- About
- Editorial board
- Articles
- Special issues
- Highlight articles
- Manuscript tracking
- Book reviews
- Subscribe to alerts
- Peer review
- For authors
- For reviewers
- EGU publications
Journal cover
Journal topic
Nonlinear Processes in Geophysics
An interactive open-access journal of the European Geosciences Union
Journal topic
- About
- Editorial board
- Articles
- Special issues
- Highlight articles
- Manuscript tracking
- Book reviews
- Subscribe to alerts
- Peer review
- For authors
- For reviewers
- EGU publications
Journal metrics
Journal metrics
IF 1.558
1.475CiteScore
2.8SNIP 0.921
SJR 0.571
index 55h5-index 22
Abstracted/indexed
Abstracted/indexed
NPG | Articles | Volume 25, issue 2
Nonlin. Processes Geophys., 25, 387–412, 2018
https://doi.org/10.5194/npg-25-387-2018
© Author(s) 2018. This work is distributed under
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.
Special issue: Numerical modeling, predictability and data assimilation in...
Nonlin. Processes Geophys., 25, 387–412, 2018
https://doi.org/10.5194/npg-25-387-2018
© Author(s) 2018. This work is distributed under
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.
Research article 28 May 2018
Research article | 28 May 2018
Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models
Lesley De Cruz et al.
Related authors
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. Discuss., https://doi.org/10.5194/gmd-2019-368, https://doi.org/10.5194/gmd-2019-368, 2020
Revised manuscript under review for GMD
Short summary
Short summary
Detailed climate data is needed to assess the impact of climate change on human and natural systems. The model 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. Both models are able to reproduce the observed spatial patterns for temperature and precipitation, making their produced climate data suitable for climate impact studies over the Central Asia region.
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
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.
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. Discuss., https://doi.org/10.5194/gmd-2019-368, https://doi.org/10.5194/gmd-2019-368, 2020
Revised manuscript under review for GMD
Short summary
Short summary
Detailed climate data is needed to assess the impact of climate change on human and natural systems. The model 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. Both models are able to reproduce the observed spatial patterns for temperature and precipitation, making their produced climate data suitable for climate impact studies over the Central Asia region.
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
Revised manuscript has not been submitted
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, Data Assimilation | Topic: Climate, Atmosphere, Ocean, Hydrology, Cryosphere, Biosphere
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
Application of a local attractor dimension to reduced space strongly coupled data assimilation for chaotic multiscale systems
Order of operation for multi-stage post-processing of ensemble wind forecast trajectories
Generalization properties of feed-forward neural networks trained on Lorenz systems
Revising the stochastic iterative ensemble smoother
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
Non-Gaussian statistics in global atmospheric dynamics: a study with a 10 240-member ensemble Kalman filter using an intermediate atmospheric general circulation model
Fluctuations of finite-time Lyapunov exponents in an intermediate-complexity atmospheric model: a multivariate and large-deviation perspective
Data assimilation using adaptive, non-conservative, moving mesh models
Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models
A Bayesian approach to multivariate adaptive localization in ensemble-based data assimilation with time-dependent extensions
Exploring the sensitivity of Northern Hemisphere atmospheric circulation to different surface temperature forcing using a statistical–dynamical atmospheric model
Review article: Comparison of local particle filters and new implementations
Data assimilation of radar reflectivity volumes in a LETKF scheme
Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling
Nonlinear effects in 4D-Var
A novel approach for solving CNOPs and its application in identifying sensitive regions of tropical cyclone adaptive observations
Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error
Ensemble variational assimilation as a probabilistic estimator – Part 1: The linear and weak non-linear case
Ensemble variational assimilation as a probabilistic estimator – Part 2: The fully non-linear case
OSSE for a sustainable marine observing network in the Sea of Marmara
Parametric covariance dynamics for the nonlinear diffusive Burgers equation
Sensitivity analysis with respect to observations in variational data assimilation for parameter estimation
Feature-based data assimilation in geophysics
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother
Accelerating assimilation development for new observing systems using EFSO
Optimal transport for variational data assimilation
The Onsager–Machlup functional for data assimilation
Impact of an observational time window on coupled data assimilation: simulation with a simple climate model
Remote sensing of ocean surface currents: a review of what is being observed and what is being assimilated
Non-Gaussian data assimilation of satellite-based leaf area index observations with an individual-based dynamic global vegetation model
Data assimilation for moving mesh methods with an application to ice sheet modelling
Regularization destriping of remote sensing imagery
Controllability, not chaos, key criterion for ocean state estimation
An estimate of the inflation factor and analysis sensitivity in the ensemble Kalman filter
Formulation of scale transformation in a stochastic data assimilation framework
Insights on the role of accurate state estimation in coupled model parameter estimation by a conceptual climate model study
Conditional nonlinear optimal perturbations based on the particle swarm optimization and their applications to the predictability problems
Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction
Constraining ecosystem model with adaptive Metropolis algorithm using boreal forest site eddy covariance measurements
A local particle filter for high-dimensional geophysical systems
Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model
An improved global zenith tropospheric delay model GZTD2 considering diurnal variations
Hybrid Levenberg–Marquardt and weak-constraint ensemble Kalman smoother method
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.
