• Acheson, D. J., 1990: Elementary Fluid Dynamics. Oxford University Press, 397 pp.

  • Aligo, E., B. S. Ferrier, J. Carley, E. Rogers, M. Pyle, S. J. Weiss, and I. L. Jirak, 2014: Modified microphysics for use in high resolution NAM forecasts. 27th Conf. on Severe Local Storms, Madison, WI, Amer. Meteor. Soc., 16A.1, https://ams.confex.com/ams/27SLS/webprogram/Paper255732.html.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 28842903, https://doi.org/10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2010: A non-Gaussian ensemble filter update for data assimilation. Mon. Wea. Rev., 138, 41864198, https://doi.org/10.1175/2010MWR3253.1.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2020: A marginal adjustment rank histogram filter for non-Gaussian ensemble data assimilation. Mon. Wea. Rev., 148, 33613378, https://doi.org/10.1175/MWR-D-19-0307.1.

    • Search Google Scholar
    • Export Citation
  • Atlas, R., V. Tallapragada, and S. G. Gopalakrishnan, 2015: Advances in tropical cyclone intensity forecasts. Mar. Technol. J., 49, 149160, https://doi.org/10.4031/MTSJ.49.6.2.

    • Search Google Scholar
    • Export Citation
  • Bannister, R. N., 2017: A review of operational methods of variational and ensemble-variational data assimilation. Quart. J. Roy. Meteor. Soc., 143, 607633, https://doi.org/10.1002/qj.2982.

    • Search Google Scholar
    • Export Citation
  • Bengtsson, T., C. Snyder, and D. Nychka, 2003: Toward a nonlinear ensemble filter for high dimensional systems. J. Geophys. Res., 108, 8775, https://doi.org/10.1029/2002JD002900.

    • Search Google Scholar
    • Export Citation
  • Bishop, C. H., 2016: The GIGG-EnKF: Ensemble Kalman filtering for highly skewed non-negative uncertainty distributions. Quart. J. Roy. Meteor. Soc., 142, 13951412, https://doi.org/10.1002/qj.2742.

    • Search Google Scholar
    • Export Citation
  • Bishop, C. H., B. J. Etherton, and S. J. Majumdar, 2000: Adaptive sampling with the ensemble transform Kalman filter. Mon. Wea. Rev., 129, 420436, https://doi.org/10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Biswas, M. K., and Coauthors, 2018: Hurricane Weather Research and Forecasting (HWRF) model: 2017 Scientific documentation. NCAR Tech. Note NCAR/TN-544+STR, 111 pp., https://opensky.ucar.edu/islandora/object/technotes%3A563/datastream/PDF/view.

    • Search Google Scholar
    • Export Citation
  • Bloom, S. C., L. L. Takacs, A. M. da Silva, and D. Ledvina, 1996: Data assimilation using incremental analysis updates. Mon. Wea. Rev., 124, 12561271, https://doi.org/10.1175/1520-0493(1996)124<1256:DAUIAU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., P. L. Houtekamer, C. Charette, H. Mitchell, and B. He, 2010a: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experiments. Mon. Wea. Rev., 138, 15501566, https://doi.org/10.1175/2009MWR3157.1.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., P. L. Houtekamer, C. Charette, H. Mitchell, and B. He, 2010b: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: One-month experiments with real observations. Mon. Wea. Rev., 138, 15671586, https://doi.org/10.1175/2009MWR3158.1.

    • Search Google Scholar
    • Export Citation
  • Chen, Y., and C. Snyder, 2007: Assimilating vortex position with an ensemble Kalman filter. Mon. Wea. Rev., 135, 18281845, https://doi.org/10.1175/MWR3351.1.

    • Search Google Scholar
    • Export Citation
  • Courtier, P., J.-N. Thepáut, and A. Hollingsworth, 1994: A strategy for operational implementation of 4D-Var, using an incremental approach. Quart. J. Roy. Meteor. Soc., 120, 13671387, https://doi.org/10.1002/qj.49712051912.

    • Search Google Scholar
    • Export Citation
  • Dirren, S., M. Didone, and H. C. Davies, 2003: Diagnosis of “forecast-analysis” differences of a weather prediction system. Geophys. Res. Lett., 30, 2060, https://doi.org/10.1029/2003GL017986.

    • Search Google Scholar
    • Export Citation
  • Doucet, A., N. de Freitas, and N. Gordon, 2001: An introduction to sequential Monte Carlo methods. Sequential Monte Carlo Methods in Practice, A. Doucet, N. de Freitas, and N. Gordon. Eds., Springer-Verlag, 214.

