Articles | Volume 25, issue 2
https://doi.org/10.5194/npg-25-387-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-25-387-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
28 May 2018
Research article |
| 28 May 2018
| 28 May 2018
Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models
Royal Meteorological Institute of Belgium, Brussels, Belgium
Sebastian Schubert
Meteorological Institute, CEN, University of Hamburg, Hamburg, Germany
Jonathan Demaeyer
Royal Meteorological Institute of Belgium, Brussels, Belgium
Valerio Lucarini
Meteorological Institute, CEN, University of Hamburg, Hamburg, Germany
Department of Mathematics and Statistics, University of Reading, Reading, UK
Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
Stéphane Vannitsem
Royal Meteorological Institute of Belgium, Brussels, Belgium
Related authors
Vera Melinda Galfi, Tommaso Alberti, Lesley De Cruz, Christian L. E. Franzke, and Valerio Lembo
Nonlin. Processes Geophys., 31, 185–193, https://doi.org/10.5194/npg-31-185-2024, https://doi.org/10.5194/npg-31-185-2024, 2024
Short summary
Short summary
In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.
Nicolas Ghilain, Stéphane Vannitsem, Quentin Dalaiden, Hugues Goosse, Lesley De Cruz, and Wenguang Wei
Earth Syst. Sci. Data, 14, 1901–1916, https://doi.org/10.5194/essd-14-1901-2022, https://doi.org/10.5194/essd-14-1901-2022, 2022
Short summary
Short summary
Modeling the climate at high resolution is crucial to represent the snowfall accumulation over the complex orography of the Antarctic coast. While ice cores provide a view constrained spatially but over centuries, climate models can give insight into its spatial distribution, either at high resolution over a short period or vice versa. We downscaled snowfall accumulation from climate model historical simulations (1850–present day) over Dronning Maud Land at 5.5 km using a statistical method.
Sara Top, Lola Kotova, Lesley De Cruz, Svetlana Aniskevich, Leonid Bobylev, Rozemien De Troch, Natalia Gnatiuk, Anne Gobin, Rafiq Hamdi, Arne Kriegsmann, Armelle Reca Remedio, Abdulla Sakalli, Hans Van De Vyver, Bert Van Schaeybroeck, Viesturs Zandersons, Philippe De Maeyer, Piet Termonia, and Steven Caluwaerts
Geosci. Model Dev., 14, 1267–1293, https://doi.org/10.5194/gmd-14-1267-2021, https://doi.org/10.5194/gmd-14-1267-2021, 2021
Short summary
Short summary
Detailed climate data are needed to assess the impact of climate change on human and natural systems. The performance of two high-resolution regional climate models, ALARO-0 and REMO2015, was investigated over central Asia, a vulnerable region where detailed climate information is scarce. In certain subregions the produced climate data are suitable for impact studies, but bias adjustment is required for subregions where significant biases have been identified.
Maite Bauwens, Trissevgeni Stavrakou, Jean-François Müller, Bert Van Schaeybroeck, Lesley De Cruz, Rozemien De Troch, Olivier Giot, Rafiq Hamdi, Piet Termonia, Quentin Laffineur, Crist Amelynck, Niels Schoon, Bernard Heinesch, Thomas Holst, Almut Arneth, Reinhart Ceulemans, Arturo Sanchez-Lorenzo, and Alex Guenther
Biogeosciences, 15, 3673–3690, https://doi.org/10.5194/bg-15-3673-2018, https://doi.org/10.5194/bg-15-3673-2018, 2018
Short summary
Short summary
Biogenic isoprene fluxes are simulated over Europe with the MEGAN–MOHYCAN model for the recent past and end-of-century climate at high spatiotemporal resolution (0.1°, 3 min). Due to climate change, fluxes increased by 40 % over 1979–2014. Climate scenarios for 2070–2099 suggest an increase by 83 % due to climate, and an even stronger increase when the potential impact of CO2 fertilization is considered (up to 141 %). Accounting for CO2 inhibition cancels out a large part of these increases.
Lesley De Cruz, Jonathan Demaeyer, and Stéphane Vannitsem
Geosci. Model Dev., 9, 2793–2808, https://doi.org/10.5194/gmd-9-2793-2016, https://doi.org/10.5194/gmd-9-2793-2016, 2016
Short summary
Short summary
Large-scale weather patterns such as the North Atlantic Oscillation, which dictates the harshness of European winters, vary over the course of years. By recreating it in a simple ocean-atmosphere model, we hope to understand what drives this slow, hard-to-predict variability. MAOOAM is such a model, in which the resolution and included physical processes can easily be modified. The modular system allowed us to show the robustness of the slow variability against changes in model resolution.
Olivier Giot, Piet Termonia, Daan Degrauwe, Rozemien De Troch, Steven Caluwaerts, Geert Smet, Julie Berckmans, Alex Deckmyn, Lesley De Cruz, Pieter De Meutter, Annelies Duerinckx, Luc Gerard, Rafiq Hamdi, Joris Van den Bergh, Michiel Van Ginderachter, and Bert Van Schaeybroeck
Geosci. Model Dev., 9, 1143–1152, https://doi.org/10.5194/gmd-9-1143-2016, https://doi.org/10.5194/gmd-9-1143-2016, 2016
Short summary
Short summary
The Royal Meteorological Institute of Belgium and Ghent University have performed two simulations with different horizontal resolutions of the past observed climate of Europe for the period 1979–2010. Of special interest is the new way of handling convective precipitation in the model that was used. Results show that the model is capable of representing the European climate and comparison with other models reveals that precipitation patterns are well represented.
S. Vannitsem and L. De Cruz
Geosci. Model Dev., 7, 649–662, https://doi.org/10.5194/gmd-7-649-2014, https://doi.org/10.5194/gmd-7-649-2014, 2014
Stéphane Vannitsem, X. San Liang, and Carlos A. Pires
EGUsphere, https://doi.org/10.5194/egusphere-2024-3308, https://doi.org/10.5194/egusphere-2024-3308, 2024
Short summary
Short summary
Large-scale modes of variability are present in the climate system. These modes are known to have influences on each other, but usually viewed as linear influences. The nonlinear connections among a set of key climate indices are here explored using tools from information theory, which allow for characterizing the causality between indices. It is found that quadratic nonlinear dependencies between climate indices are present at low-frequencies, reflecting the complex nature of its dynamics.
Anupama K. Xavier, Jonathan Demaeyer, and Stéphane Vannitsem
Earth Syst. Dynam., 15, 893–912, https://doi.org/10.5194/esd-15-893-2024, https://doi.org/10.5194/esd-15-893-2024, 2024
Short summary
Short summary
This research focuses on understanding different atmospheric patterns like blocking, zonal, and transition regimes and analyzing their predictability. We used an idealized land–atmosphere coupled model to simulate Earth's atmosphere. Then we identified these blocking, zonal, and transition regimes using Gaussian mixture clustering and studied their predictability using Lyapunov exponents.
Vera Melinda Galfi, Tommaso Alberti, Lesley De Cruz, Christian L. E. Franzke, and Valerio Lembo
Nonlin. Processes Geophys., 31, 185–193, https://doi.org/10.5194/npg-31-185-2024, https://doi.org/10.5194/npg-31-185-2024, 2024
Short summary
Short summary
In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.
David Docquier, Giorgia Di Capua, Reik V. Donner, Carlos A. L. Pires, Amélie Simon, and Stéphane Vannitsem
Nonlin. Processes Geophys., 31, 115–136, https://doi.org/10.5194/npg-31-115-2024, https://doi.org/10.5194/npg-31-115-2024, 2024
Short summary
Short summary
Identifying causes of specific processes is crucial in order to better understand our climate system. Traditionally, correlation analyses have been used to identify cause–effect relationships in climate studies. However, correlation does not imply causation, which justifies the need to use causal methods. We compare two independent causal methods and show that these are superior to classical correlation analyses. We also find some interesting differences between the two methods.
Michel Journée, Edouard Goudenhoofdt, Stéphane Vannitsem, and Laurent Delobbe
Hydrol. Earth Syst. Sci., 27, 3169–3189, https://doi.org/10.5194/hess-27-3169-2023, https://doi.org/10.5194/hess-27-3169-2023, 2023
Short summary
Short summary
The exceptional flood of July 2021 in central Europe impacted Belgium severely. This study aims to characterize rainfall amounts in Belgium from 13 to 16 July 2021 based on observational data (i.e., rain gauge data and a radar-based rainfall product). The spatial and temporal distributions of rainfall during the event aredescribed. In order to document such a record-breaking event as much as possible, the rainfall data are shared with the scientific community on Zenodo for further studies.
Lucy G. Recchia and Valerio Lucarini
Earth Syst. Dynam., 14, 697–722, https://doi.org/10.5194/esd-14-697-2023, https://doi.org/10.5194/esd-14-697-2023, 2023
Short summary
Short summary
Simulations are performed with an intermediate-complexity climate model, PLASIM, to assess the future response of monsoons to changing concentrations of aerosols and greenhouse gases. The aerosol loading is applied to India, Southeast Asia, and eastern China, both concurrently and independently, to assess linearity. The primary effect of increased aerosol loading is a decrease in summer precipitation in the vicinity of the applied forcing, although the regional response varies significantly.
Jonathan Demaeyer, Jonas Bhend, Sebastian Lerch, Cristina Primo, Bert Van Schaeybroeck, Aitor Atencia, Zied Ben Bouallègue, Jieyu Chen, Markus Dabernig, Gavin Evans, Jana Faganeli Pucer, Ben Hooper, Nina Horat, David Jobst, Janko Merše, Peter Mlakar, Annette Möller, Olivier Mestre, Maxime Taillardat, and Stéphane Vannitsem
Earth Syst. Sci. Data, 15, 2635–2653, https://doi.org/10.5194/essd-15-2635-2023, https://doi.org/10.5194/essd-15-2635-2023, 2023
Short summary
Short summary
A benchmark dataset is proposed to compare different statistical postprocessing methods used in forecasting centers to properly calibrate ensemble weather forecasts. This dataset is based on ensemble forecasts covering a portion of central Europe and includes the corresponding observations. Examples on how to download and use the data are provided, a set of evaluation methods is proposed, and a first benchmark of several methods for the correction of 2 m temperature forecasts is performed.