Courtney Quinn, Terence J. O'Kane, and Vassili Kitsios
Nonlin. Processes Geophys., 27, 51–74, https://doi.org/10.5194/npg-27-51-2020, https://doi.org/10.5194/npg-27-51-2020, 2020
Short summary
Short summary
This study presents a novel method for reduced-rank data assimilation of multiscale highly nonlinear systems. Time-varying dynamical properties are used to determine the rank and projection of the system onto a reduced subspace. The variable reduced-rank method is shown to succeed over other fixed-rank methods. This work provides implications for performing strongly coupled data assimilation with a limited number of ensemble members on high-dimensional coupled climate models.
Nina Schuhen
Nonlin. Processes Geophys., 27, 35–49, https://doi.org/10.5194/npg-27-35-2020, https://doi.org/10.5194/npg-27-35-2020, 2020
Short summary
Short summary
We present a new way to adaptively improve weather forecasts by incorporating last-minute observation information. The recently measured error, together with a statistical model, gives us an indication of the expected future error of wind speed forecasts, which are then adjusted accordingly. This new technique can be especially beneficial for customers in the wind energy industry, where it is important to have reliable short-term forecasts, as well as providers of extreme weather warnings.
Sebastian Scher and Gabriele Messori
Nonlin. Processes Geophys., 26, 381–399, https://doi.org/10.5194/npg-26-381-2019, https://doi.org/10.5194/npg-26-381-2019, 2019
Short summary
Short summary
Neural networks are a technique that is widely used to predict the time evolution of physical systems. For this the past evolution of the system is shown to the neural network – it is
trained– and then can be used to predict the evolution in the future. We show some limitations in this approach for certain systems that are important to consider when using neural networks for climate- and weather-related applications.
Patrick Nima Raanes, Andreas Størksen Stordal, and Geir Evensen
Nonlin. Processes Geophys., 26, 325–338, https://doi.org/10.5194/npg-26-325-2019, https://doi.org/10.5194/npg-26-325-2019, 2019
Short summary
Short summary
A popular variational ensemble smoother for data assimilation and history matching is simplified. An exact relationship between ensemble linearizations (linear regression) and adjoints (analytic derivatives) is established.
Fei Lu, Nils Weitzel, and Adam H. Monahan
Nonlin. Processes Geophys., 26, 227–250, https://doi.org/10.5194/npg-26-227-2019, https://doi.org/10.5194/npg-26-227-2019, 2019
Short summary
Short summary
ll-posedness of the inverse problem and sparse noisy data are two major challenges in the modeling of high-dimensional spatiotemporal processes. We present a Bayesian inference method with a strongly regularized posterior to overcome these challenges, enabling joint state-parameter estimation and quantifying uncertainty in the estimation. We demonstrate the method on a physically motivated nonlinear stochastic partial differential equation arising from paleoclimate construction.
Keiichi Kondo and Takemasa Miyoshi
Nonlin. Processes Geophys., 26, 211–225, https://doi.org/10.5194/npg-26-211-2019, https://doi.org/10.5194/npg-26-211-2019, 2019
Short summary
Short summary
This study investigates non-Gaussian statistics of the data from a 10240-member ensemble Kalman filter. The large ensemble size can resolve the detailed structures of the probability density functions (PDFs) and indicates that the non-Gaussian PDF is caused by multimodality and outliers. While the outliers appear randomly, large multimodality corresponds well with large analysis error, mainly in the tropical regions and storm track regions where highly nonlinear processes appear frequently.
