• Aksoy, A., , D. C. Dowell, , and C. Snyder, 2010: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part II: Short-range ensemble forecasts. Mon. Wea. Rev., 138, 12731292.

    • Search Google Scholar
    • Export Citation
  • Baldwin, M. E., , S. Lakshmivarahan, , and J. S. Kain, 2001: Verification of mesoscale features in NWP models. Preprints, Ninth Conf. on Mesoscale Processes, Fort Lauderdale, FL, Amer. Meteor. Soc., 255–257.

  • Bowler, N. E., , and K. R. Mylne, 2009: Ensemble transform Kalman filter perturbations for a regional ensemble prediction system. Quart. J. Roy. Meteor. Soc., 135, 757766.

    • Search Google Scholar
    • Export Citation
  • Brier, G. W., 1950: Verification of weather forecasts expressed in terms of probability. Mon. Wea. Rev., 78, 13.

  • Brotzge, J., , K. Hondle, , B. Philips, , L. Lemon, , E. Bass, , D. Rude, , and D. Andra Jr., 2010: Evaluation of distributed collaborative adaptive sensing for detection of low-level circulations and implications for severe weather operations. Wea. Forecasting, 25, 173189.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., 1997: Potential forecast skill of ensemble prediction and spread and skill distributions of the ECMWF ensemble prediction system. Mon. Wea. Rev., 125, 99119.

    • Search Google Scholar
    • Export Citation
  • Carbone, R. E., , J. D. Tuttle, , D. A. Ahijevych, , and S. B. Trier, 2002: Inferences of predictability associated with warm season precipitation episodes. J. Atmos. Sci., 59, 20332056.

    • Search Google Scholar
    • Export Citation
  • Dawson, D. T., II, 2009: Impacts of single- and multi-moment microphysics on numerical simulations of supercells and tornadoes of the 3 May 1999 Oklahoma tornado outbreak. Ph.D. dissertation, School of Meteorology, University of Oklahoma, 173 pp.

  • Dowell, D. C., , L. J. Wicker, , and D. J. Stensrud, 2004: High resolution analyses of the 8 May 2003 Oklahoma City storm. Part II: EnKF data assimilation and forecast experiments. Preprints, 22nd Conf. on Severe Local Storms, Hyannis, MA, Amer. Meteor. Soc., 12.5. [Available online at http://ams.confex.com/ams/pdfpapers/81393.pdf.]

  • Du, J., , G. DiMego, , S. Tracton, , and B. Zhou, 2003: NCEP short-range ensemble forecasting (SREF) system: Multi-IC, multi-model, and multi-physics approach. Research Activities in Atmospheric and Oceanic Modelling, Rep. 33, WMO Tech. Doc. 1161, J. Cote, Ed., CAS/JSC Working Group Numerical Experimentation (WGNE), 5.09–5.10.

  • Ebert, E. E., 2001: Ability of a poor man’s ensemble to predict the probability and distribution of precipitation. Mon. Wea. Rev., 129, 24612480.

    • Search Google Scholar
    • Export Citation
  • Edwards, R., , S. F. Corfidi, , R. L. Thompson, , J. S. Evans, , J. P. Craven, , J. P. Racy, , D. W. McCarthy, , and M. D. Vescio, 2002: Storm Prediction Center forecasting issues related to the 3 May 1999 tornado outbreak. Wea. Forecasting, 17, 544558.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53, 343367.

  • Hamill, T. M., , J. S. Whitaker, , M. Fiorino, , and S. G. Benjamin, 2011: Global ensemble predictions of 2009’s tropical cyclones initialized with an ensemble Kalman filter. Mon. Wea. Rev., 139, 668688.

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

  • Houtekamer, P. L., , L. Lefaivre, , J. Derome, , H. Ritchie, , and H. L. Mitchell, 1996: A system simulation approach to ensemble prediction. Mon. Wea. Rev., 124, 12251242.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , H. L. Mitchell, , G. Pellerin, , M. Buehner, , M. Charron, , L. Spacek, , and B. Hansen, 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133, 604620.

    • Search Google Scholar
    • Export Citation
  • Hu, M., , M. Xue, , and K. Brewster, 2006: 3DVAR and cloud analysis with WSR-88D level-II data for the prediction of Fort Worth tornadic thunderstorms. Part I: Cloud analysis and its impact. Mon. Wea. Rev., 134, 675698.

    • Search Google Scholar
    • Export Citation
  • Kong, F., , K. K. Droegemeier, , and N. L. Hickmon, 2006: Multi-resolution ensemble forecasts of an observed tornadic thunderstorm system. Part I: Comparison of coarse- and fine-grid experiments. Mon. Wea. Rev., 134, 807833.

    • Search Google Scholar
    • Export Citation
  • Kong, F., and Coauthors, 2011: Evaluation of CAPS multi-model storm-scale ensemble forecast for the NOAA HWT 2010 Spring Experiment. Preprints, 24th Conf. on Weather Forecasting/20th Conf. on Numerical Weather Prediction, Seattle, WA, Amer. Meteor. Soc., 457. [Available online at http://ams.confex.com/ams/91Annual/webprogram/Paper181680.html.]

  • Leith, C. E., 1974: Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev., 102, 409418.

  • Lilly, D. K., 1990: Numerical prediction of thunderstorms—Has its time come? Quart. J. Roy. Meteor. Soc., 116, 779798.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1969: The predictability of a flow which possesses many scales of motion. Tellus, 21, 289307.

  • Mason, S. J., , and N. E. Graham, 1999: Conditional probabilities, relative operating characteristics, and relative operating levels. Wea. Forecasting, 14, 713725.

    • Search Google Scholar
    • Export Citation
  • McLaughlin, D., and Coauthors, 2009: Short-wavelength technology and the potential for distributed networks of small radar systems. Bull. Amer. Meteor. Soc., 90, 17971817.

    • Search Google Scholar
    • Export Citation
  • NRC, 2006: Completing the Forecast: Characterizing and Communicating Uncertainty for Better Decisions Using Weather and Climate Forecasts. National Academies Press, 112 pp.

  • Potvin, C. K., , A. Shapiro, , T.-Y. Yu, , J. Gao, , and M. Xue, 2009: Using a low-order model to detect and characterize tornadoes in multiple-Doppler radar data. Mon. Wea. Rev., 137, 12301249.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Schenkman, A., , M. Xue, , A. Shapiro, , K. Brewster, , and J. Gao, 2011: The analysis and prediction of the 8-9 May 2007 Oklahoma tornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVAR. Mon. Wea. Rev., 139, 224246.

    • Search Google Scholar
    • Export Citation
  • Schultz, P., 1995: An explicit cloud physics parameterization for operational numerical weather prediction. Mon. Wea. Rev., 123, 33313343.

    • Search Google Scholar
    • Export Citation
  • Schwartz, C. S., and Coauthors, 2009: Optimizing probabilistic high-resolution ensemble guidance for hydrologic prediction. Preprints, 23rd Conf. on Hydrology, Phoenix, AZ, Amer. Meteor. Soc., 9.4. [Available online at http://ams.confex.com/ams/pdfpapers/147171.pdf.]

  • Schwartz, C. S., and Coauthors, 2010: Toward improved convection-allowing ensembles: Model physics sensitivities and optimizing probabilistic guidance with small ensemble membership. Wea. Forecasting, 25, 263280.

    • Search Google Scholar
    • Export Citation
  • Snook, N., , and M. Xue, 2008: Effects of microphysical drop size distribution on tornadogenesis in supercell thunderstorms. Geophys. Res. Lett., 35, L24803, doi:10.1029/2008GL035866.

    • Search Google Scholar
    • Export Citation
  • Snook, N., , M. Xue, , and Y. Jung, 2011: Analysis of a tornadic meoscale convective vortex based on ensemble Kalman filter assimilation of CASA X-band and WSR-88D radar data. Mon. Wea. Rev., 139, 34463468.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., , and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 16631677.

    • Search Google Scholar
    • Export Citation
  • Stensrud, D. J., , and J. Gao, 2010: Importance of horizontally inhomogeneous environmental initial conditions to ensemble storm-scale radar data assimilation and very short-range forecasts. Mon. Wea. Rev., 138, 12501272.

    • Search Google Scholar
    • Export Citation
  • Stensrud, D. J., and Coauthors, 2009: Convective-scale warn-on-forecast system: A vision for 2020. Bull. Amer. Meteor. Soc., 90, 14871499.

    • Search Google Scholar
    • Export Citation
  • Sun, J., , and N. A. Crook, 1998: Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part II: Retrieval experiments of an observed Florida convective storm. J. Atmos. Sci., 55, 835852.

    • Search Google Scholar
    • Export Citation
  • Sun, J., , D. W. Flicker, , and D. K. Lilly, 1991: Recovery of three-dimensional wind and temperature fields from simulated single-Doppler radar data. J. Atmos. Sci., 48, 876890.

    • Search Google Scholar
    • Export Citation
  • Theis, S. E., , A. Hense, , and U. Damrath, 2005: Probabilistic precipitation forecasts from a deterministic model: A pragmatic approach. Meteor. Appl., 12, 257268.

    • Search Google Scholar
    • Export Citation
  • Tong, M., 2006: Ensemble Kalman filter assimilation of Doppler radar data for the initialization and prediction of convective storms. Ph.D. dissertation, School of Meteorology, University of Oklahoma, 243 pp.

  • Tong, M., , and M. Xue, 2005a: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments. Mon. Wea. Rev., 133, 17891807.

    • Search Google Scholar
    • Export Citation
  • Tong, M., , and M. Xue, 2005b: Simultaneous retrieval of microphysical parameters and atmospheric state variables with radar data and ensemble Kalman filter method. Preprints, 17th Conf. on Numerical Weather Prediction, Washington, DC, Amer. Meteor. Soc., P1.30. [Available online at http://ams.confex.com/ams/pdfpapers/95042.pdf.]

  • Tong, M., , and M. Xue, 2008: Simultaneous estimation of microphysical parameters and atmospheric state with radar data and ensemble square-root Kalman filter. Part I: Sensitivity analysis and parameter identifiability. Mon. Wea. Rev., 136, 16301648.

    • Search Google Scholar
    • Export Citation
  • Toth, Z., , and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc., 74, 23172330.

