1. Introduction
National Weather Service forecasters' ability to provide advanced warning of supercell tornadoes currently relies heavily upon the detection (by radar or human observers) of strong low-level rotation (LLR) in storms. This paradigm hinders the tornado-warning process in three important ways. First, tornado-warning lead times are significantly limited in cases where the onset of strong LLR precedes tornadogenesis by only several minutes. It is therefore not surprising that the average warning lead time for events in which the warning precedes the tornado, about 17 min, did not increase from 1986 to 2006 (Stensrud et al. 2013). Second, the existence of mesocyclone-scale LLR, however intense, does not guarantee tornadogenesis. Achieving a satisfactory probability of detection (POD; currently ~80%) while maintaining sufficiently long warning lead times therefore results in a high false alarm rate (FAR; currently ~75%). Third, much of the lowest 1–3 km of the atmosphere lies below the Weather Surveillance Radar-1988 Doppler (WSR-88D) domain (Maddox et al. 2002), precluding low-level radar observations of many storms. The trade-off between the POD and FAR is sharpened in those cases.
These problems will hopefully be mitigated under the envisioned “warn on forecast” (WoF) paradigm (Stensrud et al. 2009), in which forecasters would utilize short-term (e.g., 0–60 min) storm-scale ensemble numerical weather prediction (NWP) model output to increase tornado (as well as severe thunderstorm and flash flood) warning lead times and possibly reduce the FAR. Available computational resources will presumably constrain the horizontal grid spacing of initial operational warn-on-forecast systems to 1 km or larger, thus precluding direct simulation of tornadoes (thus, the second limitation listed above may not be addressed by early WoF systems). Fortunately, 1-km horizontal grid spacing is sufficiently fine to permit the simulation of low-level mesocyclones (LLMs). Using a large and geographically diverse dataset, Trapp et al. (2005) determined that 40% of mesocyclones with bases below 1 km AGL were tornadic, versus only 15% of mesocyclones with bases 3–5 km AGL. Furthermore, recent observational studies strongly suggest a positive correlation between tornado and LLM intensity (e.g., Kingfield et al. 2012; LaDue et al. 2012; Toth et al. 2013). The potential utility of ensemble systems to LLR forecasts and thereby to tornado-warning operations therefore merits serious consideration. Toward that end, this study adopts an observing system simulation experiment (OSSE) framework to estimate the maximum accuracy with which near-term-realizable ensemble forecast systems can predict LLM path, timing, and intensity.
Due largely to the nonlinearities associated with convective instability and cloud microphysics, moist convection is chaotic [i.e., initial condition errors grow rapidly, especially as finer scales are simulated; e.g., Zhang et al. (2003); Hohenegger and Schär (2007)]. Numerical forecasts of supercell thunderstorms, therefore, are sensitive to errors in the initial state estimate provided by the data assimilation procedure. Such errors inevitably arise from deficiencies in 1) the assimilated observations (e.g., data gaps, measurement errors), 2) the assimilation system (e.g., simplified forward operators) and, in cycled data assimilation methods, 3) the NWP model (e.g., discretization and physical parameterization errors). Additional errors occur as the model is integrated forward from the initial conditions. In this study, we introduce model error into our experiments by using a finer horizontal grid for the truth simulation than for the ensemble analysis–forecasting system.
In deducing implications of our idealized forecasts for near-future WoF ensemble systems, it is important to consider how the predictability of the supercells simulated in our experiments compares to the predictability of real supercells. The grid resolution in our “truth” simulations (described in section 2a) is coarse relative to the inertial subrange of cumulus convection (Bryan et al. 2003). The resulting absence in the simulations of the smallest supercell scales of motion artificially reduces upscale error growth (Lorenz 1969) in forecasts. This suggests the intrinsic predictability (i.e., the predictability that would be achieved given a perfect forecast model and very small initial condition uncertainty) of our simulated supercells is greater than that of atmospheric supercells. Moreover, since errors arise in current convection-permitting models from a multitude of sources, our use of a model that, apart from its coarsened resolution, is identical to the model used to generate truth presumably leads to our simulated supercells having greater practical predictability (i.e., the predictability given the constraints of the observational network, data assimilation techniques, and NWP model) than atmospheric supercells. Assuming that current model errors contribute much more than current data assimilation deficiencies to errors in storm-scale ensemble forecasts, the results of this study are therefore best viewed as estimating the upper limit of the accuracy with which early WoF systems will forecast LLMs in the simple supercell scenario examined (no interactions with other storms, orography, nor larger-scale boundaries). Establishing such baselines is critical to assessing the feasibility of long-term tornado warnings under the WoF paradigm.