    • Search Google Scholar
    • Export Citation
  • Emerick, A. A., and A. C. Reynolds, 2012: History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations. Comput. Geosci., 16, 639659, https://doi.org/10.1007/s10596-012-9275-5.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10 14310 162, https://doi.org/10.1029/94JC00572.

    • Search Google Scholar
    • Export Citation
  • Farchi, A., and M. Bocquet, 2018: Review article: Comparison of local particle filters and new implementations. Nonlinear Processes Geophys., 25, 765807, https://doi.org/10.5194/npg-25-765-2018.

    • Search Google Scholar
    • Export Citation
  • Feng, J., X. Wang, and J. Poterjoy, 2020: A comparison of two local moment-matching nonlinear filters: Local particle filter (LPF) and local nonlinear ensemble transform filter (LNETF). Mon. Wea. Rev., 148, 43774395, https://doi.org/10.1175/MWR-D-19-0368.1.

    • Search Google Scholar
    • Export Citation
  • Fletcher, S. J., and M. Zupanski, 2006: A data assimilation method for log-normally distributed observational errors. Quart. J. Roy. Meteor. Soc., 132, 25052519, https://doi.org/10.1256/qj.05.222.

    • Search Google Scholar
    • Export Citation
  • Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723757, https://doi.org/10.1002/qj.49712555417.

    • Search Google Scholar
    • Export Citation
  • Gopalakrishnan, S. G., Q. Liu, T. Marchok, D. Sheinin, N. Surgi, R. Tuleya, R. Yablonsky, and X. Zhang, 2010: Hurricane Weather Research and Forecasting (HWRF) model scientific documentation. NCAR Tech. Note, 75 pp.

    • Search Google Scholar
    • Export Citation
  • Gordon, N. J., D. J. Salmond, and A. F. M. Smith, 1993: Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc., 140, 107113, https://doi.org/10.1049/ip-f-2.1993.0015.

    • Search Google Scholar
    • Export Citation
  • Greybush, S. J., E. Kalnay, T. Miyoshi, K. Ide, and B. Hunt, 2011: Balance and ensemble Kalman filter localization techniques. Mon. Wea. Rev., 139, 511522, https://doi.org/10.1175/2010MWR3328.1.

    • Search Google Scholar
    • Export Citation
  • Hodyss, D., 2012: Accounting for skewness in ensemble data assimilation. Mon. Wea. Rev., 140, 23462358, https://doi.org/10.1175/MWR-D-11-00198.1.

    • Search Google Scholar
    • Export Citation
  • Hodyss, D., and P. A. Reinecke, 2013: Skewness of the prior through position errors and its impact on data assimilation. Data Assimilation for Atmospheric, Oceanic, and Hydrologic Applications, S. K. Park and L. Xu, Eds., Vol. II, Springer, 147175.

    • Search Google Scholar
    • Export Citation
  • Hoffman, R. N., Z. Liu, J. Louis, and C. Grassoti, 1995: Distortion representation of forecast errors. Mon. Wea. Rev., 123, 27582770, https://doi.org/10.1175/1520-0493(1995)123<2758:DROFE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Jazwinski, A. H., 1970: Stochastic Processes and Filtering Theory. Academic Press, 376 pp.

  • Kepert, J. D., 2009: Covariance localisation and balance in an ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 135, 11571176, https://doi.org/10.1002/qj.443.

    • Search Google Scholar
    • Export Citation
  • Kleist, D. T., and K. Ide, 2015: An OSSE-based evaluation of hybrid variational–ensemble data assimilation for the NCEP GFS. Part II: 4DEnVar and hybrid variants. Mon. Wea. Rev., 143, 452470, https://doi.org/10.1175/MWR-D-13-00350.1.

    • Search Google Scholar
    • Export Citation
  • Knaff, J. A., S. P. Longmore, R. T. DeMaria, and D. A. Molenar, 2015: Improved tropical cyclone flight-level wind estimates using routine infrared satellite reconnaissance. J. Appl. Meteor. Climatol., 54, 463478, https://doi.org/10.1175/JAMC-D-14-0112.1.

    • Search Google Scholar
    • Export Citation
  • Kurosawa, K., and J. Poterjoy, 2021: Data assimilation challenges posed by nonlinear measurement operators: A comparative study using a simplified model. Mon. Wea. Rev., 149, 23692389, https://doi.org/10.1175/MWR-D-20-0368.1.

    • Search Google Scholar
    • Export Citation
  • Landsea, C. W., and J. L. Franklin, 2013: Atlantic hurricane database uncertainty and presentation of a new database format. Mon. Wea. Rev., 141, 35763592, https://doi.org/10.1175/MWR-D-12-00254.1.