Frank Kwasniok
Nonlin. Processes Geophys., 26, 195–209, https://doi.org/10.5194/npg-26-195-2019, https://doi.org/10.5194/npg-26-195-2019, 2019
Short summary
Short summary
The stability properties as characterized by finite-time Lyapunov exponents are investigated in an intermediate-complexity atmospheric model. Firstly, the dominant patterns of collective excitation are identified by an empirical orthogonal function analysis of the fluctuation field of all of the finite-time Lyapunov exponents. Secondly, a large-deviation principle is established for all of the Lyapunov exponents and the large-deviation rate functions are estimated.
Ali Aydoğdu, Alberto Carrassi, Colin T. Guider, Chris K. R. T Jones, and Pierre Rampal
Nonlin. Processes Geophys., 26, 175–193, https://doi.org/10.5194/npg-26-175-2019, https://doi.org/10.5194/npg-26-175-2019, 2019
Short summary
Short summary
Computational models involving adaptive meshes can both evolve dynamically and be remeshed. Remeshing means that the state vector dimension changes in time and across ensemble members, making the ensemble Kalman filter (EnKF) unsuitable for assimilation of observational data. We develop a modification in which analysis is performed on a fixed uniform grid onto which the ensemble is mapped, with resolution relating to the remeshing criteria. The approach is successfully tested on two 1-D models.
Marc Bocquet, Julien Brajard, Alberto Carrassi, and Laurent Bertino
Nonlin. Processes Geophys., 26, 143–162, https://doi.org/10.5194/npg-26-143-2019, https://doi.org/10.5194/npg-26-143-2019, 2019
Short summary
Short summary
This paper describes an innovative way to use data assimilation to infer the dynamics of a physical system from its observation only. The method can operate with noisy and partial observation of the physical system. It acts as a deep learning technique specialised to dynamical models without the need for machine learning tools. The method is successfully tested on chaotic dynamical systems: the Lorenz-63, Lorenz-96, and Kuramoto–Sivashinski models and a two-scale Lorenz model.
Andrey A. Popov and Adrian Sandu
Nonlin. Processes Geophys., 26, 109–122, https://doi.org/10.5194/npg-26-109-2019, https://doi.org/10.5194/npg-26-109-2019, 2019
Short summary
Short summary
This work has to do with a small part of existing algorithms that are used in applications such as predicting the weather. We provide empirical evidence that our new technique works well on small but representative models. This might lead to creation of a better weather forecast and potentially save lives as in the case of hurricane prediction.
Sonja Totz, Stefan Petri, Jascha Lehmann, Erik Peukert, and Dim Coumou
Nonlin. Processes Geophys., 26, 1–12, https://doi.org/10.5194/npg-26-1-2019, https://doi.org/10.5194/npg-26-1-2019, 2019
Alban Farchi and Marc Bocquet
Nonlin. Processes Geophys., 25, 765–807, https://doi.org/10.5194/npg-25-765-2018, https://doi.org/10.5194/npg-25-765-2018, 2018
Short summary
Short summary
Data assimilation looks for an optimal way to learn from observations of a dynamical system to improve the quality of its predictions. The goal is to filter out the noise (both observation and model noise) to retrieve the true signal. Among all possible methods, particle filters are promising; the method is fast and elegant, and it allows for a Bayesian analysis. In this review paper, we discuss implementation techniques for (local) particle filters in high-dimensional systems.
Thomas Gastaldo, Virginia Poli, Chiara Marsigli, Pier Paolo Alberoni, and Tiziana Paccagnella
Nonlin. Processes Geophys., 25, 747–764, https://doi.org/10.5194/npg-25-747-2018, https://doi.org/10.5194/npg-25-747-2018, 2018
Short summary
Short summary
Accuracy of numerical weather prediction forecasts is strongly related to the quality of initial conditions employed. To improve them, it seems advantageous to use radar reflectivity observations because of their high spatial and temporal resolution. This is tested in a high-resolution model whose domain covers Italy. Results show that the employment of reflectivity observations improves precipitation forecast accuracy, but the positive impact is lost after a few hours of forecast.
Sangeetika Ruchi and Svetlana Dubinkina
Nonlin. Processes Geophys., 25, 731–746, https://doi.org/10.5194/npg-25-731-2018, https://doi.org/10.5194/npg-25-731-2018, 2018
Short summary
Short summary
Accurate estimation of subsurface geological parameters is essential for the oil industry. This is done by combining observations with an estimation from a model. Ensemble Kalman filter is a widely used method for inverse modeling, while ensemble transform particle filtering is a recently developed method that has been applied to estimate only a small number of parameters and in fluids. We show that for a high-dimensional inverse problem it is superior to an ensemble Kalman filter.
