Particle Filtering and Gaussian Mixtures – On a Localized Mixture Coefficients Particle Filter (LMCPF) for Global NWP
In a global numerical weather prediction (NWP) modeling framework we study the implementation of Gaussian uncertainty of individual particles into the assimilation step of a localized adaptive particle filter (LAPF). We obtain a local representation of the prior distribution as a mixture of basis fu...
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| Published in | Journal of the Meteorological Society of Japan Vol. 101; no. 4; pp. 233 - 253 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Meteorological Society of Japan
2023
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0026-1165 2186-9057 |
| DOI | 10.2151/jmsj.2023-015 |
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| Abstract | In a global numerical weather prediction (NWP) modeling framework we study the implementation of Gaussian uncertainty of individual particles into the assimilation step of a localized adaptive particle filter (LAPF). We obtain a local representation of the prior distribution as a mixture of basis functions. In the assimilation step, the filter calculates the individual weight coefficients and new particle locations. It can be viewed as a combination of the LAPF and a localized version of a Gaussian mixture filter, i.e., a “Localized Mixture Coefficients Particle Filter (LMCPF)”.Here, we investigate the feasibility of the LMCPF within a global operational framework and evaluate the relationship between prior and posterior distributions and observations. Our simulations are carried out in a standard pre-operational experimental set-up with the full global observing system, 52 km global resolution and 106 model variables. Statistics of particle movement in the assimilation step are calculated. The mixture approach is able to deal with the discrepancy between prior distributions and observation location in a real-world framework and to pull the particles towards the observations in a much better way than the pure LAPF. This shows that using Gaussian uncertainty can be an important tool to improve the analysis and forecast quality in a particle filter framework. |
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| AbstractList | In a global numerical weather prediction (NWP) modeling framework we study the implementation of Gaussian uncertainty of individual particles into the assimilation step of a localized adaptive particle filter (LAPF). We obtain a local representation of the prior distribution as a mixture of basis functions. In the assimilation step, the filter calculates the individual weight coefficients and new particle locations. It can be viewed as a combination of the LAPF and a localized version of a Gaussian mixture filter, i.e., a “Localized Mixture Coefficients Particle Filter (LMCPF)”.Here, we investigate the feasibility of the LMCPF within a global operational framework and evaluate the relationship between prior and posterior distributions and observations. Our simulations are carried out in a standard pre-operational experimental set-up with the full global observing system, 52 km global resolution and 106 model variables. Statistics of particle movement in the assimilation step are calculated. The mixture approach is able to deal with the discrepancy between prior distributions and observation location in a real-world framework and to pull the particles towards the observations in a much better way than the pure LAPF. This shows that using Gaussian uncertainty can be an important tool to improve the analysis and forecast quality in a particle filter framework. |
| ArticleNumber | 2023-015 |
