Articles | Volume 24, issue 3
https://doi.org/10.5194/npg-24-307-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-24-307-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
30 Jun 2017
Research article |
| 30 Jun 2017
Subvisible cirrus clouds – a dynamical system approach
Elisa Johanna Spreitzer
Institute for Atmospheric Physics, Johannes Gutenberg
University Mainz, Mainz, Germany
now at: Institute for Atmospheric and Climate Science, ETH
Zurich, Zurich, Switzerland
Manuel Patrik Marschalik
Institute for Atmospheric Physics, Johannes Gutenberg
University Mainz, Mainz, Germany
now at: Fritz-Haber-Institut der Max-Planck-Gesellschaft,
Berlin, Germany
Institute for Atmospheric Physics, Johannes Gutenberg
University Mainz, Mainz, Germany
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Roman Attinger, Elisa Spreitzer, Maxi Boettcher, Heini Wernli, and Hanna Joos
Weather Clim. Dynam., 2, 1073–1091, https://doi.org/10.5194/wcd-2-1073-2021, https://doi.org/10.5194/wcd-2-1073-2021, 2021
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Diabatic processes affect the development of extratropical cyclones. This work provides a systematic assessment of the diabatic processes that modify potential vorticity (PV) in model simulations. PV is primarily produced by condensation and convection. Given favorable environmental conditions, long-wave radiative cooling and turbulence become the primary process at the cold and warm fronts, respectively. Turbulence and long-wave radiative heating produce negative PV anomalies at the fronts.
Gabriel Vollenweider, Elisa Spreitzer, and Sebastian Schemm
Weather Clim. Dynam. Discuss., https://doi.org/10.5194/wcd-2021-31, https://doi.org/10.5194/wcd-2021-31, 2021
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The interactions between the dry and moist components of the atmosphere and the influence of, for example, the phase transition of water on the atmospheric circulation are often studied from the potential vorticity (PV) framework. Changes in the PV due to, for example, condensation can relate to changes in the static stability or vorticity. To better the interaction between these two drivers of PV changes, we explore the usefulness of a novel vorticity-and-stability diagram.
Alena Kosareva, Stamen Dolaptchiev, Peter Spichtinger, and Ulrich Achatz
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-193, https://doi.org/10.5194/gmd-2024-193, 2024
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This study improves how we predict ice formation in clouds by accounting for variable ice sizes and different weather conditions. Using simulations, we developed a more accurate method that works efficiently, making it suitable for application in weather and climate prediction models. The new approach is numerically verified and provides precise predictions of ice formation events and reliable estimates of key parameters.
Daniel Köhler, Philipp Reutter, and Peter Spichtinger
Atmos. Chem. Phys., 24, 10055–10072, https://doi.org/10.5194/acp-24-10055-2024, https://doi.org/10.5194/acp-24-10055-2024, 2024
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In this work, the influence of humidity on the properties of the tropopause is studied. The tropopause is the interface between the troposphere and the stratosphere and represents a barrier for the transport of air masses between the troposphere and the stratosphere. We consider not only the tropopause itself, but also a layer around it called the tropopause inversion layer (TIL). It is shown that the moister the underlying atmosphere is, the more this layer acts as a barrier.
Tim Lüttmer, Peter Spichtinger, and Axel Seifert
EGUsphere, https://doi.org/10.5194/egusphere-2024-2157, https://doi.org/10.5194/egusphere-2024-2157, 2024
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We investigate ice formation pathways in idealized convective clouds using a novel microphysics scheme, that distinguishes between five ice classes each with their unique formation mechanism. Ice crystals from rime splintering forms the lowermost layer of ice crystals around the updraft core. The majority of ice crystals in the anvil of the convective cloud stems from frozen droplets. Ice stemming from homogeneous and deposition nucleation was only relevant in the overshoot.
Stefan Niebler, Annette Miltenberger, Bertil Schmidt, and Peter Spichtinger
Weather Clim. Dynam., 3, 113–137, https://doi.org/10.5194/wcd-3-113-2022, https://doi.org/10.5194/wcd-3-113-2022, 2022
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We use machine learning to create a network that detects and classifies four types of synoptic-scale weather fronts from ERA5 atmospheric reanalysis data. We present an application of our method, showing its use case in a scientific context. Additionally, our results show that multiple sources of training data are necessary to perform well on different regions, implying differences within those regions. Qualitative evaluation shows that the results are physically plausible.
