Articles | Volume 25, issue 3
https://doi.org/10.5194/npg-25-481-2018
© 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-25-481-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| Highlight paper
| 
09 Jul 2018
Research article | Highlight paper |
| 09 Jul 2018
| 09 Jul 2018
Parametric covariance dynamics for the nonlinear diffusive Burgers equation
Olivier Pannekoucke
CORRESPONDING AUTHOR
INPT-ENM, CNRM UMR 3589, Météo-France/CNRS, CERFACS, Toulouse, France
Marc Bocquet
CEREA, Joint Laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France
Richard Ménard
ARQI/Air Quality Research Division, Environment and Climate Change Canada, Dorval (Québec), Canada
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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
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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.
Olivier Pannekoucke and Ronan Fablet
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Colin Grudzien, Marc Bocquet, and Alberto Carrassi
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Thomas Lauvaux, Liza I. Díaz-Isaac, Marc Bocquet, and Nicolas Bousserez
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Marc Bocquet, Julien Brajard, Alberto Carrassi, and Laurent Bertino
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Julien Brajard, Alberto Carrassi, Marc Bocquet, and Laurent Bertino
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2019-136, https://doi.org/10.5194/gmd-2019-136, 2019
Revised manuscript not accepted
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Liza I. Díaz-Isaac, Thomas Lauvaux, Marc Bocquet, and Kenneth J. Davis
Atmos. Chem. Phys., 19, 5695–5718, https://doi.org/10.5194/acp-19-5695-2019, https://doi.org/10.5194/acp-19-5695-2019, 2019
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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
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Colin Grudzien, Alberto Carrassi, and Marc Bocquet
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Sergey Skachko, Richard Ménard, Quentin Errera, Yves Christophe, and Simon Chabrillat
Geosci. Model Dev., 9, 2893–2908, https://doi.org/10.5194/gmd-9-2893-2016, https://doi.org/10.5194/gmd-9-2893-2016, 2016
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In the present work, we performed a comparison of two broadly used data assimilation algorithms, 4D-Var and EnKF, applied to a state-of-the-art atmospheric chemistry transport model. The comparison is carried out using carefully calibrated error statistics. The paper discusses the advantages and disadvantages of each method applied to real-life conditions of a numerical atmospheric chemistry data assimilation.
J.-M. Haussaire and M. Bocquet
Geosci. Model Dev., 9, 393–412, https://doi.org/10.5194/gmd-9-393-2016, https://doi.org/10.5194/gmd-9-393-2016, 2016
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The focus is on the development of low-order models of atmospheric transport and chemistry and their use for data assimilation purposes. A new low-order coupled chemistry meteorology model is developed. It consists of the Lorenz40-variable model used as a wind field coupled with a simple ozone photochemistry module. Advanced ensemble variational methods are applied to this model to obtain insights on the use of data assimilation with coupled models, in an offline mode or in an online mode.
M. Bocquet, P. N. Raanes, and A. Hannart
Nonlin. Processes Geophys., 22, 645–662, https://doi.org/10.5194/npg-22-645-2015, https://doi.org/10.5194/npg-22-645-2015, 2015
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The popular data assimilation technique known as the ensemble Kalman filter (EnKF) suffers from sampling errors due to the limited size of the ensemble. This deficiency is usually cured by inflating the sampled error covariances and by using localization. This paper further develops and discusses the finite-size EnKF, or EnKF-N, a variant of the EnKF that does not require inflation. It expands the use of the EnKF-N to a wider range of dynamical regimes.
M. Bocquet, H. Elbern, H. Eskes, M. Hirtl, R. Žabkar, G. R. Carmichael, J. Flemming, A. Inness, M. Pagowski, J. L. Pérez Camaño, P. E. Saide, R. San Jose, M. Sofiev, J. Vira, A. Baklanov, C. Carnevale, G. Grell, and C. Seigneur
Atmos. Chem. Phys., 15, 5325–5358, https://doi.org/10.5194/acp-15-5325-2015, https://doi.org/10.5194/acp-15-5325-2015, 2015
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Data assimilation is used in atmospheric chemistry models to improve air quality forecasts, construct re-analyses of concentrations, and perform inverse modeling. Coupled chemistry meteorology models (CCMM) are atmospheric chemistry models that simulate meteorological processes and chemical transformations jointly. We review here the current status of data assimilation in atmospheric chemistry models, with a particular focus on future prospects for data assimilation in CCMM.
