Articles | Volume 25, issue 2
https://doi.org/10.5194/npg-25-315-2018
© 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-25-315-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
27 Apr 2018
Research article |
| 27 Apr 2018
| 27 Apr 2018
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother
Anthony Fillion
CORRESPONDING AUTHOR
CEREA, Joint Laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France
CERFACS, Toulouse, France
Marc Bocquet
CEREA, Joint Laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France
Serge Gratton
INPT-IRIT, Toulouse, France
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Charlotte Durand, Tobias Sebastian Finn, Alban Farchi, Marc Bocquet, Julien Brajard, and Laurent Bertino
EGUsphere, https://doi.org/10.5194/egusphere-2024-4028, https://doi.org/10.5194/egusphere-2024-4028, 2025
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This paper presents a four-dimensional variational data assimilation system based on a neural network emulator for sea-ice thickness, learned from neXtSIM simulation outputs. Testing with simulated and real observation retrievals, the system improves forecasts and bias error, performing comparably to operational methods, demonstrating the promise of sea-ice data-driven data assimilation systems.
Simon Driscoll, Alberto Carrassi, Julien Brajard, Laurent Bertino, Einar Ólason, Marc Bocquet, and Amos Lawless
EGUsphere, https://doi.org/10.5194/egusphere-2024-2476, https://doi.org/10.5194/egusphere-2024-2476, 2024
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The formation and evolution of sea ice melt ponds (ponds of melted water) are complex, insufficiently understood and represented in models with considerable uncertainty. These uncertain representations are not traditionally included in climate models potentially causing the known underestimation of sea ice loss in climate models. Our work creates the first observationally based machine learning model of melt ponds that is also a ready and viable candidate to be included in climate models.
Joffrey Dumont Le Brazidec, Pierre Vanderbecken, Alban Farchi, Grégoire Broquet, Gerrit Kuhlmann, and Marc Bocquet
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-156, https://doi.org/10.5194/gmd-2024-156, 2024
Revised manuscript accepted for GMD
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We developed a deep learning method to estimate CO2 emissions from power plants using satellite images. Trained and validated on simulated data, our model accurately predicts emissions despite challenges like cloud cover. When applied to real OCO3 satellite image, the results closely match reported emissions. This study shows that neural networks trained on simulations can effectively analyse real satellite data, offering a new way to monitor CO2 emissions from space.
Tobias Sebastian Finn, Lucas Disson, Alban Farchi, Marc Bocquet, and Charlotte Durand
Nonlin. Processes Geophys., 31, 409–431, https://doi.org/10.5194/npg-31-409-2024, https://doi.org/10.5194/npg-31-409-2024, 2024
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We train neural networks as denoising diffusion models for state generation in the Lorenz 1963 system and demonstrate that they learn an internal representation of the system. We make use of this learned representation and the pre-trained model in two downstream tasks: surrogate modelling and ensemble generation. For both tasks, the diffusion model can outperform other more common approaches. Thus, we see a potential of representation learning with diffusion models for dynamical systems.
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.
Yumeng Chen, Polly Smith, Alberto Carrassi, Ivo Pasmans, Laurent Bertino, Marc Bocquet, Tobias Sebastian Finn, Pierre Rampal, and Véronique Dansereau
The Cryosphere, 18, 2381–2406, https://doi.org/10.5194/tc-18-2381-2024, https://doi.org/10.5194/tc-18-2381-2024, 2024
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We explore multivariate state and parameter estimation using a data assimilation approach through idealised simulations in a dynamics-only sea-ice model based on novel rheology. We identify various potential issues that can arise in complex operational sea-ice models when model parameters are estimated. Even though further investigation will be needed for such complex sea-ice models, we show possibilities of improving the observed and the unobserved model state forecast and parameter accuracy.
Charlotte Durand, Tobias Sebastian Finn, Alban Farchi, Marc Bocquet, Guillaume Boutin, and Einar Ólason
The Cryosphere, 18, 1791–1815, https://doi.org/10.5194/tc-18-1791-2024, https://doi.org/10.5194/tc-18-1791-2024, 2024
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This paper focuses on predicting Arctic-wide sea-ice thickness using surrogate modeling with deep learning. The model has a predictive power of 12 h up to 6 months. For this forecast horizon, persistence and daily climatology are systematically outperformed, a result of learned thermodynamics and advection. Consequently, surrogate modeling with deep learning proves to be effective at capturing the complex behavior of sea ice.
Joffrey Dumont Le Brazidec, Pierre Vanderbecken, Alban Farchi, Grégoire Broquet, Gerrit Kuhlmann, and Marc Bocquet
Geosci. Model Dev., 17, 1995–2014, https://doi.org/10.5194/gmd-17-1995-2024, https://doi.org/10.5194/gmd-17-1995-2024, 2024
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Our research presents an innovative approach to estimating power plant CO2 emissions from satellite images of the corresponding plumes such as those from the forthcoming CO2M satellite constellation. The exploitation of these images is challenging due to noise and meteorological uncertainties. To overcome these obstacles, we use a deep learning neural network trained on simulated CO2 images. Our method outperforms alternatives, providing a positive perspective for the analysis of CO2M images.