  • Trapp, R. J., , and M. L. Weisman, 2003: Low-level mesovortices within squall lines and bow echoes. Part II: Their genesis and implications. Mon. Wea. Rev., 131, 28042823.

    • Search Google Scholar
    • Export Citation
  • Wandishin, M. S., , D. J. Stensrud, , S. L. Mullen, , and L. J. Wicker, 2010: On the predictability of mesoscale convective systems: Three-dimensional simulations. Mon. Wea. Rev., 138, 863885.

    • Search Google Scholar
    • Export Citation
  • Xue, M., , D.-H. Wang, , J.-D. Gao, , K. Brewster, , and K. K. Droegemeier, 2003: The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation. Meteor. Atmos. Phys., 82, 139170.

    • Search Google Scholar
    • Export Citation
  • Xue, M., and Coauthors, 2008: CAPS realtime storm-scale ensemble and high-resolution forecasts as part of the NOAA Hazardous Weather Testbed 2008 Spring Experiment. Preprints, 24th Conf. on Several Local Storms, Savannah, GA, Amer. Meteor. Soc., 12.2. [Available online at http://ams.confex.com/ams/pdfpapers/142036.pdf.]

  • Xue, M., and Coauthors, 2011: Realtime convection-permitting ensemble and convection-resolving deterministic forecasts of CAPS for the Hazardous Weather Testbed 2010 Spring Experiment. Preprints, 25th Conf. on Wea. Forecasting/20th Conf. on Numerical Weather Prediction, Seattle, WA, Amer. Meteor. Soc., 9A.2. [Available online at http://ams.confex.com/ams/91Annual/flvgateway.cgi/id/17650?recordingid=17650.]

  • Zhang, F., , Y. Weng, , J. A. Sippel, , Z. Meng, , and C. H. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 137, 21052125.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., , Y. Weng, , Y.-H. Kuo, , J. S. Whitaker, , and B. Xie, 2010: Predicting Typhoon Morakot’s catastrophic rainfall with a convection-permitting mesoscale ensemble system. Wea. Forecasting, 25, 18161825.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Geographic extent of the model domain. Shading indicates surface elevation in meters MSL. The forecast verification subdomain used for skill score calculations in Fig. 8b is indicated by the black box in the northeastern portion of the forecast domain.

  • View in gallery

    Composite radar reflectivity (dBZ) of the ensemble mean analysis state at 0200 UTC 9 May 2007 for (a) CNTL, (b) NoMMP, and (c) NoCASA, from which the deterministic forecasts in Fig. 4 were launched; also shown is (d) composite radar reflectivity (dBZ) observed by WSR-88Ds KAMA, KDYX, KFWS, KLBB,, and KTLX at 0200 UTC 9 May 2007. The 30-km CASA radar range rings are included for reference. This figure is a reproduction of Fig. 4 of SXJ11.

  • View in gallery

    Forecast diagram detailing the analysis and forecast periods for experiments CNTL, NoMMP, and NoCASA.

  • View in gallery

    Storm-relative radial velocity from observed level-III WSR-88D data for the 1.5° elevation scan of KTLX at (a) 0400, (b) 0420, and (c) 0440 UTC 9 May 2007. Mesovortices associated with the reported tornadoes are circled. Urban and county boundaries are shown.

  • View in gallery

    Probability-matched ensemble mean forecasts of reflectivity (dBZ, shaded) at model grid level 10 (approximately 2 km AGL) for (a)–(c) CNTL, (d)–(f) CNTL_LIN, and (g)–(i) NoMMP at (left to right) 0300, 0400, and 0500 UTC. Also shown is (j)–(l) reflectivity observed by the WSR-88D network, interpolated to the same model grid level. The center of the line-end vortex in the observations is indicated by the black marker in (j)–(l).

  • View in gallery

    Neighborhood ensemble probabilities (shaded) of reflectivity exceeding 25 dBZ, P(Z > 25 dBZ), at model grid level 10 (approximately 2 km above the surface) in an area surrounding the CASA domain at (left to right) 0300, 0400, and 0500 UTC for (a)–(c) CNTL at; (d)–(f) CNTL_LIN; and (g)–(i) NoMMP. The 25-dBZ radar reflectivity contours observed by the WSR-88Ds at the same time are in bold black contours.

  • View in gallery

    As in Fig. 6, but for spaghetti plots of the ensemble forecasts of the 25-dBZ radar reflectivity contours. Contours for individual ensemble members are shown as thin gray lines; those for the deterministic forecasts initialized from the ensemble mean at 0200 UTC are in thick gray lines. The 25-dBZ radar reflectivity contour observed by the WSR-88D network at the corresponding time is indicated by the thick black contour.

  • View in gallery

    As in Fig. 6, but for P(Z > 40 dBZ) and the 40-dBZ radar reflectivity contour.

  • View in gallery

    ROC skill score for 1-, 2-, and 3-h forecasts of radar reflectivity at the 25-dBZ threshold on vertical grid level k = 10 (slightly more than 2 km MSL) calculated over (a) the entire horizontal model domain and (b) the equitable threat score (ETS) verification subdomain as depicted by the black outline in Fig. 1.

  • View in gallery

    Domainwide histograms of reflectivity intensity in ensemble forecast experiment CNTL during (left to right) the 3-h forecast period. Shown are (a)–(d) WSR-88D observations interpolated to the model grid, (e)–(h) the ensemble mean, and (i)–(l) individual ensemble members normalized by the size of the ensemble. The vertical axis indicates the number of model grid volumes (in thousands) containing reflectivity of a given intensity.

  • View in gallery

    Ensemble mean convergence (s−1; shaded) at (a) 0300 and (b) 0400 UTC, as well as horizontal winds (barbs) and potential temperature (K; shaded) at (c) 0300 and (d) 0400 UTC in CNTL at the first model grid level above the surface.

  • View in gallery

    RMS innovation of radar reflectivity during the forecast period for ensemble forecasts (left) CNTL and (right) CNTL_LIN. The ensemble mean forecast is indicated by the thick, solid black line, while the probability-matched ensemble mean forecast is indicated by the dashed black line. The thin gray lines indicate innovation within individual ensemble members, with different shades of gray used for members using differing microphysical parameterization schemes.

  • View in gallery

    Ensemble-based forecast of P(low-level circulation with vertical vorticity ζ > 0.02 s−1 within 25 km of a point) for (left to right) 0400, 0420, and 0440 UTC: (a)–(c) CNTL, (d)–(f) NoMMP , and (g)–(i) NoCASA. The triangles indicate the reported locations of the tornadoes at (a),(d),(g) 0354 UTC, (b),(e),(h) 0426 UTC, and (c),(f),(i) 0443 UTC.

  • View in gallery

    Locations of significant (vertical vorticity ζ > 0.02 s−1), discernible, low-level (grid level 10, approximately 2 km above the surface) mesovortex centers for all ensemble members at 0400 UTC in experiments (a) CNTL, (b) NoMMP, and (c) NoCASA. Individual members are coded by microphysical type: Lin microphysics (L), WSM-6 microphysics (W), and NEM microphysics (N). The ensemble mean vortex location is marked EM. The location of the EF-1 tornado reported at 0354 UTC is marked by the black triangle.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 29 29 7
PDF Downloads 36 36 19

Ensemble Probabilistic Forecasts of a Tornadic Mesoscale Convective System from Ensemble Kalman Filter Analyses Using WSR-88D and CASA Radar Data

View More View Less
  • 1 School of Meteorology, and Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma
  • 2 Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma
© Get Permissions
Full access

Abstract

This study examines the ability of a storm-scale numerical weather prediction (NWP) model to predict precipitation and mesovortices within a tornadic mesoscale convective system that occurred over Oklahoma on 8–9 May 2007, when the model is initialized from ensemble Kalman filter (EnKF) analyses including data from four Engineering Research Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) X-band and five Weather Surveillance Radar-1988 Doppler (WSR-88D) S-band radars. Ensemble forecasts are performed and probabilistic forecast products generated, focusing on prediction of radar reflectivity (a proxy of quantitative precipitation) and mesovortices (an indication of tornado potential).

Assimilating data from both the CASA and WSR-88D radars for the ensemble and using a mixed-microphysics ensemble during data assimilation produces the best probabilistic mesovortex forecast. The use of multiple microphysics schemes within the ensemble aims to address at least partially the model physics uncertainty and effectively plays a role of flow-dependent inflation (in precipitation regions) during EnKF data assimilation. The ensemble predicts with high probability (approximately 0.65) the near-surface mesovortex associated with the first of three reported tornadoes. Though a bias toward stronger precipitation is noted in the ensemble forecasts, all experiments produce skillful probabilistic forecasts of radar reflectivity on a 0–3-h time scale as evaluated by multiple probabilistic verification metrics. These results suggest that both the inclusion of CASA radar data and use of a mixed-microphysics ensemble during EnKF data assimilation positively impact the skill of 2–3-h ensemble forecasts of mesovortices, despite having little impact on the quality of precipitation forecasts (analyzed in terms of predicted radar reflectivity), and are important steps toward an operational EnKF-based ensemble analysis and probabilistic forecast system to support convective-scale warn-on-forecast operations.

Corresponding author address: Nathan Snook, Center for Analysis and Prediction of Storms, University of Oklahoma, 120 David Boren Blvd., Room 4104, Norman, OK 73072. E-mail: nsnook@ou.edu

Abstract

This study examines the ability of a storm-scale numerical weather prediction (NWP) model to predict precipitation and mesovortices within a tornadic mesoscale convective system that occurred over Oklahoma on 8–9 May 2007, when the model is initialized from ensemble Kalman filter (EnKF) analyses including data from four Engineering Research Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) X-band and five Weather Surveillance Radar-1988 Doppler (WSR-88D) S-band radars. Ensemble forecasts are performed and probabilistic forecast products generated, focusing on prediction of radar reflectivity (a proxy of quantitative precipitation) and mesovortices (an indication of tornado potential).

