Articles | Volume 29, issue 1
https://doi.org/10.5194/npg-29-77-2022
© 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/npg-29-77-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Ensemble Riemannian data assimilation: towards large-scale dynamical systems
Department of Civil, Environmental and Geo-Engineering and Saint Anthony Falls Laboratory, University of Minnesota-Twin Cities, Twin Cities, Minnesota, USA
Ardeshir Ebtehaj
Department of Civil, Environmental and Geo-Engineering and Saint Anthony Falls Laboratory, University of Minnesota-Twin Cities, Twin Cities, Minnesota, USA
Peter Jan van Leeuwen
Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado, USA
Gilad Lerman
School of Mathematics, University of Minnesota-Twin Cities, Twin Cities, Minnesota, USA
Efi Foufoula-Georgiou
Department of Civil and Environmental Engineering and Department of Earth System Science, University of California Irvine, Irvine, California, USA
Related authors
Sagar K. Tamang, Ardeshir Ebtehaj, Peter J. van Leeuwen, Dongmian Zou, and Gilad Lerman
Nonlin. Processes Geophys., 28, 295–309, https://doi.org/10.5194/npg-28-295-2021, https://doi.org/10.5194/npg-28-295-2021, 2021
Short summary
Short summary
Data assimilation aims to improve hydrologic and weather forecasts by combining available information from Earth system models and observations. The classical approaches to data assimilation usually proceed with some preconceived assumptions about the shape of their probability distributions. As a result, when such assumptions are invalid, the forecast accuracy suffers. In the proposed methodology, we relax such assumptions and demonstrate improved performance.
Nicholas Williams, Nicholas Byrne, Daniel Feltham, Peter Jan Van Leeuwen, Ross Bannister, David Schroeder, Isobel Lawrence, Lars Nerger, Jack Landy, and Geoffrey Dawson
EGUsphere, https://doi.org/10.5194/egusphere-2026-742, https://doi.org/10.5194/egusphere-2026-742, 2026
This preprint is open for discussion and under review for The Cryosphere (TC).
Short summary
Short summary
In this study we present three satellite era Arctic sea ice reanalyses, each assimilating different combinations of sea ice concentration and thickness observations. Results show that using year-round thickness observations substantially improves reanalysis compared to winter-only data. The best-performing reanalysis reveals a seasonally compensating bias cycle, suggesting errors in ice growth, leads, refreezing, marginal ice zone dynamics, redistribution, and melt timing mask model errors.
Tianjia Liu, James T. Randerson, Yang Chen, Douglas C. Morton, Elizabeth B. Wiggins, Padhraic Smyth, Efi Foufoula-Georgiou, Roy Nadler, and Omer Nevo
Earth Syst. Sci. Data, 16, 1395–1424, https://doi.org/10.5194/essd-16-1395-2024, https://doi.org/10.5194/essd-16-1395-2024, 2024
Short summary
Short summary
To improve our understanding of extreme wildfire behavior, we use geostationary satellite data to develop the GOFER algorithm and track the hourly fire progression of large wildfires. GOFER fills a key temporal gap present in other fire tracking products that rely on low-Earth-orbit imagery and reveals considerable variability in fire spread rates on diurnal timescales. We create a product of hourly fire perimeters, active-fire lines, and fire spread rates for 28 fires in California.
Nicholas Williams, Nicholas Byrne, Daniel Feltham, Peter Jan Van Leeuwen, Ross Bannister, David Schroeder, Andrew Ridout, and Lars Nerger
The Cryosphere, 17, 2509–2532, https://doi.org/10.5194/tc-17-2509-2023, https://doi.org/10.5194/tc-17-2509-2023, 2023
Short summary
Short summary
Observations show that the Arctic sea ice cover has reduced over the last 40 years. This study uses ensemble-based data assimilation in a stand-alone sea ice model to investigate the impacts of assimilating three different kinds of sea ice observation, including the novel assimilation of sea ice thickness distribution. We show that assimilating ice thickness distribution has a positive impact on thickness and volume estimates within the ice pack, especially for very thick ice.