    • Search Google Scholar
    • Export Citation
  • Lawson, W. G., and J. A. Hansen, 2005: Alignment error models and ensemble-based data assimilation. Mon. Wea. Rev., 133, 16871709, https://doi.org/10.1175/MWR2945.1.

    • Search Google Scholar
    • Export Citation
  • Lee, Y., and A. J. Majda, 2016: State estimation and prediction using clustered particle filters. Proc. Natl. Acad. Sci. USA, 113, 14 60914 614, https://doi.org/10.1073/pnas.1617398113.

    • Search Google Scholar
    • Export Citation
  • Leeuwen, V., 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, 23352365, https://doi.org/10.1002/qj.3551.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1969: The predictability of a flow which possesses many scales of motion. Tellus, 21, 289307, https://doi.org/10.3402/tellusa.v21i3.10086.

    • Search Google Scholar
    • Export Citation
  • Lynch, P., and X.-Y. Huang, 1992: Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 120, 10191034, https://doi.org/10.1175/1520-0493(1992)120<1019:IOTHMU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Marks, F., N. Kurkowski, M. DeMaria, and M. Brennan, 2019: Hurricane forecast improvement program five-year plan: 2019–2024. NOAA, 86 pp., https://hfip.org/sites/default/files/documents/hfip-strategic-plan-20190625-final.pdf.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., K. Kondo, and T. Imamura, 2014: The 10,240-member ensemble Kalman filtering with an intermediate AGCM. Geophys. Res. Lett., 41, 52645271, https://doi.org/10.1002/2014GL060863.

    • Search Google Scholar
    • Export Citation
  • Molinari, J., S. Skubis, D. Vollaro, F. Alsheimer, and H. E. Willoughby, 1998: Potential vorticity analysis of tropical cyclone intensification. J. Atmos. Sci., 55, 26322644, https://doi.org/10.1175/1520-0469(1998)055<2632:PVAOTC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Morzfeld, M., and D. Hodyss, 2019: Gaussian approximations in filters and smoothers for data assimilation. Tellus, 71A, 1600344, https://doi.org/10.1080/16000870.2019.1600344.

    • Search Google Scholar
    • Export Citation
  • Morzfeld, M., D. Hodyss, and J. Poterjoy, 2018: Variational particle smoothers and their localization. Quart. J. Roy. Meteor. Soc., 144, 806825, https://doi.org/10.1002/qj.3256.

    • Search Google Scholar
    • Export Citation
  • Nehrkorn, T., B. Woods, R. N. Hoffman, and T. Auligné, 2015: Correcting for position errors in variational data assimilation. Mon. Wea. Rev., 143, 13681381, https://doi.org/10.1175/MWR-D-14-00127.1.

    • Search Google Scholar
    • Export Citation
  • NWS, 2018: Average NHC Atlantic track forecast errors: 2010–2018. National Hurricane Center Forecast Verification, accessed 20 June 2019, https://www.nhc.noaa.gov/verification/verify5.shtml.

    • Search Google Scholar
    • Export Citation
  • Penny, S. G., and T. Miyoshi, 2016: A local particle filter for high dimensional geophysical systems. Nonlinear Processes Geophys., 23, 391405, https://doi.org/10.5194/npg-23-391-2016.

    • Search Google Scholar
    • Export Citation
  • Posselt, D. J., and C. H. Bishop, 2012: Nonlinear parameter estimation: Comparison of an ensemble Kalman smoother with a Markov chain Monte Carlo algorithm. Mon. Wea. Rev., 140, 19571974, https://doi.org/10.1175/MWR-D-11-00242.1.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., 2016: A localized particle filter for high-dimensional nonlinear systems. Mon. Wea. Rev., 144, 5976, https://doi.org/10.1175/MWR-D-15-0163.1.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., 2022: Regularization and tempering for a moment-matching localized particle filter. Quart. J. Roy. Meteor. Soc., in press.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., and F. Zhang, 2011: Dynamics and structure of forecast error covariance in the core of a developing hurricane. J. Atmos. Sci., 68, 15861606, https://doi.org/10.1175/2011JAS3681.1.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., and F. Zhang, 2014: Intercomparison and coupling of ensemble and variational data assimilation approaches for the analysis and forecasting of Hurricane Karl (2010). Mon. Wea. Rev., 142, 33473364, https://doi.org/10.1175/MWR-D-13-00394.1.

