Impacts of Methods for Estimating the Observation Error Variance for the Frequent Assimilation of Thermodynamic Profilers on Convective-Scale Forecasts

Samuel K. Degelia aSchool of Meteorology, University of Oklahoma, Norman, Oklahoma

Search for other papers by Samuel K. Degelia in
Current site
Google Scholar
PubMed
Close
https://orcid.org/0000-0002-0901-5837
and
Xuguang Wang aSchool of Meteorology, University of Oklahoma, Norman, Oklahoma

Search for other papers by Xuguang Wang in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The observation error covariance partially controls the weight assigned to an observation during data assimilation (DA). True observation error statistics are rarely known and likely vary depending on the meteorological state. However, operational DA systems often apply static methods that assign constant observation errors across a dataset. Previous studies show that these methods can degrade forecast quality when assimilating ground-based remote sensing datasets. To improve the impact of assimilating such observations, we propose two novel methods for estimating the observation error variance for high-frequency thermodynamic profilers. These methods include an adaptive observation error inflation technique and the Desroziers method that directly estimates the observation error variances using paired innovation and analysis residuals. Each method is compared for a nocturnal mesoscale convective system (MCS) observed during the Plains Elevated Convection at Night (PECAN) experiment. In general, we find that these novel methods better represent the large variability of observation error statistics for high-frequency profiles collected by Atmospheric Emitted Radiance Interferometers (AERIs). When assimilating AERIs by statically inflating retrieval error variances, the trailing stratiform region of the MCS is degraded compared to a baseline simulation with no AERI data assimilated. Assimilating the AERIs using the adaptive inflation or Desroziers method results in better maintenance of the trailing stratiform region and additional suppression of spurious convection. The forecast improvements from these novel methods are primarily linked to increased error variances for some moisture retrievals. These results indicate the importance of accurately estimating observation error statistics for convective-scale DA and suggest that accounting for flow dependence can improve the impacts from assimilating remote sensing datasets.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the PECAN:Plains Elevated Convection At Night Special Collection.

Corresponding author: Samuel K. Degelia, sdegelia@ou.edu

Abstract

The observation error covariance partially controls the weight assigned to an observation during data assimilation (DA). True observation error statistics are rarely known and likely vary depending on the meteorological state. However, operational DA systems often apply static methods that assign constant observation errors across a dataset. Previous studies show that these methods can degrade forecast quality when assimilating ground-based remote sensing datasets. To improve the impact of assimilating such observations, we propose two novel methods for estimating the observation error variance for high-frequency thermodynamic profilers. These methods include an adaptive observation error inflation technique and the Desroziers method that directly estimates the observation error variances using paired innovation and analysis residuals. Each method is compared for a nocturnal mesoscale convective system (MCS) observed during the Plains Elevated Convection at Night (PECAN) experiment. In general, we find that these novel methods better represent the large variability of observation error statistics for high-frequency profiles collected by Atmospheric Emitted Radiance Interferometers (AERIs). When assimilating AERIs by statically inflating retrieval error variances, the trailing stratiform region of the MCS is degraded compared to a baseline simulation with no AERI data assimilated. Assimilating the AERIs using the adaptive inflation or Desroziers method results in better maintenance of the trailing stratiform region and additional suppression of spurious convection. The forecast improvements from these novel methods are primarily linked to increased error variances for some moisture retrievals. These results indicate the importance of accurately estimating observation error statistics for convective-scale DA and suggest that accounting for flow dependence can improve the impacts from assimilating remote sensing datasets.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the PECAN:Plains Elevated Convection At Night Special Collection.

Corresponding author: Samuel K. Degelia, sdegelia@ou.edu
Save
  • Bormann, N., M. Bonavita, R. Dragani, R. Eresmaa, M. Matricardi, and A. McNally, 2016: Enhancing the impact of IASI observations through an updated observation-error covariance matrix. Quart. J. Roy. Meteor. Soc., 142, 17671780, https://doi.org/10.1002/qj.2774.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, 2010: 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
  • Campbell, W. F., E. A. Satterfield, B. Ruston, and N. L. Baker, 2017: Accounting for correlated observation error in a dual-formulation 4D variational data assimilation system. Mon. Wea. Rev., 145, 10191032, https://doi.org/10.1175/MWR-D-16-0240.1.

