Articles | Volume 24, issue 3
https://doi.org/10.5194/npg-24-535-2017
© 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-24-535-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
05 Sep 2017
Research article |
| 05 Sep 2017
On the CCN (de)activation nonlinearities
Sylwester Arabas
CORRESPONDING AUTHOR
Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland
Chatham Financial Corporation Europe, Cracow, Poland
Shin-ichiro Shima
CORRESPONDING AUTHOR
Graduate School of Simulation Studies, University of Hyogo, Kobe, Japan
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Emily de Jong, John Ben Mackay, Oleksii Bulenok, Anna Jaruga, and Sylwester Arabas
Geosci. Model Dev., 16, 4193–4211, https://doi.org/10.5194/gmd-16-4193-2023, https://doi.org/10.5194/gmd-16-4193-2023, 2023
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In clouds, collisional breakup occurs when two colliding droplets splinter into new, smaller fragments. Particle-based modeling approaches often do not represent breakup because of the computational demands of creating new droplets. We present a particle-based breakup method that preserves the computational efficiency of these methods. In a series of simple demonstrations, we show that this representation alters cloud processes in reasonable and expected ways.
Michael A. Olesik, Jakub Banaśkiewicz, Piotr Bartman, Manuel Baumgartner, Simon Unterstrasser, and Sylwester Arabas
Geosci. Model Dev., 15, 3879–3899, https://doi.org/10.5194/gmd-15-3879-2022, https://doi.org/10.5194/gmd-15-3879-2022, 2022
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In systems such as atmospheric clouds, droplets undergo growth through condensation of vapor. The broadness of the resultant size spectrum of droplets influences precipitation likelihood and the radiative properties of clouds. One of the inherent limitations of simulations of the problem is the so-called numerical diffusion causing overestimation of the spectrum width, hence the term numerical broadening. In the paper, we take a closer look at one of the algorithms used in this context: MPDATA.
S. Arabas, A. Jaruga, H. Pawlowska, and W. W. Grabowski
Geosci. Model Dev., 8, 1677–1707, https://doi.org/10.5194/gmd-8-1677-2015, https://doi.org/10.5194/gmd-8-1677-2015, 2015
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This paper introduces a free and open-source C++ library of algorithms for representing cloud microphysics in numerical models. In the current release, the library covers three warm-rain schemes: the single- and double-moment bulk schemes, and the particle-based scheme with Monte Carlo coalescence. The three schemes are intended for modelling frameworks of different dimensionalities and complexities ranging from parcel models to multi-dimensional cloud-resolving (e.g. large-eddy) simulations.
A. Jaruga, S. Arabas, D. Jarecka, H. Pawlowska, P. K. Smolarkiewicz, and M. Waruszewski
Geosci. Model Dev., 8, 1005–1032, https://doi.org/10.5194/gmd-8-1005-2015, https://doi.org/10.5194/gmd-8-1005-2015, 2015
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This paper accompanies the first release of libmpdata++, a C++ library implementing the multidimensional positive-definite advection transport algorithm (MPDATA) on a regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide.
Ruyi Zhang, Limin Zhou, Shin-ichiro Shima, and Huawei Yang
Geosci. Model Dev., 17, 6761–6774, https://doi.org/10.5194/gmd-17-6761-2024, https://doi.org/10.5194/gmd-17-6761-2024, 2024
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Solar activity weakly ionises Earth's atmosphere, charging cloud droplets. Electro-coalescence is when oppositely charged droplets stick together. We introduce an analytical expression of electro-coalescence probability and use it in a warm-cumulus-cloud simulation. Results show that charge cases increase rain and droplet size, with the new method outperforming older ones. The new method requires longer computation time, but its impact on rain justifies inclusion in meteorology models.
