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Accounting for observation uncertainty and bias due to unresolved scales with the Schmidt-Kalman filter Cover

Accounting for observation uncertainty and bias due to unresolved scales with the Schmidt-Kalman filter

Open Access
|Jan 2020

References

  1. Aravéquia, J. A. , Szunyogh, I. , Fertig, E. J. , Kalnay, E. , Kuhl, D. and co-authors. 2011. Evaluation of a strategy for the assimilation of satellite radiance observations with the local ensemble transform Kalman filter. Mon. Weather Rev. 139 , 19321951. doi:10.1175/2010MWR3515.1
  2. Asher, R. B. , Herring, K. D. and Ryles, J. C. 1976. Bias, variance, and estimation error in reduced order filters. Automatica 12 , 589600. doi:10.1016/0005-1098(76)90040-6
  3. Asher, R. B. and Reeves, R. M. 1975. Performance evaluation of suboptimal filters. IEEE Trans. Aerosp. Electron. Syst. AES-11 , 400405. doi:10.1109/TAES.1975.308092
  4. Brown, R. G. and Hwang, P. Y. 2012. Introduction to Random Signals and Applied Kalman Filtering . John Wiley & Sons, Hoboken, NJ, p. 192, Chapter 5.
  5. Brown, R. and Sage, A. 1971. Analysis of modeling and bias errors in discrete-time state estimation. IEEE Trans. Aerosp. Electron. Syst. AES-7 , 340354. doi:10.1109/TAES.1971.310375
  6. Cordoba, M. , Dance, S. L. , Kelly, G. A. , Nichols, N. K. and Waller, J. A. 2017. Diagnosing atmospheric motion vector observation errors for an operational high-resolution data assimilation system. Q. Meteorol. Soc. 143 , 333341. doi:10.1002/qj.2925
  7. Daley, R. 1993. Estimating observation error statistics for atmospheric data assimilation. Ann. Geophysicae 11 , 634647.
  8. Dee, D. P. 2005. Bias and data assimilation. Q. J. R. Meteorol. Soc. 131 , 33233343. doi:10.1256/qj.05.137
  9. Dee, D. 2004. Variational bias correction of radiance data in the ECMWF system. In: Proceedings of the ECMWF Workshop on Assimilation of High Spectral Resolution Sounders in NWP , Reading, UK, ECMWF.
  10. Derber, J. C. and Wu, W.-S. 1998. The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system. Mon. Wea. Rev. 126 , 22872299. doi:10.1175/1520-0493(1998)126<;2287:TUOTCC>2.0.CO;2
  11. Desroziers, G. , Berre, L. , Chapnik, B. and Poli, P. 2005. Diagnosis of observation, background and analysis-error statistics in observation space. Q. J. R. Meteorol. Soc. 131 , 33853396. doi:10.1256/qj.05.108
  12. Eyre, J. 2016. Observation bias correction schemes in data assimilation systems: a theoretical study of some of their properties. Q. J. R. Meteorol. Soc. 142 , 22842291. doi:10.1002/qj.2819
  13. Fertig, E. , Baek, S.-J. , Hunt, B. , Ott, E. , Szunyogh, I. and co-authors. 2009. Observation bias correction with an ensemble Kalman filter. Tellus A: Dyn. Meteorol. Oceanogr. 61 , 210226. doi:10.1111/j.1600-0870.2008.00378.x
  14. Fielding, M. and Stiller, O. 2019. Characterizing the representativity error of cloud profiling observations for data assimilation. J. Geophys. Res. Atmos. 124 , 40864103. doi:10.1029/2018JD029949
  15. Friedland, B. 1969. Treatment of bias in recursive filtering. IEEE Trans. Automat. Contr. 14 , 359367. doi:10.1109/TAC.1969.1099223
  16. Gelb, A. 1974. Applied Optimal Estimation . MIT Press, Cambridge, MA, and London, UK, Chapter 8, pp. 305306.
  17. Grooms, I. , Lee, Y. and Majda, A. J. 2014. Ensemble Kalman filters for dynamical systems with unresolved turbulence. Comput. Phys. 273 , 435452. doi:10.1016/j.jcp.2014.05.037
  18. Hodyss, D. and Satterfield, E. 2016. Mathematical concepts of data assimilation. In: Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (eds. S. K. Park and L. Xu ) Vol. 3. Springer, Berlin, pp. 177194.
  19. Ignagni, M. 1981. An alternate derivation and extension of Friendland’s two-stage Kalman estimator. IEEE Trans. Automat. Contr. 26 , 746750. doi:10.1109/TAC.1981.1102697
  20. Janjić, T. , Bormann, N. , Bocquet, M. , Carton, J. , Cohn, S. and co-authors. 2018. On the representation error in data assimilation. Q. J. R. Meteorol. Soc. 144 , 12571278. doi:10.1002/qj.3130
  21. Janjić, T. and Cohn, S. E. 2006. Treatment of observation error due to unresolved scales in atmospheric data assimilation. Mon. Weather Rev. 134 , 29002915. doi:10.1175/MWR3229.1
  22. Jazwinski, A. H. 1970. Stochastic Processes and Filtering Theory . Academic Press, New York, NY, Chapter 7, p. 212.