David Docquier, Stéphane Vannitsem, and Alessio Bellucci
Earth Syst. Dynam., 14, 577–591, https://doi.org/10.5194/esd-14-577-2023, https://doi.org/10.5194/esd-14-577-2023, 2023
Short summary
Short summary
The climate system is strongly regulated by interactions between the ocean and atmosphere. However, many uncertainties remain in the understanding of these interactions. Our analysis uses a relatively novel approach to quantify causal links between the ocean surface and lower atmosphere based on satellite observations. We find that both the ocean and atmosphere influence each other but with varying intensity depending on the region, demonstrating the power of causal methods.
Stéphane Vannitsem
Nonlin. Processes Geophys., 30, 1–12, https://doi.org/10.5194/npg-30-1-2023, https://doi.org/10.5194/npg-30-1-2023, 2023
Short summary
Short summary
The impact of climate change on weather pattern dynamics over the North Atlantic is explored through the lens of information theory. These tools allow the predictability of the succession of weather patterns and the irreversible nature of the dynamics to be clarified. It is shown that the predictability is increasing in the observations, while the opposite trend is found in model projections. The irreversibility displays an overall increase in time in both the observations and the model runs.
David Docquier, Stéphane Vannitsem, Alessio Bellucci, and Claude Frankignoul
EGUsphere, https://doi.org/10.5194/egusphere-2022-1340, https://doi.org/10.5194/egusphere-2022-1340, 2022
Preprint withdrawn
Short summary
Short summary
Understanding whether variations in ocean heat content are driven by air-sea heat fluxes or by ocean dynamics is of crucial importance to enhance climate projections. We use a relatively novel causal method to quantify interactions between ocean heat budget terms based on climate models. We find that low-resolution models overestimate the influence of ocean dynamics in the upper ocean, and that changes in ocean heat content are dominated by air-sea fluxes at high resolution.
Valerio Lembo, Federico Fabiano, Vera Melinda Galfi, Rune Grand Graversen, Valerio Lucarini, and Gabriele Messori
Weather Clim. Dynam., 3, 1037–1062, https://doi.org/10.5194/wcd-3-1037-2022, https://doi.org/10.5194/wcd-3-1037-2022, 2022
Short summary
Short summary
Eddies in mid-latitudes characterize the exchange of heat between the tropics and the poles. This exchange is largely uneven, with a few extreme events bearing most of the heat transported across latitudes in a season. It is thus important to understand what the dynamical mechanisms are behind these events. Here, we identify recurrent weather regime patterns associated with extreme transports, and we identify scales of mid-latitudinal eddies that are mostly responsible for the transport.
Valerio Lucarini, Larissa Serdukova, and Georgios Margazoglou
Nonlin. Processes Geophys., 29, 183–205, https://doi.org/10.5194/npg-29-183-2022, https://doi.org/10.5194/npg-29-183-2022, 2022
Short summary
Short summary
In most of the investigations on metastable systems, the stochastic forcing is modulated by Gaussian noise. Lévy noise laws, which describe jump processes, have recently received a lot of attention, but much less is known. We study stochastic versions of the Ghil–Sellers energy balance model, and we highlight the fundamental difference between how transitions are performed between the competing warm and snowball states, depending on whether Gaussian or Lévy noise acts as forcing.
Nicolas Ghilain, Stéphane Vannitsem, Quentin Dalaiden, Hugues Goosse, Lesley De Cruz, and Wenguang Wei
Earth Syst. Sci. Data, 14, 1901–1916, https://doi.org/10.5194/essd-14-1901-2022, https://doi.org/10.5194/essd-14-1901-2022, 2022
Short summary
Short summary
Modeling the climate at high resolution is crucial to represent the snowfall accumulation over the complex orography of the Antarctic coast. While ice cores provide a view constrained spatially but over centuries, climate models can give insight into its spatial distribution, either at high resolution over a short period or vice versa. We downscaled snowfall accumulation from climate model historical simulations (1850–present day) over Dronning Maud Land at 5.5 km using a statistical method.
Yumeng Chen, Alberto Carrassi, and Valerio Lucarini
Nonlin. Processes Geophys., 28, 633–649, https://doi.org/10.5194/npg-28-633-2021, https://doi.org/10.5194/npg-28-633-2021, 2021
Short summary
Short summary
Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial conditions. However, obtaining the instability properties is burdensome for complex problems, both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.
Tommaso Alberti, Reik V. Donner, and Stéphane Vannitsem
Earth Syst. Dynam., 12, 837–855, https://doi.org/10.5194/esd-12-837-2021, https://doi.org/10.5194/esd-12-837-2021, 2021
Short summary
Short summary
We provide a novel approach to diagnose the strength of the ocean–atmosphere coupling by using both a reduced order model and reanalysis data. Our findings suggest the ocean–atmosphere dynamics presents a rich variety of features, moving from a chaotic to a coherent coupled dynamics, mainly attributed to the atmosphere and only marginally to the ocean. Our observations suggest further investigations in characterizing the occurrence and spatial dependency of the ocean–atmosphere coupling.
Sara Top, Lola Kotova, Lesley De Cruz, Svetlana Aniskevich, Leonid Bobylev, Rozemien De Troch, Natalia Gnatiuk, Anne Gobin, Rafiq Hamdi, Arne Kriegsmann, Armelle Reca Remedio, Abdulla Sakalli, Hans Van De Vyver, Bert Van Schaeybroeck, Viesturs Zandersons, Philippe De Maeyer, Piet Termonia, and Steven Caluwaerts
Geosci. Model Dev., 14, 1267–1293, https://doi.org/10.5194/gmd-14-1267-2021, https://doi.org/10.5194/gmd-14-1267-2021, 2021
Short summary
Short summary
Detailed climate data are needed to assess the impact of climate change on human and natural systems. The performance of two high-resolution regional climate models, ALARO-0 and REMO2015, was investigated over central Asia, a vulnerable region where detailed climate information is scarce. In certain subregions the produced climate data are suitable for impact studies, but bias adjustment is required for subregions where significant biases have been identified.
Stephan Hemri, Sebastian Lerch, Maxime Taillardat, Stéphane Vannitsem, and Daniel S. Wilks
Nonlin. Processes Geophys., 27, 519–521, https://doi.org/10.5194/npg-27-519-2020, https://doi.org/10.5194/npg-27-519-2020, 2020
Veronika Eyring, Lisa Bock, Axel Lauer, Mattia Righi, Manuel Schlund, Bouwe Andela, Enrico Arnone, Omar Bellprat, Björn Brötz, Louis-Philippe Caron, Nuno Carvalhais, Irene Cionni, Nicola Cortesi, Bas Crezee, Edouard L. Davin, Paolo Davini, Kevin Debeire, Lee de Mora, Clara Deser, David Docquier, Paul Earnshaw, Carsten Ehbrecht, Bettina K. Gier, Nube Gonzalez-Reviriego, Paul Goodman, Stefan Hagemann, Steven Hardiman, Birgit Hassler, Alasdair Hunter, Christopher Kadow, Stephan Kindermann, Sujan Koirala, Nikolay Koldunov, Quentin Lejeune, Valerio Lembo, Tomas Lovato, Valerio Lucarini, François Massonnet, Benjamin Müller, Amarjiit Pandde, Núria Pérez-Zanón, Adam Phillips, Valeriu Predoi, Joellen Russell, Alistair Sellar, Federico Serva, Tobias Stacke, Ranjini Swaminathan, Verónica Torralba, Javier Vegas-Regidor, Jost von Hardenberg, Katja Weigel, and Klaus Zimmermann
Geosci. Model Dev., 13, 3383–3438, https://doi.org/10.5194/gmd-13-3383-2020, https://doi.org/10.5194/gmd-13-3383-2020, 2020
Short summary
Short summary
The Earth System Model Evaluation Tool (ESMValTool) is a community diagnostics and performance metrics tool designed to improve comprehensive and routine evaluation of earth system models (ESMs) participating in the Coupled Model Intercomparison Project (CMIP). It has undergone rapid development since the first release in 2016 and is now a well-tested tool that provides end-to-end provenance tracking to ensure reproducibility.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 27, 307–327, https://doi.org/10.5194/npg-27-307-2020, https://doi.org/10.5194/npg-27-307-2020, 2020
Short summary
Short summary
Postprocessing schemes used to correct weather forecasts are no longer efficient when the model generating the forecasts changes. An approach based on response theory to take the change into account without having to recompute the parameters based on past forecasts is presented. It is tested on an analytical model and a simple model of atmospheric variability. We show that this approach is effective and discuss its potential application for an operational environment.
Michiel Van Ginderachter, Daan Degrauwe, Stéphane Vannitsem, and Piet Termonia
Nonlin. Processes Geophys., 27, 187–207, https://doi.org/10.5194/npg-27-187-2020, https://doi.org/10.5194/npg-27-187-2020, 2020
Short summary
Short summary
A generic methodology is developed to estimate the model error and simulate the model uncertainty related to a specific physical process. The method estimates the model error by comparing two different representations of the physical process in otherwise identical models. The found model error can then be used to perturb the model and simulate the model uncertainty. When applying this methodology to deep convection an improvement in the probabilistic skill of the ensemble forecast is found.
Emmanuel Roulin and Stéphane Vannitsem
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2019-45, https://doi.org/10.5194/npg-2019-45, 2019
Preprint withdrawn
Short summary
Short summary
We need seasonal predictions of temperature and precipitation to prepare hydrological outlooks. Since the skill is limited, statistical correction and combination of outputs from multiple models are necessary. We use the forecasts of past situations from the EUROSIP multi-model system for 6 case studies in Western Europe and the Mediterranean Region. We identify skill for spring temperature in most areas and winter precipitation in Sweden and Greece. Sample size for training appears crucial.
Valerio Lembo, Frank Lunkeit, and Valerio Lucarini
Geosci. Model Dev., 12, 3805–3834, https://doi.org/10.5194/gmd-12-3805-2019, https://doi.org/10.5194/gmd-12-3805-2019, 2019
Short summary
Short summary
The Thermodynamic Diagnostic Tool (TheDiaTo v1.0) is a collection of diagnostics for the study of the thermodynamics of the climate system in climate models. This is fundamental in order to understand where the imbalances affecting climate projections come from and also to allow for easy comparison of different scenarios and atmospheric regimes. The tool is currently being developed for the assessment of models that are part of the next phase of the Coupled Model Intercomparison Project (CMIP).