    • Search Google Scholar
    • Export Citation
  • 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, 20072020, https://doi.org/10.1175/MWR-D-15-0322.1.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., R. A. Sobash, and J. L. Anderson, 2017: Convective-scale data assimilation for the Weather Research and Forecasting Model using the local particle filter. Mon. Wea. Rev., 145, 18971918, https://doi.org/10.1175/MWR-D-16-0298.1.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., L. Wicker, and M. Buehner, 2019: Progress toward the application of a localized particle filter for numerical weather prediction. Mon. Wea. Rev., 147, 11071126, https://doi.org/10.1175/MWR-D-17-0344.1.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., G. Alaka, and H. Winterbottom, 2021: The irreplaceable utility of sequential data assimilation for model development: Lessons learned from an experimental HWRF system. Wea. Forecasting, 36, 661677, https://doi.org/10.1175/WAF-D-20-0204.1.

    • Search Google Scholar
    • Export Citation
  • Potthast, R., A. Walter, and A. Rhodin, 2019: A localized adaptive particle filter within an operational NWP framework. Mon. Wea. Rev., 147, 345362, https://doi.org/10.1175/MWR-D-18-0028.1.

    • Search Google Scholar
    • Export Citation
  • Ravela, S., K. Emanuel, and D. McLaughlin, 2007: Data assimilation by field alignment. Physica D, 230, 127145, https://doi.org/10.1016/j.physd.2006.09.035.

    • Search Google Scholar
    • Export Citation
  • Reich, S., and C. Cotter, Eds., 2015: Introduction to probability. Probabilistic Forecasting and Bayesian Data Assimilation. Cambridge University Press, 3364.

    • Search Google Scholar
    • Export Citation
  • Robert, S., D. Leuenberger, and H. R. Kunsch, 2018: A local ensemble transform Kalman particle filter for convective-scale data assimilation. Quart. J. Roy. Meteor. Soc., 144, 12791296, https://doi.org/10.1002/qj.3116.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., and C. Snyder, 2008: A generalization of Lorenz’s model for the predictability of flows with many scales of motion. J. Atmos. Sci., 65, 10631076, https://doi.org/10.1175/2007JAS2449.1.

    • Search Google Scholar
    • Export Citation
  • Slivinski, L., and C. Snyder, 2016: Exploring practical estimates of the ensemble size necessary for particle filters. Mon. Wea. Rev., 144, 861875, https://doi.org/10.1175/MWR-D-14-00303.1.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., T. Bengtsson, and M. Morzfeld, 2015: Performance bounds for particle filters using optimal proposal. Mon. Wea. Rev., 143, 47504761, https://doi.org/10.1175/MWR-D-15-0144.1.

    • Search Google Scholar
    • Export Citation
  • Stensrud, D. J., 2007: Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models. 1st ed. Cambridge University Press, 480 pp.

    • Search Google Scholar
    • Export Citation
  • Stratman, D. R., C. K. Potvin, and L. J. Wicker, 2018: Correcting storm displacement errors in ensemble using the Feature Alignment Technique (FAT). Mon. Wea. Rev., 146, 21252145, https://doi.org/10.1175/MWR-D-17-0357.1.

    • Search Google Scholar
    • Export Citation
  • Thepáut, J.-N., and P. Courtie, 1991: Four-dimensional variational data assimilation using the adjoint of a multilevel primitive-equation model. Quart. J. Roy. Meteor. Soc., 117, 12251254, https://doi.org/10.1002/qj.49711750206.

    • Search Google Scholar
    • Export Citation
  • Weng, Y., and F. Zhang, 2012: Assimilating airborne Doppler radar observations with an ensemble Kalman filter for convection-permitting hurricane initialization and prediction: Katrina (2005). Mon. Wea. Rev., 140, 841859, https://doi.org/10.1175/2011MWR3602.1.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924, https://doi.org/10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and T. M. Hamill, 2012: Evaluating methods to account for system errors in ensemble data assimilation. Mon. Wea. Rev., 140, 30783089, https://doi.org/10.1175/MWR-D-11-00276.1.

    • Search Google Scholar
    • Export Citation
  • Ying, Y., 2019: A multiscale alignment method for ensemble filtering with displacement errors. Mon. Wea. Rev., 147, 45534565, https://doi.org/10.1175/MWR-D-19-0170.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132, 12381253, https://doi.org/10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., M. Zhang, and J. A. Hansen, 2009: Coupling ensemble Kalman filter with four dimensional variational data assimilation. Adv. Atmos. Sci., 26, 18, https://doi.org/10.1007/s00376-009-0001-8.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., Y. Weng, J. F. Gamache, and F. D. Marks, 2011: Performance of convection-permitting hurricane initialization and prediction during 2008–2010 with ensemble data assimilation of inner-core airborne Doppler radar observations. Geophys. Res. Lett., 38, L15810, https://doi.org/10.1029/2011GL048469.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 330 330 70
Full Text Views 174 174 22
PDF Downloads 178 178 26