Nicholas J. Kedzuf, J. Christine Chiu, V. Chandrasekar, Sounak Biswas, Shashank S. Joshil, Yinghui Lu, Peter Jan van Leeuwen, Christopher Westbrook, Yann Blanchard, and Sebastian O'Shea
Atmos. Meas. Tech., 14, 6885–6904, https://doi.org/10.5194/amt-14-6885-2021, https://doi.org/10.5194/amt-14-6885-2021, 2021
Short summary
Short summary
Ice clouds play a key role in our climate system due to their strong controls on precipitation and the radiation budget. However, it is difficult to characterize co-existing ice species using radar observations. We present a new method that separates the radar signals of pristine ice embedded in snow aggregates and retrieves their respective abundances and sizes for the first time. The ability to provide their quantitative microphysical properties will open up many research opportunities.
Concetta Di Mauro, Renaud Hostache, Patrick Matgen, Ramona Pelich, Marco Chini, Peter Jan van Leeuwen, Nancy K. Nichols, and Günter Blöschl
Hydrol. Earth Syst. Sci., 25, 4081–4097, https://doi.org/10.5194/hess-25-4081-2021, https://doi.org/10.5194/hess-25-4081-2021, 2021
Short summary
Short summary
This study evaluates how the sequential assimilation of flood extent derived from synthetic aperture radar data can help improve flood forecasting. In particular, we carried out twin experiments based on a synthetically generated dataset with controlled uncertainty. Our empirical results demonstrate the efficiency of the proposed data assimilation framework, as forecasting errors are substantially reduced as a result of the assimilation.
Sagar K. Tamang, Ardeshir Ebtehaj, Peter J. van Leeuwen, Dongmian Zou, and Gilad Lerman
Nonlin. Processes Geophys., 28, 295–309, https://doi.org/10.5194/npg-28-295-2021, https://doi.org/10.5194/npg-28-295-2021, 2021
Short summary
Short summary
Data assimilation aims to improve hydrologic and weather forecasts by combining available information from Earth system models and observations. The classical approaches to data assimilation usually proceed with some preconceived assumptions about the shape of their probability distributions. As a result, when such assumptions are invalid, the forecast accuracy suffers. In the proposed methodology, we relax such assumptions and demonstrate improved performance.
Cited articles
Altman, A. and Gondzio, J.: Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization, Optim. Method. Softw., 11, 275–302, 1999. a
Anderson, J. and Lei, L.: Empirical localization of observation impact in ensemble Kalman filters, Mon. Weather Rev., 141, 4140–4153, 2013. a
Anderson, J. L.: An ensemble adjustment Kalman filter for data assimilation, Mon. Weather Rev., 129, 2884–2903, 2001. a
Anderson, J. L.: Reducing correlation sampling error in ensemble Kalman filter data assimilation, Mon. Weather Rev., 144, 913–925, 2016. a
Bigot, J. and Klein, T.: Characterization of barycenters in the Wasserstein space by averaging optimal transport maps, ESAIM-Probab. Stat., 22, 35–57, https://doi.org/10.1051/ps/2017020, 2018.
a
Bishop, C. H., Etherton, B. J., and Majumdar, S. J.: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects, Mon.
Weather Rev., 129, 420–436, 2001. a
Borobia, A. and Cantó, R.: Matrix scaling: A geometric proof of sinkhorn's theorem, Linear Algebra Appl., 268, 1–8, 1998. a
Brajard, J., Carrassi, A., Bocquet, M., and Bertino, L.: Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model, Journal of Computational Science, 44, 101171, https://doi.org/10.1016/j.jocs.2020.101171, 2020. a
Brenier, Y.: Décomposition polaire et réarrangement monotone des champs de vecteurs, C. R. Acad. Sci. Paris, Série I Math., 305, 805–808, 1987. a
Burgers, G., Jan van Leeuwen, P., and Evensen, G.: Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126, 1719–1724, 1998. a