Manuel Baumgartner, Christian Rolf, Jens-Uwe Grooß, Julia Schneider, Tobias Schorr, Ottmar Möhler, Peter Spichtinger, and Martina Krämer
Atmos. Chem. Phys., 22, 65–91, https://doi.org/10.5194/acp-22-65-2022, https://doi.org/10.5194/acp-22-65-2022, 2022
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An important mechanism for the appearance of ice particles in the upper troposphere at low temperatures is homogeneous nucleation. This process is commonly described by the
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Roman Attinger, Elisa Spreitzer, Maxi Boettcher, Heini Wernli, and Hanna Joos
Weather Clim. Dynam., 2, 1073–1091, https://doi.org/10.5194/wcd-2-1073-2021, https://doi.org/10.5194/wcd-2-1073-2021, 2021
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Diabatic processes affect the development of extratropical cyclones. This work provides a systematic assessment of the diabatic processes that modify potential vorticity (PV) in model simulations. PV is primarily produced by condensation and convection. Given favorable environmental conditions, long-wave radiative cooling and turbulence become the primary process at the cold and warm fronts, respectively. Turbulence and long-wave radiative heating produce negative PV anomalies at the fronts.
Ralf Weigel, Christoph Mahnke, Manuel Baumgartner, Martina Krämer, Peter Spichtinger, Nicole Spelten, Armin Afchine, Christian Rolf, Silvia Viciani, Francesco D'Amato, Holger Tost, and Stephan Borrmann
Atmos. Chem. Phys., 21, 13455–13481, https://doi.org/10.5194/acp-21-13455-2021, https://doi.org/10.5194/acp-21-13455-2021, 2021
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In July and August 2017, the StratoClim mission took place in Nepal with eight flights of the M-55 Geophysica at up to 20 km in the Asian monsoon anticyclone. New particle formation (NPF) next to cloud ice was detected in situ by abundant nucleation-mode aerosols (> 6 nm) along with ice particles (> 3 µm). NPF was observed mainly below the tropopause, down to 15 % being non-volatile residues. Observed intra-cloud NPF indicates its importance for the composition in the tropical tropopause layer.
Gabriel Vollenweider, Elisa Spreitzer, and Sebastian Schemm
Weather Clim. Dynam. Discuss., https://doi.org/10.5194/wcd-2021-31, https://doi.org/10.5194/wcd-2021-31, 2021
Publication in WCD not foreseen
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Manuel Baumgartner, Ralf Weigel, Allan H. Harvey, Felix Plöger, Ulrich Achatz, and Peter Spichtinger
Atmos. Chem. Phys., 20, 15585–15616, https://doi.org/10.5194/acp-20-15585-2020, https://doi.org/10.5194/acp-20-15585-2020, 2020
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The potential temperature is routinely used in atmospheric science. We review its derivation and suggest a new potential temperature, based on a temperature-dependent parameterization of the dry air's specific heat capacity. Moreover, we compare the new potential temperature to the common one and discuss the differences which become more important at higher altitudes. Finally, we indicate some consequences of using the new potential temperature in typical applications.
Martina Krämer, Christian Rolf, Nicole Spelten, Armin Afchine, David Fahey, Eric Jensen, Sergey Khaykin, Thomas Kuhn, Paul Lawson, Alexey Lykov, Laura L. Pan, Martin Riese, Andrew Rollins, Fred Stroh, Troy Thornberry, Veronika Wolf, Sarah Woods, Peter Spichtinger, Johannes Quaas, and Odran Sourdeval
Atmos. Chem. Phys., 20, 12569–12608, https://doi.org/10.5194/acp-20-12569-2020, https://doi.org/10.5194/acp-20-12569-2020, 2020
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To improve the representations of cirrus clouds in climate predictions, extended knowledge of their properties and geographical distribution is required. This study presents extensive airborne in situ and satellite remote sensing climatologies of cirrus and humidity, which serve as a guide to cirrus clouds. Further, exemplary radiative characteristics of cirrus types and also in situ observations of tropical tropopause layer cirrus and humidity in the Asian monsoon anticyclone are shown.