    • Search Google Scholar
    • Export Citation
  • Chandramouli, K., X. Wang, A. Johnson, and J. Otkin, 2021: Online nonlinear bias correction in ensemble Kalman filter to assimilate GOES-R all-sky radiances for the analysis and prediction of rapidly developing supercells. J. Adv. Model. Earth Syst., 14, e2021MS002711, https://doi.org/10.1029/2021MS002711.

    • Search Google Scholar
    • Export Citation
  • Chipilski, H. G., X. Wang, and D. B. Parsons, 2020: Impact of assimilating PECAN profilers on the prediction of bore-driven nocturnal convection: A multi-scale forecast evaluation for the 6 July 2015 case study. Mon. Wea. Rev., 148, 11471175, https://doi.org/10.1175/MWR-D-19-0171.1.

    • Search Google Scholar
    • Export Citation
  • Cordoba, M., S. L. Dance, G. A. Kelly, N. K. Nichols, and J. A. Waller, 2017: Diagnosing atmospheric motion vector observation errors for an operational high-resolution data assimilation system. Quart. J. Roy. Meteor. Soc., 143, 333341, https://doi.org/10.1002/qj.2925.

    • Search Google Scholar
    • Export Citation
  • Degelia, S. K., X. Wang, and D. J. Stensrud, 2019: An evaluation of the impact of assimilating AERI retrievals, kinematic profilers, rawinsondes, and surface observations on a forecast of a nocturnal convection initiation event during the PECAN field campaign. Mon. Wea. Rev., 147, 27392764, https://doi.org/10.1175/MWR-D-18-0423.1.

    • Search Google Scholar
    • Export Citation
  • Degelia, S. K., X. Wang, D. J. Stensrud, and D. D. Turner, 2020: Systematic evaluation of the impact of assimilating a network of ground-based remote sensing profilers for forecasts of nocturnal convection initiation during PECAN. Mon. Wea. Rev., 148, 47034728, https://doi.org/10.1175/MWR-D-20-0118.1.

    • Search Google Scholar
    • Export Citation
  • Desroziers, G., L. Berre, B. Chapnik, and P. Poli, 2005: Diagnosis of observation, background and analysis-error statistics in observation space. Quart. J. Roy. Meteor. Soc., 131, 33853396, https://doi.org/10.1256/qj.05.108.

    • Search Google Scholar
    • Export Citation
  • Du, J., and Coauthors, 2014: NCEP regional ensemble update: Current systems and planned storm-scale ensembles. 26th Conf. on Weather Analysis and Forecasting/22nd Conf. on Numerical Weather Prediction, Atlanta, GA, Amer. Meteor. Soc., J1.4, https://ams.confex.com/ams/94Annual/webprogram/Paper239030.html.

  • Ek, M. B., K. E. Mitchell, Y. Lin, E. Rogers, P. Grunmann, V. Koren, G. Gayno, and J. Tarpley, 2003: Implementation of Noah land surface model advances in the National Centers for Environmental Prediction operational mesoscale Eta model. J. Geophys. Res., 108, 8851, https://doi.org/10.1029/2002JD003296.

    • Search Google Scholar
    • Export Citation
  • Feltz, W. F., W. L. Smith, H. B. Howell, R. O. Knuteson, H. Woolf, and H. E. Revercomb, 2003: Near-continuous profiling of temperature, moisture, and atmospheric stability using the atmospheric emitted radiance interferometer (AERI). J. Appl. Meteor., 42, 584597, https://doi.org/10.1175/1520-0450(2003)042<0584:NPOTMA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fielding, M. D., and M. Janiskova, 2018: Assimilating profiles of cloud radar and lidar observations into the ECMWF 4D-Var system. Sixth Int. Symp. on Data Assimilation (2018), Munich, Germany, Universität München Schellingstraße, 3.6, https://isda2018.wavestoweather.de/.

  • Fielding, M. D., and O. Stiller, 2019: Characterizing the representativity error of cloud profiling observations for data assimilation. J. Geophys. Res. Atmos., 124, 40864103, https://doi.org/10.1029/2018JD029949.

    • Search Google Scholar
    • Export Citation
  • Fowler, A., and P. J. Van Leeuwen, 2013: Observation impact in data assimilation: The effect of non-Gaussian observation error. Tellus, 65A, 20035, https://doi.org/10.3402/tellusa.v65i0.20035.