Carrassi, A. and Vannitsem, S.: State and parameter estimation with the extended Kalman filter: an alternative formulation of the model error dynamics, Q. J. Roy. Meteor. Soc., 137, 435–451, 2011. a
Carrassi, A., Bocquet, M., Bertino, L., and Evensen, G.: Data assimilation in the geosciences: An overview of methods, issues, and perspectives, WIREs Clim. Change, 9, e535, https://doi.org/10.1002/wcc.535, 2018. a
Chen, B., Dang, L., Gu, Y., Zheng, N., and Prıncipe, J. C.: Minimum Error Entropy Kalman Filter, arXiv [preprint], arXiv:1904.06617, 17 April 2019. a
Chen, J., Chen, Y., Wu, H., and Yang, D.: The quadratic Wasserstein metric for earthquake location, J. Comput. Phys., 373, 188–209, 2018. a
Chen, Y., Georgiou, T. T., and Tannenbaum, A.: Matrix optimal mass transport: a quantum mechanical approach, IEEE T. Automat. Contr., 63, 2612–2619, 2017. a
Chen, Y., Georgiou, T. T., and Tannenbaum, A.: Wasserstein geometry of quantum states and optimal transport of matrix-valued measures, in: Emerging Applications of Control and Systems Theory, Springer,
139–150, https://doi.org/10.1007/978-3-319-67068-3_10, 2018. a
Chepurin, G. A., Carton, J. A., and Dee, D.: Forecast model bias correction in ocean data assimilation, Mon. Weather Rev., 33, 1328–1342, 2005. a
Chianese, E., Galletti, A., Giunta, G., Landi, T., Marcellino, L., Montella, R., and Riccio, A.: Spatiotemporally resolved ambient particulate matter concentration by fusing observational data and ensemble chemical transport model simulations, Ecol. Model., 385, 173–181, 2018. a
Cotter, C., Crisan, D., Holm, D., Pan, W., and Shevchenko, I.: Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model, Foundations of Data Science, 2, 173–205, 2020. a
Courtier, P., Thépaut, J.-N., and Hollingsworth, A.: A strategy for operational implementation of 4D-Var, using an incremental approach, Q. J. Roy. Meteor. Soc., 120, 1367–1387, 1994. a
Courtier, P., Andersson, E., Heckley, W., Vasiljevic, D., Hamrud, M., Hollingsworth, A., Rabier, F., Fisher, M., and Pailleux, J.: The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation, Q. J. Roy. Meteor. Soc., 124, 1783–1807, 1998. a
Cramér, H.: Mathematical methods of statistics, Princeton University Press, vol. 9, ISBN: 9780691005478, 1999. a
Cuturi, M.: Sinkhorn distances: Lightspeed computation of optimal transport, in: Advances in neural information processing systems,
edited by: Burges, C. J. C., Bottou, L., Welling, M., Ghahramani, Z., and Weinberger, K. Q., Curran Associates, Inc., 26, 2292–2300, https://proceedings.neurips.cc/paper/2013/file/af21d0c97db2e27e13572cbf59eb343d-Paper.pdf (last access: 9 February 2022), 2013. a, b
Cuturi, M. and Peyré, G.: Semidual regularized optimal transport, SIAM Rev., 60, 941–965, 2018. a
Dantzig, G. B., Orden, A., and Wolfe, P.: The generalized simplex method for minimizing a linear form under linear inequality restraints, Pac. J. Math., 5, 183–195, 1955. a
Dee, D. P. and Da Silva, A. M.: Data assimilation in the presence of forecast bias, Q. J. Roy. Meteor. Soc., 124, 269–295, 1998. a
De Lannoy, G. J., Reichle, R. H., Houser, P. R., Pauwels, V., and Verhoest, N. E.: Correcting for forecast bias in soil moisture assimilation with the ensemble Kalman filter, Water Resour. Res., 43, W09410, https://doi.org/10.1029/2006WR005449, 2007. a
Dobrushin, R. L.: Prescribing a system of random variables by conditional distributions, Theor. Probab. Appl., 15, 458–486, 1970. a
Evensen, G.: Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model, J. Geophys. Res., 97, 17905–17924, 1992. a
Evensen, G.: The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dynam., 53, 343–367, 2003. a
Evensen, G. and Van Leeuwen, P. J.: Assimilation of Geosat altimeter data for the Agulhas current using the ensemble Kalman filter with a quasigeostrophic model, Mon. Weather Rev., 124, 85–96, 1996. a
