Articles | Volume 15, issue 20
https://doi.org/10.5194/gmd-15-7641-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-15-7641-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
20 Oct 2022
Development and technical paper |
| 20 Oct 2022
| 20 Oct 2022
A fast, single-iteration ensemble Kalman smoother for sequential data assimilation
Center for Western Weather and Water Extremes (CW3E), Scripps Institution of Oceanography, University of California San Diego, San Diego, CA, USA
Department of Mathematics and Statistics, University of Nevada, Reno, Reno, Nevada, USA
Marc Bocquet
CEREA, École des Ponts and EDF R&D, Île-de-France, France
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Marc Bocquet, Tobias Sebastian Finn, Sibo Cheng, and Alban Farchi
Nonlin. Processes Geophys., 33, 401–424, https://doi.org/10.5194/npg-33-401-2026, https://doi.org/10.5194/npg-33-401-2026, 2026
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Deep learning has been used to discover new data assimilation methods to track chaotic dynamical systems. Strikingly, these data assimilation networks can match the accuracy of ensemble-based methods using only a single state forecast. This paper first investigates the reasons for this efficacy, and then shows that their performance in more nonlinear regimes matches that of the most accurate scalable data assimilation methods, with greater efficiency and robustness.
Wenbo Yu, Anirbit Ghosh, Tobias Sebastian Finn, Rossella Arcucci, Marc Bocquet, and Sibo Cheng
Geosci. Model Dev., 19, 1027–1054, https://doi.org/10.5194/gmd-19-1027-2026, https://doi.org/10.5194/gmd-19-1027-2026, 2026
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We introduce the first denoising diffusion model for wildfire spread prediction, a new kind of generative AI model that learns to simulate fires not just as one fixed outcome, but as a range of possible scenarios. This allows us to capture the inherent uncertainty of wildfire dynamics. Our model produces ensembles of forecasts that reflect physically meaningful distributions of where fire might go next.
Charlotte Durand, Tobias Sebastian Finn, Alban Farchi, Marc Bocquet, Julien Brajard, and Laurent Bertino
The Cryosphere, 19, 5613–5637, https://doi.org/10.5194/tc-19-5613-2025, https://doi.org/10.5194/tc-19-5613-2025, 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 (neXt generation Sea Ice Model) 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.
Joffrey Dumont Le Brazidec, Pierre Vanderbecken, Alban Farchi, Grégoire Broquet, Gerrit Kuhlmann, and Marc Bocquet
Geosci. Model Dev., 18, 3607–3622, https://doi.org/10.5194/gmd-18-3607-2025, https://doi.org/10.5194/gmd-18-3607-2025, 2025
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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 images, 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.
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
Preprint archived
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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.
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.
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.
Cited articles
Ait-El-Fquih, B. and Hoteit, I.: Filtering with One-Step-Ahead Smoothing for
Efficient Data Assimilation, in: Data Assimilation for Atmospheric, Oceanic
and Hydrologic Applications (Vol. IV), edited by: Park, S. K. and Xu, L.,
Springer, Cham, 69–96, https://doi.org/10.1007/978-3-030-77722-7_1, 2022. a, b
Ait-El-Fquih, B., El Gharamti, M., and Hoteit, I.: A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology, Hydrol. Earth Syst. Sci., 20, 3289–3307, https://doi.org/10.5194/hess-20-3289-2016, 2016. a
Bannister, R. N.: A review of operational methods of variational and
ensemble-variational data assimilation, Q. J. Roy. Meteor. Soc., 143,
607–633, https://doi.org/10.1002/qj.2982, 2017. a
Bezanson, J., Edelman, A., Karpinski, S., and Shah, V.: Julia: A
fresh approach to numerical computing, SIAM Rev., 59, 65–98, https://doi.org/10.1137/141000671, 2017. a
Bocquet, M.: Ensemble Kalman filtering without the intrinsic need for inflation, Nonlin. Processes Geophys., 18, 735–750, https://doi.org/10.5194/npg-18-735-2011, 2011. a
Bocquet, M.: Localization and the iterative ensemble Kalman smoother, Q. J. Roy.