    • Search Google Scholar
    • Export Citation
  • Geer, A. J., and P. Bauer, 2011: Observation errors in all-sky data assimilation. Quart. J. Roy. Meteor. Soc., 137, 20242037, https://doi.org/10.1002/qj.830.

    • Search Google Scholar
    • Export Citation
  • Geer, A. J., and Coauthors, 2018: All-sky satellite data assimilation at operational weather forecasting centres. Quart. J. Roy. Meteor. Soc., 144, 11911217, https://doi.org/10.1002/qj.3202.

    • Search Google Scholar
    • Export Citation
  • Geerts, B., and Coauthors, 2017: The 2015 plains elevated convection at night field project. Bull. Amer. Meteor. Soc., 98, 767786, https://doi.org/10.1175/BAMS-D-15-00257.1.

    • Search Google Scholar
    • Export Citation
  • Grasmick, C., B. Geerts, D. D. Turner, Z. Wang, and T. M. Weckwerth, 2018: The relation between nocturnal MCS evolution and its outflow boundaries in the stable boundary layer: An observational study of the 15 July 2015 MCS in PECAN. Mon. Wea. Rev., 146, 32033226, https://doi.org/10.1175/MWR-D-18-0169.1.

    • Search Google Scholar
    • Export Citation
  • Grell, G. A., and S. R. Freitas, 2013: A scale and aerosol aware stochastic convective parameterization for weather and air quality modeling. Atmos. Chem. Phys., 13, 23 84523 893, https://doi.org/10.5194/acpd-13-23845-2013.

    • Search Google Scholar
    • Export Citation
  • Hodyss, D., and N. Nichols, 2015: The error of representation: Basic understanding. Tellus, 67A, 24822, https://doi.org/10.3402/tellusa.v67.24822.

    • Search Google Scholar
    • Export Citation
  • Hodyss, D., and E. Satterfield, 2017: The treatment, estimation, and issues with representation error modeling. Data Assimilation for Atmospheric, Oceanic, and Hydrologic Applications, S. K. Park and L. Xu, Eds., Vol. III, Springer International Publishing, 177–194.

  • Hong, S.-Y., and J. J. Lim, 2006: The WRF single-moment 6-class microphysics scheme (WSM6). J. Korean Meteor. Soc., 42, 129151.

  • Hu, J., N. Yussouf, D. D. Turner, T. A. Jones, and X. Wang, 2019: Impact of ground-based remote sensing boundary layer observations on short-term probabilistic forecasts of a tornadic supercell event. Wea. Forecasting, 34, 14531476, https://doi.org/10.1175/WAF-D-18-0200.1.

    • Search Google Scholar
    • Export Citation
  • Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, 2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, D13103, https://doi.org/10.1029/2008JD009944.

    • Search Google Scholar
    • Export Citation
  • Janjić, T., and Coauthors, 2018: On the representation error in data assimilation. Quart. J. Roy. Meteor. Soc., 144, 12571278, https://doi.org/10.1002/qj.3130.

    • Search Google Scholar
    • Export Citation
  • Johnson, A., X. Wang, J. R. Carley, L. J. Wicker, and C. Karstens, 2015: A comparison of multiscale GSI-based EnKF and 3DVar data assimilation using radar and conventional observations for midlatitude convective-scale precipitation forecasts. Mon. Wea. Rev., 143, 30873108, https://doi.org/10.1175/MWR-D-14-00345.1.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation, and Predictability. Cambridge University Press, 368 pp.

  • Lakshmanan, V., T. Smith, G. Stumpf, and K. Hondl, 2007: The Warning Decision Support System–Integrated Information. Wea. Forecasting, 22, 596612, https://doi.org/10.1175/WAF1009.1.

    • Search Google Scholar
    • Export Citation
  • Lange, H., and T. Janjić, 2016: Assimilation of mode-S EHS aircraft observations in COSMO- KENDA. Mon. Wea. Rev., 144, 16971711, https://doi.org/10.1175/MWR-D-15-0112.1.

    • Search Google Scholar
    • Export Citation
  • Lin, Y.-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 10651092, https://doi.org/10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ménard, R., 2016: Error covariance estimation methods based on analysis residuals: Theoretical foundation and convergence properties derived from simplified observation networks. Quart. J. Roy. Meteor. Soc., 142, 257273, https://doi.org/10.1002/qj.2650.