Tobias Sebastian Finn, Charlotte Durand, Alban Farchi, Marc Bocquet, Yumeng Chen, Alberto Carrassi, and Véronique Dansereau
The Cryosphere, 17, 2965–2991, https://doi.org/10.5194/tc-17-2965-2023, https://doi.org/10.5194/tc-17-2965-2023, 2023
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We combine deep learning with a regional sea-ice model to correct model errors in the sea-ice dynamics of low-resolution forecasts towards high-resolution simulations. The combined model improves the forecast by up to 75 % and thereby surpasses the performance of persistence. As the error connection can additionally be used to analyse the shortcomings of the forecasts, this study highlights the potential of combined modelling for short-term sea-ice forecasting.
Joffrey Dumont Le Brazidec, Pierre Vanderbecken, Alban Farchi, Marc Bocquet, Jinghui Lian, Grégoire Broquet, Gerrit Kuhlmann, Alexandre Danjou, and Thomas Lauvaux
Geosci. Model Dev., 16, 3997–4016, https://doi.org/10.5194/gmd-16-3997-2023, https://doi.org/10.5194/gmd-16-3997-2023, 2023
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Monitoring of CO2 emissions is key to the development of reduction policies. Local emissions, from cities or power plants, may be estimated from CO2 plumes detected in satellite images. CO2 plumes generally have a weak signal and are partially concealed by highly variable background concentrations and instrument errors, which hampers their detection. To address this problem, we propose and apply deep learning methods to detect the contour of a plume in simulated CO2 satellite images.
Pierre J. Vanderbecken, Joffrey Dumont Le Brazidec, Alban Farchi, Marc Bocquet, Yelva Roustan, Élise Potier, and Grégoire Broquet
Atmos. Meas. Tech., 16, 1745–1766, https://doi.org/10.5194/amt-16-1745-2023, https://doi.org/10.5194/amt-16-1745-2023, 2023
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Instruments dedicated to monitoring atmospheric gaseous compounds from space will provide images of urban-scale plumes. We discuss here the use of new metrics to compare observed plumes with model predictions that will be less sensitive to meteorology uncertainties. We have evaluated our metrics on diverse plumes and shown that by eliminating some aspects of the discrepancies, they are indeed less sensitive to meteorological variations.
Joffrey Dumont Le Brazidec, Marc Bocquet, Olivier Saunier, and Yelva Roustan
Geosci. Model Dev., 16, 1039–1052, https://doi.org/10.5194/gmd-16-1039-2023, https://doi.org/10.5194/gmd-16-1039-2023, 2023
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When radionuclides are released into the atmosphere, the assessment of the consequences depends on the evaluation of the magnitude and temporal evolution of the release, which can be highly variable as in the case of Fukushima Daiichi.
Here, we propose Bayesian inverse modelling methods and the reversible-jump Markov chain Monte Carlo technique, which allows one to evaluate the temporal variability of the release and to integrate different types of information in the source reconstruction.
Colin Grudzien and Marc Bocquet
Geosci. Model Dev., 15, 7641–7681, https://doi.org/10.5194/gmd-15-7641-2022, https://doi.org/10.5194/gmd-15-7641-2022, 2022
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Iterative optimization techniques, the state of the art in data assimilation, have largely focused on extending forecast accuracy to moderate- to long-range forecast systems. However, current methodology may not be cost-effective in reducing forecast errors in online, short-range forecast systems. We propose a novel optimization of these techniques for online, short-range forecast cycles, simultaneously providing an improvement in forecast accuracy and a reduction in the computational cost.
Joffrey Dumont Le Brazidec, Marc Bocquet, Olivier Saunier, and Yelva Roustan
Atmos. Chem. Phys., 21, 13247–13267, https://doi.org/10.5194/acp-21-13247-2021, https://doi.org/10.5194/acp-21-13247-2021, 2021
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The assessment of the environmental consequences of a radionuclide release depends on the estimation of its source. This paper aims to develop inverse Bayesian methods which combine transport models with measurements, in order to reconstruct the ensemble of possible sources.
Three methods to quantify uncertainties based on the definition of probability distributions and the physical models are proposed and evaluated for the case of 106Ru releases over Europe in 2017.
Colin Grudzien, Marc Bocquet, and Alberto Carrassi
Geosci. Model Dev., 13, 1903–1924, https://doi.org/10.5194/gmd-13-1903-2020, https://doi.org/10.5194/gmd-13-1903-2020, 2020
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All scales of a dynamical physical process cannot be resolved accurately in a multiscale, geophysical model. The behavior of unresolved scales of motion are often parametrized by a random process to emulate their effects on the dynamically resolved variables, and this results in a random–dynamical model. We study how the choice of a numerical discretization of such a system affects the model forecast and estimation statistics, when the random–dynamical model is unbiased in its parametrization.
