Skip to main content
SpringerLink
Log in

An Efficient Algorithm for Stochastic Ensemble Smoothing

  • Published:
Numerical Analysis and Applications Aims and scope Submit manuscript

ABSTRACT

The state of the environment is assessed with a mathematical model and observational data by using a data assimilation procedure. At present the ensemble Kalman filter is one of the most popular data assimilation algorithms. An important component of the data assimilation procedure is assessment not only of the predicted values, but also of parameters that are not described by the model. A single correction procedure from observational data in the ensemble Kalman filter may not provide the required accuracy. In this regard, an ensemble smoothing algorithm in which data from a certain time interval are used to estimate values at a given time is becoming increasingly popular. This paper considers a generalization of a previously proposed algorithm which is a version of the stochastic ensemble Kalman filter. The generalized algorithm is an ensemble smoothing algorithm in which smoothing is performed for the sample mean, and then the ensemble of perturbations is transformed. The transformation matrix proposed in this paper is used to estimate both the predicted value and the parameter. An important advantage of the algorithm is its locality, which makes it possible to estimate the parameter in a given domain. The paper provides a justification of the applicability of this algorithm to ensemble smoothing. Test calculations are performed with a one-dimensional model of transport and diffusion of a passive pollutant. The algorithm is efficient and can be used to assess the state of the environment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Klimova, E.G., A Stochastic Ensemble Kalman Filter with Perturbation Ensemble Transformation, Num. An. Appl., 2019, vol. 12, no. 1, pp. 27–40.

  2. Spravochnik po teorii avtomaticheskogo upravleniya (Handbook on Automatic Control Theory), Krasovskii, A.A., Ed., Moscow: Nauka, 1987.

  3. Carrassi, A., Bocquet, M., Bertino, L., and Evensen, G., Data Assimilation in the Geosciences: An Overview of Methods, Issuers and Perspectives, Wiley Interdisciplinary Rev.: Climate Change, 2018, vol. 9, iss. 5, pp. e535; DOI: 10.1002/wcc535.

  4. Evensen, G., Data Assimilation. The Ensemble Kalman Filter, Heideberg: Spriger-Verlag, 2009.

  5. Evensen, G. and van Leeuwen, P.J., An Ensemble Kalman Smoother for Nonlinear Dynamics, Monthly Weather Rev., 2000, vol. 128, pp. 1852–1867.

  6. Feng, L., Palmer, P.I., et al., Consistent Regional Fluxes of CH4 and CO2 Inferred from GOSAT Proxy XCH4:XCO2 Retrievals, 2010–2014, Atmospheric Chem. Phys., 2017, vol. 17, iss. 7, pp. 4781–4797.

  7. Fisher, M., Leutbecher, M., and Kelly, G.A., On the Equivalence between Kalman Smoothing and Weak-Constraint Four-Dimensional Variational Data Assimilation, Quart. J. Royal Meteorolog. Soc., 2005, vol. 131, pp. 3235–3246.

  8. Houtekamer, H.L. and Zhang, F., Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation, Monthly Weather Rev., 2016, vol. 144, iss. 12, pp. 4489–4532.

  9. Hunt, B.R., Kostelich, E.J., and Szunyogh, I., Efficient Data Assimilation for Statiotemporal Chaos: A Local Ensemble Transform Kalman Filter, Phys. D, 2007, vol. 230, pp. 112–126.

  10. Jazwinski, A.H., Stochastic Processes and Filtering Theory, New York: Academic Press, 1970.

  11. Klimova, E., A Suboptimal Data Assimilation Algorithm Based on the Ensemble Kalman Filter, Quart. J. Royal Meteorolog. Soc., 2012, vol. 138, iss. 669, pp. 2079–2085.

  12. Lei, J., Bickel, P., and Shyder, C., Comparison of Ensemble Kalman Filters under Non-Gaussianity, Monthly Weather Rev., 2010, vol. 138, pp. 1293–1306.

  13. Tsuruta, A., Aalto, T., et al., Global Methane Emission Estimation for 2010–2012 from Carbon Tracker Europe-CH4 v1.0., Geosci. Model Devel., 2017, vol. 10, no. 3, pp. 1261–1287.

Download references

Author information

Authors and Affiliations

  1. Federal Research Center for Information and Computational Technologies, 630090, Novosibirsk, Russia

    E. G. Klimova

Authors
  1. E. G. Klimova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. G. Klimova.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klimova, E.G. An Efficient Algorithm for Stochastic Ensemble Smoothing. Numer. Analys. Appl. 13, 321–331 (2020). https://doi.org/10.1134/S1995423920040035

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995423920040035

Search

Navigation