Mallory Carlu, Francesco Ginelli, Valerio Lucarini, and Antonio Politi
Nonlin. Processes Geophys., 26, 73–89, https://doi.org/10.5194/npg-26-73-2019, https://doi.org/10.5194/npg-26-73-2019, 2019
Short summary
Short summary
We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96, to unravel key mechanisms of interaction between scales of different resolutions and time scales. To do so, we use a mathematical machinery known as Lyapunov analysis, allowing us to capture the degrees of chaoticity associated with fundamental directions of instability. We find a non-trivial group of such directions projecting significantly on slow variables, associated with long term dynamics.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 25, 605–631, https://doi.org/10.5194/npg-25-605-2018, https://doi.org/10.5194/npg-25-605-2018, 2018
Short summary
Short summary
We investigate the modeling of the effects of the unresolved scales on the large scales of the coupled ocean–atmosphere model MAOOAM. Two different physically based stochastic methods are considered and compared, in various configurations of the model. Both methods show remarkable performances and are able to model fundamental changes in the model dynamics. Ways to improve the parameterizations' implementation are also proposed.
Stéphane Vannitsem and Pierre Ekelmans
Earth Syst. Dynam., 9, 1063–1083, https://doi.org/10.5194/esd-9-1063-2018, https://doi.org/10.5194/esd-9-1063-2018, 2018
Short summary
Short summary
The El Niño–Southern Oscillation phenomenon is a slow dynamics present in the coupled ocean–atmosphere tropical Pacific system which has important teleconnections with the northern extratropics. These teleconnections are usually believed to be the source of an enhanced predictability in the northern extratropics at seasonal to decadal timescales. This question is challenged by investigating the causality between these regions using an advanced technique known as convergent cross mapping.
Maite Bauwens, Trissevgeni Stavrakou, Jean-François Müller, Bert Van Schaeybroeck, Lesley De Cruz, Rozemien De Troch, Olivier Giot, Rafiq Hamdi, Piet Termonia, Quentin Laffineur, Crist Amelynck, Niels Schoon, Bernard Heinesch, Thomas Holst, Almut Arneth, Reinhart Ceulemans, Arturo Sanchez-Lorenzo, and Alex Guenther
Biogeosciences, 15, 3673–3690, https://doi.org/10.5194/bg-15-3673-2018, https://doi.org/10.5194/bg-15-3673-2018, 2018
Short summary
Short summary
Biogenic isoprene fluxes are simulated over Europe with the MEGAN–MOHYCAN model for the recent past and end-of-century climate at high spatiotemporal resolution (0.1°, 3 min). Due to climate change, fluxes increased by 40 % over 1979–2014. Climate scenarios for 2070–2099 suggest an increase by 83 % due to climate, and an even stronger increase when the potential impact of CO2 fertilization is considered (up to 141 %). Accounting for CO2 inhibition cancels out a large part of these increases.
Gabriele Vissio and Valerio Lucarini
Nonlin. Processes Geophys., 25, 413–427, https://doi.org/10.5194/npg-25-413-2018, https://doi.org/10.5194/npg-25-413-2018, 2018
Short summary
Short summary
Constructing good parametrizations is key when studying multi-scale systems. We consider a low-order model and derive a parametrization via a recently developed statistical mechanical approach. We show how the method allows for seamlessly treating the case when the unresolved dynamics is both faster and slower than the resolved one. We test the skill of the parametrization by using the formalism of the Wasserstein distance, which allows for measuring how different two probability measures are.
Tamás Bódai, Valerio Lucarini, and Frank Lunkeit
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2018-30, https://doi.org/10.5194/esd-2018-30, 2018
Revised manuscript not accepted
Short summary
Short summary
We establish a framework to conduct a scenario analysis of the best possible outcomes under geoengineering. The scenarios may consist of scenarios of greenhouse gas emission the choice of the quantity that we want to keep under control. The motivation is the desire of an efficient way of assessing the side-effects of geoengineering, concerning the unwanted and uncontrolled changes. Countering CO2 emission by modulating insolation, we find considerable changes in local temperatures or rainfall.
Lesley De Cruz, Jonathan Demaeyer, and Stéphane Vannitsem
Geosci. Model Dev., 9, 2793–2808, https://doi.org/10.5194/gmd-9-2793-2016, https://doi.org/10.5194/gmd-9-2793-2016, 2016
Short summary
Short summary
Large-scale weather patterns such as the North Atlantic Oscillation, which dictates the harshness of European winters, vary over the course of years. By recreating it in a simple ocean-atmosphere model, we hope to understand what drives this slow, hard-to-predict variability. MAOOAM is such a model, in which the resolution and included physical processes can easily be modified. The modular system allowed us to show the robustness of the slow variability against changes in model resolution.
Olivier Giot, Piet Termonia, Daan Degrauwe, Rozemien De Troch, Steven Caluwaerts, Geert Smet, Julie Berckmans, Alex Deckmyn, Lesley De Cruz, Pieter De Meutter, Annelies Duerinckx, Luc Gerard, Rafiq Hamdi, Joris Van den Bergh, Michiel Van Ginderachter, and Bert Van Schaeybroeck
Geosci. Model Dev., 9, 1143–1152, https://doi.org/10.5194/gmd-9-1143-2016, https://doi.org/10.5194/gmd-9-1143-2016, 2016
Short summary
Short summary
The Royal Meteorological Institute of Belgium and Ghent University have performed two simulations with different horizontal resolutions of the past observed climate of Europe for the period 1979–2010. Of special interest is the new way of handling convective precipitation in the model that was used. Results show that the model is capable of representing the European climate and comparison with other models reveals that precipitation patterns are well represented.
S. Hasson, V. Lucarini, M. R. Khan, M. Petitta, T. Bolch, and G. Gioli
Hydrol. Earth Syst. Sci., 18, 4077–4100, https://doi.org/10.5194/hess-18-4077-2014, https://doi.org/10.5194/hess-18-4077-2014, 2014
S. Vannitsem and L. De Cruz
Geosci. Model Dev., 7, 649–662, https://doi.org/10.5194/gmd-7-649-2014, https://doi.org/10.5194/gmd-7-649-2014, 2014
S. Hasson, V. Lucarini, S. Pascale, and J. Böhner
Earth Syst. Dynam., 5, 67–87, https://doi.org/10.5194/esd-5-67-2014, https://doi.org/10.5194/esd-5-67-2014, 2014
R. Deidda, M. Marrocu, G. Caroletti, G. Pusceddu, A. Langousis, V. Lucarini, M. Puliga, and A. Speranza
Hydrol. Earth Syst. Sci., 17, 5041–5059, https://doi.org/10.5194/hess-17-5041-2013, https://doi.org/10.5194/hess-17-5041-2013, 2013
S. Hasson, V. Lucarini, and S. Pascale
Earth Syst. Dynam., 4, 199–217, https://doi.org/10.5194/esd-4-199-2013, https://doi.org/10.5194/esd-4-199-2013, 2013
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
A comparison of two nonlinear data assimilation methods
Prognostic assumed-probability-density-function (distribution density function) approach: further generalization and demonstrations
Bridging classical data assimilation and optimal transport: the 3D-Var case
Leading the Lorenz 63 system toward the prescribed regime by model predictive control coupled with data assimilation
Selecting and weighting dynamical models using data-driven approaches
Improving ensemble data assimilation through Probit-space Ensemble Size Expansion for Gaussian Copulas (PESE-GC)
A quest for precipitation attractors in weather radar archives
Quantum data assimilation: a new approach to solving data assimilation on quantum annealers
Evolution of small-scale turbulence at large Richardson numbers
Inferring flow energy, space and time scales: freely-drifting vs fixed point observations
Robust weather-adaptive post-processing using model output statistics random forests
Comparative study of strongly and weakly coupled data assimilation with a global land–atmosphere coupled model
How far can the statistical error estimation problem be closed by collocated data?
Using orthogonal vectors to improve the ensemble space of the ensemble Kalman filter and its effect on data assimilation and forecasting
Review article: Towards strongly coupled ensemble data assimilation with additional improvements from machine learning
Reducing manipulations in a control simulation experiment based on instability vectors with the Lorenz-63 model
Control simulation experiments of extreme events with the Lorenz-96 model
Toward a multivariate formulation of the parametric Kalman filter assimilation: application to a simplified chemical transport model
Data-driven reconstruction of partially observed dynamical systems
A range of outcomes: the combined effects of internal variability and anthropogenic forcing on regional climate trends over Europe
Extending ensemble Kalman filter algorithms to assimilate observations with an unknown time offset
Guidance on how to improve vertical covariance localization based on a 1000-member ensemble
Weather pattern dynamics over western Europe under climate change: predictability, information entropy and production
Using a hybrid optimal interpolation–ensemble Kalman filter for the Canadian Precipitation Analysis
Applying prior correlations for ensemble-based spatial localization
A stochastic covariance shrinkage approach to particle rejuvenation in the ensemble transform particle filter
Control simulation experiment with Lorenz's butterfly attractor
Ensemble Riemannian data assimilation: towards large-scale dynamical systems
Inferring the instability of a dynamical system from the skill of data assimilation exercises
Reduced non-Gaussianity by 30 s rapid update in convective-scale numerical weather prediction
Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system
A study of capturing Atlantic meridional overturning circulation (AMOC) regime transition through observation-constrained model parameters
Calibrated ensemble forecasts of the height of new snow using quantile regression forests and ensemble model output statistics
Enhancing geophysical flow machine learning performance via scale separation
Improving the potential accuracy and usability of EURO-CORDEX estimates of future rainfall climate using frequentist model averaging
Ensemble Riemannian data assimilation over the Wasserstein space
An early warning sign of critical transition in the Antarctic ice sheet – a data-driven tool for a spatiotemporal tipping point
Training a convolutional neural network to conserve mass in data assimilation
Behavior of the iterative ensemble-based variational method in nonlinear problems
Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation
A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective
A method for predicting the uncompleted climate transition process
Statistical postprocessing of ensemble forecasts for severe weather at Deutscher Wetterdienst
Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network
From research to applications – examples of operational ensemble post-processing in France using machine learning
Correcting for model changes in statistical postprocessing – an approach based on response theory
Brief communication: Residence time of energy in the atmosphere
Simulating model uncertainty of subgrid-scale processes by sampling model errors at convective scales
Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty
Seasonal statistical–dynamical prediction of the North Atlantic Oscillation by probabilistic post-processing and its evaluation
Vivian A. Montiforte, Hans E. Ngodock, and Innocent Souopgui
Nonlin. Processes Geophys., 31, 463–476, https://doi.org/10.5194/npg-31-463-2024, https://doi.org/10.5194/npg-31-463-2024, 2024
Short summary
Short summary
Advanced data assimilation methods are complex and computationally expensive. We compare two simpler methods, diffusive back-and-forth nudging and concave–convex nonlinearity, which account for change over time with the potential of providing accurate results with a reduced computational cost. We evaluate the accuracy of the two methods by implementing them within simple chaotic models. We conclude that the length and frequency of observations impact which method is better suited for a problem.