Massimo Bonavita, Peter Lean, and Elias Holm
Nonlin. Processes Geophys., 25, 713–729, https://doi.org/10.5194/npg-25-713-2018, https://doi.org/10.5194/npg-25-713-2018, 2018
Short summary
Short summary
This paper deals with the effects of nonlinearity in a state-of-the-art atmospheric global data assimilation system. It is shown that these effects have become increasingly important over the years due to increased model resolution and use of nonlinear observations. The ability to deal with nonlinearities has thus become a crucial asset of data assimilation algorithms. At ECMWF this is done in a perturbative fashion. Advantages and limitations of this technique are discussed.
Linlin Zhang, Bin Mu, Shijin Yuan, and Feifan Zhou
Nonlin. Processes Geophys., 25, 693–712, https://doi.org/10.5194/npg-25-693-2018, https://doi.org/10.5194/npg-25-693-2018, 2018
Short summary
Short summary
We propose a novel approach to solve conditional nonlinear optimal perturbation for identifying sensitive areas for tropical cyclone adaptive observations. This method is free of adjoint models and overcomes two obstacles, not having adjoint models and having dimensions higher than the problem space. All experimental results prove that it is a meaningful and effective method for solving CNOP and provides a new way for such research. This work aims to solve CNOP and identify sensitive areas.
Colin Grudzien, Alberto Carrassi, and Marc Bocquet
Nonlin. Processes Geophys., 25, 633–648, https://doi.org/10.5194/npg-25-633-2018, https://doi.org/10.5194/npg-25-633-2018, 2018
Short summary
Short summary
Using the framework Lyapunov vectors, we analyze the asymptotic properties of ensemble based Kalman filters and how these are influenced by dynamical chaos, especially in the context of random model errors and small ensemble sizes. Particularly, we show a novel derivation of the evolution of forecast uncertainty for ensemble-based Kalman filters with weakly-nonlinear error growth, and discuss its impact for filter design in geophysical models.
Mohamed Jardak and Olivier Talagrand
Nonlin. Processes Geophys., 25, 565–587, https://doi.org/10.5194/npg-25-565-2018, https://doi.org/10.5194/npg-25-565-2018, 2018
Short summary
Short summary
Ensemble variational assimilation (EnsVAR) has been implemented on two small-dimension non-linear chaotic toy models, as well as on a linearized version of those models. In the linear case, EnsVAR is exactly Bayesian and produced
highly reliable ensembles. In the non-linear case, EnsVAR, implemented on temporal windows on the order of magnitude of the predictability time of the systems, shows as good performance as in the exactly linear case. EnsVar is as good an estimator as EnKF and PF.
Mohamed Jardak and Olivier Talagrand
Nonlin. Processes Geophys., 25, 589–604, https://doi.org/10.5194/npg-25-589-2018, https://doi.org/10.5194/npg-25-589-2018, 2018
Short summary
Short summary
EnsVAR is fundamentally successful in that, even in conditions where Bayesianity cannot be expected, it produces ensembles which possess a high degree of statistical reliability. In non-linear strong-constraint cases, EnsVAR has been successful here only through the use of quasi-static variational assimilation. In the weak-constraint case, without QSVA, EnsVAR provided new evidence as to the favourable effect.
Ali Aydoğdu, Timothy J. Hoar, Tomislava Vukicevic, Jeffrey L. Anderson, Nadia Pinardi, Alicia Karspeck, Jonathan Hendricks, Nancy Collins, Francesca Macchia, and Emin Özsoy
Nonlin. Processes Geophys., 25, 537–551, https://doi.org/10.5194/npg-25-537-2018, https://doi.org/10.5194/npg-25-537-2018, 2018
Short summary
Short summary
This study presents, to our knowledge, the first data assimilation experiments in the Sea of Marmara. We propose a FerryBox network for monitoring the state of the sea and show that assimilation of the temperature and salinity improves the forecasts in the basin. The flow of the Bosphorus helps to propagate the error reduction. The study can be taken as a step towards a marine forecasting system in the Sea of Marmara that will help to improve the forecasts in the adjacent Black and Aegean seas.