Assimilating data from both the CASA and WSR-88D radars for the ensemble and using a mixed-microphysics ensemble during data assimilation produces the best probabilistic mesovortex forecast. The use of multiple microphysics schemes within the ensemble aims to address at least partially the model physics uncertainty and effectively plays a role of flow-dependent inflation (in precipitation regions) during EnKF data assimilation. The ensemble predicts with high probability (approximately 0.65) the near-surface mesovortex associated with the first of three reported tornadoes. Though a bias toward stronger precipitation is noted in the ensemble forecasts, all experiments produce skillful probabilistic forecasts of radar reflectivity on a 0–3-h time scale as evaluated by multiple probabilistic verification metrics. These results suggest that both the inclusion of CASA radar data and use of a mixed-microphysics ensemble during EnKF data assimilation positively impact the skill of 2–3-h ensemble forecasts of mesovortices, despite having little impact on the quality of precipitation forecasts (analyzed in terms of predicted radar reflectivity), and are important steps toward an operational EnKF-based ensemble analysis and probabilistic forecast system to support convective-scale warn-on-forecast operations.

Corresponding author address: Nathan Snook, Center for Analysis and Prediction of Storms, University of Oklahoma, 120 David Boren Blvd., Room 4104, Norman, OK 73072. E-mail: nsnook@ou.edu

1. Introduction

Since the inception of explicit numerical weather prediction (NWP) of severe convective storms (Lilly 1990), assimilation of Doppler weather radar data has been shown to be critical and often effective for initializing such model predictions (e.g., Sun et al. 1991; Sun and Crook 1998; Xue et al. 2003; Hu et al. 2006). Recent studies have produced promising results assimilating Doppler radar data for convective-scale NWP in real time and over large domains (e.g., Xue et al. 2008). The ensemble Kalman filter (EnKF) technique, initially developed by Evensen (1994, 2003), has been gaining popularity as an effective method of radar data assimilation for storm-scale NWP (e.g., Snyder and Zhang 2003; Dowell et al. 2004; Tong and Xue 2005b, 2008). Though EnKF is more computationally expensive than the three-dimensional variational data assimilation method (3DVAR) widely used operationally, it provides flow-dependent multivariate background error covariances and cross-covariances that 3DVAR cannot. Such cross-covariances are essential for radar data assimilation, because most state variables are not directly observed (Tong and Xue 2005a, 2008). Additional comments on the relative merits of various radar data assimilation methods including 3DVAR, 4DVAR, and EnKF for convective storm analysis can be found in Tong and Xue (2005a). As available computational power increases, it will soon become feasible to run a real-time convective-scale forecast system that assimilates data via EnKF (Zhang et al. 2009) and produces convective-scale ensemble forecasts (e.g., Xue et al. 2008).

One of the major goals of the National Weather Service (NWS) in the coming decade is to develop a warn-on-forecast paradigm for convective-scale severe weather warnings (e.g., tornado, severe thunderstorm, and flash flood warnings) to increase warning lead time beyond what is possible with nowcasting techniques alone. Such an increase in warning lead time would allow entities such as hospitals and stadiums sufficient time to respond in the event of a warning (Stensrud et al. 2009). To achieve this goal, reliable short-term (0–3 h) forecasts at the convective scale will be vital.

Because of the chaotic nature of the atmosphere, and inevitable errors in observations and NWP models, weather forecasts always contain uncertainty. No forecast is therefore complete without a description of its uncertainty (NRC 2006), which is often expressed in terms of forecast probability. Ensemble forecasting offers a practical way to provide a probabilistic forecast (Leith 1974). Global and regional ensemble forecasting has been operational for nearly two decades (e.g., Toth and Kalnay 1993; Houtekamer et al. 1996; Du et al. 2003; Bowler and Mylne 2009); by comparison, convective-scale ensemble forecasting is still in its infancy (Kong et al. 2006; Xue et al. 2011), though a few recent papers have sought to address the topic. Wandishin et al. (2010) use an idealized two-dimensional model to investigate the predictability of ensemble forecasts of mesoscale convective systems (MCSs), while Aksoy et al. (2010) used the Weather Research and Forecasting Model (WRF) to assimilate Doppler radar observations and perform idealized ensemble predictions of storms with both supercellular and linear convective modes. Stensrud and Gao (2010) assimilate radar data using 3DVAR and perform short-range ensemble forecasts of a supercell case. All three of these recent studies demonstrate the value of using ensembles for short-range convective NWP. Convective-scale weather poses a greater prediction challenge because of its intermittent nature, smaller spatial and temporal scale, higher nonlinearity, and often incomplete observation coverage; these challenges increase the forecast uncertainty, making probabilistic forecasting even more crucial (Stensrud et al. 2009; Xue et al. 2011).

While it is possible to obtain probabilistic forecast products from a single deterministic forecast by examining the occurrence of an event at the surrounding grid points (Theis et al. 2005; Schwartz et al. 2009), the capability of such a method is limited by inherent biases and errors in the deterministic forecast used. One such source of error is microphysical parameterization; Snook and Xue (2008) and Dawson (2009) found that the choice of microphysical scheme (and the parameter settings therein) strongly impacts the mode and intensity of the convection predicted. Furthermore, such probabilistic forecast products are inadequate in addressing uncertainty in the initial condition and dynamic error growth. Convective-scale errors generally grow very quickly (Lorenz 1969), greatly limiting the utility of a single deterministic forecast.

EnKF provides a set of analyses that, in principle, best characterize the analysis uncertainty, making them desirable initial conditions for ensemble forecasts. At the global scale, ensembles using EnKF analysis initial conditions have shown superior probabilistic forecasting performance compared to those using more traditional perturbation methods (Houtekamer et al. 2005; Hamill et al. 2011). EnKF methods have proven effective in generating dynamically consistent wind, temperature, and microphysical fields for convective storms when assimilating Doppler radar reflectivity and radial velocity data (e.g., Dowell et al. 2004; Tong 2006; Snook et al. 2011, hereafter SXJ11) but probabilistic forecasts at the convective scale using EnKF analyses have so far received limited attention. Zhang et al. (2010) is an example where convection-permitting-resolution ensemble forecasts of a tropical cyclone were initialized from global EnKF analyses.

This study details the results of ensemble forecasts produced from the EnKF analyses of the 8–9 May 2007 tornadic mesoscale convective system presented in SXJ11, with the goal of evaluating the suitability of EnKF analyses of radar data for initializing an ensemble for the short-term convective-scale probabilistic forecast goals of “warn-on-forecast” (Stensrud et al. 2009). We use a neighborhood ensemble probability (NEP) approach (Schwartz et al. 2010) to obtain probabilistic forecasts of radar reflectivity, and an object-based ensemble approach to obtain probabilistic forecasts of near-surface mesovortices. The value of assimilating X-band radar data by the Engineering Research Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) (McLaughlin et al. 2009) for improving the forecasts is evaluated, and the impact of microphysical parameterization during analysis and forecast periods is examined.

The remainder of this paper is organized as follows: section 2 discusses the methodology used in the ensemble forecasts, as well as techniques used to generate probabilistic forecast products. Section 3 examines the results of ensemble and probabilistic forecasts in terms of simulated radar reflectivity and low-level mesovortices and verifies them against observations. Finally, section 4 contains a summary of analysis and forecast results, as well as concluding remarks.

2. Forecast setup and verification methodology

Ensemble forecasts have become an indispensable part of convective-scale NWP in operational and research settings, providing valuable information about forecast sensitivity and uncertainty, as well as probabilistic forecast guidance (NRC 2006). In this study, 3-h storm-scale ensemble forecasts are examined for the tornadic mesoscale convective system that occurred over southwestern and central Oklahoma on 8–9 May 2007; this was the first tornadic event observed by the then newly deployed CASA Integrated Project 1 (IP-1) radar network (McLaughlin et al. 2009; Brotzge et al. 2010). During this event, a pronounced line-end vortex (LEV) developed within the MCS and moved through much of southwest-central Oklahoma, passing directly over the CASA IP-1 network. The MCS spawned two confirmed EF-1 tornadoes and one confirmed EF-0 tornado in central Oklahoma between 0354 and 0443 UTC, just north of the CASA radar network. Additional details regarding the 8–9 May 2007 MCS can be found in SXJ11.

To quantify the impact of the new CASA radar data in storm-scale NWP, SXJ11 assimilated data from four CASA IP-1 radars and five Weather Surveillance Radar-1988 Doppler (WSR-88D) radars using the Advanced Regional Prediction System (ARPS) EnKF system configured with full model physics and real terrain. The ensemble contained 40 members, and radar data are assimilated every 5 min for 1 h. While the assimilation of WSR-88D data alone produced a reasonably accurate analysis of the convective system, assimilating CASA data in addition to WSR-88D data was found to improve the resulting analysis. Use of a mixed-microphysics ensemble was found to alleviate underdispersion by increasing the ensemble spread.

In this study, the EnKF ensemble analyses produced by SXJ11, valid at 0200 UTC 9 May 2007, are used to initialize 3-h ensemble forecasts. The model setup and naming convention used for these forecast experiments follow those of SXJ11. The computational domain has 256 × 256 × 40 grid points with a 2-km horizontal grid spacing and stretched vertical grid spacing (see Fig. 1). The analyses used as initial conditions were produced by assimilating radar data at 5-min intervals for 1 h, and provide an initial model state that closely matches the observations (SXJ11); the ongoing MCS is represented relatively well, as shown in the comparison of the mean analyses of composite radar reflectivity in the ensemble to that observed by the WSR-88D network (Fig. 2). Results from three ensemble forecast experiments are presented here. The control experiment (CNTL) assimilates both CASA and WSR-88D radar data and contains 40 ARPS ensemble members; 16 of these use the Lin ice microphysical scheme (Lin et al. 1983), 16 use the WRF single-moment 6-class (WSM-6) ice microphysics scheme (Hong and Lim 2006), and the remaining 8 members use the NWP explicit microphysics (NEM) scheme developed by Schultz (1995). The second experiment, NoMMP, assimilates the same data as CNTL but uses the Lin microphysics scheme in all 40 of its ensemble members. The third experiment, NoCASA, uses the same ensemble setup as CNTL but does not assimilate CASA data.

Fig. 1.
Fig. 1.

Geographic extent of the model domain. Shading indicates surface elevation in meters MSL. The forecast verification subdomain used for skill score calculations in Fig. 8b is indicated by the black box in the northeastern portion of the forecast domain.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

Fig. 2.
Fig. 2.

