. Processes Geophys., 22, 275–288, https://doi.org/10.5194/npg-22-275-2015, https://doi.org/10.5194/npg-22-275-2015, 2015
Short summary
Short summary
Our conceptual model describes global temperature and vegetation extent. We use elements from Daisyworld and classical energy balance models and add an ocean with sea ice. The model exhibits oscillatory behavior within a plausible range of parameter values.
Its periodic solutions have sawtooth behavior that is characteristic of relaxation oscillations, as well as suggestive of Quaternary glaciation cycles. The model is one of the simplest of its kind to produce such oscillatory behavior.
P. C. Yan, G. L. Feng, and W. Hou
Nonlin. Processes Geophys., 22, 249–258, https://doi.org/10.5194/npg-22-249-2015, https://doi.org/10.5194/npg-22-249-2015, 2015
Short summary
Short summary
A novel method is created to detect the process of the abrupt change, which has not been mentioned yet in traditional research. By building an ideal time series with a transition process, the results show that the process could be detected clearly. When applied to a climate index, this method detects five processes, and all of them have reappeared via the “start-end states” phase diagram. Additionally, it is detectable that the persist time of the process is related to global warming.
N. Tartaglione
Nonlin. Processes Geophys., 22, 173–185, https://doi.org/10.5194/npg-22-173-2015, https://doi.org/10.5194/npg-22-173-2015, 2015
Short summary
Short summary
At the Equator, where the heating is larger than that at other latitudes, air rises and diverges poleward in the upper troposphere, descending more or less at 30° latitude; this circulation is the Hadley cell.
We studied the impact of different meridional and vertical temperature distributions on a few features of the Hadley cell. Some parameters show a regular dependence on these distributions; others remain rather stable with distributions, but when they change, they do it in an abrupt way.
Cited articles
Abramov, R. V. and Majda, A.: New approximations and tests of linear
fluctuation-response for chaotic nonlinear forced-dissipative dynamical
systems, J. Nonlinear Sci., 18, 303–341, https://doi.org/10.1007/s00332-007-9011-9,
2007. a
Aurell, E., Boffetta, G., Crisanti, A., Paladin, G., and Vulpiani, A.:
Predictability in the large: an extension of the concept of Lyapunov
exponent, J. Phys. A, 30 1, https://doi.org/10.1088/0305-4470/30/1/003, 1997. a, b
Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J. M.: Lyapunov
characteristic exponents for smooth dynamical systems and for Hamiltonian
systems; a method for computing all of them. Part 1: Theory, Meccanica, 15,
https://doi.org/10.1007/BF02128236, 1980. a
Berner, J., et al.: Stochastic
parametrization: Toward a new view of weather and climate models, B. Am.
Meteorol. Soc., 98, 565, https://doi.org/10.1175/BAMS-D-15-00268.1, 2017. a
Blender, R., Lucarini, V., and Wouters, J.: Avalanches, breathers, and flow
reversal in a continuous Lorenz-96 model, Phys. Rev. E, 88, 013201,
https://doi.org/10.1103/PhysRevE.88.013201, 2013. a
Bochi, J. and Viana, M.: The Lyapunov exponents of generic volume-preserving
and symplectic maps, Ann. Math., 161, 1423–1485, 2005. a
Boffetta, G., Giuliani, P., Paladin, G., and Vulpiani, A. J.: An Extension of
the Lyapunov Analysis for the Predictability Problem, Atmos. Sci., 55, 3409,
https://doi.org/10.1175/1520-0469(1998)055<3409:AEOTLA>2.0.CO;2, 1998. a
Chekroun, M. D., Liu, H., and Wang, S.: Approximation of Stochastic Invariant
