 values associated with an operationally useful forecast (AUC > 0.7). The red region indicates forecasts with no skill (AUC < 0.5).
Reliability and sharpness diagrams for NEP forecasts of P[Z > 25 dBZ] for all experiments at (a) 0200, (b) 0300, (c) 0400, and (d) 0500 UTC calculated over the Oklahoma verification subdomain (the red box in Fig. 2). Forecast probability bins are spaced at intervals of 0.05.
Hourly, domain-wide histograms of forecast radar reflectivity for all ensemble forecast experiments, compared to WSR-88D observed reflectivity interpolated to the ensemble forecast grid. Bins are placed every 1 dBZ. The vertical axis indicates the number of model grid volumes within each bin; for the ensemble forecasts these values are normalized by the size of the ensemble.
Ensemble-based probability of a significant near-surface mesovortex occurring within 25 km of a point (shaded) at 0400 UTC for (a) RADCONV, (b) RAD, (c) CONV, and (d) CNTL. The location of the observed tornadic mesovortex (located within the line-end vortex of the MCS) at 0400 UTC is indicated by the green triangle in each panel. Urban boundaries are shown in purple.
Contours of the difference between ensemble mean surface (2 m) temperature forecast and Oklahoma Mesonet observations at 0400 UTC for (a) RADCONV, (b) RAD, (c) CONV, and (d) CNTL. Red areas indicate an ensemble mean temperature warmer than observed by the mesonet, while blue areas indicate an ensemble mean colder than observations.
Contours of the difference between ensemble mean surface (2 m) dewpoint forecast and Oklahoma Mesonet observations at 0400 UTC for (a) RADCONV, (b) RAD, (c) CONV, and (d) CNTL. Green areas indicate an ensemble mean dewpoint higher than observed by the mesonet, while brown areas indicate an ensemble mean dewpoint lower than observations.
Observed surface (2 m) temperature (°F) (solid black lines) at 5-min intervals between 0100 and 0500 UTC from Oklahoma Mesonet sites at (a)–(d) Marena (MARE), (e)–(h) Norman (NRMN), and (i)–(l) Grandfield (GRA2). Also shown are ensemble mean (thick colored lines) and the 5th–95th percentile range (shaded colored regions) for experiments RADCONV [purple; (a),(e), and (i)]; RAD [blue; (b),(f), and (j)]; CONV [red; (c),(g), and (k)]; and CNTL [gray; (d),(h), and (l)] interpolated to the location of the corresponding Oklahoma Mesonet sites. The vertical dotted line in each panel denotes the end of the DA period at 0200 UTC.
As in Fig. 14, but for observed surface (2 m) dewpoint (solid black lines) and ensemble mean (thick colored lines) and the 5th–95th percentile range within the ensemble (shaded colored regions) of dewpoint interpolated to the corresponding Oklahoma Mesonet site.
Neighborhood ensemble probability (shaded) of radar reflectivity exceeding 25 dBZ, P[Z > 25 dBZ], at model grid level 10 (approximately 2 km above the surface) at (a),(b) 0300; (c),(d) 0400; and (e),(f) 0500 UTC for (right) CONV and (left) a variant of CONV using reduced localization radii for conventional data assimilation, at 0300, 0400, and 0500 UTC. The region of radar reflectivity exceeding 25 dBZ observed by the WSR-88D network at the corresponding time is outlined by a bold black contour. Urban boundaries are shown in purple. The localization radius used to assimilate surface and upper-air data is noted in each panel.
Ensemble-based probability of a significant near-surface mesovortex occurring within 25 km of a point (shaded) at 0400 UTC for (a) RADCONV, (b) a variant of RADCONV using reduced localization radii for conventional data assimilation, (c) CONV, and (d) a variant of CONV using reduced localization radii for conventional data assimilation. The location of the observed tornadic mesovortex at 0400 UTC is indicated by the green triangle in each panel. Urban boundaries are shown in purple. The localization radius used to assimilate surface, upper-air, and (if used) radar observations, is noted in each panel.