Studies of the 4–5 May 2007 Greensburg, Kansas, tornadic thunderstorm by Stensrud and Gao (2010) and Dawson et al. (2012) demonstrate that operationally useful ensemble forecasts of low-level vorticity can be achieved for at least some supercells despite current observational, model, and data assimilation method limitations. The experiments of Snook et al. (2012) support a similar hypothesis for 0–3-h forecasts of mesoscale convective system mesovortices. Assessing the generality of these results, and identifying scenarios that pose a particularly significant challenge to ensemble LLR forecasts, requires that such forecasts be performed and evaluated for a large number of cases spanning a range of radar–storm geometries and atmospheric environments.
The OSSE framework provides a powerful complement to real case studies of such problems, for two primary reasons. First, since the truth is known, analysis errors and their sensitivity to important experimental parameters (e.g., radar cross-beam angle) can be precisely determined. Second, there is no need to collect and quality control numerous observation sets meeting specific desired criteria. In this paper, we simulate scenarios where a supercell is observed by two WSR-88D radars and we evaluate LLR forecasts for different radar–storm distances, radar cross-beam angles, and data assimilation period lengths. The simulated supercell used as truth in the majority of our experiments rapidly develops an intense LLM-like vortex (hereafter, simply LLM) that undergoes cyclic low-level mesocyclogenesis through the remainder of the simulation. Evaluations of those forecasts focus upon the timing of the development of the initial LLM, as well as the path and rotational intensity of the LLM “family.” To test the ability of the ensemble system to distinguish between supercells that develop very different magnitudes of LLR, we also perform experiments in which the “true” storm develops a weaker LLM, or fails to sustain strong LLR at all (null case).
The rest of the paper is organized as follows. Section 2 describes the model configuration for our supercell simulations, the procedure for emulating radar observations of the simulated storms, the ensemble data assimilation and forecast system, and our verification methods. The results of the LLR forecasts are described in section 3. Implications of the forecast results for the proposed WoF paradigm are discussed in section 4.
2. Methods
a. “Truth” simulations
The two truth simulations for our experiments were generated by the National Severe Storms Laboratory Collaborative Model for Multiscale Atmospheric Simulation (NCOMMAS; Wicker and Skamarock 2002; Coniglio et al. 2006). The NCOMMAS is a nonhydrostatic, compressible cloud model designed to simulate convective storms in a simplified setting (e.g., flat surface, no surface fluxes nor radiative transfer, and horizontally uniform base state). The prognostic variables in NCOMMAS are the wind components u, υ, and w; the Exner function π; the turbulent mixing coefficient Km; the potential temperature θ; the water vapor mixing ratio qυ; and the microphysical parameterization (MP) scheme variables (listed below). The supercell simulations proceeded on a stationary 200 km × 200 km × 20 km domain with horizontal grid spacing ΔH = ⅓ km and vertical spacing increasing from 200 m over the lowest 1 km to 600 m above z = 5.2 km. Both simulations were integrated for 2 h using large and small time steps of 4 and ⅔ s, respectively.