  23. Kalman, R. E. 1960. A new approach to linear filtering and prediction problems. Journal of Basic Engineering 82 , 3545. doi:10.1115/1.3662552
  24. Karspeck, A. R. 2016. An ensemble approach for the estimation of observational error illustrated for a nominal 1° global ocean model. Mon. Wea. Rev. 144 , 17131728. doi:10.1175/MWR-D-14-00336.1
  25. Lea, D. , Drecourt, J.-P. , Haines, K. and Martin, M. 2008. Ocean altimeter assimilation with observational-and model-bias correction. Q. J. R. Meteorol. Soc. 134 , 17611774. doi:10.1002/qj.320
  26. Liu, Z.-Q. and Rabier, F. 2002. The interaction between model resolution, observation resolution and observation density in data assimilation: A one-dimensional study. Q J. R Meteorol. Soc. 128 , 13671386. doi:10.1256/003590002320373337
  27. Ménard, R. 2010. Bias estimation. In: Data Assimilation: making Sense of Observations (eds. W. Lahoz , B. Khattatov and R. Menard ). Springer, Berlin, pp. 113135.
  28. Miyoshi, T. , Sato, Y. and Kadowaki, T. 2010. Ensemble Kalman filter and 4D-Var intercomparison with the Japanese operational global analysis and prediction system. Mon. Weather Rev. 138 , 28462866. doi:10.1175/2010MWR3209.1
  29. Moodey, A. J. 2013. Instability and regularization for data assimilation. PhD thesis, University of Reading.
  30. Nichols, N. 2010. Mathematical concepts of data assimilation. In: Data Assimilation: making Sense of Observations (eds. W. Lahoz , B. Khattatov and R. Menard ). Springer, Berlin, pp. 1339.
  31. Oke, P. R. and Sakov, P. 2008. Representation error of oceanic observations for data assimilation. J. Atmos. Oceanic Technol. 25 , 10041017. doi:10.1175/2007JTECHO558.1
  32. Satterfield, E. , Hodyss, D. , Kuhl, D. D. and Bishop, C. H. 2017. Investigating the use of ensemble variance to predict observation error of representation. Mon. Weather Rev. 145 , 653667. doi:10.1175/MWR-D-16-0299.1
  33. Schmidt, S. F. 1966. Application of state-space methods to navigation problems. In: Advances in Control Systems (ed. C. T. Leondes) Vol. 3. Elsevier, Amsterdam, pp. 293340.
  34. Schutgens, N. A. , Gryspeerdt, E. , Weigum, N. , Tsyro, S. , Goto, D. and co-authors. 2016. Will a perfect model agree with perfect observations? The impact of spatial sampling. Atmos. Chem. Phys. 16 , 63356353. doi:10.5194/acp-16-6335-2016
  35. Simon, D. 2006. Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches . Wiley-Blackwell, Hoboken, NJ, pp. 309312, Chapter 10.
  36. Stewart, L. M. , Dance, S. L. , Nichols, N. K. , Eyre, J. R. and Cameron, J. 2014. Estimating interchannel observation-error correlations for IASI radiance data in the Met Office system. Q. J. R. Meteorol. Soc. 140 , 12361244. doi:10.1002/qj.2211
  37. Todling, R. and Cohn, S. E. 1994. Suboptimal schemes for atmospheric data assimilation based on the Kalman filter. Mon. Wea. Rev. 122 , 25302557. doi:10.1175/1520-0493(1994)122<;2530:SSFADA>2.0.CO;2
  38. Waller, J. A. , Ballard, S. P. , Dance, S. L. , Kelly, G. , Nichols, N. K. and co-authors. 2016a. Diagnosing horizontal and inter-channel observation error correlations for SEVIRI observations using observation-minus-background and observation-minus-analysis statistics. Remote Sens. 8 , 581. doi:10.3390/rs8070581
  39. Waller, J. A. , Dance, S. L. , Lawless, A. S. , Nichols, N. K. and Eyre, J. 2014. Representativity error for temperature and humidity using the Met Office high-resolution model. Q. J. R. Meteorol. Soc. 140 , 11891197. doi:10.1002/qj.2207
  40. Waller, J. A. , Simonin, D. , Dance, S. L. , Nichols, N. K. and Ballard, S. P. 2016b. Diagnosing observation error correlations for Doppler radar radial winds in the Met Office UKV model using observation-minus-background and observation-minus-analysis statistics. Mon. Wea. Rev. 144 , 35333551. doi:10.1175/MWR-D-15-0340.1
  41. Zhu, Y. , Derber, J. , Collard, A. , Dee, D. , Treadon, R. and co-authors. 2014. Enhanced radiance bias correction in the National Centers for Environmental Prediction’s gridpoint statistical interpolation data assimilation system. Q. J. R. Meteorol. Soc. 140 , 14791492. doi:10.1002/qj.2233
Language: English
Page range: 1831830 - 1831830
Published on: Jan 1, 2020
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services

© 2020 Zackary Bell, Sarah L. Dance, Joanne A. Waller, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.