Y. Wang, K. N. Sartelet, M. Bocquet, P. Chazette, M. Sicard, G. D'Amico, J. F. Léon, L. Alados-Arboledas, A. Amodeo, P. Augustin, J. Bach, L. Belegante, I. Binietoglou, X. Bush, A. Comerón, H. Delbarre, D. García-Vízcaino, J. L. Guerrero-Rascado, M. Hervo, M. Iarlori, P. Kokkalis, D. Lange, F. Molero, N. Montoux, A. Muñoz, C. Muñoz, D. Nicolae, A. Papayannis, G. Pappalardo, J. Preissler, V. Rizi, F. Rocadenbosch, K. Sellegri, F. Wagner, and F. Dulac
Atmos. Chem. Phys., 14, 12031–12053, https://doi.org/10.5194/acp-14-12031-2014, https://doi.org/10.5194/acp-14-12031-2014, 2014
Y. Wang, K. N. Sartelet, M. Bocquet, and P. Chazette
Atmos. Chem. Phys., 14, 3511–3532, https://doi.org/10.5194/acp-14-3511-2014, https://doi.org/10.5194/acp-14-3511-2014, 2014
E. Emili, B. Barret, S. Massart, E. Le Flochmoen, A. Piacentini, L. El Amraoui, O. Pannekoucke, and D. Cariolle
Atmos. Chem. Phys., 14, 177–198, https://doi.org/10.5194/acp-14-177-2014, https://doi.org/10.5194/acp-14-177-2014, 2014
O. Saunier, A. Mathieu, D. Didier, M. Tombette, D. Quélo, V. Winiarek, and M. Bocquet
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M. R. Koohkan, M. Bocquet, Y. Roustan, Y. Kim, and C. Seigneur
Atmos. Chem. Phys., 13, 5887–5905, https://doi.org/10.5194/acp-13-5887-2013, https://doi.org/10.5194/acp-13-5887-2013, 2013
S. Barthélémy, S. Ricci, O. Pannekoucke, O. Thual, and P. O. Malaterre
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-10-6963-2013, https://doi.org/10.5194/hessd-10-6963-2013, 2013
Preprint withdrawn
Y. Wang, K. N. Sartelet, M. Bocquet, and P. Chazette
Atmos. Chem. Phys., 13, 269–283, https://doi.org/10.5194/acp-13-269-2013, https://doi.org/10.5194/acp-13-269-2013, 2013
Related subject area
Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
Explaining the high skill of reservoir computing methods in El Niño prediction
Multilevel Monte Carlo methods for ensemble variational data assimilation
Dynamic–statistic combined ensemble prediction and impact factors of China's summer precipitation
Bridging Data Assimilation and Control: Ensemble Model Predictive Control for High-Dimensional Nonlinear Systems
Evaluation of Effectiveness of Intervention Strategy in Control Simulation Experiment through Comparison with Model Predictive Control
Long-window hybrid variational data assimilation methods for chaotic climate models tested with the Lorenz 63 system
Inferring flow energy, space scales, and timescales: freely drifting vs. fixed-point observations
Simulation and Data Assimilation in an Idealized Coupled Atmosphere-Ocean-Sea Ice Floe Model with Cloud Effects
A comparison of two nonlinear data assimilation methods
On Process-Oriented Conditional Targeted Covariance Inflation (TCI) for 3D-Volume Radar Data Assimilation
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
Robust weather-adaptive post-processing using model output statistics random forests
Computation of covariant lyapunov vectors using data assimilation
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
Francesco Guardamagna, Claudia Wieners, and Henk A. Dijkstra
Nonlin. Processes Geophys., 32, 201–224, https://doi.org/10.5194/npg-32-201-2025, https://doi.org/10.5194/npg-32-201-2025, 2025
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Artificial intelligence (AI) has recently shown promising results in ENSO (El Niño–Southern Oscillation) forecasting, outperforming traditional models. Yet AI models deliver accurate predictions without showing the underlying mechanisms. Our study examines a specific AI model, the reservoir computer (RC). Our results show that the RC is less sensitive to initial perturbations than the traditional Zebiak–Cane (ZC) model. This reduced sensitivity can explain the RC's superior skills.
Mayeul Destouches, Paul Mycek, Selime Gürol, Anthony T. Weaver, Serge Gratton, and Ehouarn Simon
Nonlin. Processes Geophys., 32, 167–187, https://doi.org/10.5194/npg-32-167-2025, https://doi.org/10.5194/npg-32-167-2025, 2025
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Can multilevel Monte Carlo methods improve ensemble variational data assimilation without increasing its computational cost? By shifting part of the ensemble generation cost to coarser simulation grids, larger ensemble sizes become affordable. This gives smaller sampling errors without introducing any coarse-grid bias. Numerical experiments with a quasi-geostrophic model demonstrate the potential of the approach and highlight the challenges of operational implementation.
Xiaojuan Wang, Zihan Yang, Shuai Li, Qingquan Li, and Guolin Feng
Nonlin. Processes Geophys., 32, 117–130, https://doi.org/10.5194/npg-32-117-2025, https://doi.org/10.5194/npg-32-117-2025, 2025
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Unequal-weighted ensemble prediction (UWE) using outputs of the dynamic–statistic prediction is presented, and its possible impact factors are also analysed. Results indicate that the UWE has shown promise in improving the prediction skill of summer precipitation in China on account of the fact that UWE can overcome the shortcomings of the structural inadequacy of individual dynamic–statistic predictions, reducing formulation uncertainties and resulting in more stable and accurate predictions.