Meteor. Soc., 142, 1075–1089, https://doi.org/10.1002/qj.2711, 2016. a, b
Bocquet, M. and Carrassi, A.: Four-dimensional ensemble variational data
assimilation and the unstable subspace, Tellus A, 69, 1304504, https://doi.org/10.1080/16000870.2017.1304504, 2017. a
Bocquet, M. and Sakov, P.: Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems, Nonlin. Processes Geophys., 19, 383–399, https://doi.org/10.5194/npg-19-383-2012, 2012. a, b
Bocquet, M. and Sakov, P.: Joint state and parameter estimation with an iterative ensemble Kalman smoother, Nonlin. Processes Geophys., 20, 803–818, https://doi.org/10.5194/npg-20-803-2013, 2013. a, b
Bocquet, M., Raanes, P. N., and Hannart, A.: Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation, Nonlin. Processes Geophys., 22, 645–662, https://doi.org/10.5194/npg-22-645-2015, 2015. a, b, c
Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Bayesian inference of
chaotic dynamics by merging data assimilation, machine learning and
expectation-maximization, Foundations of Data Science, 2, 55–80, https://doi.org/10.3934/fods.2020004, 2020. a
Carrassi, A., Bocquet, M., Bertino, L., and Evensen, G.: Data Assimilation in
the Geosciences-An overview on methods, issues and perspectives, WIREs Clim.
Change, 9, e535, https://doi.org/10.1002/wcc.535, 2018. a
Carrassi, A., Bocquet, M., Demaeyer, J., Grudzien, C., Raanes, P., and
Vannitsem, S.: Data Assimilation for Chaotic Dynamics, in: Data Assimilation
for Atmospheric, Oceanic and Hydrologic Applications (Vol. IV), edited by:
Park, S. K. and Xu, L., Springer, Cham, 1–42,
https://doi.org/10.1007/978-3-030-77722-7_1, 2022. a
Chen, Y. and Oliver, D. S.: Ensemble randomized maximum likelihood method as an
iterative ensemble smoother, Math. Geosci., 44, 1–26, https://doi.org/10.1007/s11004-011-9376-z, 2012. a
Corazza, M., Kalnay, E., Patil, D. J., Yang, S.-C., Morss, R., Cai, M., Szunyogh, I., Hunt, B. R., and Yorke, J. A.: Use of the breeding technique to estimate the structure of the analysis “errors of the day”, Nonlin. Processes Geophys., 10, 233–243, https://doi.org/10.5194/npg-10-233-2003, 2003. a
Cosme, E., Verron, J., Brasseur, P., Blum, J., and Auroux, D.: Smoothing
problems in a Bayesian framework and their linear Gaussian solutions,
Mon. Weather Rev., 140, 683–695, https://doi.org/10.1175/MWR-D-10-05025.1, 2012. a
Desbouvries, F., Petetin, Y., and Ait-El-Fquih, B.: Direct, prediction-and
smoothing-based Kalman and particle filter algorithms, Signal Process.,
91, 2064–2077, https://doi.org/10.1016/j.sigpro.2011.03.013, 2011. a
Emerick, A. A. and Reynolds, A. C.: Ensemble smoother with multiple data
assimilation, Comput. Geosci., 55, 3–15, https://doi.org/10.1016/j.cageo.2012.03.011, 2013. a, b
Evensen, G.: Analysis of iterative ensemble smoothers for solving inverse
problems, Comput. Geosci., 22, 885–908, https://doi.org/10.1007/s10596-018-9731-y, 2018. a
Evensen, G. and Van Leeuwen, P. J.: An ensemble Kalman smoother for nonlinear
dynamics, Mon. Weather Rev., 128, 1852–1867, https://doi.org/10.1175/1520-0493(2000)128<1852:AEKSFN>2.0.CO;2, 2000. a
Fertig, E. J., Harlim, J., and Hunt, B. R.: A comparative study of 4D-VAR and
a 4D ensemble Kalman filter: Perfect model simulations with
Lorenz-96, Tellus A, 59, 96–100, https://doi.org/10.1111/j.1600-0870.2006.00205.x, 2007. a
Fillion, A., Bocquet, M., and Gratton, S.: Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother, Nonlin. Processes Geophys., 25, 315–334, https://doi.org/10.5194/npg-25-315-2018, 2018. a
Fillion, A., Bocquet, M., Gratton, S., Görol, S., and Sakov, P.: An
iterative ensemble Kalman smoother in presence of additive model error,
SIAM/ASA J. Uncertainty Quantification, 8, 198–228, 2020. a
Gharamti, M. E., Ait-El-Fquih, B., and Hoteit, I.: An iterative ensemble
Kalman filter with one-step-ahead smoothing for state-parameters estimation
of contaminant transport models, J. Hydrol., 527, 442–457, https://doi.org/10.1016/j.jhydrol.2015.05.004, 2015. a
Grudzien, C. and Bocquet, M.: A Tutorial on Bayesian Data Assimilation, arXiv
[preprint],
https://doi.org/10.48550/arXiv.2112.07704, 2021. a
Grudzien, C., Carrassi, A., and Bocquet, M.: Asymptotic forecast uncertainty
and the unstable subspace in the presence of additive model error, SIAM/ASA
J. Uncertainty Quantification, 6, 1335–1363, https://doi.org/10.1137/17M114073X, 2018. a
Gu, Y. and Oliver, D. S.: An iterative ensemble Kalman filter for multiphase
fluid flow data assimilation, SPE J., 12, 438–446, https://doi.org/10.2118/108438-PA, 2007. a
Harlim, J. and Hunt, B. R.: Four-dimensional local ensemble transform Kalman
filter: numerical experiments with a global circulation model, Tellus A, 59,
731–748, https://doi.org/10.1111/j.1600-0870.2007.00255.x, 2007. a
Hunt, B. R., Kalnay, E., Kostelich, E. J., Ott, E., Patil, D. J., Sauer, T.,
Szunyogh, I., Yorke, J. A., and Zimin, A. V.: Four-dimensional ensemble
Kalman filtering, Tellus A, 56, 273–277, https://doi.org/10.3402/tellusa.v56i4.14424, 2004. a, b
Hunt, B. R., Kostelich, E. J., and Szunyogh, I.: Efficient data assimilation
for spatiotemporal chaos: A local ensemble transform Kalman filter, Phys.