Jun-Ichi Yano
Nonlin. Processes Geophys., 31, 359–380, https://doi.org/10.5194/npg-31-359-2024, https://doi.org/10.5194/npg-31-359-2024, 2024
Short summary
Short summary
A methodology for directly predicting the time evolution of the assumed parameters for the distribution densities based on the Liouville equation, as proposed earlier, is extended to multidimensional cases and to cases in which the systems are constrained by integrals over a part of the variable range. The extended methodology is tested against a convective energy-cycle system as well as the Lorenz strange attractor.
Marc Bocquet, Pierre J. Vanderbecken, Alban Farchi, Joffrey Dumont Le Brazidec, and Yelva Roustan
Nonlin. Processes Geophys., 31, 335–357, https://doi.org/10.5194/npg-31-335-2024, https://doi.org/10.5194/npg-31-335-2024, 2024
Short summary
Short summary
A novel approach, optimal transport data assimilation (OTDA), is introduced to merge DA and OT concepts. By leveraging OT's displacement interpolation in space, it minimises mislocation errors within DA applied to physical fields, such as water vapour, hydrometeors, and chemical species. Its richness and flexibility are showcased through one- and two-dimensional illustrations.
Fumitoshi Kawasaki and Shunji Kotsuki
Nonlin. Processes Geophys., 31, 319–333, https://doi.org/10.5194/npg-31-319-2024, https://doi.org/10.5194/npg-31-319-2024, 2024
Short summary
Short summary
Recently, scientists have been looking into ways to control the weather to lead to a desirable direction for mitigating weather-induced disasters caused by torrential rainfall and typhoons. This study proposes using the model predictive control (MPC), an advanced control method, to control a chaotic system. Through numerical experiments using a low-dimensional chaotic system, we demonstrate that the system can be successfully controlled with shorter forecasts compared to previous studies.
Pierre Le Bras, Florian Sévellec, Pierre Tandeo, Juan Ruiz, and Pierre Ailliot
Nonlin. Processes Geophys., 31, 303–317, https://doi.org/10.5194/npg-31-303-2024, https://doi.org/10.5194/npg-31-303-2024, 2024
Short summary
Short summary
The goal of this paper is to weight several dynamic models in order to improve the representativeness of a system. It is illustrated using a set of versions of an idealized model describing the Atlantic Meridional Overturning Circulation. The low-cost method is based on data-driven forecasts. It enables model performance to be evaluated on their dynamics. Taking into account both model performance and codependency, the derived weights outperform benchmarks in reconstructing a model distribution.
Man-Yau Chan
Nonlin. Processes Geophys., 31, 287–302, https://doi.org/10.5194/npg-31-287-2024, https://doi.org/10.5194/npg-31-287-2024, 2024
Short summary
Short summary
Forecasts have uncertainties. It is thus essential to reduce these uncertainties. Such reduction requires uncertainty quantification, which often means running costly models multiple times. The cost limits the number of model runs and thus the quantification’s accuracy. This study proposes a technique that utilizes users’ knowledge of forecast uncertainties to improve uncertainty quantification. Tests show that this technique improves uncertainty reduction.
Loris Foresti, Bernat Puigdomènech Treserras, Daniele Nerini, Aitor Atencia, Marco Gabella, Ioannis V. Sideris, Urs Germann, and Isztar Zawadzki
Nonlin. Processes Geophys., 31, 259–286, https://doi.org/10.5194/npg-31-259-2024, https://doi.org/10.5194/npg-31-259-2024, 2024
Short summary
Short summary
We compared two ways of defining the phase space of low-dimensional attractors describing the evolution of radar precipitation fields. The first defines the phase space by the domain-scale statistics of precipitation fields, such as their mean, spatial and temporal correlations. The second uses principal component analysis to account for the spatial distribution of precipitation. To represent different climates, radar archives over the United States and the Swiss Alpine region were used.
Shunji Kotsuki, Fumitoshi Kawasaki, and Masanao Ohashi
Nonlin. Processes Geophys., 31, 237–245, https://doi.org/10.5194/npg-31-237-2024, https://doi.org/10.5194/npg-31-237-2024, 2024
Short summary
Short summary
In Earth science, data assimilation plays an important role in integrating real-world observations with numerical simulations for improving subsequent predictions. To overcome the time-consuming computations of conventional data assimilation methods, this paper proposes using quantum annealing machines. Using the D-Wave quantum annealer, the proposed method found solutions with comparable accuracy to conventional approaches and significantly reduced computational time.
Lev Ostrovsky, Irina Soustova, Yuliya Troitskaya, and Daria Gladskikh
Nonlin. Processes Geophys., 31, 219–227, https://doi.org/10.5194/npg-31-219-2024, https://doi.org/10.5194/npg-31-219-2024, 2024
Short summary
Short summary
The nonstationary kinetic model of turbulence is used to describe the evolution and structure of the upper turbulent layer with the parameters taken from in situ observations. As an example, we use a set of data for three cruises made in different areas of the world ocean. With the given profiles of current shear and buoyancy frequency, the theory yields results that satisfactorily agree with the measurements of the turbulent dissipation rate.
Aurelien Luigi Serge Ponte, Lachlan Astfalck, Matthew Rayson, Andrew Zulberti, and Nicole Jones
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-10, https://doi.org/10.5194/npg-2024-10, 2024
Revised manuscript accepted for NPG
Short summary
Short summary
We propose a novel method for the estimation of ocean flow properties in terms of its energy, spatial and temporal scales. The method relies on flow observations that are either collected at a fixed location or along the flow as they would if inferred from the trajectory of freely-drifting platforms. The accuracy of the method is quantified in different experimental configurations. We demonstrate freely drifting platforms can, even in isolation, enable to capture flow properties is a first.
Thomas Muschinski, Georg J. Mayr, Achim Zeileis, and Thorsten Simon
Nonlin. Processes Geophys., 30, 503–514, https://doi.org/10.5194/npg-30-503-2023, https://doi.org/10.5194/npg-30-503-2023, 2023
Short summary
Short summary
Statistical post-processing is necessary to generate probabilistic forecasts from physical numerical weather prediction models. To allow for more flexibility, there has been a shift in post-processing away from traditional parametric regression models towards modern machine learning methods. By fusing these two approaches, we developed model output statistics random forests, a new post-processing method that is highly flexible but at the same time also very robust and easy to interpret.
Kenta Kurosawa, Shunji Kotsuki, and Takemasa Miyoshi
Nonlin. Processes Geophys., 30, 457–479, https://doi.org/10.5194/npg-30-457-2023, https://doi.org/10.5194/npg-30-457-2023, 2023
Short summary
Short summary
This study aimed to enhance weather and hydrological forecasts by integrating soil moisture data into a global weather model. By assimilating atmospheric observations and soil moisture data, the accuracy of forecasts was improved, and certain biases were reduced. The method was found to be particularly beneficial in areas like the Sahel and equatorial Africa, where precipitation patterns vary seasonally. This new approach has the potential to improve the precision of weather predictions.
Annika Vogel and Richard Ménard
Nonlin. Processes Geophys., 30, 375–398, https://doi.org/10.5194/npg-30-375-2023, https://doi.org/10.5194/npg-30-375-2023, 2023
Short summary
Short summary
Accurate estimation of the error statistics required for data assimilation remains an ongoing challenge, as statistical assumptions are required to solve the estimation problem. This work provides a conceptual view of the statistical error estimation problem in light of the increasing number of available datasets. We found that the total number of required assumptions increases with the number of overlapping datasets, but the relative number of error statistics that can be estimated increases.
Yung-Yun Cheng, Shu-Chih Yang, Zhe-Hui Lin, and Yung-An Lee
Nonlin. Processes Geophys., 30, 289–297, https://doi.org/10.5194/npg-30-289-2023, https://doi.org/10.5194/npg-30-289-2023, 2023
Short summary
Short summary
In the ensemble Kalman filter, the ensemble space may not fully capture the forecast errors due to the limited ensemble size and systematic model errors, which affect the accuracy of analysis and prediction. This study proposes a new algorithm to use cost-free pseudomembers to expand the ensemble space effectively and improve analysis accuracy during the analysis step, without increasing the ensemble size during forecasting.
Eugenia Kalnay, Travis Sluka, Takuma Yoshida, Cheng Da, and Safa Mote
Nonlin. Processes Geophys., 30, 217–236, https://doi.org/10.5194/npg-30-217-2023, https://doi.org/10.5194/npg-30-217-2023, 2023
Short summary
Short summary
Strongly coupled data assimilation (SCDA) generates coherent integrated Earth system analyses by assimilating the full Earth observation set into all Earth components. We describe SCDA based on the ensemble Kalman filter with a hierarchy of coupled models, from a coupled Lorenz to the Climate Forecast System v2. SCDA with a sufficiently large ensemble can provide more accurate coupled analyses compared to weakly coupled DA. The correlation-cutoff method can compensate for a small ensemble size.
Mao Ouyang, Keita Tokuda, and Shunji Kotsuki
Nonlin. Processes Geophys., 30, 183–193, https://doi.org/10.5194/npg-30-183-2023, https://doi.org/10.5194/npg-30-183-2023, 2023
Short summary
Short summary
This research found that weather control would change the chaotic behavior of an atmospheric model. We proposed to introduce chaos theory in the weather control. Experimental results demonstrated that the proposed approach reduced the manipulations, including the control times and magnitudes, which throw light on the weather control in a real atmospheric model.