The sounding (Fig. 1a) that provided the model base state for the default supercell simulation (used in most of our experiments) is a composite of the wind profile from the 1200 UTC 3 April 1974 Covington, Kentucky, rawinsonde, modified to yield a storm motion slow enough to permit the use of a stationary model grid, and a thermodynamic profile similar to that of Weisman and Klemp (1982, 1984) with some modifications to increase the low-level stability below 800 mb to introduce a weak capping inversion more indicative of supercell environments (G. Bryan 2011, personal communication). The sounding used in the second simulation has the same thermodynamic profile as that used in the default simulation, but the wind profile is modified to reduce the wind shear by ⅓ (Fig. 1b). In both simulations, the storm was initiated with an ellipsoidal 4-K thermal bubble with horizontal and vertical radii of 10 and 1.4 km, respectively. A fully dual-moment version of the Ziegler (1985) MP scheme (Mansell et al. 2010) was used. The scheme predicts the mixing ratio and number concentration for distributions of cloud droplets, rain, cloud ice crystals, snow, graupel, and hail, as well as the bulk concentration of cloud condensation nuclei, average bulk densities of graupel and hail, and the melted fractional diameters of graupel and hail.
Model base state (a) thermodynamic profile used in both simulations and (b) hodographs used in default (solid) and lower-shear (dashed) simulations. Heights (km) are indicated for three points on each hodograph.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
In both supercell simulations, the initial supercell splits several times during the course of the model integration, consistent with the straight-line hodographs above z = 1 km. We restrict our attention to the initial supercell pair in the default simulation and to the initial right-moving supercell in the weaker-shear simulation. Cursory inspection of the simulated low-level reflectivity fields reveals marked differences in the evolution of the three supercells (Fig. 2). Time–height plots of the horizontal-domain maximum-amplitude cyclonic (anticyclonic) vorticity, ζmax, are shown for the right-moving supercells (left-moving supercell) in Figs. 3a–c (discussion of Figs. 3d-f is deferred to section 2d). The presence of a mesocyclone at the middle levels is indicated by ζmax > 0.02 s−1 in all three storms. Cyclic low-level mesocyclogenesis occurs in both default-simulation supercells; this process is reflected in the temporal oscillations in ζmax in the lowest 1 km (Figs. 3a and 3b). Series of LLMs from the same storm are considered a single object for the purpose of the verification. The right-moving supercell in the default simulation, supA, develops a fairly intense LLM just after t = 60 min; the LLM weakens after t = 65 min, rapidly reintensifies after t = 75 min, and remains strong through the end of the simulation (Fig. 3a). The evolution of the LLM of the left-moving supercell in the default simulation, supB, bears qualitative similarities to that of the supA LLM (Fig. 3b). However, low-level mesocyclogenesis is delayed relative to supA, and ζmax is generally smaller above z = 1 km. The latter difference is at least partly attributable to the fact that both storms experience positive storm-relative environmental helicity, the tilting of which enhances the (cyclonic) LLM in supA but weakens the (anticyclonic) LLM in supB. The supercell in the weaker-shear simulation, supC, fails to sustain strong LLR (Fig. 2c). This is the intended consequence of reducing the environmental vertical wind shear. The large differences in evolution between the three supercells allow us to pose a more varied, meaningful challenge to the ensemble analysis–forecasting system.
Horizontal cross sections of z = 1 km reflectivity (shading; dBZ) and w (contoured at 5 and 10 m s−1) at t = 30, 60, 90, and 120 min: (a) default and (b) lower-shear simulations.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
(left) Time–height plots of maximum-amplitude (a) cyclonic vertical vorticity (s−1) in supA, (b) anticyclonic vertical vorticity magnitude in supB, and (c) cyclonic vertical vorticity in supC. (right) Time series of VT for (d) supA, (e) supB, and (f) supC.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
As with any OSSE study, the relevance of our results to real-data applications is largely determined by the physical realism of the truth simulations. Encouragingly, the storm morphology and evolution (not shown) comport with real supercell observations in many important ways. These include the bowing of the rear-flank downdraft (RFD) gust front by surging outflow and the attendant horseshoe-shaped updraft; the existence of a vertical vorticity dipole straddling the hook echo; the diffuse nature of the forward-flank downdraft “gust front”; and the similarity of the surface gradients and maximum deficits of perturbation virtual potential temperature in the simulations to those in observational studies (Shabbott and Markowski 2006; Markowski et al. 2002). Confidence in the realism of the simulations is further enhanced by our use of a double-moment MP scheme, which affords greater flexibility in hydrometeor size distributions than do single-moment schemes, presumably improving the representation of hydrometeor size sorting and other processes (e.g., Milbrandt and Yau 2006; Dawson et al. 2010).