Olivier Pannekoucke, Marc Bocquet, and Richard Ménard
Nonlin. Processes Geophys., 25, 481–495, https://doi.org/10.5194/npg-25-481-2018, https://doi.org/10.5194/npg-25-481-2018, 2018
Short summary
Short summary
The forecast of weather prediction uncertainty is a real challenge and is crucial for risk management. However, uncertainty prediction is beyond the capacity of supercomputers, and improvements of the technology may not solve this issue. A new uncertainty prediction method is introduced which takes advantage of fluid equations to predict simple quantities which approximate real uncertainty but at a low numerical cost. A proof of concept is shown by an academic model derived from fluid dynamics.
Victor Shutyaev, Francois-Xavier Le Dimet, and Eugene Parmuzin
Nonlin. Processes Geophys., 25, 429–439, https://doi.org/10.5194/npg-25-429-2018, https://doi.org/10.5194/npg-25-429-2018, 2018
Short summary
Short summary
The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters of the model. The observation data, and hence the optimal solution, may contain uncertainties. A response function is considered as a functional of the optimal solution after assimilation. The sensitivity of the response function to the observation data is studied. The results are relevant for monitoring and prediction of sea and ocean states.
Matthias Morzfeld, Jesse Adams, Spencer Lunderman, and Rafael Orozco
Nonlin. Processes Geophys., 25, 355–374, https://doi.org/10.5194/npg-25-355-2018, https://doi.org/10.5194/npg-25-355-2018, 2018
Short summary
Short summary
Many applications in science require that computational models and data be combined. In a Bayesian framework, this is usually done by defining likelihoods based on the mismatch of model outputs and data. However, matching model outputs and data in this way can be unnecessary or impossible. This issue can be addressed by selecting features of the data, and defining likelihoods based on the features, rather than by the usual mismatch of model output and data.
Anthony Fillion, Marc Bocquet, and Serge Gratton
Nonlin. Processes Geophys., 25, 315–334, https://doi.org/10.5194/npg-25-315-2018, https://doi.org/10.5194/npg-25-315-2018, 2018
Short summary
Short summary
This study generalizes a paper by Pires et al. (1996) to state-of-the-art data assimilation techniques, such as the iterative ensemble Kalman smoother (IEnKS). We show that the longer the time window over which observations are assimilated, the better the accuracy of the IEnKS. Beyond a critical time length that we estimate, we show that this accuracy finally degrades. We show that the use of the quasi-static minimizations but generalized to the IEnKS yields a significantly improved accuracy.
Guo-Yuan Lien, Daisuke Hotta, Eugenia Kalnay, Takemasa Miyoshi, and Tse-Chun Chen
Nonlin. Processes Geophys., 25, 129–143, https://doi.org/10.5194/npg-25-129-2018, https://doi.org/10.5194/npg-25-129-2018, 2018
Short summary
Short summary
The ensemble forecast sensitivity to observation (EFSO) method can efficiently clarify under what conditions observations are beneficial or detrimental for assimilation. Based on EFSO, an offline assimilation method is proposed to accelerate the development of data selection strategies for new observing systems. The usefulness of this method is demonstrated with the assimilation of global satellite precipitation data.
Nelson Feyeux, Arthur Vidard, and Maëlle Nodet
Nonlin. Processes Geophys., 25, 55–66, https://doi.org/10.5194/npg-25-55-2018, https://doi.org/10.5194/npg-25-55-2018, 2018
Short summary
Short summary
In geophysics, numerical models are generally initialized through so-called data assimilation methods. They require computation of a distance between model fields and physical observations. The most common choice is the Euclidian distance. However, due to its local nature it is not well suited for capturing position errors. This papers investigates theoretical aspects of the use of the optimal transport-based Wasserstein distance in this context and shows that it is able to capture such errors.
Nozomi Sugiura
Nonlin. Processes Geophys., 24, 701–712, https://doi.org/10.5194/npg-24-701-2017, https://doi.org/10.5194/npg-24-701-2017, 2017
Short summary
Short summary
The optimisation of simulation paths is sometimes misleading. We can find a path with the highest probability by the method of least squares. However, it is not necessarily the route where the paths are most concentrated. This paper clarifies how we can find the mode of a distribution of paths by optimisation.