Qiwen Sun, Takemasa Miyoshi, and Serge Richard
Nonlin. Processes Geophys., 30, 117–128, https://doi.org/10.5194/npg-30-117-2023, https://doi.org/10.5194/npg-30-117-2023, 2023
Short summary
Short summary
This paper is a follow-up of a work by Miyoshi and Sun which was published in NPG Letters in 2022. The control simulation experiment is applied to the Lorenz-96 model for avoiding extreme events. The results show that extreme events of this partially and imperfectly observed chaotic system can be avoided by applying pre-designed small perturbations. These investigations may be extended to more realistic numerical weather prediction models.
Antoine Perrot, Olivier Pannekoucke, and Vincent Guidard
Nonlin. Processes Geophys., 30, 139–166, https://doi.org/10.5194/npg-30-139-2023, https://doi.org/10.5194/npg-30-139-2023, 2023
Short summary
Short summary
This work is a theoretical contribution that provides equations for understanding uncertainty prediction applied in air quality where multiple chemical species can interact. A simplified minimal test bed is introduced that shows the ability of our equations to reproduce the statistics estimated from an ensemble of forecasts. While the latter estimation is the state of the art, solving equations is numerically less costly, depending on the number of chemical species, and motivates this research.
Pierre Tandeo, Pierre Ailliot, and Florian Sévellec
Nonlin. Processes Geophys., 30, 129–137, https://doi.org/10.5194/npg-30-129-2023, https://doi.org/10.5194/npg-30-129-2023, 2023
Short summary
Short summary
The goal of this paper is to obtain probabilistic predictions of a partially observed dynamical system without knowing the model equations. It is illustrated using the three-dimensional Lorenz system, where only two components are observed. The proposed data-driven procedure is low-cost, is easy to implement, uses linear and Gaussian assumptions and requires only a small amount of data. It is based on an iterative linear Kalman smoother with a state augmentation.
Clara Deser and Adam S. Phillips
Nonlin. Processes Geophys., 30, 63–84, https://doi.org/10.5194/npg-30-63-2023, https://doi.org/10.5194/npg-30-63-2023, 2023
Short summary
Short summary
Past and future climate change at regional scales is a result of both human influences and natural (internal) variability. Here, we provide an overview of recent advances in climate modeling and physical understanding that has led to new insights into their respective roles, illustrated with original results for the European climate. Our findings highlight the confounding role of internal variability in attribution, climate model evaluation, and accuracy of future projections.
Elia Gorokhovsky and Jeffrey L. Anderson
Nonlin. Processes Geophys., 30, 37–47, https://doi.org/10.5194/npg-30-37-2023, https://doi.org/10.5194/npg-30-37-2023, 2023
Short summary
Short summary
Older observations of the Earth system sometimes lack information about the time they were taken, posing problems for analyses of past climate. To begin to ameliorate this problem, we propose new methods of varying complexity, including methods to estimate the distribution of the offsets between true and reported observation times. The most successful method accounts for the nonlinearity in the system, but even the less expensive ones can improve data assimilation in the presence of time error.
Tobias Necker, David Hinger, Philipp Johannes Griewank, Takemasa Miyoshi, and Martin Weissmann
Nonlin. Processes Geophys., 30, 13–29, https://doi.org/10.5194/npg-30-13-2023, https://doi.org/10.5194/npg-30-13-2023, 2023
Short summary
Short summary
This study investigates vertical localization based on a convection-permitting 1000-member ensemble simulation. We derive an empirical optimal localization (EOL) that minimizes sampling error in 40-member sub-sample correlations assuming 1000-member correlations as truth. The results will provide guidance for localization in convective-scale ensemble data assimilation systems.
Stéphane Vannitsem
Nonlin. Processes Geophys., 30, 1–12, https://doi.org/10.5194/npg-30-1-2023, https://doi.org/10.5194/npg-30-1-2023, 2023
Short summary
Short summary
The impact of climate change on weather pattern dynamics over the North Atlantic is explored through the lens of information theory. These tools allow the predictability of the succession of weather patterns and the irreversible nature of the dynamics to be clarified. It is shown that the predictability is increasing in the observations, while the opposite trend is found in model projections. The irreversibility displays an overall increase in time in both the observations and the model runs.
Dikraa Khedhaouiria, Stéphane Bélair, Vincent Fortin, Guy Roy, and Franck Lespinas
Nonlin. Processes Geophys., 29, 329–344, https://doi.org/10.5194/npg-29-329-2022, https://doi.org/10.5194/npg-29-329-2022, 2022
Short summary
Short summary
This study introduces a well-known use of hybrid methods in data assimilation (DA) algorithms that has not yet been explored for precipitation analyses. Our approach combined an ensemble-based DA approach with an existing deterministically based DA. Both DA scheme families have desirable aspects that can be leveraged if combined. The DA hybrid method showed better precipitation analyses in regions with a low rate of assimilated surface observations, which is typically the case in winter.
Chu-Chun Chang and Eugenia Kalnay
Nonlin. Processes Geophys., 29, 317–327, https://doi.org/10.5194/npg-29-317-2022, https://doi.org/10.5194/npg-29-317-2022, 2022
Short summary
Short summary
This study introduces a new approach for enhancing the ensemble data assimilation (DA), a technique that combines observations and forecasts to improve numerical weather predictions. Our method uses the prescribed correlations to suppress spurious errors, improving the accuracy of DA. The experiments on the simplified atmosphere model show that our method has comparable performance to the traditional method but is superior in the early stage and is more computationally efficient.
Andrey A. Popov, Amit N. Subrahmanya, and Adrian Sandu
Nonlin. Processes Geophys., 29, 241–253, https://doi.org/10.5194/npg-29-241-2022, https://doi.org/10.5194/npg-29-241-2022, 2022
Short summary
Short summary
Numerical weather prediction requires the melding of both computational model and data obtained from sensors such as satellites. We focus on one algorithm to accomplish this. We aim to aid its use by additionally supplying it with data obtained from separate models that describe the average behavior of the computational model at any given time. We show that our approach outperforms the standard approaches to this problem.
Takemasa Miyoshi and Qiwen Sun
Nonlin. Processes Geophys., 29, 133–139, https://doi.org/10.5194/npg-29-133-2022, https://doi.org/10.5194/npg-29-133-2022, 2022
Short summary
Short summary
The weather is chaotic and hard to predict, but the chaos implies an effective control where a small control signal grows rapidly to make a big difference. This study proposes a control simulation experiment where we apply a small signal to control
naturein a computational simulation. Idealized experiments with a low-order chaotic system show successful results by small control signals of only 3 % of the observation error. This is the first step toward realistic weather simulations.
Sagar K. Tamang, Ardeshir Ebtehaj, Peter Jan van Leeuwen, Gilad Lerman, and Efi Foufoula-Georgiou
Nonlin. Processes Geophys., 29, 77–92, https://doi.org/10.5194/npg-29-77-2022, https://doi.org/10.5194/npg-29-77-2022, 2022
Short summary
Short summary
The outputs from Earth system models are optimally combined with satellite observations to produce accurate forecasts through a process called data assimilation. Many existing data assimilation methodologies have some assumptions regarding the shape of the probability distributions of model output and observations, which results in forecast inaccuracies. In this paper, we test the effectiveness of a newly proposed methodology that relaxes such assumptions about high-dimensional models.
Yumeng Chen, Alberto Carrassi, and Valerio Lucarini
Nonlin. Processes Geophys., 28, 633–649, https://doi.org/10.5194/npg-28-633-2021, https://doi.org/10.5194/npg-28-633-2021, 2021
Short summary
Short summary
Chaotic dynamical systems are sensitive to the initial conditions, which are crucial for climate forecast. These properties are often used to inform the design of data assimilation (DA), a method used to estimate the exact initial conditions. However, obtaining the instability properties is burdensome for complex problems, both numerically and analytically. Here, we suggest a different viewpoint. We show that the skill of DA can be used to infer the instability properties of a dynamical system.
Juan Ruiz, Guo-Yuan Lien, Keiichi Kondo, Shigenori Otsuka, and Takemasa Miyoshi
Nonlin. Processes Geophys., 28, 615–626, https://doi.org/10.5194/npg-28-615-2021, https://doi.org/10.5194/npg-28-615-2021, 2021
Short summary
Short summary
Effective use of observations with numerical weather prediction models, also known as data assimilation, is a key part of weather forecasting systems. For precise prediction at the scales of thunderstorms, fast nonlinear processes pose a grand challenge because most data assimilation systems are based on linear processes and normal distribution errors. We investigate how, every 30 s, weather radar observations can help reduce the effect of nonlinear processes and nonnormal distributions.
Zofia Stanley, Ian Grooms, and William Kleiber
Nonlin. Processes Geophys., 28, 565–583, https://doi.org/10.5194/npg-28-565-2021, https://doi.org/10.5194/npg-28-565-2021, 2021
Short summary
Short summary
In weather forecasting, observations are incorporated into a model of the atmosphere through a process called data assimilation. Sometimes observations in one location may impact the weather forecast in another faraway location in undesirable ways. The impact of distant observations on the forecast is mitigated through a process called localization. We propose a new method for localization when a model has multiple length scales, as in a model spanning both the ocean and the atmosphere.
Zhao Liu, Shaoqing Zhang, Yang Shen, Yuping Guan, and Xiong Deng
Nonlin. Processes Geophys., 28, 481–500, https://doi.org/10.5194/npg-28-481-2021, https://doi.org/10.5194/npg-28-481-2021, 2021
Short summary
Short summary
A general methodology is introduced to capture regime transitions of the Atlantic meridional overturning circulation (AMOC). The assimilation models with different parameters simulate different paths for the AMOC to switch between equilibrium states. Constraining model parameters with observations can significantly mitigate the model deviations, thus capturing AMOC regime transitions. This simple model study serves as a guideline for improving coupled general circulation models.
Guillaume Evin, Matthieu Lafaysse, Maxime Taillardat, and Michaël Zamo
Nonlin. Processes Geophys., 28, 467–480, https://doi.org/10.5194/npg-28-467-2021, https://doi.org/10.5194/npg-28-467-2021, 2021
Short summary
Short summary
Forecasting the height of new snow is essential for avalanche hazard surveys, road and ski resort management, tourism attractiveness, etc. Météo-France operates a probabilistic forecasting system using a numerical weather prediction system and a snowpack model. It provides better forecasts than direct diagnostics but exhibits significant biases. Post-processing methods can be applied to provide automatic forecasting products from this system.