D, 230, 112–126, https://doi.org/10.1016/j.physd.2006.11.008, 2007. a, b, c, d
Iglesias, M. A., Law, K. J. H., and Stuart, A. M.: Ensemble Kalman methods for
inverse problems, Inverse Problems, 29, 045001, https://doi.org/10.1088/0266-5611/29/4/045001, 2013. a
Kalnay, E. and Yang, S. C.: Accelerating the spin-up of ensemble Kalman
filtering, Q. J. Roy. Meteor. Soc., 136, 1644–1651, https://doi.org/10.1002/qj.652, 2010. a
Kalnay, E., Li, H., Miyoshi, T., Yang, S.-C., and Ballabrera-Poy, J.:
4-D-Var or ensemble Kalman filter?, Tellus A, 59, 758–773, https://doi.org/10.1111/j.1600-0870.2007.00261.x, 2007. a
Kovachki, N. B. and Stuart, A. M.: Ensemble Kalman inversion: a derivative-free
technique for machine learning tasks, Inverse Problems, 35, 095005, https://doi.org/10.1088/1361-6420/ab1c3a, 2019. a
Liu, C., Xiao, Q., and Wang, B.: An Ensemble-Based Four-Dimensional Variational
Data Assimilation Scheme. Part I: Technical Formulation and Preliminary
Test, Mon. Weather Rev., 136, 3363–3373, https://doi.org/10.1175/2008MWR2312.1, 2008. a
Lorenc, A. C.: The potential of the ensemble Kalman filter for NWP – A
comparison with 4D-Var, Q. J. Roy. Meteor. Soc., 129, 3183–3203, https://doi.org/10.1256/qj.02.132, 2003. a, b
Lorenz, E. N.: Predictability: A problem partly solved, in: Proc. Seminar on
predictability, vol. 1, https://www.ecmwf.int/node/10829 (last access: 10 October 2022), 1996. a
Lorenz, E. N. and Emanuel, K. A.: Optimal sites for supplementary weather
observations: Simulation with a small model, J. Atmos. Sci., 55, 399–414, https://doi.org/10.1175/1520-0469(1998)055<0399:OSFSWO>2.0.CO;2,
1998. a
Neal, R. M.: Sampling from multimodal distributions using tempered transitions,
Stat. Comput., 6, 353–366, https://doi.org/10.1007/BF00143556, 1996. a
Nerger, L., Schulte, S., and Bunse-Gerstner, A.: On the influence of model
nonlinearity and localization on ensemble Kalman smoothing, Q. J. Roy.
Meteor. Soc., 140, 2249–2259, https://doi.org/10.1002/qj.2293, 2014. a
Nocedal, J. and Wright, S.: Numerical optimization, Springer Science &
Business Media, https://doi.org/10.1007/978-0-387-40065-5, 2006. a
Pulido, M., Tandeo, P., Bocquet, M., Carrassi, A., and Lucini, M.: Stochastic
parameterization identification using ensemble Kalman filtering combined
with maximum likelihood methods, Tellus A, 70, 1442099, https://doi.org/10.1080/16000870.2018.1442099, 2018. a
Raanes, P. N.: On the ensemble Rauch-Tung-Striebel smoother and its
equivalence to the ensemble Kalman smoother, Q. J. Roy. Meteor. Soc., 142,
1259–1264, https://doi.org/10.1002/qj.2728, 2016. a
Raanes, P. N., Bocquet, M., and Carrassi, A.: Adaptive covariance inflation in
the ensemble Kalman filter by Gaussian scale mixtures, Q. J. Roy. Meteor.