Composite radar reflectivity (dBZ) of the ensemble mean analysis state at 0200 UTC 9 May 2007 for (a) CNTL, (b) NoMMP, and (c) NoCASA, from which the deterministic forecasts in Fig. 4 were launched; also shown is (d) composite radar reflectivity (dBZ) observed by WSR-88Ds KAMA, KDYX, KFWS, KLBB,, and KTLX at 0200 UTC 9 May 2007. The 30-km CASA radar range rings are included for reference. This figure is a reproduction of Fig. 4 of SXJ11.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

To isolate the impact of using a mixed-microphysics ensemble during the forecast period, two more ensemble forecast experiments are run in addition to the three mentioned above. Experiments CNTL_LIN and NoCASA_LIN are initialized from the CNTL and NoCASA initial conditions (respectively), but use a single-microphysics forecast ensemble consisting of 40 ARPS members using the Lin microphysics scheme, as in NoMMP. Though the number of microphysical species is the same in the Lin, WSM-6, and NEM microphysical schemes, the WSM-6 scheme uses graupel whereas the Lin and NEM schemes use hail. To solve this inconsistency, hail and graupel are treated as interchangeable when initializing a Lin forecast ensemble member from a WSM-6 member analysis in CNTL_LIN and NoCASA_LIN. A summary of all forecast experiments included in this study is provided in Table 1.

Table 1.

Summary of forecast experiments.

Table 1.

In all experiments, a reduced rain intercept parameter of 8 × 105 was used, consistent with Snook and Xue (2008), who found that reducing the rain intercept parameter yielded more realistic cold-pool structure. A timeline for these experiments is presented in Fig. 3. Lateral boundary conditions for all ensemble members are obtained from the National Centers for Environmental Prediction (NCEP) North American Mesoscale Model (NAM) 6-hourly analyses and intervening 3-h forecasts. Because of the relatively short forecast period and the use of a relatively large domain, the absence of boundary condition perturbations did not negatively impact ensemble data assimilation and prediction in the main regions of interest.

Fig. 3.
Fig. 3.

Forecast diagram detailing the analysis and forecast periods for experiments CNTL, NoMMP, and NoCASA.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

Forecast verification is performed for radar reflectivity at 0300, 0400, and 0500 UTC, and for low-level mesovortices at 0400, 0420, and 0440 UTC; the latter times correspond closely to tornado reports received during this event at 0354, 0426, and 0443 UTC (see section 2 of SXJ11). Given the 2-km horizontal grid spacing used, tornado-scale circulations cannot be resolved; therefore we focus on prediction of resolvable low-level circulations linked to the observed tornadoes, rather than on the tornadoes themselves. With the 2-km horizontal grid spacing used, the mesovortices (Trapp and Weisman 2003) that were present in this case can be resolved.

Because convective cells are highly localized, even small displacement errors in a storm-scale forecast can result in very low objective skill scores when verified on a point-by-point basis, even though the forecast being scored may still be quite valuable to researchers and operational meteorologists (Baldwin et al. 2001; Schwartz et al. 2009). To alleviate this problem, Schwartz et al. (2009) applied a probabilistic “neighborhood” approach following Roberts and Lean (2008), where the probability of an event (e.g., radar reflectivity > 40 dBZ; rainfall rate > 2.0 cm h−1; hail mixing ratio > 0) at a grid point is determined by conditions at all grid points within a given radius of influence r from that grid point; this collection of points composes the neighborhood for the selected grid point. In this study, as was done in Schwartz et al. (2010), the neighborhood is extended to include all grid points on the same model level within the radius of influence from every ensemble member. Thus, drawing from Schwartz et al. (2009, 2010), the forecast probability (Pi) of an event at the ith grid point of the ensemble forecast is defined by
e1
where N is the unique collection of all points composing the neighborhood for point i and Bj is the binary probability at the jth grid point of the neighborhood, defined to be 1 if the event was observed at that grid point and 0 if it was not. Schwartz et al. (2010) call Pi the neighborhood ensemble probability; further discussion can be found in that paper.
Mesovortices and other circulations cannot easily be treated as point variables, and are therefore not well-suited to an NEP method. Thus, for prediction of mesovortices, we instead apply an object-based ensemble verification approach. Significant low-level circulations are manually identified for each ensemble member in forecasts valid at 0400, 0420, and 0440 UTC. For a feature to count as a significant circulation, three criteria must be met: (i) vertical vorticity must exceed 0.02 s−1 at 2 km above ground level, (ii) discernable rotation must be present in the horizontal wind field at this level, and (iii) the feature must be located within a convective region with radar reflectivity exceeding 30 dBZ. These criteria were chosen to discriminate true mesovortices from other phenomena, such as shear zones occurring along outflow boundaries. The binary probability Bim for the ith model grid volume of the mth ensemble member is calculated such that Bim = 1 if the center of that grid volume lies within a predefined distance (in this study, 25 km) from a circulation center identified in the forecast for that ensemble member, and Bim = 0 otherwise. A purely ensemble-based probability results in
e2
where Nens is the number of members in the ensemble. In essence, Pi from Eq. (2) can be viewed as the predicted probability of a strong near-surface vortex being present within 25 km of a given point; this forecast methodology is analogous to that used operationally by the Storm Prediction Center in their Day-1 tornado, hail, and wind outlook products, which forecast the probability of an event occurring within a 25-mile radius of a given point (Edwards et al. 2002).

3. Forecast results and analysis

We begin by presenting the results of ensemble and probabilistic forecasts of radar reflectivity (Z) for CNTL, CNTL_LIN, and NoMMP. Radar reflectivity, closely linked to precipitation, is a field of meteorological interest that can be directly verified against WSR-88D radar observations over the entire area of the convective system. Ensemble and probabilistic forecasts of low-level vortices are then analyzed; near-surface mesovortices were closely collocated with the observed tornadoes in this event, as demonstrated by the proximity of rotational signatures in the KTLX storm-relative radial velocity observations (Fig. 4) to the tornadoes reported in association with them (SXJ11, their Fig. 1). Both the impact of assimilating CASA data and the use of a mixed-microphysics ensemble during the analysis and forecast periods are considered in evaluating the performance of the ensemble mesovortex forecasts.

Fig. 4.
Fig. 4.

Storm-relative radial velocity from observed level-III WSR-88D data for the 1.5° elevation scan of KTLX at (a) 0400, (b) 0420, and (c) 0440 UTC 9 May 2007. Mesovortices associated with the reported tornadoes are circled. Urban and county boundaries are shown.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

a. Probability-matched ensemble mean forecasts of radar reflectivity

In ensemble forecasting, particularly at the convective scale, averaging the individual ensemble members to produce ensemble mean fields for precipitation-related variables (such as radar reflectivity) often leads to a smoother distribution with increased geographic extent and a low bias in intensity. To counteract the low-bias tendency in the ensemble mean, it is often desirable to reassign the values of precipitation-related fields using values from the component ensemble members used to compute the mean; the result of this process (Ebert 2001) is the probability-matched (PM) mean. The PM mean is a useful tool for forecasters, producing a single “best-estimate” deterministic forecast; such ensemble mean products for precipitation fields often outperform most or all of the ensemble members used to produce them (Ebert 2001). The PM mean of Z is calculated at approximately 2 km above the surface for CNTL (Figs. 5a–c), CNTL_LIN (Figs. 5d–f), and NoMMP (Figs. 5g–i) at 1, 2, and 3 h of forecast time, and compared with Z as observed by the WSR-88D network and interpolated to the model grid at the corresponding times (Figs. 5j–l).

Fig. 5.
Fig. 5.

Probability-matched ensemble mean forecasts of reflectivity (dBZ, shaded) at model grid level 10 (approximately 2 km AGL) for (a)–(c) CNTL, (d)–(f) CNTL_LIN, and (g)–(i) NoMMP at (left to right) 0300, 0400, and 0500 UTC. Also shown is (j)–(l) reflectivity observed by the WSR-88D network, interpolated to the same model grid level. The center of the line-end vortex in the observations is indicated by the black marker in (j)–(l).

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

In all experiments, the dominant convective mode is predicted with reasonable success (Fig. 5); the forecast ensembles predict a large mesoscale convective system with a trailing convective line in a similar location to the corresponding features in the WSR-88D observations (Figs. 5j–l). There are noticeable errors in the PM mean forecasts, however; in particular, the leading convective line, extending southeast from the region of the LEV in the observations (Figs. 5j–l), is not captured in the forecast ensemble. In addition, the southern portion of the trailing convective line decays too quickly in the ensemble forecast at 0400 UTC and beyond in all forecast experiments (Figs. 5b,c,f–i). Because of the prevailing south and south-southwesterly flow during this case, the prediction of the southern portion of the trailing convective line is likely to have been affected by the flow conditions at the southern boundary of the model domain at the later times; the role of data assimilation tends to be diminished near the inflow boundaries.

The Lin microphysics scheme, used in all 40 members of the NoMMP experiment during both the analysis and forecast periods, produces greater precipitation coverage than the NEM and WSM-6 schemes for this case (not shown). In addition, the reduced spread among NoMMP ensemble members as compared to the CNTL ensemble (SXJ11) results in much less variation in position (and thus higher ensemble mean values) in the trailing line, resulting in a more intense trailing line in the PM mean (Figs. 5g–i). In contrast, CNTL used a mixed-microphysics ensemble containing members from the WSM-6 and NEM microphysical schemes, both of which favored solutions with fewer regions of light precipitation. Combined with greater variation among ensemble members, the result is a PM mean field with a weaker trailing line and less extensive regions of lighter precipitation in the northern portion of the system in CNTL (Figs. 5c,f,i).

b. Probabilistic predictions of radar reflectivity

Fast error growth and high levels of uncertainty from various sources make probabilistic forecast products potentially very valuable at the convective scale. Using an NEP method, as described in section 2, P(Z > 25 dBZ) (Fig. 6) is calculated at 0300, 0400, and 0500 UTC for CNTL, CNTL_LIN, and NoMMP, and compared with the corresponding reflectivity contour observed by the WSR-88D network. A neighborhood radius of 5 km was used, resulting in a neighborhood consisting of 21 points in each ensemble member; thus, for the 40-member ensemble used, the ensemblewide neighborhood consists of 840 forecast values.

Fig. 6.
Fig. 6.