Feyeux, N., Vidard, A., and Nodet, M.: Optimal transport for variational data assimilation, Nonlin. Processes Geophys., 25, 55–66, https://doi.org/10.5194/npg-25-55-2018, 2018. a, b
Fisher, M. and Gürol, S.: Parallelization in the time dimension of four-dimensional variational data assimilation, Q. J. Roy. Meteor. Soc., 143, 1136–1147, 2017. a
Fréchet, M.: Les éléments aléatoires de nature quelconque dans un espace distancié, Annales de l'institut Henri Poincaré, 10, 215–310, 1948 (in French). a
Gaspari, G. and Cohn, S. E.: Construction of correlation functions in two and three dimensions, Q. J. Roy. Meteor. Soc., 125, 723–757, 1999. a
Hamill, T. M.: Interpretation of rank histograms for verifying ensemble forecasts, Mon. Weather Rev., 129, 550–560, 2001. a
Hamill, T. M., Whitaker, J. S., and Snyder, C.: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter, Mon. Weather Rev., 129, 2776–2790, 2001. a
Hellinger, E.: Neue begründung der theorie quadratischer formen von unendlichvielen veränderlichen, J. Reine Angew. Math., 1909, 210–271, 1909 (in German). a
Houtekamer, P. L. and Mitchell, H. L.: Data assimilation using an ensemble Kalman filter technique, Mon. Weather Rev., 126, 796–811, 1998. a
Houtekamer, P. L. and Mitchell, H. L.: A sequential ensemble Kalman filter for atmospheric data assimilation, Mon. Weather Rev., 129, 123–137, 2001. a
Houtekamer, P. L. and Zhang, F.: Review of the ensemble Kalman filter for atmospheric data assimilation, Mon. Weather Rev., 144, 4489–4532, 2016. a
Kalman, R. E.: A New Approach to Linear Filtering and Prediction Problems, J. Basic Eng.-T. ASME, 82, 35–45, https://doi.org/10.1115/1.3662552, 1960. a
Kalnay, E.: Atmospheric modeling, data assimilation and predictability, Cambridge University Press, Cambridge, ISBN: 9780511802270, 2003. a
Kapur, J. N.: Measures of information and their applications, Wiley-Interscience, https://doi.org/10.2307/2533186, 1994. a
Kolouri, S., Park, S. R., Thorpe, M., Slepcev, D., and Rohde, G. K.: Optimal mass transport: Signal processing and machine-learning applications, IEEE Signal Proc. Mag., 34, 43–59, 2017. a
Kullback, S. and Leibler, R. A.: On information and sufficiency, Ann. Math. Stat., 22, 79–86, 1951. a
Kutta, W.: Beitrag zur naherungsweisen Integration totaler Differentialgleichungen, Z. Math. Phys., 46, 435–453, 1901 (in German). a
Lei, J. and Bickel, P.: A moment matching ensemble filter for nonlinear non-Gaussian data assimilation, Mon. Weather Rev., 139, 3964–3973, 2011. a
Lei, L., Whitaker, J. S., and Bishop, C.: Improving assimilation of radiance observations by implementing model space localization in an ensemble Kalman filter, J. Adv. Model. Earth Sy., 10, 3221–3232, 2018. a
Lguensat, R., Tandeo, P., Ailliot, P., Pulido, M., and Fablet, R.: The analog data assimilation, Mon. Weather Rev., 145, 4093–4107, 2017. a
Li, L., Vidard, A., Le Dimet, F.-X., and Ma, J.: Topological data assimilation using Wasserstein distance, Inverse Problems, 35, 015006, https://doi.org/10.1088/1361-6420/aae993, 2018. a
Li, R., Jan, N. M., Huang, B., and Prasad, V.: Constrained ensemble Kalman filter based on Kullback–Leibler divergence, J. Process Contr., 81, 150–161, 2019. a
Li, T., Bolic, M., and Djuric, P. M.: Resampling methods for particle filtering: classification, implementation, and strategies, IEEE Signal Proc. Mag., 32, 70–86, 2015. a
Li, Z., Zang, Z., Li, Q. B., Chao, Y., Chen, D., Ye, Z., Liu, Y., and Liou, K. N.: A three-dimensional variational data assimilation system for multiple aerosol species with WRF/Chem and an application to PM2.5 prediction, Atmos. Chem. Phys., 13, 4265–4278, https://doi.org/10.5194/acp-13-4265-2013, 2013. a
Lin, L.-F., Ebtehaj, A. M., Flores, A. N., Bastola, S., and Bras, R. L.: Combined assimilation of satellite precipitation and soil moisture: A case study using trmm and smos data, Mon. Weather Rev., 145, 4997–5014, 2017. a