| Author | LEEUWEN, Peter Jan VAN ROJAHN, Anne SCHENK, Nora POTTHAST, Roland |
| Author_xml | – sequence: 1 fullname: ROJAHN, Anne organization: Data Assimilation Unit, Deutscher Wetterdienst, Germany – sequence: 1 fullname: LEEUWEN, Peter Jan VAN organization: Departement of Atmospheric Science, Colorado State University, Colorado, USA – sequence: 1 fullname: POTTHAST, Roland organization: Data Assimilation Unit, Deutscher Wetterdienst, Germany – sequence: 1 fullname: SCHENK, Nora organization: Data Assimilation Unit, Deutscher Wetterdienst, Germany |
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| Cites_doi | 10.3389/fams.2022.920186 10.1007/978-3-319-18347-3 10.1175/MWR-D-18-0367.1 10.1002/qj.2742 10.1029/94JC00572 10.1002/qj.3116 10.1214/074921708000000228 10.1016/j.jhydrol.2016.01.048 10.1080/16000870.2018.1445364 10.1093/biomet/ast020 10.1175/MWR-D-15-0322.1 10.1175/2007MWR1927.1 10.1175/2009MWR2835.1 10.1175/1520-0493(2000)128<1852:AEKSFN>2.0.CO;2 10.1175/2008MWR2529.1 10.1007/978-0-387-76896-0 10.1002/qj.49712656417 10.1029/2002JD002900 10.1017/CBO9781107706804 10.1175/MWR-D-15-0144.1 10.1088/978-0-7503-1218-9 10.1002/qj.2378 10.1002/qj.3551 10.1007/978-3-642-03711-5 10.1175/MWR-D-14-00292.1 10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2 10.1175/MWR-D-16-0298.1 10.5194/npg-25-765-2018 10.1175/MWR-D-18-0028.1 10.1002/qj.699 10.1016/j.physd.2006.11.008 10.5194/npg-23-391-2016 |
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| References | Liu, B., M. E. Gharamti, and I. Hoteit, 2016b: Assessing clustering strategies for Gaussian mixture filtering a subsurface contaminant model. J. Hydrol., 535, 1–21. Bickel, P., B. Li, and T. Bengtsson, 2008: Sharp failure rates for the bootstrap particle filter in high dimensions. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh. vol.3, IMS Collections, 318–329. Potthast, R., A. Walter, and A. Rhodin, 2019: A localized adaptive particle filter within an operational nwp framework. Mon. Wea. Rev., 147, 345–362. Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10143–10162. van Leeuwen, P. J., 2010: Nonlinear data assimilation in geosciences: An extremely efficient particle filter. Quart. J. Roy. Meteor. Soc., 136, 1991–1999. Liu, B., B. Ait-El-Fquih, and I. 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Reich, 2019: Particle filters for high-dimensional geoscience applications: A review. Quart. J. Roy. Meteor. Soc., 145, 2335–2365. Penny, S. G., and T. Miyoshi, 2016: A local particle filter for high-dimensional geophysical systems. Nonlinear Processes Geophys., 23, 391–405. van Leeuwen, P. J., Y. Cheng, and S. Reich, 2015: Nonlinear Data Assimilation. Frontiers in Applied Dynamical Systems: Reviews and Tutorials, vol. 2, Springer Cham, 130 pp. Poterjoy, J., R. A. Sobash, and J. L. Anderson, 2017: Convective-scale data assimilation for the weather research forecasting model using the local particle filter. Mon. Wea. Rev., 145, 1897–1918. Vetra-Carvalho, S., P. J. van Leeuwen, L. Nerger, A. Barth, M. U. Altaf, P. Brasseur, P. Kirchgessner, and J.-M. Beckers, 2018: State-of-the-art stochastic data assimilation methods for high-dimensional non-Gaussian problems. Tellus A, 70, 1–43. Hoteit, I., D.-T. Pham, G. Triantafyllou, and G. 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Math. Stat., 8, doi:10.3389/fams.2022.920186. Anderson, J. L., and S. L. Anderson, 1999: A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Wea. Rev., 127, 2741–2758. Snyder, C., T. Bengtsson, P. Bickel, and J. Anderson, 2008: Obstacles to high-dimensional particle filtering. Mon. Wea. Rev., 136, 4629–4640. Hunt, B. R., E. J. Kostelich, and I. Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Phys. D, 230, 112–126. Reich, S., and C. Cotter, 2015: Probabilistic Forecatsing and Bayesian Data Assimilation. Cambridge University Press, 308 pp. 22 23 24 25 26 27 28 29 30 31 10 32 11 33 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 20 21 |