Kenta Kurosawa, Atsushi Okazaki, Fumitoshi Kawasaki, and Shunji Kotsuki
EGUsphere, https://doi.org/10.5194/egusphere-2025-595, https://doi.org/10.5194/egusphere-2025-595, 2025
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We propose Ensemble Model Predictive Control (EnMPC), a novel method that improves control of complex systems like weather by integrating control theory with data assimilation. Unlike traditional methods, which are computationally expensive, EnMPC uses ensemble simulations to efficiently handle uncertainties and optimize solutions. This approach reduces computational cost while maintaining accuracy, making it a promising step toward real-world applications in dynamic system control.
Rikuto Nagai, Yang Bai, Masaki Ogura, Shunji Kotsuki, and Naoki Wakamiya
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-26, https://doi.org/10.5194/npg-2024-26, 2024
Revised manuscript accepted for NPG
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Controlling chaotic systems is a key step toward weather control. The Control Simulation Experiment (CSE) modifies weather systems using small perturbations, as shown in studies with the Lorenz-63 model. However, the effectiveness of CSE compared to other methods is unclear. This study evaluates CSE against Model Predictive Control (MPC). Simulations reveal that MPC achieves higher success rates with less effort under certain conditions, linking control theory and atmospheric science.
Philip David Kennedy, Abhirup Banerjee, Armin Köhl, and Detlef Stammer
EGUsphere, https://doi.org/10.48550/arXiv.2403.03166, https://doi.org/10.48550/arXiv.2403.03166, 2024
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This work introduces and evaluates two hybrid data assimilation techniques. The first uses two syncronsied forward model runs before a single adjoint model run to consistently increase the precision of the parameter estimation. The second uses a lower resolution model with adjoint equations to drive a higher resolution ‘target’ model through data assimilation with no loss in precision compared to data assimilation without hybrid methods.
Aurelien Luigi Serge Ponte, Lachlan C. Astfalck, Matthew D. Rayson, Andrew P. Zulberti, and Nicole L. Jones
Nonlin. Processes Geophys., 31, 571–586, https://doi.org/10.5194/npg-31-571-2024, https://doi.org/10.5194/npg-31-571-2024, 2024
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We propose a novel method for the estimation of ocean surface flow properties in terms of its energy and spatial and temporal scales. The method relies on flow observations collected either at a fixed location or along the flow, as would be inferred from the trajectory of freely drifting platforms. The accuracy of the method is quantified in several experimental configurations. We innovatively demonstrate that freely drifting platforms, even in isolation, can be used to capture flow properties.
Changhong Mou, Samuel N. Stechmann, and Nan Chen
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-21, https://doi.org/10.5194/npg-2024-21, 2024
Revised manuscript accepted for NPG
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Sea ice is crucial in the climate system, especially in the Marginal Ice Zone (MIZ). As the MIZ expands, understanding its dynamics is essential for predicting climate impacts. This paper addresses the largely overlooked role of clouds, developing an idealized atmosphere-ocean-ice model with cloud effects, tackling both simulation and data assimilation. The results imply the potential of integrating idealized models with data assimilation for understanding of Arctic dynamics and predictions.
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
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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.
Klaus Vobig, Roland Potthast, and Klaus Stephan
EGUsphere, https://doi.org/10.5194/egusphere-2024-2876, https://doi.org/10.5194/egusphere-2024-2876, 2024
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We present a novel approach to targeted covariance inflation (TCI) which aims to improve the assimilation of 3D radar reflectivity and, eventually, the short-term forecast of reflectivity and precipitation.
Using an operational numerical weather prediction framework, our numerical results show that TCI makes the system accurately generate new reflectivity cells and significantly improves the fractional skill score of forecasts over lead times of up to six hours by up to 10 %.
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
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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
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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
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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
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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
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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
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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
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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
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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.
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
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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.
Shashank Kumar Roy and Amit Apte
EGUsphere, https://doi.org/10.5194/egusphere-2023-2168, https://doi.org/10.5194/egusphere-2023-2168, 2023
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We focus on the computation of Lyapunov vectors for dynamical systems using partial and noisy observations using data assimilation. We study how the errors in the approximated LVs are implicitly affected by the errors in the estimated trajectory. Our results reveal the difference in sensitivity of the individual vectors in low and high dimensions. Additionally, we find that the subspaces defined by the LVs computed from the approximate trajectory are less sensitive than the individual vectors.
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
The forecast of weather prediction uncertainty is a real challenge and is crucial for risk...