Implications of Multivariate Non-Gaussian Data Assimilation for Multiscale Weather Prediction

Jonathan PoterjoyaDepartment of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland
bNOAA/Atlantic Oceanographic and Meteorological Laboratory, Miami, Florida

Search for other papers by Jonathan Poterjoy in
Current site
Google Scholar
PubMed
Close
https://orcid.org/0000-0003-3927-4642
Restricted access

Abstract

Weather prediction models currently operate within a probabilistic framework for generating forecasts conditioned on recent measurements of Earth’s atmosphere. This framework can be conceptualized as one that approximates parts of a Bayesian posterior density estimated under assumptions of Gaussian errors. Gaussian error approximations are appropriate for synoptic-scale atmospheric flow, which experiences quasi-linear error evolution over time scales depicted by measurements, but are often hypothesized to be inappropriate for highly nonlinear, sparsely observed mesoscale processes. The current study adopts an experimental regional modeling system to examine the impact of Gaussian prior error approximations, which are adopted by ensemble Kalman filters (EnKFs) to generate probabilistic predictions. The analysis is aided by results obtained using recently introduced particle filter (PF) methodology that relies on an implicit nonparametric representation of prior probability densities—but with added computational expense. The investigation focuses on EnKF and PF comparisons over monthlong experiments performed using an extensive domain, which features the development and passage of numerous extratropical and tropical cyclones. The experiments reveal spurious small-scale corrections in EnKF members, which come about from inappropriate Gaussian approximations for priors dominated by alignment uncertainty in mesoscale weather systems. Similar behavior is found in PF members, owing to the use of a localization operator, but to a much lesser extent. This result is reproduced and studied using a low-dimensional model, which permits the use of large sample estimates of the Bayesian posterior distribution. Findings from this study motivate the use of data assimilation techniques that provide a more appropriate specification of multivariate non-Gaussian prior densities or a multiscale treatment of alignment errors during data assimilation.

Significance Statement

Numerical predictions of Earth’s atmosphere require computer models, which represent known physical processes governing the evolution of atmospheric flow, and a clever use of statistical methods to construct a complete model representation of the true atmosphere from incomplete measurements. The second requirement is built on assumptions for the shape of error distributions for variables that are input into the model for generating predictions. The present study explores the fidelity of these error assumptions for regional weather forecasting using a novel technique that avoids common approximations that go into operational weather prediction systems.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jonathan Poterjoy, poterjoy@umd.edu

Abstract

Weather prediction models currently operate within a probabilistic framework for generating forecasts conditioned on recent measurements of Earth’s atmosphere. This framework can be conceptualized as one that approximates parts of a Bayesian posterior density estimated under assumptions of Gaussian errors. Gaussian error approximations are appropriate for synoptic-scale atmospheric flow, which experiences quasi-linear error evolution over time scales depicted by measurements, but are often hypothesized to be inappropriate for highly nonlinear, sparsely observed mesoscale processes. The current study adopts an experimental regional modeling system to examine the impact of Gaussian prior error approximations, which are adopted by ensemble Kalman filters (EnKFs) to generate probabilistic predictions. The analysis is aided by results obtained using recently introduced particle filter (PF) methodology that relies on an implicit nonparametric representation of prior probability densities—but with added computational expense. The investigation focuses on EnKF and PF comparisons over monthlong experiments performed using an extensive domain, which features the development and passage of numerous extratropical and tropical cyclones. The experiments reveal spurious small-scale corrections in EnKF members, which come about from inappropriate Gaussian approximations for priors dominated by alignment uncertainty in mesoscale weather systems. Similar behavior is found in PF members, owing to the use of a localization operator, but to a much lesser extent. This result is reproduced and studied using a low-dimensional model, which permits the use of large sample estimates of the Bayesian posterior distribution. Findings from this study motivate the use of data assimilation techniques that provide a more appropriate specification of multivariate non-Gaussian prior densities or a multiscale treatment of alignment errors during data assimilation.

Significance Statement

Numerical predictions of Earth’s atmosphere require computer models, which represent known physical processes governing the evolution of atmospheric flow, and a clever use of statistical methods to construct a complete model representation of the true atmosphere from incomplete measurements. The second requirement is built on assumptions for the shape of error distributions for variables that are input into the model for generating predictions. The present study explores the fidelity of these error assumptions for regional weather forecasting using a novel technique that avoids common approximations that go into operational weather prediction systems.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jonathan Poterjoy, poterjoy@umd.edu
Save