Yuxin Zhao, Xiong Deng, Shaoqing Zhang, Zhengyu Liu, Chang Liu, Gabriel Vecchi, Guijun Han, and Xinrong Wu
Nonlin. Processes Geophys., 24, 681–694, https://doi.org/10.5194/npg-24-681-2017, https://doi.org/10.5194/npg-24-681-2017, 2017
Short summary
Short summary
Here with a simple coupled model that simulates typical scale interactions in the climate system, we study the optimal OTWs for the coupled media so that climate signals can be most accurately recovered by CDA. Results show that an optimal OTW determined from the de-correlation timescale provides maximal observational information that best fits the characteristic variability of the coupled medium during the data blending process.
Jordi Isern-Fontanet, Joaquim Ballabrera-Poy, Antonio Turiel, and Emilio García-Ladona
Nonlin. Processes Geophys., 24, 613–643, https://doi.org/10.5194/npg-24-613-2017, https://doi.org/10.5194/npg-24-613-2017, 2017
Short summary
Short summary
Ocean currents play a key role in Earth’s climate – they are of major importance for navigation and human activities at sea and impact almost all processes that take place in the ocean. Nevertheless, their observation and forecasting are still difficult. Here, we review the main techniques used to derive surface currents from satellite measurements and the existing approaches to assimilate this information into ocean models.
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
Short summary
Short summary
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.
Bertrand Bonan, Nancy K. Nichols, Michael J. Baines, and Dale Partridge
Nonlin. Processes Geophys., 24, 515–534, https://doi.org/10.5194/npg-24-515-2017, https://doi.org/10.5194/npg-24-515-2017, 2017
Short summary
Short summary
We develop data assimilation techniques for numerical models using moving mesh methods. Moving meshes are valuable for explicitly tracking interfaces and boundaries in evolving systems. The application of the techniques is demonstrated on a one-dimensional
model of an ice sheet. It is shown, using various types of observations, that
the techniques predict the evolution of the edges of the ice sheet and its height accurately and efficiently.
Ranil Basnayake, Erik Bollt, Nicholas Tufillaro, Jie Sun, and Michelle Gierach
Nonlin. Processes Geophys., 24, 367–378, https://doi.org/10.5194/npg-24-367-2017, https://doi.org/10.5194/npg-24-367-2017, 2017
Geoffrey Gebbie and Tsung-Lin Hsieh
Nonlin. Processes Geophys., 24, 351–366, https://doi.org/10.5194/npg-24-351-2017, https://doi.org/10.5194/npg-24-351-2017, 2017
Short summary
Short summary
The best reconstructions of the past ocean state involve the statistical combination of numerical models and observations; however, the computationally efficient method that produces physically interpretable fields is thought to not be applicable to chaotic dynamical systems, such as ocean models with eddies. Here we use a model of the chaotic, forced pendulum to show that the most popular existing method is successful so long as there are enough uncertain boundary conditions through time.
Guocan Wu and Xiaogu Zheng
Nonlin. Processes Geophys., 24, 329–341, https://doi.org/10.5194/npg-24-329-2017, https://doi.org/10.5194/npg-24-329-2017, 2017
Short summary
Short summary
The accuracy of the assimilation results crucially relies on the estimate accuracy of forecast error covariance matrix in data assimilation. Ensemble Kalman filter estimates the forecast error covariance matrix as the sampling covariance matrix of the ensemble forecast states, which need to be further inflated. The experiment results on the Lorenz-96 model show that the analysis error is reduced and the analysis sensitivity to observations is improved using the proposed inflation technique.
Feng Liu and Xin Li
Nonlin. Processes Geophys., 24, 279–291, https://doi.org/10.5194/npg-24-279-2017, https://doi.org/10.5194/npg-24-279-2017, 2017
Short summary
Short summary
This is the first mathematical definitions of the spatial scale and its transformation based on Lebesgue measure. An Ito process-formed geophysical variable with respect to scale was also provided. The stochastic calculus for data assimilation discovered the new expressions of error caused by spatial scale transformation. The results improve the ability to understand the spatial scale transformation and related uncertainties in Earth observation, modelling and data assimilation.
Xiaolin Yu, Shaoqing Zhang, Xiaopei Lin, and Mingkui Li
Nonlin. Processes Geophys., 24, 125–139, https://doi.org/10.5194/npg-24-125-2017, https://doi.org/10.5194/npg-24-125-2017, 2017
Short summary
Short summary
Parameter estimation (PE) with a global coupled data assimilation (CDA) system can improve the runs, but the improvement remains in a limited range. We have to come back to simple models to sort out the sources of noises. Incomplete observations and the chaotic nature of the atmosphere have much stronger influences on the PE through the state estimation (SE) process. Here, we propose the guidelines of how to enhance the signal-to-noise ratio under partial SE status.