Davide Faranda, Mathieu Vrac, Pascal Yiou, Flavio Maria Emanuele Pons, Adnane Hamid, Giulia Carella, Cedric Ngoungue Langue, Soulivanh Thao, and Valerie Gautard
Nonlin. Processes Geophys., 28, 423–443, https://doi.org/10.5194/npg-28-423-2021, https://doi.org/10.5194/npg-28-423-2021, 2021
Short summary
Short summary
Machine learning approaches are spreading rapidly in climate sciences. They are of great help in many practical situations where using the underlying equations is difficult because of the limitation in computational power. Here we use a systematic approach to investigate the limitations of the popular echo state network algorithms used to forecast the long-term behaviour of chaotic systems, such as the weather. Our results show that noise and intermittency greatly affect the performances.
Stephen Jewson, Giuliana Barbato, Paola Mercogliano, Jaroslav Mysiak, and Maximiliano Sassi
Nonlin. Processes Geophys., 28, 329–346, https://doi.org/10.5194/npg-28-329-2021, https://doi.org/10.5194/npg-28-329-2021, 2021
Short summary
Short summary
Climate model simulations are uncertain. In some cases this makes it difficult to know how to use them. Significance testing is often used to deal with this issue but has various shortcomings. We describe two alternative ways to manage uncertainty in climate model simulations that avoid these shortcomings. We test them on simulations of future rainfall over Europe and show they produce more accurate projections than either using unadjusted climate model output or statistical testing.
Sagar K. Tamang, Ardeshir Ebtehaj, Peter J. van Leeuwen, Dongmian Zou, and Gilad Lerman
Nonlin. Processes Geophys., 28, 295–309, https://doi.org/10.5194/npg-28-295-2021, https://doi.org/10.5194/npg-28-295-2021, 2021
Short summary
Short summary
Data assimilation aims to improve hydrologic and weather forecasts by combining available information from Earth system models and observations. The classical approaches to data assimilation usually proceed with some preconceived assumptions about the shape of their probability distributions. As a result, when such assumptions are invalid, the forecast accuracy suffers. In the proposed methodology, we relax such assumptions and demonstrate improved performance.
Abd AlRahman AlMomani and Erik Bollt
Nonlin. Processes Geophys., 28, 153–166, https://doi.org/10.5194/npg-28-153-2021, https://doi.org/10.5194/npg-28-153-2021, 2021
Short summary
Short summary
This paper introduces a tool for data-driven discovery of early warning signs of critical transitions in ice shelves from remote sensing data. Our directed spectral clustering method considers an asymmetric affinity matrix along with the associated directed graph Laplacian. We applied our approach to reprocessing the ice velocity data and remote sensing satellite images of the Larsen C ice shelf.
Yvonne Ruckstuhl, Tijana Janjić, and Stephan Rasp
Nonlin. Processes Geophys., 28, 111–119, https://doi.org/10.5194/npg-28-111-2021, https://doi.org/10.5194/npg-28-111-2021, 2021
Short summary
Short summary
The assimilation of observations using standard algorithms can lead to a violation of physical laws (e.g. mass conservation), which is shown to have a detrimental impact on the system's forecast. We use a neural network (NN) to correct this mass violation, using training data generated from expensive algorithms that can constrain such physical properties. We found that, in an idealized set-up, the NN can match the performance of these expensive algorithms at negligible computational costs.
Shin'ya Nakano
Nonlin. Processes Geophys., 28, 93–109, https://doi.org/10.5194/npg-28-93-2021, https://doi.org/10.5194/npg-28-93-2021, 2021
Short summary
Short summary
The ensemble-based variational method is a method for solving nonlinear data assimilation problems by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to analyze its behavior in high-dimensional nonlinear problems and discuss the convergence.
Sangeetika Ruchi, Svetlana Dubinkina, and Jana de Wiljes
Nonlin. Processes Geophys., 28, 23–41, https://doi.org/10.5194/npg-28-23-2021, https://doi.org/10.5194/npg-28-23-2021, 2021
Short summary
Short summary
To infer information of an unknown quantity that helps to understand an associated system better and to predict future outcomes, observations and a physical model that connects the data points to the unknown parameter are typically used as information sources. Yet this problem is often very challenging due to the fact that the unknown is generally high dimensional, the data are sparse and the model can be non-linear. We propose a novel approach to address these challenges.
Olivier Pannekoucke, Richard Ménard, Mohammad El Aabaribaoune, and Matthieu Plu
Nonlin. Processes Geophys., 28, 1–22, https://doi.org/10.5194/npg-28-1-2021, https://doi.org/10.5194/npg-28-1-2021, 2021
Short summary
Short summary
Numerical weather prediction involves numerically solving the mathematical equations, which describe the geophysical flow, by transforming them so that they can be computed. Through this transformation, it appears that the equations actually solved by the machine are then a modified version of the original equations, introducing an error that contributes to the model error. This work helps to characterize the covariance of the model error that is due to this modification of the equations.
Pengcheng Yan, Guolin Feng, Wei Hou, and Ping Yang
Nonlin. Processes Geophys., 27, 489–500, https://doi.org/10.5194/npg-27-489-2020, https://doi.org/10.5194/npg-27-489-2020, 2020
Short summary
Short summary
A system transiting from one stable state to another has to experience a period. Can we predict the end moment (state) if the process has not been completed? This paper presents a method to solve this problem. This method is based on the quantitative relationship among the parameters, which is used to describe the transition process of the abrupt change. By using the historical data, we extract some parameters for predicting the uncompleted climate transition process.
Reinhold Hess
Nonlin. Processes Geophys., 27, 473–487, https://doi.org/10.5194/npg-27-473-2020, https://doi.org/10.5194/npg-27-473-2020, 2020
Short summary
Short summary
Forecasts of ensemble systems are statistically aligned to synoptic observations at DWD in order to provide support for warning decision management. Motivation and design consequences for extreme and rare meteorological events are presented. Especially for probabilities of severe wind gusts global logistic parameterisations are developed that generate robust statistical forecasts for extreme events, while local characteristics are preserved.
Ashesh Chattopadhyay, Pedram Hassanzadeh, and Devika Subramanian
Nonlin. Processes Geophys., 27, 373–389, https://doi.org/10.5194/npg-27-373-2020, https://doi.org/10.5194/npg-27-373-2020, 2020
Short summary
Short summary
The performance of three machine-learning methods for data-driven modeling of a multiscale chaotic Lorenz 96 system is examined. One of the methods is found to be able to predict the future evolution of the chaotic system well from just knowing the past observations of the large-scale component of the multiscale state vector. Potential applications to data-driven and data-assisted surrogate modeling of complex dynamical systems such as weather and climate are discussed.
Maxime Taillardat and Olivier Mestre
Nonlin. Processes Geophys., 27, 329–347, https://doi.org/10.5194/npg-27-329-2020, https://doi.org/10.5194/npg-27-329-2020, 2020
Short summary
Short summary
Statistical post-processing of ensemble forecasts is now a well-known procedure in order to correct biased and misdispersed ensemble weather predictions. But practical application in European national weather services is in its infancy. Different applications of ensemble post-processing using machine learning at an industrial scale are presented. Forecast quality and value are improved compared to the raw ensemble, but several facilities have to be made to adjust to operational constraints.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 27, 307–327, https://doi.org/10.5194/npg-27-307-2020, https://doi.org/10.5194/npg-27-307-2020, 2020
Short summary
Short summary
Postprocessing schemes used to correct weather forecasts are no longer efficient when the model generating the forecasts changes. An approach based on response theory to take the change into account without having to recompute the parameters based on past forecasts is presented. It is tested on an analytical model and a simple model of atmospheric variability. We show that this approach is effective and discuss its potential application for an operational environment.
Carlos Osácar, Manuel Membrado, and Amalio Fernández-Pacheco
Nonlin. Processes Geophys., 27, 235–237, https://doi.org/10.5194/npg-27-235-2020, https://doi.org/10.5194/npg-27-235-2020, 2020
Short summary
Short summary
We deduce that after a global thermal perturbation, the Earth's
atmosphere would need about a couple of months to come back to equilibrium.
Michiel Van Ginderachter, Daan Degrauwe, Stéphane Vannitsem, and Piet Termonia
Nonlin. Processes Geophys., 27, 187–207, https://doi.org/10.5194/npg-27-187-2020, https://doi.org/10.5194/npg-27-187-2020, 2020
Short summary
Short summary
A generic methodology is developed to estimate the model error and simulate the model uncertainty related to a specific physical process. The method estimates the model error by comparing two different representations of the physical process in otherwise identical models. The found model error can then be used to perturb the model and simulate the model uncertainty. When applying this methodology to deep convection an improvement in the probabilistic skill of the ensemble forecast is found.
Valentin Resseguier, Wei Pan, and Baylor Fox-Kemper
Nonlin. Processes Geophys., 27, 209–234, https://doi.org/10.5194/npg-27-209-2020, https://doi.org/10.5194/npg-27-209-2020, 2020
Short summary
Short summary
Geophysical flows span a broader range of temporal and spatial scales than can be resolved numerically. One way to alleviate the ensuing numerical errors is to combine simulations with measurements, taking account of the accuracies of these two sources of information. Here we quantify the distribution of numerical simulation errors without relying on high-resolution numerical simulations. Specifically, small-scale random vortices are added to simulations while conserving energy or circulation.
André Düsterhus
Nonlin. Processes Geophys., 27, 121–131, https://doi.org/10.5194/npg-27-121-2020, https://doi.org/10.5194/npg-27-121-2020, 2020
Short summary
Short summary
Seasonal prediction of the of the North Atlantic Oscillation (NAO) has been improved in recent years by improving dynamical models and ensemble predictions. One step therein was the so-called sub-sampling, which combines statistical and dynamical predictions. This study generalises this approach and makes it much more accessible. Furthermore, it presents a new verification approach for such predictions.
Cited articles
Abarbanel, H. D., Brown, R., and Kennel, M. B.: Variation of Lyapunov
exponents on a strange attractor, J. Nonlinear Sci., 1, 175–199,
https://doi.org/10.1007/BF01209065, 1991. a
Barsugli, J. J. and Battisti, D. S.: The Basic Effects of Atmosphere-Ocean
Thermal Coupling on Midlatitude Variability, J. Atmos.