    • Search Google Scholar
    • Export Citation
  • Ménard, R., Y. Yang, and Y. Rochon, 2009: Convergence and stability of estimated error variances derived from assimilation residuals in observation space. ECMWF Workshop on Diagnostics of Data Assimilation System Performance, Reading, United Kingdom, ECMWF, 133–143, https://www.ecmwf.int/sites/default/files/elibrary/2009/75646-convergence-and-stability-estimated-error-variances-derived-assimilation-residuals-observation_0.pdf.

  • Minamide, M., and F. Zhang, 2017: Adaptive observation error inflation for assimilating all-sky satellite radiance. Mon. Wea. Rev., 145, 10631081, https://doi.org/10.1175/MWR-D-16-0257.1.

    • Search Google Scholar
    • Export Citation
  • Nakanishi, M., and H. Niino, 2006: An improved Mellor–Yamada level-3 model: Its numerical stability and application to a regional prediction of advection fog. Bound.-Layer Meteor., 119, 397407, https://doi.org/10.1007/s10546-005-9030-8.

    • Search Google Scholar
    • Export Citation
  • Roberts, N. M., and H. W. Lean, 2008: Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events. Mon. Wea. Rev., 136, 7897, https://doi.org/10.1175/2007MWR2123.1.

    • Search Google Scholar
    • Export Citation
  • Satterfield, E., D. Hodyss, D. D. Kuhl, and C. H. Bishop, 2017: Investigating the use of ensemble variance to predict observation error of representation. Mon. Wea. Rev., 145, 653667, https://doi.org/10.1175/MWR-D-16-0299.1.

    • Search Google Scholar
    • Export Citation
  • Schwartz, C. S., and R. A. Sobash, 2017: Generating probabilistic forecasts from convection- allowing ensembles using neighborhood approaches: A review and recommendations. Mon. Wea. Rev., 145, 33973418, https://doi.org/10.1175/MWR-D-16-0400.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

  • Stewart, L. M., S. L. Dance, N. K. Nichols, J. R. Eyre, and J. Cameron, 2014: Estimating interchannel observation-error correlations for IASI radiance data in the Met Office system. Quart. J. Roy. Meteor. Soc., 140, 12361244, https://doi.org/10.1002/qj.2211.

    • Search Google Scholar
    • Export Citation
  • Tandeo, P., P. Ailliot, M. Bocquiet, A. Carrassi, T. Miyoshi, M. Pulido, and Y. Zhen, 2020: A review of innovation-based methods to jointly estimate model and observation error covariance matrices in ensemble data assimilation. Mon. Wea. Rev., 148, 39733994, https://doi.org/10.1175/MWR-D-19-0240.1.

    • Search Google Scholar
    • Export Citation
  • Tao, W.-K., and Coauthors, 2003: Microphysics, radiation and surface processes in the Goddard cumulus ensemble (GCE) model. Meteor. Atmos. Phys., 82, 97137, https://doi.org/10.1007/s00703-001-0594-7.

    • Search Google Scholar
    • Export Citation
  • Turner, D. D., and U. Löhnert, 2014: Information content and uncertainties in thermodynamic profiles and liquid cloud properties retrieved from the ground-based atmospheric emitted radiance interferometer (AERI). J. Appl. Meteor. Climatol., 53, 752771, https://doi.org/10.1175/JAMC-D-13-0126.1.

    • Search Google Scholar
    • Export Citation
  • Turner, D. D., and W. G. Blumberg, 2019: Improvements to the AERIoe thermodynamic profile retrieval algorithm. IEEE Sel. Top. Appl. Earth Obs. Remote Sens., 12, 13391354, https://doi.org/10.1109/JSTARS.2018.2874968.

    • Search Google Scholar
    • Export Citation
  • Vaisala, 2017: Vaisala radiosonde RS41 measurement performance. Vaisala white paper, Ref. B211356EN-B, 28 pp., https://www.vaisala.com/sites/default/files/documents/WEA-MET-RS41-Performance-White-paper-B211356EN-B-LOW-v3.pdf.

  • Waller, J. A., S. L. Dance, and N. K. Nichols, 2016a: Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics. Quart. J. Roy. Meteor. Soc., 142, 418431, https://doi.org/10.1002/qj.2661.