Qin Zheng, Zubin Yang, Jianxin Sha, and Jun Yan
Nonlin. Processes Geophys., 24, 101–112, https://doi.org/10.5194/npg-24-101-2017, https://doi.org/10.5194/npg-24-101-2017, 2017
Short summary
Short summary
When the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model on the prediction variable will lead to failure of the ADJ-CNOP method; when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making false estimations of the lower bound of maximum predictable time.
Zhe An, Daniel Rey, Jingxin Ye, and Henry D. I. Abarbanel
Nonlin. Processes Geophys., 24, 9–22, https://doi.org/10.5194/npg-24-9-2017, https://doi.org/10.5194/npg-24-9-2017, 2017
Jarmo Mäkelä, Jouni Susiluoto, Tiina Markkanen, Mika Aurela, Heikki Järvinen, Ivan Mammarella, Stefan Hagemann, and Tuula Aalto
Nonlin. Processes Geophys., 23, 447–465, https://doi.org/10.5194/npg-23-447-2016, https://doi.org/10.5194/npg-23-447-2016, 2016
Short summary
Short summary
The land-based hydrological cycle is one of the key processes controlling the growth and wilting of plants and the amount of carbon vegetation can assimilate. Recent studies have shown that many land surface models have biases in this area. We optimized parameters in one such model (JSBACH) and were able to enhance the model performance in many respects, but the response to drought remained unaffected. Further studies into this aspect should include alternative stomatal conductance formulations.
Stephen G. Penny and Takemasa Miyoshi
Nonlin. Processes Geophys., 23, 391–405, https://doi.org/10.5194/npg-23-391-2016, https://doi.org/10.5194/npg-23-391-2016, 2016
Short summary
Short summary
Particle filters in their basic form have been shown to be unusable for large geophysical systems because the number of required particles grows exponentially with the size of the system. We have applied the ideas of localized analyses at each model grid point and use ensemble weight smoothing to blend each local analysis with its neighbors. This new local particle filter (LPF) makes large geophysical applications tractable for particle filters and is competitive with a popular EnKF alternative.
Bo-Wen Shen
Nonlin. Processes Geophys., 23, 189–203, https://doi.org/10.5194/npg-23-189-2016, https://doi.org/10.5194/npg-23-189-2016, 2016
Short summary
Short summary
We construct a seven-dimensional Lorenz model (7DLM) to discuss the impact of an extended nonlinear feedback loop on solutions' stability and illustrate the hierarchical scale dependence of chaotic solutions. The 7DLM requires a much larger critical value for the Rayleigh parameter (rc ∼ 116.9) for the onset of chaos. For chaotic solutions with r = 120, high correlation coefficients among the modes at different scales indicate hierarchical scale dependence.
Yibin Yao, Yufeng Hu, Chen Yu, Bao Zhang, and Jianjian Guo
Nonlin. Processes Geophys., 23, 127–136, https://doi.org/10.5194/npg-23-127-2016, https://doi.org/10.5194/npg-23-127-2016, 2016
Short summary
Short summary
By considering the diurnal variations in zenith tropospheric delay (ZTD) and modifying the model expansion function, we developed an improved global empirical ZTD model GZTD2 with higher temporal and spatial resolutions compared to our previous GZTD model. The external validation testing with IGS ZTD data shows the bias and rms for GZTD2 are −0.3 and 3.9 cm respectively, indicating higher accuracy and reliability for geodesy technology compared to GZTD and other commonly used ZTD models.
J. Mandel, E. Bergou, S. Gürol, S. Gratton, and I. Kasanický
Nonlin. Processes Geophys., 23, 59–73, https://doi.org/10.5194/npg-23-59-2016, https://doi.org/10.5194/npg-23-59-2016, 2016
Short summary
Short summary
A stochastic method, the ensemble Kalman smoother (EnKS), is proposed as a linear solver in four-dimensional variational data assimilation (4DVAR). The method approaches 4DVAR for large ensembles. Regularization provides global convergence, and it is implemented as an additional artificial observation. Since the EnKS is uncoupled from the insides of the 4DVAR, any version of EnKS can be used.
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
Search articles
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...
Nonlinear Processes in Geophysics
An interactive open-access journal of the European Geosciences Union
All site content, except where otherwise noted, is licensed under the Creative Commons Attribution 4.0 License.