Lorenc, A. C., Ballard, S. P., Bell, R. S., Ingleby, N. B., Andrews, P. L. F., Barker, D. M., Bray, J. R., Clayton, A. M., Dalby, T., Li, D., Payne, T. J., and Saunders, F. W.: The Met. Office global three-dimensional variational data assimilation scheme, Q. J. Roy. Meteor. Soc., 126, 2991–3012, 2000. a
Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130–141, 1963. a
Lorenz, E. N.: Predictability – a problem partly solved, in: Predictability of Weather and Climate, Seminar on Predictability, Shinfield Park, Reading, UK, 4–8 September 1995, ECMWF, https://doi.org/10.1017/CBO9780511617652.004, 1995. a, b, c
Maclean, J., Santitissadeekorn, N., and Jones, C. K.: A coherent structure approach for parameter estimation in Lagrangian Data Assimilation, Physica D, 360, 36–45, 2017. a
McCann, R. J.: A convexity principle for interacting gases, Adv. Math., 128, 153–179, 1997. a
Nerger, L., Janjić, T., Schröter, J., and Hiller, W.: A regulated localization scheme for ensemble-based Kalman filters, Q. J. Roy. Meteor. Soc., 138, 802–812, 2012a. a
Nerger, L., Janjić, T., Schröter, J., and Hiller, W.: A unification of ensemble square root Kalman filters, Mon. Weather Rev., 140, 2335–2345, 2012b. a
Pass, B.: Multi-marginal optimal transport: theory and applications, ESAIM-Math. Model. Num., 49, 1771–1790, 2015. a
Pedlosky, J.: Geophysical fluid dynamics, Springer, vol. 710, https://doi.org/10.1007/978-1-4612-4650-3, 1987. a, b
Penny, S., Bach, E., Bhargava, K., Chang, C.-C., Da, C., Sun, L., and Yoshida, T.: Strongly coupled data assimilation in multiscale media: Experiments using a quasi-geostrophic coupled model, J. Adv. Model. Earth Sy., 11, 1803–1829, 2019. a
Pitt, M. K. and Shephard, N.: Filtering via simulation: Auxiliary particle filters, J. Am. Stat. Assoc., 94, 590–599, 1999. a
Poterjoy, J. and Zhang, F.: Intercomparison and coupling of ensemble and four-dimensional variational data assimilation methods for the analysis and forecasting of Hurricane Karl (2010), Mon. Weather Rev., 142, 3347–3364, 2014. a
Pulido, M. and van Leeuwen, P. J.: Sequential Monte Carlo with kernel embedded mappings: The mapping particle filter, J. Comput. Phys., 396, 400–415, 2019. a
Rabier, F., Järvinen, H., Klinker, E., Mahfouf, J.-F., and Simmons, A.: The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics, Q. J. Roy. Meteor. Soc., 126, 1143–1170, 2000. a
Rabin, J., Peyré, G., Delon, J., and Bernot, M.: Wasserstein barycenter and its application to texture mixing, in: International Conference on Scale Space and Variational Methods in Computer Vision, Springer,
435–446, ISBN: 9783642247859, 2011. a
Rao, C. R., Rao, C. R., Statistiker, M., Rao, C. R., and Rao, C. R.: Linear statistical inference and its applications, Wiley New York, vol. 2, ISBN: 9780471708230, 1973. a
Reich, S.: A nonparametric ensemble transform method for Bayesian inference, SIAM J. Sci. Comput., 35, A2013–A2024, 2013. a
Reichle, R. H., McLaughlin, D. B., and Entekhabi, D.: Hydrologic data assimilation with the ensemble Kalman filter, Mon. Weather Rev., 130, 103–114, 2002. a
Reichle, R. H., Koster, R. D., Dong, J., and Berg, A. A.: Global Soil Moisture from Satellite Observations, Land Surface Models, and Ground Data: Implications for Data Assimilation, J. Hydrometeorol., 5, 430–442, https://doi.org/10.1175/1525-7541(2004)005<0430:GSMFSO>2.0.CO;2, 2004. a
Runge, C.: Über die numerische Auflösung von Differentialgleichungen, Mathematische Annalen, 46, 167–178, 1895 (in German). a
Shen, Z. and Tang, Y.: A modified ensemble Kalman particle filter for non-Gaussian systems with nonlinear measurement functions, J. Adv. Model. Earth Sy., 7, 50–66, 2015. a
Sinkhorn, R.: Diagonal Equivalence to Matrices with Prescribed Row and Column Sums, Am. Math. Mon., 74, 402–405, https://doi.org/10.2307/2314570, 1967. a, b