Neighborhood ensemble probabilities (shaded) of reflectivity exceeding 25 dBZ, P(Z > 25 dBZ), at model grid level 10 (approximately 2 km above the surface) in an area surrounding the CASA domain at (left to right) 0300, 0400, and 0500 UTC for (a)–(c) CNTL at; (d)–(f) CNTL_LIN; and (g)–(i) NoMMP. The 25-dBZ radar reflectivity contours observed by the WSR-88Ds at the same time are in bold black contours.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

The observed 25-dBZ threshold (the thick contour in Fig. 6) encompasses large areas, including the entire region surrounding the LEV circulation and much of the convective line extending to the south and southwest; areas with a high NEP of reflectivity (exceeding 25 dBZ) closely match regions where observed reflectivity exceeds 25 dBZ over the northern portion of the system throughout the forecast period (Fig. 6), though the forecast precipitation region does not extend quite as far north and east as in observations at 0400 and 0500 UTC. The presence of the trailing convective line to the south and southwest is strongly indicated in the probabilistic forecasts, particularly in the NoMMP ensemble (Figs. 6g–i), though the decay of the southern portion of the line discussed in section 3a is evident in all experiments.

Particularly at the 25-dBZ threshold, the spread among ensemble members in the single-microphysics forecast ensemble of NoMMP (Figs. 7g–i) is considerably less than in the mixed-microphysics ensemble of CNTL (Figs. 7a–c), and also somewhat less than in CNTL_LIN (Figs. 7d–f), which uses the same microphysical makeup as NoMMP but begins from an initial condition obtained using a mixed-microphysics analysis ensemble. Both CNTL (Figs. 7a–c) and CNTL_LIN (Figs. 7d–f) exhibit greater variation among ensemble members; the difference is most prominent in the trailing convective line. Almost all members of NoMMP agree on a wide area of precipitation in excess of 25 dBZ in the trailing convective line at 0400 and 0500 UTC (Figs. 7h,i), giving rise to high probability there (Figs. 6h,i). In CNTL (Figs. 6b,c), many members predict the precipitation in the trailing line, but there is much greater variation in the location and extent of that precipitation than in NoMMP. Variation among ensemble members in CNTL_LIN (Figs. 7e,f) is greater than in NoMMP, but far less than in CNTL. The greater coverage of light precipitation in members using the Lin scheme and the reduced variation among ensemble members as a result of the use of a single-microphysics ensemble result in a large region of very high probability of Z > 25 dBZ associated with the trailing line in NoMMP, particularly at 0400 and 0500 UTC (Figs. 6h,i). In general, the use of a mixed-microphysics ensemble results in increased ensemble spread in a variety of model fields, particularly those closely related to precipitation processes, because of variation in hydrometeor type and distribution resulting from the different treatment of microphysical processes. Increased spread alone does not necessarily improve the derived probabilistic forecast products, however, as we will consider later in this section through skill score analyses. Yet it does seem to help better account for model uncertainty with precipitation physics during the EnKF analysis.

Fig. 7.
Fig. 7.

As in Fig. 6, but for spaghetti plots of the ensemble forecasts of the 25-dBZ radar reflectivity contours. Contours for individual ensemble members are shown as thin gray lines; those for the deterministic forecasts initialized from the ensemble mean at 0200 UTC are in thick gray lines. The 25-dBZ radar reflectivity contour observed by the WSR-88D network at the corresponding time is indicated by the thick black contour.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

Using the NEP method, P(Z > 40 dBZ) is also calculated for CNTL, CNTL_LIN, and NoMMP; the results are shown in Fig. 8. The 40-dBZ threshold is exceeded only in small, localized areas in the WSR-88D observations (Fig. 8), in individual convective elements within the core of the LEV, and the leading convective line. Near the LEV (cf. Figs. 5i–l) where observed radar reflectivity exceeds 40 dBZ, moderate–high NEP values are found (Fig. 8), although observed reflectivity exceeding 40 dBZ in the leading convective line is largely missed by the forecast ensembles. Particularly at later forecast times, all experiments strongly overestimate the geographic coverage of 40-dBZ echoes, due in part to spurious convection that develops near the CASA radar network (Figs. 8c,f,i). The causes of this spurious convection are considered in section 3c. The intensity of the trailing convective line extending southeast and south of the CASA domain into north-central Texas (Fig. 8) is also overestimated; moderate–high NEP values are present in areas where no reflectivity exceeding 40 dBZ was observed. The ensemble adequately forecasts the extent and location of regions of moderate precipitation within the system (Fig. 6), but a combination of position error, intensity error, and the development of spurious convection limits forecast skill for more intense convective cores (Fig. 8).

Fig. 8.
Fig. 8.

As in Fig. 6, but for P(Z > 40 dBZ) and the 40-dBZ radar reflectivity contour.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

To more quantitatively evaluate the skill of the NEP forecasts of radar reflectivity, we next examine their performance using the relative operating characteristic (ROC) skill score (RSS; Mason and Graham 1999). The RSS is derived from the area under the ROC curve (AROC; Mason and Graham 1999), and is given by . The RSS has a maximum value of 1.0 for a perfect probabilistic forecast, and a minimum of −1.0, with scores at or below 0.0 indicating forecasts with no skill. The ROC measures probability of detection and probability of false detection at varying probability thresholds (Mason and Graham 1999); thus, RSS is a summary statistic providing information on the ability of the probabilistic forecast system to correctly discriminate between events and nonevents. RSS is calculated for forecasts of reflectivity exceeding 25 dBZ at grid level 10, over the entire model domain (Fig. 9a) as well as over a verification subdomain (Fig. 9b) located within and downwind of the CASA radar network (see Fig. 1). In all experiments, the RSS is considerably higher over the verification subdomain (Fig. 9b) than over the entire domain (Fig. 9a), because of error associated with the trailing convective line south and southwest of the CASA network.

Fig. 9.
Fig. 9.

ROC skill score for 1-, 2-, and 3-h forecasts of radar reflectivity at the 25-dBZ threshold on vertical grid level k = 10 (slightly more than 2 km MSL) calculated over (a) the entire horizontal model domain and (b) the equitable threat score (ETS) verification subdomain as depicted by the black outline in Fig. 1.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

All forecast ensembles show considerable skill in forecasting reflectivity exceeding 25 dBZ. The 1-h ensemble forecasts (valid at 0300 UTC) show the greatest skill, with verification subdomain RSSs ranging from 0.84 to 0.89. RSSs steadily decrease between 0300 and 0500 UTC (Fig. 9), with domainwide values (Fig. 9a) remaining slightly lower than those over the verification subdomain (Fig. 9b). The minimum RSS of 0.40, obtained for NoCASA_LIN on the full domain at 0500 UTC, corresponds to an area under the ROC curve of 0.70; an ROC area of 0.70 is often considered to be the lower bound for a skillful forecast (Buizza 1997; Kong et al. 2011), thus all experiments produced skillful 1-, 2-, and 3-h NEP forecasts for regions of Z exceeding 25 dBZ.

NoMMP has the highest domainwide RSS (Fig. 9a) throughout the forecast period and the highest RSS within the verification subdomain (Fig. 9b) at 0300 and 0400 UTC; at 0500 UTC, however, NoMMP actually has the lowest RSS in the subdomain, while CNTL_LIN has the highest. For this case, ensemble members using Lin microphysics showed, on average, slightly better agreement with observed Z than members using WSM-6 or NEM microphysics. When ROC skill scores are calculated for three subensembles within CNTL, grouped by the microphysics scheme used, the Lin subensemble produces the highest RSS, while the NEM subensemble produces the lowest (not shown). Similarly, within the verification subdomain, RSSs decrease more slowly with time for CNTL_LIN and NoCASA_LIN than for their mixed-microphysics counterparts CNTL and NoCASA (Fig. 9b). The slightly improved RSS performance in CNTL_LIN and NoCASA_LIN at later times appears to be in part due to slightly faster movement of the trailing convective line, in better agreement with observations. These results suggest a positive impact when using a mixed-microphysics ensemble during the assimilation period but an improved forecast error trend when using a Lin-only ensemble during the subsequent forecast, at least for this case. The difference in the error trend is especially notable at longer forecast ranges when the impact of the initial condition is reduced relative to the impact of the forecast model. This is believed to be due to the relatively better performance of the Lin scheme, especially when compared to the simplified NEM scheme.

When the ensemble forecasts are evaluated using the Brier score (Brier 1950) (not shown), another metric commonly used in probabilistic forecast evaluation, the conclusions drawn from verification using the RSS remain valid. Brier scores for CNTL_LIN and NoCASA_LIN deteriorate more slowly with time than those of their mixed-microphysics counterparts, CNTL and NoCASA, a result that matches the improved error trend of the single-microphysics forecast ensembles seen in verification using the RSS. Also, as with the RSS, NoMMP initially yields a good Brier score compared to the ensembles that used mixed microphysics during data assimilation, but exhibits the fastest deterioration of Brier score during the forecast period (and, by 0500 UTC, the worst Brier scores of any experiment).

c. Prominent biases and errors within the ensemble forecasts

During the discussion of the NEP forecasts of radar reflectivity exceeding 40 dBZ (Fig. 8), we noted that the ensemble forecasts predict high probabilities of reflectivity exceeding 40 dBZ in regions where no 40-dBZ reflectivity values were observed, particularly at 0400 and 0500 UTC. To more closely examine biases in reflectivity within the ensemble forecasts, we construct domainwide histograms of radar reflectivity each hour from 0200 to 0500 UTC in the ensemble mean and ensemble member forecasts of CNTL, and compare them to histograms constructed from radar reflectivity observed by the WSR-88D network and interpolated to the model grid. Bins are placed at intervals of 1 dBZ between 15 and 65 dBZ, and histograms constructed using the individual ensemble members are normalized by the size of the ensemble. The resulting histograms are shown in Fig. 10.

Fig. 10.
Fig. 10.

Domainwide histograms of reflectivity intensity in ensemble forecast experiment CNTL during (left to right) the 3-h forecast period. Shown are (a)–(d) WSR-88D observations interpolated to the model grid, (e)–(h) the ensemble mean, and (i)–(l) individual ensemble members normalized by the size of the ensemble. The vertical axis indicates the number of model grid volumes (in thousands) containing reflectivity of a given intensity.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

Two prominent biases are evident in the histograms of Z for both the ensemble mean and the ensemble members: an underprediction (low bias) of weak-precipitation (<25 dBZ) regions and an overprediction (high bias) of areas of intense precipitation (>40 dBZ) (Fig. 10). At the initial time (0200 UTC), only the underprediction of low Z is present in the ensemble members and the ensemble mean; the histograms match observations well for Z greater than approximately 25 dBZ (Fig. 10). By 0300 UTC both biases are present in both the ensemble mean and the ensemble members; the magnitude of these biases remains relatively constant from 0300 to 0500 UTC (Figs. 10f–h, j–l).