Chongzhi Yin, Shin-ichiro Shima, Lulin Xue, and Chunsong Lu
Geosci. Model Dev., 17, 5167–5189, https://doi.org/10.5194/gmd-17-5167-2024, https://doi.org/10.5194/gmd-17-5167-2024, 2024
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We investigate numerical convergence properties of a particle-based numerical cloud microphysics model (SDM) and a double-moment bulk scheme for simulating a marine stratocumulus case, compare their results with model intercomparison project results, and present possible explanations for the different results of the SDM and the bulk scheme. Aerosol processes can be accurately simulated using SDM, and this may be an important factor affecting the behavior and morphology of marine stratocumulus.
Toshiki Matsushima, Seiya Nishizawa, and Shin-ichiro Shima
Geosci. Model Dev., 16, 6211–6245, https://doi.org/10.5194/gmd-16-6211-2023, https://doi.org/10.5194/gmd-16-6211-2023, 2023
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A particle-based cloud model was developed for meter- to submeter-scale resolution in cloud simulations. Our new cloud model's computational performance is superior to a bin method and comparable to a two-moment bulk method. A highlight of this study is the 2 m resolution shallow cloud simulations over an area covering ∼10 km2. This model allows for studying turbulence and cloud physics at spatial scales that overlap with those covered by direct numerical simulations and field studies.
Emily de Jong, John Ben Mackay, Oleksii Bulenok, Anna Jaruga, and Sylwester Arabas
Geosci. Model Dev., 16, 4193–4211, https://doi.org/10.5194/gmd-16-4193-2023, https://doi.org/10.5194/gmd-16-4193-2023, 2023
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In clouds, collisional breakup occurs when two colliding droplets splinter into new, smaller fragments. Particle-based modeling approaches often do not represent breakup because of the computational demands of creating new droplets. We present a particle-based breakup method that preserves the computational efficiency of these methods. In a series of simple demonstrations, we show that this representation alters cloud processes in reasonable and expected ways.
Michael A. Olesik, Jakub Banaśkiewicz, Piotr Bartman, Manuel Baumgartner, Simon Unterstrasser, and Sylwester Arabas
Geosci. Model Dev., 15, 3879–3899, https://doi.org/10.5194/gmd-15-3879-2022, https://doi.org/10.5194/gmd-15-3879-2022, 2022
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In systems such as atmospheric clouds, droplets undergo growth through condensation of vapor. The broadness of the resultant size spectrum of droplets influences precipitation likelihood and the radiative properties of clouds. One of the inherent limitations of simulations of the problem is the so-called numerical diffusion causing overestimation of the spectrum width, hence the term numerical broadening. In the paper, we take a closer look at one of the algorithms used in this context: MPDATA.
Mizuo Kajino, Makoto Deushi, Tsuyoshi Thomas Sekiyama, Naga Oshima, Keiya Yumimoto, Taichu Yasumichi Tanaka, Joseph Ching, Akihiro Hashimoto, Tetsuya Yamamoto, Masaaki Ikegami, Akane Kamada, Makoto Miyashita, Yayoi Inomata, Shin-ichiro Shima, Pradeep Khatri, Atsushi Shimizu, Hitoshi Irie, Kouji Adachi, Yuji Zaizen, Yasuhito Igarashi, Hiromasa Ueda, Takashi Maki, and Masao Mikami
Geosci. Model Dev., 14, 2235–2264, https://doi.org/10.5194/gmd-14-2235-2021, https://doi.org/10.5194/gmd-14-2235-2021, 2021
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This study compares performance of aerosol representation methods of the Japan Meteorological Agency's regional-scale nonhydrostatic meteorology–chemistry model (NHM-Chem). It indicates separate treatment of sea salt and dust in coarse mode and that of light-absorptive and non-absorptive particles in fine mode could provide accurate assessments on aerosol feedback processes.
Shin-ichiro Shima, Yousuke Sato, Akihiro Hashimoto, and Ryohei Misumi
Geosci. Model Dev., 13, 4107–4157, https://doi.org/10.5194/gmd-13-4107-2020, https://doi.org/10.5194/gmd-13-4107-2020, 2020
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Using the super-droplet method, we constructed a detailed numerical model of mixed-phase clouds based on kinetic description and subsequently demonstrated that a large-eddy simulation of a cumulonimbus which predicts ice particle morphology without assuming ice categories or mass–dimension relationships is possible. Our results strongly support the particle-based modeling methodology’s efficacy for simulating mixed-phase clouds.