Spantini, A., Baptista, R., and Marzouk, Y.: Coupling techniques for nonlinear ensemble filtering, arXiv [preprint], arXiv:1907.00389, 30 June 2019. a, b, c
Spiller, E. T., Budhiraja, A., Ide, K., and Jones, C. K.: Modified particle filter methods for assimilating Lagrangian data into a point-vortex model, Physica D, 237, 1498–1506, 2008. a
Srivastava, S., Li, C., and Dunson, D. B.: Scalable Bayes via barycenter in Wasserstein space, J. Mach. Learn. Res., 19, 312–346, 2018. a
Tagade, P. and Ravela, S.: On a quadratic information measure for data assimilation, in: 2014 American Control Conference, IEEE, 598–603, https://doi.org/10.1109/ACC.2014.6859127, 2014. a
Tamang, S. K., Ebtehaj, A., van Leeuwen, P. J., Zou, D., and Lerman, G.: Ensemble Riemannian data assimilation over the Wasserstein space, Nonlin. Processes Geophys., 28, 295–309, https://doi.org/10.5194/npg-28-295-2021, 2021. a, b, c, d
tamangsk: tamangsk/EnRDA: Ensemble Riemannian Data Assimilation, Version v1.0, Zenodo [code], https://doi.org/10.5281/zenodo.5047392, 2021 (data available at:
https://github.com/tamangsk/EnRDA, last access: last access: 9 February 2022). a
Tang, Y., Deng, Z., Manoj, K., and Chen, D.: A practical scheme of the sigma-point Kalman filter for high-dimensional systems, J. Adv. Model. Earth Sy., 6, 21–37, 2014. a
Tian, X., Zhang, H., Feng, X., and Xie, Y.: Nonlinear least squares En4DVar to 4DEnVar methods for data assimilation: Formulation, analysis, and preliminary evaluation, Mon. Weather Rev., 146, 77–93, 2018. 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, 2003. a
Trevisan, A. and Palatella, L.: On the Kalman Filter error covariance collapse into the unstable subspace, Nonlin. Processes Geophys., 18, 243–250, https://doi.org/10.5194/npg-18-243-2011, 2011. a
Van Leeuwen, P. J.: Particle filtering in geophysical systems, Mon. Weather
Rev., 137, 4089–4114, 2009. a
Van Leeuwen, P. J.: A consistent interpretation of the stochastic version of the Ensemble Kalman Filter, Q. J. Roy. Meteor. Soc., 146, 2815–2825, 2020. a
Villani, C.: Topics in optimal transportation, American Mathematical Soc., Providence, RI, Volume 58, https://doi.org/10.1090/gsm/058, 2003. a, b, c
Villani, C.: Optimal transport: old and new, Springer Science & Business Media, vol. 338, ISBN 9783662501801, 2008. a
Vissio, G., Lembo, V., Lucarini, V., and Ghil, M.: Evaluating the performance of climate models based on Wasserstein distance, Geophys. Res. Lett., 47, e2020GL089385, https://doi.org/10.1029/2020GL089385, 2020. a
Yang, Y. and Engquist, B.: Analysis of optimal transport and related misfit functions in full-waveform inversion, Geophysics, 83, A7–A12, 2018. a
Yang, Y., Engquist, B., Sun, J., and Hamfeldt, B. F.: Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion, Geophysics, 83, R43–R62, 2018. a
Yong, P., Huang, J., Li, Z., Liao, W., and Qu, L.: Least-squares reverse time migration via linearized waveform inversion using a Wasserstein metric, Geophysics, 84, S411–S423, 2019. a
Zupanski, M.: Regional 4-Dimensional Variational Data Assimilation in a Quasi-Operational Forecasting Environment, Mon. Weather Rev., 121, 2396–2408, 1993. a
Short summary
The outputs from Earth system models are optimally combined with satellite observations to produce accurate forecasts through a process called data assimilation. Many existing data assimilation methodologies have some assumptions regarding the shape of the probability distributions of model output and observations, which results in forecast inaccuracies. In this paper, we test the effectiveness of a newly proposed methodology that relaxes such assumptions about high-dimensional models.
The outputs from Earth system models are optimally combined with satellite observations to...