Both the low bias in weak precipitation and the high bias in strong precipitation are smaller in magnitude for the ensemble mean than for the individual ensemble members at and after 0300 UTC (Figs. 10f–h, j–l). The primary sources of these differences are smoothing and decreased intensity of Z in the ensemble mean due to differences in the position of small-scale reflectivity features among individual ensemble members. While this smoothing leads to a distribution of Z that agrees more closely with observations in this case, such smoothing is not universally desirable; for example, in the absence of the high bias in intense precipitation seen in the ensemble members in this case, the smoothing would degrade, not improve, the distribution of Z in the ensemble mean.

In addition to the two biases identified above, a third bias is also evident in the histograms of Fig. 10: a low bias in total histogram population (i.e., the total number of gridcell volumes having radar reflectivity values ≥ 15 dBZ) in the ensemble forecast compared to the observations. This bias is present in both the ensemble mean (Figs. 10e–h) and the individual ensemble members (Figs. 10i–l), but is more prominent in the ensemble members. Because a low bias in total histogram population corresponds to smaller spatial coverage, the low bias is mitigated in the ensemble mean by the spatial smoothing inherent in the ensemble mean. This low bias results largely from the low bias of reflectivity of less than 30 dBZ in the ensemble, and appears to be a result of underprediction of the extent of stratiform precipitation within the system (see Fig. 6).

The high bias in intense precipitation observed in the ensemble can be in part attributed to spurious convection that developed in and near the CASA radar network, as noted in section 3a. To provide additional insight into the source of this spurious convection, we calculate ensemble mean horizontal wind convergence fields at the first model level above ground (Figs. 11a,b) and show them together with potential temperature and horizontal winds at the same level (Figs. 11c,d) for CNTL at 0300 and 0400 UTC (Fig. 11). In the ensemble, the cold pool in the wake of the MCS (cf. Fig. 5) is relatively weak, with temperatures at and near the surface under the MCS only around 2–3 K cooler than the surrounding area (Figs. 11c,d). By comparison, many Oklahoma mesonet sites in southwestern Oklahoma recorded temperature drops of around 4 K during the passage of the MCS (not shown). In addition, particularly at 0300 UTC (Fig. 11a), the strongest convergence near the surface occurs behind the MCS, in and near the CASA domain (Fig. 11c), where strong near-surface southeasterly and easterly flow upwind of the CASA domain transitions to weaker, more directionally varying flow within (and to the northwest of) the CASA domain (Fig. 11). The combination of low-level convergence and relatively warm, buoyant air in the wake of the MCS seems to have contributed to the development of the spurious convection in this region in the model between 0300 and 0500 UTC.

Fig. 11.
Fig. 11.

Ensemble mean convergence (s−1; shaded) at (a) 0300 and (b) 0400 UTC, as well as horizontal winds (barbs) and potential temperature (K; shaded) at (c) 0300 and (d) 0400 UTC in CNTL at the first model grid level above the surface.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

d. Impact of microphysics on ensemble reflectivity forecasts

To examine the impact of model microphysics during the ensemble forecasts, we calculate and compare the RMS innovation of radar reflectivity (Z) for ensemble forecast experiments CNTL and CNTL_LIN. As discussed in section 2, the CNTL and CNTL_LIN ensembles start from the same initial conditions, but CNTL uses a mixed-microphysics ensemble, while CNTL_LIN uses a single-microphysics ensemble consisting only of Lin microphysics members. Innovation is calculated using all grid volumes where the reflectivity observed by the WSR-88D network (interpolated to the model grid) exceeds 15 dBZ; this analysis technique is similar to that used in Aksoy et al. (2010). Innovation values for each individual ensemble member, as well as the ensemble mean and PM ensemble mean, are shown at 1, 2, and 3 h of forecast time (0300, 0400, and 0500 UTC, respectively) in Fig. 12.

Fig. 12.
Fig. 12.

RMS innovation of radar reflectivity during the forecast period for ensemble forecasts (left) CNTL and (right) CNTL_LIN. The ensemble mean forecast is indicated by the thick, solid black line, while the probability-matched ensemble mean forecast is indicated by the dashed black line. The thin gray lines indicate innovation within individual ensemble members, with different shades of gray used for members using differing microphysical parameterization schemes.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

Both CNTL and CNTL_LIN exhibit similar evolutions of RMS innovation of Z for the ensemble mean and PM mean forecasts. The ensemble mean consistently outperforms the PM mean, as well as most individual ensemble members (Fig. 12). This result is in agreement with Aksoy et al. (2010), whose ensemble mean RMS innovation of Z was also lower than most of their ensemble members. The relatively good performance of the ensemble mean can be attributed to the high bias in the reflectivity forecast (Fig. 10), discussed in section 3b, since position differences in the strongest reflectivity cores between individual members give an ensemble mean Z field that is smoother and contains lower reflectivity values than the individual members. The PM mean, though it contains the same spatial structure as the ensemble mean, has the same high bias as the individual ensemble members. Because the ensemble mean consistently outperforms the PM mean, we can conclude that it is the absence of the high bias, rather than improved spatial structure of the Z field, that results in lower RMS innovation of Z in the ensemble mean.

In the CNTL ensemble, the individual ensemble members exhibit a trimodal distribution, grouped into three clusters segregated by the microphysical scheme used in the model. The cluster of members using the Lin microphysical scheme has the lowest RMS innovation followed by the cluster of members using WSM-6 microphysics, and the cluster using NEM microphysics has the highest RMS innovation values. The strong clustering in CNTL indicates that error associated with the microphysical parameterization is a dominant factor in model error in Z during the ensemble forecast; in CNTL_LIN, where all members used the Lin microphysical scheme, the ensemble members have a unimodal distribution. Though the increased ensemble dispersion of CNTL is desirable, ensemble dispersion could also be increased using other methods, such as perturbed boundary conditions, perturbations within a microphysical scheme, and the use of different spread-maintenance techniques during the assimilation period; such methods will be a subject for future work. Because the microphysical parameterization appears to be a dominant source of error in the forecasts, using a more sophisticated two- or three-moment microphysical scheme might also be desirable to reduce overall RMS error in the ensemble; this too could be a subject for future study.

e. Ensemble and probabilistic forecasts of mesovortices

Forecast ensemble members of CNTL, NoMMP, and NoCASA were manually examined at 0400, 0420, and 0440 UTC to identify significant low-level vortices, as outlined in section 2. Such low-level vortices are considered objects for the purpose of verification. Equation (2) was then applied to generate forecasts of the probability of a significant (vertical vorticity ζ > 0.02 s−1) low-level vortex being present within 25 km of a point. The results of this analysis are presented in Fig. 13; the probabilities thus calculated are shown at 0400, 0420, and 0440 UTC for CNTL (Figs. 13a–c), NoMMP (Figs. 13d–f), and NoCASA (Figs. 13g–i), along with the locations of reported tornadoes (which were collocated with their parent mesovortices).

Fig. 13.
Fig. 13.

Ensemble-based forecast of P(low-level circulation with vertical vorticity ζ > 0.02 s−1 within 25 km of a point) for (left to right) 0400, 0420, and 0440 UTC: (a)–(c) CNTL, (d)–(f) NoMMP , and (g)–(i) NoCASA. The triangles indicate the reported locations of the tornadoes at (a),(d),(g) 0354 UTC, (b),(e),(h) 0426 UTC, and (c),(f),(i) 0443 UTC.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

All three forecast ensembles predict near-surface vortices in the vicinity of the reported tornadic activity at 0400, 0420, and 0440 UTC (Fig. 13). At 0400 and 0420 UTC, the probability field of CNTL exhibits a tight concentration of the highest probability values close to the reported tornado location (Figs. 13a,b). At 0400 UTC, the maximum near-surface vortex probability for CNTL of 0.65 (Fig. 13a) is located within 3 km of the reported tornado, and its probability field is tightly concentrated around the location of the observed tornado. In NoMMP and NoCASA (Figs. 13d,g), maximum probabilities are located approximately 10 and 20 km, respectively, from the reported tornado location. NoCASA and NoMMP forecast probabilities are only 0.43 and 0.35 (respectively) at the reported tornado location at 0400 UTC, and, especially in NoMMP (Fig. 13d), have relatively diffuse probability distributions with lower maxima. In NoMMP, this difference results from a wider spread of vortex location predictions seen within the single-microphysics ensemble. The only difference between NoCASA and CNTL, however, was the absence or presence of CASA radar data during the assimilation period, suggesting that assimilating CASA data positively impacts the prediction of low-level vortex features, yielding a higher maximum probability prediction at 0400 UTC in the vicinity of the observed tornado. This finding is consistent with that of Schenkman et al. (2011), where low-level radial velocity data from CASA radars were found to improve the LEV forecast.

The results at 0420 UTC (Figs. 13b,e,h) are similar to those at 0400 UTC: CNTL (Fig. 13b) produces the highest maximum probability (between 0.4 and 0.5) and exhibits a probability field concentrated close to the reported tornado location. NoCASA (Fig. 13h) and NoMMP (Fig. 13e) predict lower probabilities (approximately 0.2 and 0.1, respectively) of a significant low-level vortex being present in the vicinity of the observed tornado. The probability in the vicinity of the observed tornado is lower in all three experiments at 0420 UTC than at 0400 UTC. At 0440 UTC (Figs. 13g–i), CNTL and NoCASA both feature probability fields with the highest predicted probabilities in close proximity to the observed tornado. Unlike at 0400 and 0420 UTC, the probability near the reported tornado location is actually slightly higher in NoCASA than in CNTL. NoMMP performs poorly at 0440 UTC (Fig. 13h), predicting generally low probability of significant vortices, with the highest probabilities located several tens of kilometers away from the reported tornado. Because of the small size of the CASA domain and increasing impact of model factors (such as microphysical parameterization) as the forecast period proceeds, the greatest impact of CASA data from the initial condition of the ensemble would be expected at shorter forecast times, consistent with the results shown in Fig. 13.