Soc., 145, 53–75, https://doi.org/10.1002/qj.3386, 2019a. a, b
Raanes, P. N., Stordal, A. S., and Evensen, G.: Revising the stochastic iterative ensemble smoother, Nonlin. Processes Geophys., 26, 325–338, https://doi.org/10.5194/npg-26-325-2019, 2019b. a
Raanes, P. N., Grudzien, C., and14tondeu: nansencenter/DAPPER: Version 0.8, Zenodo [code],
https://doi.org/10.5281/zenodo.2029296, 2018. a
Raboudi, N. F., Ait-El-Fquih, B., and Hoteit, I.: Ensemble Kalman filtering
with one-step-ahead smoothing, Mon. Weather Rev., 146, 561–581, https://doi.org/10.1175/MWR-D-17-0175.1, 2018. a
Sakov, P. and Bertino, L.: Relation between two common localisation methods for
the EnKF, Comput. Geosci., 15, 225–237, https://doi.org/10.1007/s10596-010-9202-6, 2011. a, b
Sakov, P. and Oke, P. R.: A deterministic formulation of the ensemble Kalman
filter: an alternative to ensemble square root filters, Tellus A, 60,
361–371, https://doi.org/10.1111/j.1600-0870.2007.00299.x, 2008a. a
Sakov, P. and Oke, P. R.: Implications of the form of the ensemble
transformation in the ensemble square root filters, Mon. Weather Rev., 136,
1042–1053, https://doi.org/10.1175/2007MWR2021.1, 2008b. a, b, c
Sakov, P., Evensen, G., and Bertino, L.: Asynchronous data assimilation with
the EnKF, Tellus A, 62, 24–29, https://doi.org/10.1111/j.1600-0870.2009.00417.x, 2010. a
Sakov, P., Oliver, D. S., and Bertino, L.: An iterative EnKF for strongly
nonlinear systems, Mon. Weather Rev., 140, 1988–2004, https://doi.org/10.1175/MWR-D-11-00176.1, 2012. a, b, c
Sakov, P., Haussaire, J. M., and Bocquet, M.: An iterative ensemble Kalman
filter in presence of additive model error, Q. J. Roy. Meteor. Soc., 144, 1297–1309, https://doi.org/10.1002/qj.3213, 2018.
a
Sankhya, A.: Reprint of: Mahalanobis, P.C. (1936) “On the Generalised Distance in Statistics”, 80 (Suppl 1), 1–7, https://doi.org/10.1007/s13171-019-00164-5, 2018. a
Schillings, C. and Stuart, A. M.: Convergence analysis of ensemble Kalman
inversion: the linear, noisy case, Appl. Anal., 97, 107–123, https://doi.org/10.1080/00036811.2017.1386784, 2018. a
Tandeo, P., Ailliot, P., Bocquet, M., Carrassi, A., Miyoshi, T., Pulido, M.,
and Zhen, Y.: A review of innovation-based methods to jointly estimate model
and observation error covariance matrices in ensemble data assimilation, Mon.
Weather Rev., 148, 3973–3994, https://doi.org/10.1175/MWR-D-19-0240.1, 2020. a
Taylor, M. E.: Partial differential equations. 1, Basic theory, Springer, https://doi.org/10.1007/978-1-4419-7055-8, 1996. a
Tippett, M. K., Anderson, J. L., Bishop, C. H., Hamill, T. M., and Whitaker,
J. S.: Ensemble square root filters, Mon. Weather Rev., 131, 1485–1490, https://doi.org/10.1175/1520-0493(2003)131<1485:ESRF>2.0.CO;2, 2003. a
Whitaker, J. S. and Loughe, A. F.: The relationship between ensemble spread and
ensemble mean skill, Mon. Weather Rev., 126, 3292–3302, https://doi.org/10.1175/1520-0493(1998)126<3292:TRBESA>2.0.CO;2, 1998. a
Yang, S.-C., Lin, K. J., Miyoshi, T., and Kalnay, E.: Improving the spin-up of
regional EnKF for typhoon assimilation and forecasting with Typhoon Sinlaku
(2008), Tellus A, 65, 20804, https://doi.org/10.3402/tellusa.v65i0.20804, 2013. a
Zupanski, M.: Maximum likelihood ensemble filter: Theoretical aspects, Mon.
Weather Rev., 133, 1710–1726, https://doi.org/10.1175/MWR2946.1, 2005. a, b
Zupanski, M., Navon, I. M., and Zupanski, D.: The Maximum Likelihood Ensemble
Filter as a non-differentiable minimization algorithm, Q. J. Roy. Meteor.
Soc., 134, 1039–1050, https://doi.org/10.1002/qj.251, 2008. a
Short summary
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.
Iterative optimization techniques, the state of the art in data assimilation, have largely...