| References_xml | – reference: Nakamura, G., and R. Potthast, 2015: Inverse Modeling. IOP Publishing, 506 pp. – reference: Evensen, G., 2009: Data Assimilation: The Ensemble Kalman Filter. Earth and Environmental Science, Springer, 307 pp. – reference: Bengtsson, T., C. Snyder, and D. Nychka, 2003: Toward a nonlinear ensemble filter for high-dimensional systems. J. Geophys. Res., 108, D24, doi:10.1029/2002JD002900. – reference: van Leeuwen, P. J., Y. Cheng, and S. Reich, 2015: Nonlinear Data Assimilation. Frontiers in Applied Dynamical Systems: Reviews and Tutorials, vol. 2, Springer Cham, 130 pp. – reference: Snyder, C., T. Bengtsson, and M. Morzfeld, 2015: Performance bounds for particle filters using the optimal proposal. Mon. Wea. Rev., 143, 4750–4761. – reference: van Leeuwen, P. J., H. R. Künsch, L. Nerger, R. Potthast, and S. Reich, 2019: Particle filters for high-dimensional geoscience applications: A review. Quart. J. Roy. Meteor. Soc., 145, 2335–2365. – reference: Snyder, C., T. Bengtsson, P. Bickel, and J. Anderson, 2008: Obstacles to high-dimensional particle filtering. Mon. Wea. Rev., 136, 4629–4640. – reference: Liu, B., B. Ait-El-Fquih, and I. Hoteit, 2016a: Efficient kernel-based ensemble Gaussian mixture filtering. Mon. Wea. Rev., 144, 781–800. – reference: Schenk, N., R. Potthast, and A. Rojahn, 2022: On two localized particle filter methods for Lorenz 1963 and 1996 models. Front. Appl. Math. Stat., 8, doi:10.3389/fams.2022.920186. – reference: van Leeuwen, P. J., 2009: Particle filtering in geophysical systems. Mon. Wea. Rev., 137, 4089–4114. – reference: Crisan, D., and B. Rozovskii, 2011: The Oxford Handbook of Nonlinear Filtering. Oxford University Press, 1063 pp. – reference: Bickel, P., B. Li, and T. Bengtsson, 2008: Sharp failure rates for the bootstrap particle filter in high dimensions. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh. vol.3, IMS Collections, 318–329. – reference: Anderson, J. L., and S. L. Anderson, 1999: A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Wea. Rev., 127, 2741–2758. – reference: Evensen, G., and P. J. van Leeuwen, 2000: An ensemble Kalman smoother for nonlinear dynamics. Mon. Wea. Rev., 128, 1852–1867. – reference: Klinker, E., F. Rabier, G. Kelly, and J.-F. Mahfouf, 2000: The ECMWF operational implementation of four-dimensional variational assimilation. III: Experimental results and diagnostics with operational configuration. Quart. J. Roy. Meteor. Soc., 126, 1191–1215. – reference: Zängl, G., D. Reinert, P. Rípodas, and M. Baldauf, 2014: The ICON (ICOsahedral Non-hydrostatic) modelling framework of DWD and MPI-M: Description of the non-hydrostatic dynamical core. Quart. J. Meteor. Soc., 141, 563–579. – reference: Bain, A., and D. Crisan, 2009: Fundamentals of Stochastic Filtering. Stochastic Modelling and Applied Probability, vol. 60, Springer, 403 pp. – reference: Liu, B., M. E. Gharamti, and I. Hoteit, 2016b: Assessing clustering strategies for Gaussian mixture filtering a subsurface contaminant model. J. Hydrol., 535, 1–21. – reference: Bishop, C. H., 2016: The GIGG-EnKF: Ensemble Kalamn filtering for highly skewed non-negative uncertainty distributions. Quart. J. Roy. Meteor. Soc., 142, 1395–1412. – reference: Hoteit, I., D.-T. Pham, G. Triantafyllou, and G. Korres, 2008: A new approximate solution of the optimal nonlinear filter for data assimilation in meteorology and oceanography. Mon. Wea. Rev., 136, 317–334. – reference: Hunt, B. R., E. J. Kostelich, and I. Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Phys. D, 230, 112–126. – reference: Potthast, R., A. Walter, and A. Rhodin, 2019: A localized adaptive particle filter within an operational nwp framework. Mon. Wea. Rev., 147, 345–362. – reference: Penny, S. G., and T. Miyoshi, 2016: A local particle filter for high-dimensional geophysical systems. Nonlinear Processes Geophys., 23, 391–405. – reference: van Leeuwen, P. J., 2010: Nonlinear data assimilation in geosciences: An extremely efficient particle filter. Quart. J. Roy. Meteor. Soc., 136, 1991–1999. – reference: Frei, M., and H. Künsch, 2013: Bridging the ensemble Kalman and particle filters. Biometrika, 100, 781–800. – reference: Reich, S., and C. Cotter, 2015: Probabilistic Forecatsing and Bayesian Data Assimilation. Cambridge University Press, 308 pp. – reference: Poterjoy, J., R. A. Sobash, and J. L. Anderson, 2017: Convective-scale data assimilation for the weather research forecasting model using the local particle filter. Mon. Wea. Rev., 145, 1897–1918. – reference: Vetra-Carvalho, S., P. J. van Leeuwen, L. Nerger, A. Barth, M. U. Altaf, P. Brasseur, P. Kirchgessner, and J.-M. Beckers, 2018: State-of-the-art stochastic data assimilation methods for high-dimensional non-Gaussian problems. Tellus A, 70, 1–43. – reference: Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10143–10162. – reference: Farchi, A., and M. Bocquet, 2018: Comparison of local particle filters and new implementations. Nonlinear Processes Geophys., 25, 765–807. – reference: Kawabata, T., and G. Ueno, 2020: Non-Gaussian probability densities of convection initiation and development investigated using a particle filter with a storm-scale numerical weather prediction model. Mon. Wea. Rev., 148, 3–20. – reference: Poterjoy, J., and J. L. Anderson, 2016: Efficient assimilation of simulated observations in a high-dimensional geophysical system using a localized particle filter. Mon. Wea. Rev., 144, 2007–2020. – reference: Robert, S., D. Leuenberger, and H. R. Künsch, 2017: A local ensemble transform Kalman particle filter for convective-scale data assimilation. Quart. J. Roy. Meteor. Soc., 144, 1279–1296. – ident: 25 doi: 10.3389/fams.2022.920186 – ident: 30 doi: 10.1007/978-3-319-18347-3 – ident: 14 doi: 10.1175/MWR-D-18-0367.1 – ident: 5 doi: 10.1002/qj.2742 – ident: 7 doi: 10.1029/94JC00572 – ident: 24 doi: 10.1002/qj.3116 – ident: 4 doi: 10.1214/074921708000000228 – ident: 17 doi: 10.1016/j.jhydrol.2016.01.048 – ident: 32 doi: 10.1080/16000870.2018.1445364 – ident: 11 doi: 10.1093/biomet/ast020 – ident: 20 doi: 10.1175/MWR-D-15-0322.1 – ident: 12 doi: 10.1175/2007MWR1927.1 – ident: 28 doi: 10.1175/2009MWR2835.1 – ident: 9 doi: 10.1175/1520-0493(2000)128<1852:AEKSFN>2.0.CO;2 – ident: 26 doi: 10.1175/2008MWR2529.1 – ident: 2 doi: 10.1007/978-0-387-76896-0 – ident: 15 doi: 10.1002/qj.49712656417 – ident: 3 doi: 10.1029/2002JD002900 – ident: 23 doi: 10.1017/CBO9781107706804 – ident: 27 doi: 10.1175/MWR-D-15-0144.1 – ident: 18 doi: 10.1088/978-0-7503-1218-9 – ident: 33 doi: 10.1002/qj.2378 – ident: 31 doi: 10.1002/qj.3551 – ident: 8 doi: 10.1007/978-3-642-03711-5 – ident: 16 doi: 10.1175/MWR-D-14-00292.1 – ident: 1 doi: 10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2 – ident: 21 doi: 10.1175/MWR-D-16-0298.1 – ident: 10 doi: 10.5194/npg-25-765-2018 – ident: 22 doi: 10.1175/MWR-D-18-0028.1 – ident: 29 doi: 10.1002/qj.699 – ident: 6 – ident: 13 doi: 10.1016/j.physd.2006.11.008 – ident: 19 doi: 10.5194/npg-23-391-2016 |
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