    • Search Google Scholar
    • Export Citation
  • Waller, J. A., D. Simonin, S. L. Dance, N. K. Nichols, and S. P. Ballard, 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, https://doi.org/10.1175/MWR-D-15-0340.1.

    • Search Google Scholar
    • Export Citation
  • Waller, J. A., S. P. Ballard, S. L. Dance, G. Kelly, N. K. Nichols, and D. Simonin, 2016c: Diagnosing horizontal and inter-channel observation error correlations for SEVIRI observations using observation-minus-background and observation-minus-analysis statistics. Remote Sens., 8, 581, https://doi.org/10.3390/rs8070581.

    • Search Google Scholar
    • Export Citation
  • Waller, J. A., S. L. Dance, and N. K. Nichols, 2017: On diagnosing observation-error statistics with local ensemble data assimilation. Quart. J. Roy. Meteor. Soc., 143, 26772686, https://doi.org/10.1002/qj.3117.

    • Search Google Scholar
    • Export Citation
  • Waller, J. A., E. Bauernschubert, S. L. Dance, N. K. Nichols, R. Potthast, and D. Simonin, 2019: Observation error statistics for Doppler radar radial wind superobservations assimilated into the DWD COSMO-KENDA system. Mon. Wea. Rev., 147, 33513364, https://doi.org/10.1175/MWR-D-19-0104.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., and T. Lei, 2014: GSI-based four-dimensional ensemble–variational (4DEnsVar) data assimilation: Formulation and single-resolution experiments with real data for NCEP global forecast system. Mon. Wea. Rev., 142, 33033325, https://doi.org/10.1175/MWR-D-13-00303.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., C. Snyder, and T. M. Hamill, 2007: On the theoretical equivalence of differently proposed ensemble–3DVAR hybrid analysis schemes. Mon. Wea. Rev., 135, 222227, https://doi.org/10.1175/MWR3282.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., D. M. Barker, C. Snyder, and T. M. Hamill, 2008a: A hybrid ETKF–3DVAR data assimilation scheme for the WRF Model. Part I: Observing system simulation experiment. Mon. Wea. Rev., 136, 51165131, https://doi.org/10.1175/2008MWR2444.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., D. M. Barker, C. Snyder, and T. M. Hamill, 2008b: A hybrid ETKF–3DVAR data assimilation scheme for the WRF Model. Part II: Real observation experiments. Mon. Wea. Rev., 136, 51325147, https://doi.org/10.1175/2008MWR2445.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., T. M. Hamill, J. S. Whitaker, and C. H. Bishop, 2009: A comparison of the hybrid and EnSRF analysis schemes in the presence of model errors due to unresolved scales. Mon. Wea. Rev., 137, 32193232, https://doi.org/10.1175/2009MWR2923.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., D. Parrish, D. Kleist, and J. Whitaker, 2013: GSI 3DVar-based ensemble- variational hybrid data assimilation for NCEP global forecast system: Single resolution experiments. Mon. Wea. Rev., 141, 40984117, https://doi.org/10.1175/MWR-D-12-00141.1.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., and X. Wang, 2017: Direct assimilation of radar reflectivity without tangent linear and adjoint of the nonlinear observation operator in the GSI-Based EnVar system: Methodology and experiment with the 8 May 2003 Oklahoma City tornadic supercell. Mon. Wea. Rev., 145, 14471471, https://doi.org/10.1175/MWR-D-16-0231.1.

    • Search Google Scholar
    • Export Citation
  • Wei, M., Z. Toth, R. Wobus, and Y. Zhu, 2008: Initial perturbations based on the ensemble transform (ET) technique in the NCEP global operational forecast system. Tellus, 60A, 6279, https://doi.org/10.1111/j.1600-0870.2007.00273.x.

    • Search Google Scholar
    • Export Citation
  • Weston, P. P., W. Bell, and J. Eyre, 2014: Accounting for correlated error in the assimilation of high-resolution sounder data. Quart. J. Roy. Meteor. Soc., 140, 24202429, https://doi.org/10.1002/qj.2306.

    • 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
All Time Past Year Past 30 Days
Abstract Views 569 569 22
Full Text Views 210 210 4
PDF Downloads 240 240 8