One issue that arises when considering the prediction of tornadic mesovortices is a question of the limits of predictability for these features. Smaller features within atmospheric flows tend to exhibit error growth on shorter time scales (Lorenz 1969), and indeed, the tornadoes observed during this case formed and decayed with time scales of less than an hour. The tornadic mesovortices within the 8–9 May 2007 MCS, however, were forced by larger-scale features within the MCS that spawned them. MCSs often exhibit predictability on a significantly longer time scale (Carbone et al. 2002), therefore we believe that it is reasonable to consider ensemble predictions of the tornadic mesovortices within the MCS at time scales of 2–3 h, because of this larger-scale forcing. We do, however, note that it is impossible for the model to distinguish between tornadic and nontornadic mesovortices using a horizontal grid spacing of 2 km; probabilistic prediction of the mesovortices at this resolution can only suggest tornado potential. Explicit prediction of the timing of tornadoes would require a much higher model resolution.

We further examine the role of microphysics in vortex prediction by plotting locations of low-level vortex centers in individual ensemble members at 0400 UTC, along with the ensemble mean vortex location and the location of the EF-1 Minco, Oklahoma, tornado (reported to have begun at 0354 UTC), for CNTL (Fig. 14a), NoMMP (Fig. 14b), and NoCASA (Fig. 14c). Each low-level vortex center is marked by a letter corresponding to the microphysical scheme used in the member that produced it (“L” for Lin, “W” for WSM-6, and “N” for NEM). CNTL (Fig. 14a) exhibits the closest clustering of predicted low-level vortices around the location of the observed tornado; 26 of 40 (65%) ensemble members predict a low-level vortex center within 25 km. These 26 members include 12 of the 16 Lin members and 11 of the 16 WSM-6 members, but only 3 of the 8 NEM members. In NoCASA (Fig. 14c), 17 of 40 (43%) members predict vortex centers within 25 km of the observed tornado location; these 17 members consist of 10 Lin, 5 WSM-6, and 2 NEM members. In CNTL and NoCASA, Lin ensemble members have the least error in vortex location, while NEM members have the most; many NEM members are outliers (see Figs. 14a,c) or fail to produce significant low-level vortices. In the NoMMP ensemble (Fig. 14b), predicted vortex locations vary substantially among members; only 14 members (35%) predict low-level vortices within 25 km of the observed tornado location, underscoring the positive impact of a mixed-microphysics forecast ensemble in mesovortex prediction.

Fig. 14.
Fig. 14.

Locations of significant (vertical vorticity ζ > 0.02 s−1), discernible, low-level (grid level 10, approximately 2 km above the surface) mesovortex centers for all ensemble members at 0400 UTC in experiments (a) CNTL, (b) NoMMP, and (c) NoCASA. Individual members are coded by microphysical type: Lin microphysics (L), WSM-6 microphysics (W), and NEM microphysics (N). The ensemble mean vortex location is marked EM. The location of the EF-1 tornado reported at 0354 UTC is marked by the black triangle.

Citation: Monthly Weather Review 140, 7; 10.1175/MWR-D-11-00117.1

Despite differences in the distribution of individual members, the forecast ensemble mean low-level vortex locations (marked by “EM” in Figs. 14a–c) were similar in all three experiments. In each case the ensemble mean location was located slightly to the northwest of the observed tornado location, with the difference in position ranging from approximately 12 km in CNTL (Fig. 14a) to 18 km in NoCASA (Fig. 14c). This result underscores the importance of probabilistic information on forecast uncertainty; while CNTL produced a much sharper probabilistic forecast of the low-level vortex than NoMMP, ensemble mean vortex locations differed by only about 3 km, or 1.5 grid intervals (Figs. 14a,b), between the two experiments. Also, NoCASA forecasted a higher vortex probability with more individual members clustered around the true vortex location than NoMMP but its ensemble mean vortex location had a larger position error (Figs. 14b,c). Probabilistic information is important in assessing the reliability of these forecasts; an ensemble mean or single deterministic forecast cannot provide such information.

4. Discussion and summary

In this paper, we perform 3-h ensemble forecasts for the tornadic MCS of 8–9 May 2007 that occurred over northern Texas and southern and central Oklahoma, starting from ensemble Kalman filter analyses produced by assimilating CASA and WSR-88D radar data. We examine the impact of assimilating CASA (in addition to WSR-88D) radar data on the forecast, and the impact of the model microphysics during both the assimilation and forecast periods. The choice of microphysical scheme made a significant impact on forecast evolution for predictions of radar reflectivity and mesovortices. Ensemble members using the Lin or WSM-6 schemes performed considerably better in the prediction of low-level mesovortex locations than members using the NEM scheme, while members using the Lin microphysical scheme were found to perform best in terms of RMS innovation for prediction of radar reflectivity.

From the ensemble forecast experiments, probabilistic predictions for radar reflectivity and low-level circulations are obtained. A neighborhood ensemble probability approach (Schwartz et al. 2010) is applied to generate 60–180-min probabilistic forecasts for radar reflectivity, and an object-oriented ensemble forecast approach is used to generate 120–160-min probabilistic forecasts of low-level vortex location. Both the assimilation of CASA data and the use of a mixed-microphysics ensemble during the EnKF data assimilation cycles have a positive impact on forecasts of mesovortices.

All ensemble forecast experiments predict the dominant convective mode during the forecast period reasonably well, indicating an MCS with an embedded LEV, and a trailing convective line extending to the south, though the southern end of the convective line decays too quickly in the forecasts as compared to the observations. Two prominent biases are present in the ensemble member and ensemble mean forecasts of radar reflectivity: a low bias for light (<25 dBZ) precipitation, and a high bias for intense (>40 dBZ) precipitation. Microphysical parameterization is found to be a dominant factor in model error in reflectivity forecasts. When a single-microphysics scheme is used, the innovation of radar reflectivity within the forecast ensemble exhibits a unimodal distribution, but when a mixed-microphysics scheme containing members of three different single-moment microphysics schemes is used, a trimodal distribution results, segregated by microphysical scheme.

The ensemble forecasts predict the location of tornadic mesovortices between 120 and 160 min of forecast time with varying degrees of success. The CNTL ensemble performs particularly well, predicting a localized region of high (maximum of 0.65) neighborhood ensemble probability of a significant low-level vortex in close proximity to the observed mesovortex that spawned the 0354 UTC EF-1 Minco tornado. NoCASA and NoMMP predict comparatively diffuse probability fields with lower probability values.

The results of this study are encouraging with regard to development of a future warn-on-forecast severe weather warning system (Stensrud et al. 2009), demonstrating that, at least for the case studied, it is possible to provide useful probabilistic predictions of convective hazards, including areas of heavy precipitation and tornadic mesovortices, with lead times of 1–3 h. Significant challenges do remain; the results of this study indicate that controlling model bias and maintaining appropriate ensemble spread will be particularly important in probabilistic predictions of this kind. In addition, the robustness of such probabilistic predictions still needs to be tested and calibrated over a large number of cases including a wide range of tornadic and nontornadic convective storms. We also note that objective identification and verification of tornado-scale vortices is nontrivial (Potvin et al. 2009). At present, the high computational cost of performing such high-resolution predictions in real time remains a barrier to operational implementation, which will need to be addressed with algorithm and code optimizations and access to petascale computing systems. Further improvement in the prediction model and the inclusion of other available observations are also important; such work is ongoing with this and other cases. Despite the use of a single case in this study, we believe such careful case studies represent an essential first step toward full systematic testing and operational implementation.

Acknowledgments

This work was primarily supported by NSF Grant EEC-0313747 as part of the ERC CASA program. The second author was also supported by NSF Grants AGS-0802888 and AGS-0738370, AGS-0608168, AGS-0750790, AGS-0941491, and OCI-0905040. The first author would like to personally acknowledge Daniel Dawson and Yunheng Wang for assistance in troubleshooting ARPS, and Alex Schenkman and Robin Tanamachi for helpful discussions regarding convective forecasting. We thank three anonymous reviewers for their input, which resulted in an improved manuscript. Computing was performed at the OU Supercomputing Center for Education & Research (OSCER) at the University of Oklahoma (OU) and at the Kraken supercomputer of the National Institute for Computational Sciences (NICS).

REFERENCES

  • Aksoy, A., , D. C. Dowell, , and C. Snyder, 2010: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part II: Short-range ensemble forecasts. Mon. Wea. Rev., 138, 12731292.

    • Search Google Scholar
    • Export Citation
  • Baldwin, M. E., , S. Lakshmivarahan, , and J. S. Kain, 2001: Verification of mesoscale features in NWP models. Preprints, Ninth Conf. on Mesoscale Processes, Fort Lauderdale, FL, Amer. Meteor. Soc., 255–257.

  • Bowler, N. E., , and K. R. Mylne, 2009: Ensemble transform Kalman filter perturbations for a regional ensemble prediction system. Quart. J. Roy. Meteor. Soc., 135, 757766.

    • Search Google Scholar
    • Export Citation
  • Brier, G. W., 1950: Verification of weather forecasts expressed in terms of probability. Mon. Wea. Rev., 78, 13.

  • Brotzge, J., , K. Hondle, , B. Philips, , L. Lemon, , E. Bass, , D. Rude, , and D. Andra Jr., 2010: Evaluation of distributed collaborative adaptive sensing for detection of low-level circulations and implications for severe weather operations. Wea. Forecasting, 25, 173189.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., 1997: Potential forecast skill of ensemble prediction and spread and skill distributions of the ECMWF ensemble prediction system. Mon. Wea. Rev., 125, 99119.

    • Search Google Scholar
    • Export Citation
  • Carbone, R. E., , J. D. Tuttle, , D. A. Ahijevych, , and S. B. Trier, 2002: Inferences of predictability associated with warm season precipitation episodes. J. Atmos. Sci., 59, 20332056.

    • Search Google Scholar
    • Export Citation
  • Dawson, D. T., II, 2009: Impacts of single- and multi-moment microphysics on numerical simulations of supercells and tornadoes of the 3 May 1999 Oklahoma tornado outbreak. Ph.D. dissertation, School of Meteorology, University of Oklahoma, 173 pp.