Sci., 55, 477–493,
https://doi.org/10.1175/1520-0469(1998)055<0477:TBEOAO>2.0.CO;2, 1998. a
Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J.-M.: Lyapunov
Characteristic Exponents for smooth dynamical systems and for hamiltonian
systems; a method for computing all of them. Part 1: Theory, Meccanica, 15,
9–20, https://doi.org/10.1007/BF02128236, 1980. a
Boffetta, G., Cencini, M., Falcioni, M., and Vulpiani, A.: Predictability: a
way to characterize complexity, Phys. Rep., 356, 367–474,
https://doi.org/10.1016/S0370-1573(01)00025-4, 2002. a
Boschi, R., Lucarini, V., and Pascale, S.: Bistability of the climate around
the habitable zone: A thermodynamic investigation, Icarus, 226, 1724–1742,
https://doi.org/10.1016/j.icarus.2013.03.017, 2013. a
Carrassi, A., Trevisan, A., Descamps, L., Talagrand, O., and Uboldi, F.:
Controlling instabilities along a 3DVar analysis cycle by assimilating in the
unstable subspace: a comparison with the EnKF, Nonlin. Processes Geophys.,
15, 503–521, https://doi.org/10.5194/npg-15-503-2008, 2008. a
Cencini, M. and Ginelli, F.: Lyapunov analysis: from dynamical systems
theory
to applications, J. Phys. A-Math. Theor., 46,
250301, https://doi.org/10.1088/1751-8113/46/25/250301, 2013. a
Cencini, M., Cecconi, F., and Vulpiani, A.: Chaos: From Simple Models to
Complex Systems, vol. 17 of Series on Advances in Statistical
Mechanics, World Scientific, https://doi.org/10.1142/7351, 2010. a, b
Charney, J. G.: The Dynamics Of Long Waves In A Baroclinic Current, J.
Meteorol., 4, 136–162,
https://doi.org/10.1175/1520-0469(1947)004<0136:TDOLWI>2.0.CO;2, 1947. a, b
Charney, J. G. and Straus, D. M.: Form-Drag Instability, Multiple Equilibria
and Propagating Planetary Waves in Baroclinic, Orographically Forced,
Planetary Wave Systems, J. Atmos. Sci., 37, 1157–1176,
https://doi.org/10.1175/1520-0469(1980)037<1157:FDIMEA>2.0.CO;2, 1980. a, b
De Cruz, L., Demaeyer, J., Schubert, S., and Vannitsem, S.: MAOOAM
v1.3.1-lyapunov, Zenodo, https://doi.org/10.5281/zenodo.1198650, 2018. a
Demaeyer, J. and Vannitsem, S.: Stochastic parametrization of subgrid-scale
processes in coupled ocean–atmosphere systems: benefits and limitations of
response theory, Q. J. Roy. Meteor. Soc., 143,
881–896, https://doi.org/10.1002/qj.2973, 2016. a
Eady, E. T.: Long Waves and Cyclone Waves, Tellus, 1, 33–52,
https://doi.org/10.1111/j.2153-3490.1949.tb01265.x, 1949. a, b
Ershov, S. V. and Potapov, A. B.: On the concept of stationary Lyapunov
basis, Physica D, 118, 167–198,
https://doi.org/10.1016/S0167-2789(98)00013-X, 1998. a
Fraedrich, K. and Kirk, E.: The portable university model of the atmosphere
(PUMA): Storm track dynamics and low-frequency variability, Meteorol.
Z., 14, 735–745, https://doi.org/10.1127/0941-2948/2005/0074, 2005. a
Frederickson, P., Kaplan, J. L., Yorke, E. D., and Yorke, J. A.: The
Liapunov
dimension of strange attractors, J. Differ. Equations, 49,
185–207, https://doi.org/10.1016/0022-0396(83)90011-6, 1983. a
Fujisaka, H.: Statistical dynamics generated by fluctuations of local
Lyapunov
exponents, Prog. Theor. Phys., 70, 1264–1275,
https://doi.org/10.1143/PTP.70.1264, 1983. a
Gallavotti, G. and Cohen, E. G. D.: Dynamical Ensembles in Nonequilibrium
Statistical Mechanics, Phys. Rev. Lett., 74, 2694–2697,
https://doi.org/10.1103/PhysRevLett.74.2694, 1995. a
Gallavotti, G.: Nonequilibrium and Irreversibility, Springer, New York, USA,
2014. a
Gallavotti, G. and Lucarini, V.: Equivalence of Non-equilibrium Ensembles
and Representation of Friction in Turbulent Flows: The Lorenz 96 Model, J.
Stat. Phys., 156, 1027–1065, https://doi.org/10.1007/s10955-014-1051-6, 2014. a
Gallez, D. and Babloyantz, A.: Lyapunov exponents for nonuniform
attractors, Phys. Lett., 161, 247–254, https://doi.org/10.1016/0375-9601(91)90012-W,
1991. a
Giering, R. and Kaminski, T.: Applying TAF to generate efficient derivative
code of Fortran 77-95 programs, PAMM, 2, 54–57,
https://doi.org/10.1002/pamm.200310014, 2003. a
Ginelli, F., Poggi, P., Turchi, A., Chaté, H., Livi, R., and Politi,
A.:
Characterizing dynamics with covariant Lyapunov vectors, Phys. Rev.
Lett., 99, 130601, https://doi.org/10.1103/PhysRevLett.99.130601, 2007. a
Held, I. M. and Suarez, M. J.: A Proposal for the Intercomparison of the
Dynamical Cores of Atmospheric General Circulation Models, B.
Am. Meteorol. Soc., 75, 1825–1830,
https://doi.org/10.1175/1520-0477(1994)075<1825:APFTIO>2.0.CO;2, 1994. a
Holden, P. B., Edwards, N. R., Garthwaite, P. H., Fraedrich, K., Lunkeit, F.,
Kirk, E., Labriet, M., Kanudia, A., and Babonneau, F.: PLASIM-ENTSem v1.0: a
spatio-temporal emulator of future climate change for impacts assessment,
Geosci. Model Dev., 7, 433–451, https://doi.org/10.5194/gmd-7-433-2014, 2014. a
Holton, J. R.: An Introduction To Dynamic Meteorology, 4th edn., Academic
Press, San Diego, California, USA, 2004. a
Kalnay, E.: Atmospheric Modeling, Data Assimilation, and Predictability,
Cambridge University Press, New York, USA, 2003. a
Kaplan, J. L. and Yorke, J. A.: Chaotic behavior of multidimensional
difference
equations, in: Functional Differential Equations and Approximation of Fixed
Points: Proceedings, Bonn, July 1978, edited by: Peitgen, H.-O. and Walther,
H.-O., Springer-Verlag, Berlin, Germany, 204–227, 1979. a
Kifer, Y.: Large deviations in dynamical systems and stochastic processes,
T. Am. Math. Soc., 321, 505–524,
https://doi.org/10.1090/S0002-9947-1990-1025756-7, 1990. a, b
Klein, R.: Scale-Dependent Models for Atmospheric Flows, Annu. Rev. Fluid
Mech., 42, 249–274, https://doi.org/10.1146/annurev-fluid-121108-145537, 2010. a, b
Kuptsov, P. V. and Politi, A.: Large-deviation approach to space-time chaos,
Phys. Rev. Lett., 107, 114101, https://doi.org/10.1103/PhysRevLett.107.114101, 2011. a
Laffargue, T., Lam, K.-D. N. T., Kurchan, J., and Tailleur, J.: Large
deviations of Lyapunov exponents, J. Phys. A-Math.
Theor., 46, 254002, https://doi.org/10.1088/1751-8113/46/25/254002, 2013. a, b
Legras, B. and Ghil, M.: Persistent Anomalies, Blocking and Variations in
Atmospheric Predictability, J. Atmos. Sci., 42,
433–471, https://doi.org/10.1175/1520-0469(1985)042<0433:PABAVI>2.0.CO;2, 1985. a
Lesieur, M.: Introduction to Turbulence in Fluid Mechanics, in: Turbulence
in Fluids: Stochastic and Numerical Modelling, Springer, Dordrecht, the
Netherlands, 1–18, https://doi.org/10.1007/978-94-009-0533-7_1, 1990. a
Lorenz, E. N.: Deterministic Nonperiodic Flow, J. Atmos. Sci., 20,
130–141, https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2, 1963. a
Lucarini, V. and Fraedrich, K.: Symmetry breaking, mixing, instability, and
low-frequency variability in a minimal Lorenz-like system, Phys. Rev.
E, 80, 026313, https://doi.org/10.1103/PhysRevE.80.026313, 2009. a
Lucarini, V. and Ragone, F.: Energetics Of Climate Models: Net Energy
Balance
And Meridional Enthalpy Transport, Rev. Geophys., 49, RG1001,
https://doi.org/10.1029/2009RG000323, 2011. a
Lucarini, V., Speranza, A., and Vitolo, R.: Parametric smoothness and
self-scaling of the statistical properties of a minimal climate model: What
beyond the mean field theories?, Physica D, 234,
105–123, https://doi.org/10.1016/j.physd.2007.07.006, 2007. a, b, c
Lucarini, V., Fraedrich, K., and Lunkeit, F.: Thermodynamic analysis of
snowball earth hysteresis experiment: efficiency, entropy production and
irreversibility, Q. J. Roy. Meteor. Soc., 136,2–11, https://doi.org/10.1002/qj.543,
2010. a
Lucarini, V., Blender, R., Herbert, C., Ragone, F., Pascale, S., and Wouters,
J.: Mathematical and physical ideas for climate science, Rev.
Geophys., 52, 809–859, https://doi.org/10.1002/2013RG000446, 2014. a, b
Lucarini, V., Ragone, F., and Lunkeit, F.: Predicting climate change using
response theory: global averages and spatial patterns, J. Stat.
Phys., 166, 1036–1064, https://doi.org/10.1007/s10955-016-1506-z, 2017. a, b
Manneville, P.: Liapounov exponents for the Kuramoto-Sivashinsky model, in:
Macroscopic Modelling of Turbulent Flows, Springer
Berlin Heidelberg, Berlin, Heidelberg, Germany, vol. 230, 319–326, https://doi.org/10.1007/3-540-15644-5_26, 1985. a
Manneville, P.: Dissipative structures and weak turbulence, in: Chaos –
The Interplay Between Stochastic and Deterministic Behaviour, Springer Berlin
Heidelberg, Berlin, Heidelberg, Germany, vol. 457, 257–272,
https://doi.org/10.1007/3-540-60188-0_59, 1995. a, b
Molemaker, M. J., McWilliams, J. C., and Yavneh, I.: Baroclinic Instability
and Loss of Balance, J. Phys. Oceanogr., 35, 1505–1517,
https://doi.org/10.1175/JPO2770.1, 2005. a
Nese, J. M. and Dutton, J. A.: Quantifying predictability variations in a
low-order occan-atmosphere model: a dynamical systems approach, J.