Manifolds, Springer, Cham, 2015a. a
Chekroun, M. D., Liu, H., and Wang S.: Stochastic Parametrizing Manifolds and
Non-Markovian Reduced Equations, Springer, Cham, 2015b. a
Daido, H.: Coupling sensitivity of chaos: a new universal property of chaotic
dynamical systems, Progr. Theoret. Phys. Suppl., 79, p. 75, 1984. a
De Cruz, L., Demaeyer, J., and Vannitsem, S.: The Modular Arbitrary-Order
Ocean-Atmosphere Model: MAOOAM v1.0, Geosci. Model Dev., 9, 2793–2808,
https://doi.org/10.5194/gmd-9-2793-2016, 2016. a
De Cruz, L., Schubert, S., Demaeyer, J., Lucarini, V., and Vannitsem, S.:
Exploring the Lyapunov instability properties of high-dimensional atmospheric
and climate models, Nonlin. Processes Geophys., 25, 387–412,
https://doi.org/10.5194/npg-25-387-2018, 2018. a
Eckmann, J.-P. and Ruelle, D.: Ergodic theory of chaos and strange
attractors, Rev. Mod. Phys., 57, 617, https://doi.org/10.1007/978-0-387-21830-4_17, 1985. a, b, c, d
Fraedrich, K., Kirk, E., Luksch, U., and Lunkeit, F.: The portable university
model of the atmosphere (PUMA): Storm track dynamics and low-frequency
variability, Meteorol. Z., 14, 735–745, 2005. a
Franzke, C., Berner J., Lucarini V., OKane, T. J., and Williams P. D.:
Stochastic climate theory and modeling, WIRES Clim. Change, 6, 6378,
https://doi.org/10.1002/wcc.318, 2015. a
Gallavotti, G. and Lucarini, V.: Equivalence of nonequilibrium ensembles and
representation of friction in turbulent flows: the Lorenz 96 model, J. Stat.
Phys., 156, 1027, https://doi.org/10.1007/s10955-014-1051-6, 2014. a, b
Ginelli, F., Poggi, P., Turchi, A., Chaté, H., Livi, R., and Politi, A.:
Characterizing Dynamics with Covariant Lyapunov Vectors, Phys. Rev. Lett.,
99, 130601, https://doi.org/10.1103/PhysRevLett.99.130601, 2007. a, b
Ginelli, F., Chaté, H., Livi, R., and Politi, A.: Covariant lyapunov
vectors, J. Phys. A, 46, 254005, https://doi.org/10.1088/1751-8113/46/25/254005, 2013. a, b, c
Grassberger, P.: Information content and predictability of lumped and
distributed dynamical systems, Phys. Scripta, 40, 346, https://doi.org/10.1088/0031-8949/40/3/016, 1989. a
Hallerberg, S., Lopez, J. M., Pazo, D., and Rodriguez, M. A.: Logarithmic
bred vectors in spatiotemporal chaos: Structure and growth. Phys. Rev. E, 81,
066204, https://doi.org/10.1103/PhysRevE.81.066204, 2010. a
Herrera, S., Fernández, J., Pazó, D., and Rodríguez, M. A.: The role of
large-scale spatial patterns in the chaotic amplification of perturbations in
a Lorenz'96 model, Tellus A, 63, 978–990, 2011. a
Karimi, A. and Paul, M. R.: Extensive chaos in the Lorenz-96 model, Chaos,
20, 043105, https://doi.org/10.1063/1.3496397, 2010. a
Kuptsov, P. V. and Parlitz, U. J.: Theory and computation of covariant
Lyapunov vectors, Nonlinear Sci., 22, 727, https://doi.org/10.1007/s00332-012-9126-5, 2012. a
Livi, R., Politi, A., and Ruffo, S.: Distribution of characteristic exponents
in the thermodynamic limit, J. Phys. A, 19, 2033, https://doi.org/10.1088/0305-4470/19/11/012, 1986. a
Lucarini, V. and Sarno, S.: A statistical mechanical approach for the
computation of the climatic response to general forcings, Nonlin. Processes
Geophys., 18, 7–28, https://doi.org/10.5194/npg-18-7-2011, 2011. a
Lucarini, V., Blender, R., Herbert, C., Pascale, S., Ragone, F., and Wouters,
J.: Mathematical and physical ideas for climate science, Rev. Geophys., 52,
809859, https://doi.org/10.1002/2013RG000446, 2014. a
Molteni, F.: Atmospheric simulations using a GCM with simplified physical