Andreas Petzold, Patrick Neis, Mihal Rütimann, Susanne Rohs, Florian Berkes, Herman G. J. Smit, Martina Krämer, Nicole Spelten, Peter Spichtinger, Philippe Nédélec, and Andreas Wahner
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Manuel Baumgartner, Max Sagebaum, Nicolas R. Gauger, Peter Spichtinger, and André Brinkmann
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Numerical models in atmospheric sciences need to include physical processes through parameterizations, which are not explicitly resolved, e.g., the formation of clouds. As a consequence, the parameterizations contain uncertain parameters. We suggest using the technique of algorithmic differentiation (AD) to identify the most uncertain parameters within parameterizations. In this study, we illustrate AD by analyzing a scheme for liquid clouds incorporated into a parcel model framework.
Manuel Baumgartner and Peter Spichtinger
Atmos. Chem. Phys., 18, 2525–2546, https://doi.org/10.5194/acp-18-2525-2018, https://doi.org/10.5194/acp-18-2525-2018, 2018
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Ice crystals are surrounded by liquid cloud droplets in mixed-phase clouds. The coexistence of ice and water is thermodynamically not stable and the particles will influence their respective growth by condensation. This effect is known as the Wegener–Bergeron–Findeisen process. In current models, the local interactions of the particles are neglected and they can only interact indirectly. This work proposes an approach to include local interactions and discusses some implications.
Qing Mu, Gerhard Lammel, Christian N. Gencarelli, Ian M. Hedgecock, Ying Chen, Petra Přibylová, Monique Teich, Yuxuan Zhang, Guangjie Zheng, Dominik van Pinxteren, Qiang Zhang, Hartmut Herrmann, Manabu Shiraiwa, Peter Spichtinger, Hang Su, Ulrich Pöschl, and Yafang Cheng
Atmos. Chem. Phys., 17, 12253–12267, https://doi.org/10.5194/acp-17-12253-2017, https://doi.org/10.5194/acp-17-12253-2017, 2017
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Polycyclic aromatic hydrocarbons (PAHs) are hazardous pollutants with the largest emissions in East Asia. The regional WRF-Chem-PAH model has been developed to reflect the state-of-the-art understanding of current PAHs studies with several new or updated features. It is able to reasonably well simulate the concentration levels and particulate mass fractions of PAHs near the sources and at a remote outflow region of East Asia, in high spatial and temporal resolutions.
Marcus Klingebiel, André Ehrlich, Fanny Finger, Timo Röschenthaler, Suad Jakirlić, Matthias Voigt, Stefan Müller, Rolf Maser, Manfred Wendisch, Peter Hoor, Peter Spichtinger, and Stephan Borrmann
Atmos. Meas. Tech., 10, 3485–3498, https://doi.org/10.5194/amt-10-3485-2017, https://doi.org/10.5194/amt-10-3485-2017, 2017
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Microphysical and radiation measurements were collected with the unique AIRcraft TOwed Sensor Shuttle (AIRTOSS) – Learjet tandem platform. It is a combination of a Learjet 35A research aircraft and an instrumented aerodynamic bird, which can be detached from and retracted back to the aircraft during flight.
AIRTOSS and Learjet are equipped with radiative, cloud microphysical, trace gas,
and meteorological instruments to study cirrus clouds.
Thomas Berkemeier, Markus Ammann, Ulrich K. Krieger, Thomas Peter, Peter Spichtinger, Ulrich Pöschl, Manabu Shiraiwa, and Andrew J. Huisman
Atmos. Chem. Phys., 17, 8021–8029, https://doi.org/10.5194/acp-17-8021-2017, https://doi.org/10.5194/acp-17-8021-2017, 2017
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Kinetic process models are efficient tools used to unravel the mechanisms governing chemical and physical transformation in multiphase atmospheric chemistry. However, determination of kinetic parameters such as reaction rate or diffusion coefficients from multiple data sets is often difficult or ambiguous. This study presents a novel optimization algorithm and framework to determine these parameters in an automated fashion and to gain information about parameter uncertainty and uniqueness.