The ensemble Kalman filter (EnKF), first developed by Evensen (1994, 2003), has been successfully applied to atmospheric data assimilation (DA) using both simulated and real data from a variety of observation platforms, for models ranging from global to convective storm scales (Houtekamer and Mitchell 1998; Hamill and Snyder 2000; Anderson 2001; Whitaker and Hamill 2002; Snyder and Zhang 2003; Dowell et al. 2004; Zhang et al. 2004; Dirren et al. 2007; Tong and Xue 2008a; Xue et al. 2010; Dawson et al. 2012; Snook et al. 2011, hereafter SXJ11; Jung et al. 2012; Yussouf and Stensrud 2012; Yussouf et al. 2013). Though EnKF is rather expensive in terms of computation, requiring an ensemble of forecasts (typically using several dozen members), it provides flow-dependent multivariate background error covariances that less computationally intensive three-dimensional variational data assimilation (3DVAR) methods cannot. Cross covariances produced by the EnKF system are very valuable, especially for convective-scale DA, because state variables that are not directly observed can be retrieved (Tong and Xue 2005, 2008a). Further discussion of DA techniques commonly used for assimilation of weather observations, including 3DVAR, four-dimensional variational data assimilation (4DVAR) methods, and EnKF can be found in Tong and Xue (2005).
Analysis ensembles generated using EnKF are generally well suited as initial conditions for convective-scale ensemble forecasts. EnKF assimilation of Doppler radar data has proven to be effective in retrieving wind, temperature, and microphysical fields at the convective scale (e.g., Dowell et al. 2004; Tong 2006; SXJ11; Jung et al. 2012; Putnam et al. 2014). Furthermore, EnKF analyses, in principle, also characterize the analysis uncertainty; this is a particularly desirable quality in the ensemble forecast initial conditions. Forecast ensembles initialized from EnKF analyses have been shown to produce superior probabilistic predictions compared to ensembles initialized using traditional perturbation methods (Houtekamer et al. 2005; Hamill and Whitaker 2011). EnKF analyses have been successfully applied to ensemble forecasts of convective systems, including supercell thunderstorms (e.g., Aksoy et al. 2009, 2010; Dawson et al. 2012) and mesoscale convective systems (e.g., Snook et al. 2012, hereafter SXJ12; Putnam et al. 2014), as well as tropical cyclones (e.g., Wu et al. 2010; Aksoy et al. 2012, 2013). As available computational power increases, it will become increasingly feasible to run a real-time convective-scale ensemble analysis system (e.g., Xue et al. 2008) incorporating EnKF DA (e.g., SXJ12), as envisioned in the “warn-on-forecast” paradigm being developed by the National Weather Service (Stensrud et al. 2009). For example, the Center for Analysis and Prediction of Storms (CAPS) is actively developing a quasi-operational cycled EnKF DA and ensemble forecast system.
In SXJ11, an ensemble square root Kalman filter (EnSRF; Whitaker and Hamill 2002) is used together with the Advanced Regional Prediction System (ARPS; Xue et al. 2000, 2001) atmospheric model (Tong and Xue 2005; Xue et al. 2006; Tong and Xue 2008b) to assimilate radar reflectivity and radial velocity observations from multiple WSR-88D (Crum et al. 1993) S-band radars, and from the X-band radars deployed by the Center for Collaborative Adaptive Sensing of the Atmosphere (CASA; McLaughlin et al. 2009), for a tornadic mesoscale convective system (MCS) that occurred over Texas and Oklahoma on 9 May 2007. The 40-member ensemble mean analysis of SXJ11 produces model storms whose geographic extent, convective mode, and intensity agree well with the radar observations. Furthermore, SXJ11 finds that assimilation of CASA radar data improves the representation of near-surface circulations and cold pool structure. Ensemble forecasts initialized from the ensemble analyses of SXJ11 are subsequently examined in SXJ12. The forecast ensembles of SXJ12 produce skillful 0–3-h probabilistic forecasts for radar reflectivity and 2-h probabilistic forecasts of the presence and location of the tornadic mesovortex embedded within the MCS with probability maxima localized within several tens of kilometers of the observed tornadic mesovortex. The EnKF experiments of SXJ11 and SXJ12 did not assimilate any conventional observations, nor did they include any mesoscale perturbations in the initial ensemble or any perturbations to the lateral boundary conditions. The ensemble forecasts of SXJ12 exhibited substantial high biases