Mizuo Kajino, Makoto Deushi, Tsuyoshi Thomas Sekiyama, Naga Oshima, Keiya Yumimoto, Taichu Yasumichi Tanaka, Joseph Ching, Akihiro Hashimoto, Tetsuya Yamamoto, Masaaki Ikegami, Akane Kamada, Makoto Miyashita, Yayoi Inomata, Shin-ichiro Shima, Kouji Adachi, Yuji Zaizen, Yasuhito Igarashi, Hiromasa Ueda, Takashi Maki, and Masao Mikami
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2018-128, https://doi.org/10.5194/gmd-2018-128, 2018
Revised manuscript not accepted
Hazuki Arakida, Takemasa Miyoshi, Takeshi Ise, Shin-ichiro Shima, and Shunji Kotsuki
Nonlin. Processes Geophys., 24, 553–567, https://doi.org/10.5194/npg-24-553-2017, https://doi.org/10.5194/npg-24-553-2017, 2017
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This is the first study assimilating the satellite-based leaf area index observations every 4 days into a numerical model simulating the growth and death of individual plants. The newly developed data assimilation system successfully reduced the uncertainties of the model parameters related to phenology and carbon dynamics. It also provides better estimates of the present vegetation structure which can be used as the initial states for the simulation of the future vegetation change.
S. Arabas, A. Jaruga, H. Pawlowska, and W. W. Grabowski
Geosci. Model Dev., 8, 1677–1707, https://doi.org/10.5194/gmd-8-1677-2015, https://doi.org/10.5194/gmd-8-1677-2015, 2015
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This paper introduces a free and open-source C++ library of algorithms for representing cloud microphysics in numerical models. In the current release, the library covers three warm-rain schemes: the single- and double-moment bulk schemes, and the particle-based scheme with Monte Carlo coalescence. The three schemes are intended for modelling frameworks of different dimensionalities and complexities ranging from parcel models to multi-dimensional cloud-resolving (e.g. large-eddy) simulations.
A. Jaruga, S. Arabas, D. Jarecka, H. Pawlowska, P. K. Smolarkiewicz, and M. Waruszewski
Geosci. Model Dev., 8, 1005–1032, https://doi.org/10.5194/gmd-8-1005-2015, https://doi.org/10.5194/gmd-8-1005-2015, 2015
Short summary
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This paper accompanies the first release of libmpdata++, a C++ library implementing the multidimensional positive-definite advection transport algorithm (MPDATA) on a regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide.
Related subject area
Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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High-frequency Internal Waves, High-mode Nonlinear Waves and K-H Billows on the South China Sea's Shelf Revealed by Marine Seismic Observation
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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.
Pierre Lloret, Peter J. Diamessis, Marek Stastna, and Greg N. Thomsen
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This study presents a new approach to simulate 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 in predicting natural phenomena and their effects on environments like swash zones, where waves meet the shore.
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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
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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.
Samuel George Hartharn-Evans, Marek Stastna, and Magda Carr
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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.
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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.
Linghan Meng, Haibin Song, Yongxian Guan, Shun Yang, Kun Zhang, and Mengli Liu
EGUsphere, https://doi.org/10.5194/egusphere-2024-92, https://doi.org/10.5194/egusphere-2024-92, 2024
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In the seismic section, high-frequency and mode-2 internal waves, along with shear instability, were identified in the ocean. Strong nonlinear high-frequency waves, believed to be from shoaling, Behind them are larger mode-2 internal solitary waves. These waves show instability, notably the second mode-2 internal waves with distinct K-H billows. Seismic data revealed that diapycnal mixing from these events in the shelf area is 3.5 times greater than than that in the slope area.
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.
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.
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
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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
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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.
Cited articles
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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.
The paper bridges cloud/aerosol modelling with bifurcation analysis. It identifies two nonlinear...