Ralf Weigel, Peter Spichtinger, Christoph Mahnke, Marcus Klingebiel, Armin Afchine, Andreas Petzold, Martina Krämer, Anja Costa, Sergej Molleker, Philipp Reutter, Miklós Szakáll, Max Port, Lucas Grulich, Tina Jurkat, Andreas Minikin, and Stephan Borrmann
Atmos. Meas. Tech., 9, 5135–5162, https://doi.org/10.5194/amt-9-5135-2016, https://doi.org/10.5194/amt-9-5135-2016, 2016
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The subject of our study concerns measurements with optical array probes (OAPs) on fast-flying aircraft such as the G550 (HALO or HIAPER). At up to Mach 0.7 the effect of air compression upstream of underwing-mounted instruments and particles' inertia need consideration for determining ambient particle concentrations. Compared to conventional practices the introduced correction procedure eliminates ambiguities and exhibits consistency over flight speeds between 50 and 250 m s−.
Fanny Finger, Frank Werner, Marcus Klingebiel, André Ehrlich, Evelyn Jäkel, Matthias Voigt, Stephan Borrmann, Peter Spichtinger, and Manfred Wendisch
Atmos. Chem. Phys., 16, 7681–7693, https://doi.org/10.5194/acp-16-7681-2016, https://doi.org/10.5194/acp-16-7681-2016, 2016
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Solar spectra of optical layer properties of cirrus have been derived from the first truly collocated airborne radiation measurements using an aircraft and a towed sensor platform. The measured layer properties differ slightly due to horizontal cirrus inhomogeneities and the influence of low-level water clouds. Applying a 1-D radiative transfer model sensitivity studies were performed. It was found that if a low-level cloud is not considered, the solar cooling of the cirrus is strongly overestimated.
D. Chang, Y. Cheng, P. Reutter, J. Trentmann, S. M. Burrows, P. Spichtinger, S. Nordmann, M. O. Andreae, U. Pöschl, and H. Su
Atmos. Chem. Phys., 15, 10325–10348, https://doi.org/10.5194/acp-15-10325-2015, https://doi.org/10.5194/acp-15-10325-2015, 2015
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Atmos. Chem. Phys., 14, 7341–7365, https://doi.org/10.5194/acp-14-7341-2014, https://doi.org/10.5194/acp-14-7341-2014, 2014
H. Joos, P. Spichtinger, P. Reutter, and F. Fusina
Atmos. Chem. Phys., 14, 6835–6852, https://doi.org/10.5194/acp-14-6835-2014, https://doi.org/10.5194/acp-14-6835-2014, 2014
P. Spichtinger and M. Krämer
Atmos. Chem. Phys., 13, 9801–9818, https://doi.org/10.5194/acp-13-9801-2013, https://doi.org/10.5194/acp-13-9801-2013, 2013
E. Kienast-Sjögren, P. Spichtinger, and K. Gierens
Atmos. Chem. Phys., 13, 9021–9037, https://doi.org/10.5194/acp-13-9021-2013, https://doi.org/10.5194/acp-13-9021-2013, 2013
Related subject area
Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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
Dynamically-optimal models of atmospheric motion
A new approach to understanding fluid mixing in process-study models of stratified fluids
Sensitivity of the polar boundary layer to transient phenomena
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Existence and influence of mixed states in a model of vegetation patterns
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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
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Climatic responses to systematic time variations of parameters: a dynamical approach
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Wave propagation in the Lorenz-96 model
Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years
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Detecting changes in forced climate attractors with Wasserstein distance
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
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
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Oscillations in a simple climate–vegetation model
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Equilibrium temperature distribution and Hadley circulation in an axisymmetric model
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
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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
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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
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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
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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
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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
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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
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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.
Alexander Voronovich
EGUsphere, https://doi.org/10.5194/egusphere-2024-303, https://doi.org/10.5194/egusphere-2024-303, 2024
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The paper presents in a novel way of obtaining the ordinary differential equations representing evolution of a continuous atmosphere that is based on the least action (i.e., Hamilton’s) principle. The equations represent dynamics of the atmosphere unambiguously and in a certain sense most accurately. The algorithm possesses characteristic features which are beneficial for a dynamical core; in particular, the algorithm allows changing spatial resolution in the course of calculations.
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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.
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
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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
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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
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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.
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
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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
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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
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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
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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
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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.
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
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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
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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
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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
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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
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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
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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.
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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.
We developed a simple analytical model for describing subvisible cirrus clouds qualitatively....