Thomas Lauvaux, Liza I. Díaz-Isaac, Marc Bocquet, and Nicolas Bousserez
Atmos. Chem. Phys., 19, 12007–12024, https://doi.org/10.5194/acp-19-12007-2019, https://doi.org/10.5194/acp-19-12007-2019, 2019
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A small-size ensemble of mesoscale simulations has been filtered to characterize the spatial structures of transport errors in atmospheric CO2 mixing ratios. The extracted error structures in in situ and column CO2 show similar length scales compared to other meteorological variables, including seasonality, which could be used as proxies in regional inversion systems.
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
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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.
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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We explore the possibility of combining data assimilation with machine learning. We introduce a new hybrid method for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting its future states. Numerical experiments have been carried out using the chaotic Lorenz 96 model, proving both the convergence of the hybrid method and its statistical skills including short-term forecasting and emulation of the long-term dynamics.
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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We demonstrate that transport model errors, one of the main contributors to the uncertainty in regional CO2 inversions, can be represented by a small-size ensemble carefully calibrated with meteorological data. Our results also confirm transport model errors represent a significant fraction of the model–data mismatch in CO2 mole fractions and hence in regional inverse CO2 fluxes.
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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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.
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
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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.
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
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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.
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
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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.
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
O. Saunier, A. Mathieu, D. Didier, M. Tombette, D. Quélo, V. Winiarek, and M. Bocquet
Atmos. Chem. Phys., 13, 11403–11421, https://doi.org/10.5194/acp-13-11403-2013, https://doi.org/10.5194/acp-13-11403-2013, 2013
M. Bocquet and P. Sakov
Nonlin. Processes Geophys., 20, 803–818, https://doi.org/10.5194/npg-20-803-2013, https://doi.org/10.5194/npg-20-803-2013, 2013
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
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
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Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Correcting for model changes in statistical postprocessing – an approach based on response theory
Xiaojuan Wang, Zihan Yang, Shuai Li, Qingquan Li, and Guolin Feng
EGUsphere, https://doi.org/10.5194/egusphere-2024-3762, https://doi.org/10.5194/egusphere-2024-3762, 2024
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This study presents the Unequal-Weighted Ensemble prediction (UWE) of the dynamic-statistic schemes in order to enhance summer precipitation prediction in China. The analysis also includes an examination of factors that may impact the prediction skill of UWE, such as grid-based and station-based prediction, the calculation of prediction skill, and the influence of sample dispersion on prediction accuracy.
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.
Mayeul Destouches, Paul Mycek, Selime Gürol, Anthony T. Weaver, Serge Gratton, and Ehouarn Simon
EGUsphere, https://doi.org/10.5194/egusphere-2024-3628, https://doi.org/10.5194/egusphere-2024-3628, 2024
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We explore the potential of Multilevel Monte Carlo methods to improve ensemble-variational data assimilation without increasing the computational cost. By shifting part of the ensemble generation cost to coarser simulation grids, larger sample sizes and smaller sampling errors become affordable, while keeping the final estimate unbiased. Numerical experiments with a quasi-geostrophic model demonstrate the potential of the approach and highlight the challenges towards operational implementation.
Francesco Guardamagna, Claudia Wieners, and Henk Dijkstra
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-24, https://doi.org/10.5194/npg-2024-24, 2024
Revised manuscript accepted for NPG
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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 and Cane (ZC) model. This reduced sensitivity can explain the RC's superior skills.
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.
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.
Pengcheng Yan, Guolin Feng, Wei Hou, and Ping Yang
Nonlin. Processes Geophys., 27, 489–500, https://doi.org/10.5194/npg-27-489-2020, https://doi.org/10.5194/npg-27-489-2020, 2020
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A system transiting from one stable state to another has to experience a period. Can we predict the end moment (state) if the process has not been completed? This paper presents a method to solve this problem. This method is based on the quantitative relationship among the parameters, which is used to describe the transition process of the abrupt change. By using the historical data, we extract some parameters for predicting the uncompleted climate transition process.
Reinhold Hess
Nonlin. Processes Geophys., 27, 473–487, https://doi.org/10.5194/npg-27-473-2020, https://doi.org/10.5194/npg-27-473-2020, 2020
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Forecasts of ensemble systems are statistically aligned to synoptic observations at DWD in order to provide support for warning decision management. Motivation and design consequences for extreme and rare meteorological events are presented. Especially for probabilities of severe wind gusts global logistic parameterisations are developed that generate robust statistical forecasts for extreme events, while local characteristics are preserved.
Ashesh Chattopadhyay, Pedram Hassanzadeh, and Devika Subramanian
Nonlin. Processes Geophys., 27, 373–389, https://doi.org/10.5194/npg-27-373-2020, https://doi.org/10.5194/npg-27-373-2020, 2020
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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
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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
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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.
Cited articles
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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.
This study generalizes a paper by Pires et al. (1996) to state-of-the-art data assimilation...