Climate, 6, 185–204, https://doi.org/10.1175/1520-0442(1993)006<0185:QPVIAL>2.0.CO;2,
1993. a
Nicolis, C.: Dynamics of model error: The role of the boundary conditions,
J. Atmos. Sci., 64, 204–215,
https://doi.org/10.1175/JAS3806.1, 2007. a
Nicolis, C., Nicolis, G., and Wang, Q.: Sensitivity To Initial Conditions In
Spatially Distributed Systems, Int. J. Bifurcat.
Chaos, 02, 263–269, https://doi.org/10.1142/S0218127492000276, 1992. a
Nicolis, C., Perdigao, R. A., and Vannitsem, S.: Dynamics of prediction
errors
under the combined effect of initial condition and model errors, J. Atmos. Sci., 66, 766–778, https://doi.org/10.1175/2008JAS2781.1, 2009. a
Oseledets, V.: Oseledets theorem, Scholarpedia, 3, 1846,
https://doi.org/10.4249/scholarpedia.1846, 2008. a
Oseledets, V. I.: A multiplicative ergodic theorem. Characteristic Ljapunov,
exponents of dynamical systems, Transactions of the Moscow Mathematical
Society, 19, 179–210,
1968. a
Ott, E.: Chaos in Dynamical Systems – 2nd Edition, Cambridge University
Press, https://doi.org/10.1017/CBO9780511803260, 2002. a
Pazó, D., Szendro, I. G., López, J. M., and Rodríguez,
M. A.:
Structure of characteristic Lyapunov vectors in spatiotemporal chaos,
Phys. Rev. E, 78, 1–9, https://doi.org/10.1103/PhysRevE.78.016209, 2008. a
Pazó, D., Rodríguez, M. A., and López, J. M.:
Spatio-temporal evolution of perturbations in ensembles initialized by bred,
Lyapunov and singular vectors, Tellus A, 62, 10–23, https://doi.org/10.1111/j.1600-0870.2009.00419.x, 2010. a, b
Pazó, D., López, J. M., and Politi, A.: Universal scaling of
Lyapunov-exponent fluctuations in space-time chaos, Phys. Rev. E, 87,
062909, https://doi.org/10.1103/PhysRevE.87.062909, 2013. a, b
Pedlosky, J.: The Stability of Currents in the Atmosphere and the Ocean:
Part II, J. Atmos. Sci., 21, 201–219,
https://doi.org/10.1175/1520-0469(1964)021<0342:TSOCIT>2.0.CO;2,
1964. a, b
Pelly, J. L. and Hoskins, B. J.: A New Perspective on Blocking, J. Atmos.
Sci., 60, 743–755,
https://doi.org/10.1175/1520-0469(2003)060<0743:ANPOB>2.0.CO;2, 2003. a
Pesin, Y.: Lectures on Partial Hyperbolicity and Stable Ergodicity, European
Mathematical Society, Zurich, Switzerland, 2004. a
Pierini, S.: Low-frequency variability, coherence resonance, and phase
selection in a low-order model of the wind-driven ocean circulation, J.
Phys. Oceanogr., 41, 1585–1604, https://doi.org/10.1175/JPO-D-10-05018.1,
2011. a
Plougonven, R. and Zhang, F.: Internal gravity waves from atmospheric jets
and
fronts, Rev. Geophys., 52, 33–76, https://doi.org/10.1002/2012RG000419, 2014. a
Ragone, F., Lucarini, V., and Lunkeit, F.: A new framework for climate
sensitivity and prediction: a modelling perspective, Clim. Dynam.,
46, 1459–1471, https://doi.org/10.1007/s00382-015-2657-3, 2016. a
Ruelle, D.: Ergodic theory of differentiable dynamical systems, Publ.
Math., 50, 27–58, https://doi.org/10.1007/BF02684768, 1979. a
Ruelle, D.: A review of linear response theory for general differentiable
dynamical systems, Nonlinearity, 22, 855–870,
https://doi.org/10.1088/0951-7715/22/4/009, 2009. a
Schalge, B., Blender, R., Wouters, J., Fraedrich, K., and Lunkeit, F.:
Evidence for a fluctuation theorem in an atmospheric circulation model,
Phys. Rev. E, 87, 8760, https://doi.org/10.1103/PhysRevE.87.052113,
2013. a
Schneider, T.: The General Circulation of the Atmosphere, Annu. Rev. Earth
Pl. Sc., 34, 655–688,
https://doi.org/10.1146/annurev.earth.34.031405.125144, 2006. a
Scott, D. W.: On optimal and data-based histograms, Biometrika, 66, 605–610,
1979. a
Shimada, I. and Nagashima, T.: A Numerical Approach to Ergodic Problem of
Dissipative Dynamical Systems, Prog. Theor. Phys., 61,
1605–1616, https://doi.org/10.1143/PTP.61.1605, 1979. a
Speranza, A. and Malguzzi, P.: The Statistical Properties of a Zonal Jet in
a
Baroclinic Atmosphere: A Semilinear Approach. Part I: Quasi-geostrophic,
Two-Layer Model Atmosphere, J. Atmos. Sci., 45,
3046–3062, https://doi.org/10.1175/1520-0469(1988)045<3046:TSPOAZ>2.0.CO;2, 1988. a
Sprott, J. C.: Elegant Chaos, World Scientific, https://doi.org/10.1142/7183, 2010. a
Thompson, P. D.: Uncertainty of initial state as a factor in the
predictability
of large scale atmospheric flow patterns, Tellus, 9, 275–295,
https://doi.org/10.3402/tellusa.v9i3.9111, 1957. a
Tibaldi, S. and Molteni, F.: On the operational predictability of blocking,
Tellus A, 42, 343–365, https://doi.org/10.1034/j.1600-0870.1990.t01-2-00003.x, 1990. a
Touchette, H.: The large deviation approach to statistical mechanics, Phys.
Rep., 478, 1–69, https://doi.org/10.1016/j.physrep.2009.05.002, 2009. a, b
Trevisan, A. and Pancotti, F.: Periodic Orbits, Lyapunov Vectors, and
Singular
Vectors in the Lorenz System, J. Atmos. Sci., 55,
390–398, https://doi.org/10.1175/1520-0469(1998)055<0390:POLVAS>2.0.CO;2, 1998. a
Trevisan, A., D'Isidoro, M., and Talagrand, O.: Four-dimensional variational
assimilation in the unstable subspace and the optimal subspace dimension,
Q. J. Roy. Meteor. Soc., 136, 487–496, 2010. a
Van der Avoird, E., Dijkstra, H., Nauw, J., and Schuurmans, C.: Nonlinearly
induced low-frequency variability in a midlatitude coupled ocean-atmosphere
model of intermediate complexity, Clim. Dynam., 19, 303–320,
https://doi.org/10.1007/s00382-001-0220-x, 2002. a, b
Vannitsem, S.: Predictability of large-scale atmospheric motions: Lyapunov
exponents and error dynamics, Chaos, 27, 32101, https://doi.org/10.1063/1.4979042, 2017. a, b, c, d
Vannitsem, S. and De Cruz, L.: A 24-variable low-order coupled
ocean–atmosphere model: OA-QG-WS v2, Geosci. Model Dev., 7, 649–662,
https://doi.org/10.5194/gmd-7-649-2014, 2014. a
Vannitsem, S. and Lucarini, V.: Statistical and Dynamical Properties of
Covariant Lyapunov Vectors in a Coupled Atmosphere–Ocean Model – Multiscale
Effects, Geometric Degeneracy, and Error Dynamics, J. Phys. A-Math. Theor., 49, 224001,
https://doi.org/10.1088/1751-8113/49/22/224001, 2016. a, b, c, d, e, f, g, h, i
Vannitsem, S. and Nicolis, C.: Predictability experiments on a simplified
thermal convection model: The role of spatial scales, J. Geophys.
Res., 99, 10377, https://doi.org/10.1029/94JD00248, 1994. a
Vannitsem, S. and Nicolis, C.: Error Growth Dynamics In Spatially Extended
Systems, Int. J. Bifurcat. Chaos, 6, 2223–2235,
https://doi.org/10.1142/S0218127496001466, 1996. a
Vannitsem, S. and Nicolis, C.: Lyapunov Vectors and Error Growth Patterns in
a T21L3 Quasigeostrophic Model, J. Atmos. Sci., 54,
347–361, https://doi.org/10.1175/1520-0469(1997)054<0347:LVAEGP>2.0.CO;2, 1997. a
Vannitsem, S., Demaeyer, J., De Cruz, L., and Ghil, M.: Low-frequency
variability and heat transport in a low-order nonlinear coupled
ocean-atmosphere model, Physica D, 309, 71–85,
https://doi.org/10.1016/j.physd.2015.07.006, 2015. a, b, c, d
Wolfe, C. L. and Samelson, R. M.: An efficient method for recovering
Lyapunov
vectors from singular vectors, Tellus A, 59, 355–366,
https://doi.org/10.1111/j.1600-0870.2007.00234.x, 2007. a
Xu, M. and Paul, M. R.: Covariant Lyapunov vectors of chaotic
Rayleigh-Bénard convection, Phys. Rev. E, 93, 062208,
https://doi.org/10.1103/PhysRevE.93.062208, 2016.
a
Yamada, M. and Ohkitani, K.: Lyapunov spectrum of a model of two-dimensional
turbulence, Phys. Rev. Lett., 60, 983–986,
https://doi.org/10.1103/PhysRevLett.60.983, 1988. a
Short summary
The predictability of weather models is limited largely by the initial state error growth or decay rates. We have computed these rates for PUMA, a global model for the atmosphere, and MAOOAM, a more simplified, coupled model which includes the ocean. MAOOAM has processes at distinct timescales, whereas PUMA surprisingly does not. We propose a new programme to compute the natural directions along the flow that correspond to the growth or decay rates, to learn which components play a role.
The predictability of weather models is limited largely by the initial state error growth or...