parametrizations. I. Model climatology and variability in multi-decadal
experiments, Clim. Dynam., 20, 175–191, 2003. a
Mori, H., Fujisaka, H., and Shigematsu, H.: A new expansion of the master
equation, Prog. Theor. Phys., 51, 109122, https://doi.org/10.1143/PTP.51.109, 1974. a
Norwood, A., Kalnay, E., Ide, K., Yang, S.-C., and Wolfe, C.:
Lyapunov, singular and bred vectors in a multiscale system: an empirical exploration of vectors related to instabilities, J. Phys. A, 46,
254021, https://doi.org/10.1088/1751-8113/46/25/254021, 2013. a
Orrell, D.: Model Error and predictability over Different Timescales in the
Lorenz96 System, J. Atmos. Sci., 60, 2219–2228, 2003. a
Palmer, T. N. and Williams, P. D.: Introduction. Stochastic physics and
climate modelling, Philos. T. R. Soc. A, 366, 2421–2427, 2008. a
Pavliotis, G. A. and Stuart, A. M.: Multiscale Methods: Averaging and
Homogenization, Springer, New York, 2008. a
Peixoto, J. and Oort, A.: Physics of Climate, American Institute of Physics,
New York, 1992. a
Pugh, C., Shub, M., and Starkov, A.: Stable ergodicity, B. Am. Math. Soc.,
41, https://doi.org/10.1090/S0273-0979-03-00998-4 , 2004. a
Ruelle, D.: Thermodynamic Formalism, Addison and Wesley, Reading, MA, 1978. a
Ruelle, D.: Ergodic theory of differentiable dynamical systems, Publ. Math.
IHES, 50, https://doi.org/10.1007/BF02684768, 1979. a
Shimada, I. and Nagashima, T.: A numerical approach to ergodic problem of
dissipative dynamical systems, Prog. Theor. Phys., 61, 1605,
https://doi.org/10.1143/PTP.61.1605, 1979. a
Takeuchi, K. A., Chaté, H., Ginelli, F., Radons, G., and Yang, H.-L.:
Hyperbolic decoupling of tangent space and effective dimension of dissipative
systems, Phys. Rev. E, 84, 046214, https://doi.org/10.1103/PhysRevE.84.046214, 2011. a
Vannitsem, S. and Lucarini, V.: Statistical and dynamical properties of
covariant lyapunov vectors in a coupled atmosphere-ocean model–multiscale
effects, geometric degeneracy, and error dynamics, J. Phys. A, 49, 224001,
https://doi.org/10.1088/1751-8113/49/22/224001, 2016. a
Vissio, G. and Lucarini, V.: A proof of concept for scale adaptive
parametrizations: the case of the Lorenz '96 model, Q. J. Roy. Meteor. Soc.,
144, https://doi.org/10.1002/qj.3184, 2017. a, b, c, d
Wilks, D. S.: Effects of stochastic parametrizations in the Lorenz '96
system, Q. J. Roy. Meteor. Soc., 131, 389–407, 2006. a
Wouters, J. and Lucarini, V.: Disentangling multi-level systems: Averaging,
correlations and memory, J. Stat. Mech.-Theory E., 2012, P03003,
https://doi.org/10.1088/1742-5468/2012/03/P03003, 2012. a
Wouters, J. and Lucarini, V.: Multi-level dynamical systems: Connecting the
Ruelle response theory and the MoriZwanzig approach, J. Stat. Phys., 151,
850–860, 2013. a
Wouters, J. and Gottwald, G. A.: Edgeworth expansions for slow-fast systems
with finite time scale separation, arXiv:1708.06984, https://doi.org/10.1098/rspa.2018.0358, 2017. a
Yang, H.-L., Ginelli, F., Chaté, H., Radons, G., and Takeuchi, K. A.:
Hyperbolicity and the effective dimension of spatially extended dissipative
systems, Phys. Rev. Lett., 102, 074102, https://doi.org/10.1103/PhysRevLett.102.074102, 2009. a
Zwanzig, R.: Ensemble method in the theory of irreversibility, J. Chem.
Phys., 33, 1338–1341, 1960. a
Zwanzig, R.: Memory effects in irreversible thermodynamics, Phys. Rev., 124,
https://doi.org/10.1103/PhysRev.124.983, 1961. a
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.
We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96,...