  • Dowell, D. C., , L. J. Wicker, , and D. J. Stensrud, 2004: High resolution analyses of the 8 May 2003 Oklahoma City storm. Part II: EnKF data assimilation and forecast experiments. Preprints, 22nd Conf. on Severe Local Storms, Hyannis, MA, Amer. Meteor. Soc., 12.5. [Available online at http://ams.confex.com/ams/pdfpapers/81393.pdf.]

  • Du, J., , G. DiMego, , S. Tracton, , and B. Zhou, 2003: NCEP short-range ensemble forecasting (SREF) system: Multi-IC, multi-model, and multi-physics approach. Research Activities in Atmospheric and Oceanic Modelling, Rep. 33, WMO Tech. Doc. 1161, J. Cote, Ed., CAS/JSC Working Group Numerical Experimentation (WGNE), 5.09–5.10.

  • Ebert, E. E., 2001: Ability of a poor man’s ensemble to predict the probability and distribution of precipitation. Mon. Wea. Rev., 129, 24612480.

    • Search Google Scholar
    • Export Citation
  • Edwards, R., , S. F. Corfidi, , R. L. Thompson, , J. S. Evans, , J. P. Craven, , J. P. Racy, , D. W. McCarthy, , and M. D. Vescio, 2002: Storm Prediction Center forecasting issues related to the 3 May 1999 tornado outbreak. Wea. Forecasting, 17, 544558.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53, 343367.

  • Hamill, T. M., , J. S. Whitaker, , M. Fiorino, , and S. G. Benjamin, 2011: Global ensemble predictions of 2009’s tropical cyclones initialized with an ensemble Kalman filter. Mon. Wea. Rev., 139, 668688.

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

  • Houtekamer, P. L., , L. Lefaivre, , J. Derome, , H. Ritchie, , and H. L. Mitchell, 1996: A system simulation approach to ensemble prediction. Mon. Wea. Rev., 124, 12251242.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , H. L. Mitchell, , G. Pellerin, , M. Buehner, , M. Charron, , L. Spacek, , and B. Hansen, 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133, 604620.

    • Search Google Scholar
    • Export Citation
  • Hu, M., , M. Xue, , and K. Brewster, 2006: 3DVAR and cloud analysis with WSR-88D level-II data for the prediction of Fort Worth tornadic thunderstorms. Part I: Cloud analysis and its impact. Mon. Wea. Rev., 134, 675698.

    • Search Google Scholar
    • Export Citation
  • Kong, F., , K. K. Droegemeier, , and N. L. Hickmon, 2006: Multi-resolution ensemble forecasts of an observed tornadic thunderstorm system. Part I: Comparison of coarse- and fine-grid experiments. Mon. Wea. Rev., 134, 807833.

    • Search Google Scholar
    • Export Citation
  • Kong, F., and Coauthors, 2011: Evaluation of CAPS multi-model storm-scale ensemble forecast for the NOAA HWT 2010 Spring Experiment. Preprints, 24th Conf. on Weather Forecasting/20th Conf. on Numerical Weather Prediction, Seattle, WA, Amer. Meteor. Soc., 457. [Available online at http://ams.confex.com/ams/91Annual/webprogram/Paper181680.html.]

  • Leith, C. E., 1974: Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev., 102, 409418.

  • Lilly, D. K., 1990: Numerical prediction of thunderstorms—Has its time come? Quart. J. Roy. Meteor. Soc., 116, 779798.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1969: The predictability of a flow which possesses many scales of motion. Tellus, 21, 289307.

  • Mason, S. J., , and N. E. Graham, 1999: Conditional probabilities, relative operating characteristics, and relative operating levels. Wea. Forecasting, 14, 713725.

    • Search Google Scholar
    • Export Citation
  • McLaughlin, D., and Coauthors, 2009: Short-wavelength technology and the potential for distributed networks of small radar systems. Bull. Amer. Meteor. Soc., 90, 17971817.

    • Search Google Scholar
    • Export Citation
  • NRC, 2006: Completing the Forecast: Characterizing and Communicating Uncertainty for Better Decisions Using Weather and Climate Forecasts. National Academies Press, 112 pp.

  • Potvin, C. K., , A. Shapiro, , T.-Y. Yu, , J. Gao, , and M. Xue, 2009: Using a low-order model to detect and characterize tornadoes in multiple-Doppler radar data. Mon. Wea. Rev., 137, 12301249.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Schenkman, A., , M. Xue, , A. Shapiro, , K. Brewster, , and J. Gao, 2011: The analysis and prediction of the 8-9 May 2007 Oklahoma tornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVAR. Mon. Wea. Rev., 139, 224246.

    • Search Google Scholar
    • Export Citation
  • Schultz, P., 1995: An explicit cloud physics parameterization for operational numerical weather prediction. Mon. Wea. Rev., 123, 33313343.

    • Search Google Scholar
    • Export Citation
  • Schwartz, C. S., and Coauthors, 2009: Optimizing probabilistic high-resolution ensemble guidance for hydrologic prediction. Preprints, 23rd Conf. on Hydrology, Phoenix, AZ, Amer. Meteor. Soc., 9.4. [Available online at http://ams.confex.com/ams/pdfpapers/147171.pdf.]

  • Schwartz, C. S., and Coauthors, 2010: Toward improved convection-allowing ensembles: Model physics sensitivities and optimizing probabilistic guidance with small ensemble membership. Wea. Forecasting, 25, 263280.

    • Search Google Scholar
    • Export Citation
  • Snook, N., , and M. Xue, 2008: Effects of microphysical drop size distribution on tornadogenesis in supercell thunderstorms. Geophys. Res. Lett., 35, L24803, doi:10.1029/2008GL035866.

    • Search Google Scholar
    • Export Citation
  • Snook, N., , M. Xue, , and Y. Jung, 2011: Analysis of a tornadic meoscale convective vortex based on ensemble Kalman filter assimilation of CASA X-band and WSR-88D radar data. Mon. Wea. Rev., 139, 34463468.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., , and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 16631677.

    • Search Google Scholar
    • Export Citation
  • Stensrud, D. J., , and J. Gao, 2010: Importance of horizontally inhomogeneous environmental initial conditions to ensemble storm-scale radar data assimilation and very short-range forecasts. Mon. Wea. Rev., 138, 12501272.

    • Search Google Scholar
    • Export Citation
  • Stensrud, D. J., and Coauthors, 2009: Convective-scale warn-on-forecast system: A vision for 2020. Bull. Amer. Meteor. Soc., 90, 14871499.

    • Search Google Scholar
    • Export Citation
  • Sun, J., , and N. A. Crook, 1998: Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part II: Retrieval experiments of an observed Florida convective storm. J. Atmos. Sci., 55, 835852.

    • Search Google Scholar
    • Export Citation
  • Sun, J., , D. W. Flicker, , and D. K. Lilly, 1991: Recovery of three-dimensional wind and temperature fields from simulated single-Doppler radar data. J. Atmos. Sci., 48, 876890.

    • Search Google Scholar
    • Export Citation
  • Theis, S. E., , A. Hense, , and U. Damrath, 2005: Probabilistic precipitation forecasts from a deterministic model: A pragmatic approach. Meteor. Appl., 12, 257268.

    • Search Google Scholar
    • Export Citation
  • Tong, M., 2006: Ensemble Kalman filter assimilation of Doppler radar data for the initialization and prediction of convective storms. Ph.D. dissertation, School of Meteorology, University of Oklahoma, 243 pp.

  • Tong, M., , and M. Xue, 2005a: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments. Mon. Wea. Rev., 133, 17891807.

    • Search Google Scholar
    • Export Citation
  • Tong, M., , and M. Xue, 2005b: Simultaneous retrieval of microphysical parameters and atmospheric state variables with radar data and ensemble Kalman filter method. Preprints, 17th Conf. on Numerical Weather Prediction, Washington, DC, Amer. Meteor. Soc., P1.30. [Available online at http://ams.confex.com/ams/pdfpapers/95042.pdf.]

  • Tong, M., , and M. Xue, 2008: Simultaneous estimation of microphysical parameters and atmospheric state with radar data and ensemble square-root Kalman filter. Part I: Sensitivity analysis and parameter identifiability. Mon. Wea. Rev., 136, 16301648.

    • Search Google Scholar
    • Export Citation
  • Toth, Z., , and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc., 74, 23172330.

  • Trapp, R. J., , and M. L. Weisman, 2003: Low-level mesovortices within squall lines and bow echoes. Part II: Their genesis and implications. Mon. Wea. Rev., 131, 28042823.

    • Search Google Scholar
    • Export Citation
  • Wandishin, M. S., , D. J. Stensrud, , S. L. Mullen, , and L. J. Wicker, 2010: On the predictability of mesoscale convective systems: Three-dimensional simulations. Mon. Wea. Rev., 138, 863885.

    • Search Google Scholar
    • Export Citation
  • Xue, M., , D.-H. Wang, , J.-D. Gao, , K. Brewster, , and K. K. Droegemeier, 2003: The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation. Meteor. Atmos. Phys., 82, 139170.

    • Search Google Scholar
    • Export Citation
  • Xue, M., and Coauthors, 2008: CAPS realtime storm-scale ensemble and high-resolution forecasts as part of the NOAA Hazardous Weather Testbed 2008 Spring Experiment. Preprints, 24th Conf. on Several Local Storms, Savannah, GA, Amer. Meteor. Soc., 12.2. [Available online at http://ams.confex.com/ams/pdfpapers/142036.pdf.]

  • Xue, M., and Coauthors, 2011: Realtime convection-permitting ensemble and convection-resolving deterministic forecasts of CAPS for the Hazardous Weather Testbed 2010 Spring Experiment. Preprints, 25th Conf. on Wea. Forecasting/20th Conf. on Numerical Weather Prediction, Seattle, WA, Amer. Meteor. Soc., 9A.2. [Available online at http://ams.confex.com/ams/91Annual/flvgateway.cgi/id/17650?recordingid=17650.]

  • Zhang, F., , Y. Weng, , J. A. Sippel, , Z. Meng, , and C. H. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 137, 21052125.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., , Y. Weng, , Y.-H. Kuo, , J. S. Whitaker, , and B. Xie, 2010: Predicting Typhoon Morakot’s catastrophic rainfall with a convection-permitting mesoscale ensemble system. Wea. Forecasting, 25, 18161825.

    • Search Google Scholar
    • Export Citation
Save