b. Radar emulation and experiments
Pseudo-observations of reflectivity Zobs and Doppler velocity Vobs are generated from the model reflectivity Z, wind components (u, υ, and w), and hydrometeor fall speeds wt using a slightly modified version of the Wood et al. (2009) radar emulator (e.g., Yussouf and Stensrud 2010). This technique simulates the power-weighted averaging of radial velocities and reflectivities of scatterers within a Gaussian radar beam, and accounts for earth curvature and standard atmospheric beam refraction in computing the beam path. The same hydrometeor fall speed formula is used in the calculation of the Vobs, the Vobs forward operator in the EnKF, and the model: 
In all of our experiments, the simulated supercell is observed by two stationary radars having characteristics consistent with the WSR-88D network. Volume coverage pattern 11 (VCP-11) is used, with successively higher groups of (two or three) sweeps computed from model fields valid at successively later (in 1-min increments) simulation times. At the lowest two sweeps, superresolution data are emulated; legacy-resolution observations are generated at steeper elevation angles (Table 1). The positions of the emulated radars and the approximate paths of the main low-level updraft of each of the three supercells during the data assimilation period are depicted in Fig. 4. One radar is fixed at the same location, ~130 km east-southeast of the supA low-level updraft at t = 40 min, in all of the experiments. The second radar is repositioned from experiment to experiment to investigate the sensitivity of the LLM forecasts to the radar–storm geometry. Experiments are labeled according to the supercell being forecast, whether the second radar is near or far from the storm, and whether the radar cross-beam angles (CBAs) are good (closer to 90°) or poor (closer to 0°) during the data assimilation period (Table 2). Forecasts are initialized at t = 50 min (after 30 min of data assimilation) or t = 70 min (after 50 min of data assimilation) and suffixed accordingly (_50min-DA or _70min-DA). The t = 70 min forecasts ideally benefit from the additional 20 min of radar data assimilated, but at the cost of reduced forecast lead time.
Radar range (km) and azimuthal (°) sampling characteristics for the lowest two sweeps (superresolution) and higher sweeps (legacy resolution).
Model domain used in truth simulation and EnKF experiments. The locations of the emulated radars are indicated by large dots. The x–y coordinates of each radar site relative to the southwest corner of the domain are listed in parentheses. The experiments in which each radar site is used are listed below the radar coordinates. Also shown are the paths of the low-level updrafts of supA (squares), supB (triangles), and supC (dots) during the data assimilation period (t = 20–70 min).
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
Radar–storm geometry in each experiment.
c. Ensemble analysis–forecasting system
Initial conditions for the ensemble forecasts are obtained from assimilating the emulated radar observations using the NCOMMAS ensemble square root filter [based on the filter of Whitaker and Hamill (2002)]. Eighty ensemble members are used; repeating the far_G-CBA_supA_50min-DA forecast (section 3a) with a 120-member ensemble did not substantially improve the results. The NWP model used to advance the ensemble members to each successive assimilation time is equivalent to that used to generate the truth simulations, except that ΔH is increased from ⅓ to 1 km. The covariance localization factor is calculated using the Gaspari and Cohn (1999) correlation function with covariance estimation cutoff radii of 6 and 3 km in the horizontal and vertical directions, respectively. To imitate the practice of accounting for uncertainty in the sounding, and to mitigate ensemble underdispersion at higher altitudes, perturbations are added to the base-state u and υ of each ensemble member following the procedure of Potvin et al. (2013). The perturbations are computed by generating random sinusoidal perturbations of the form used in Aksoy et al. (2009), then scaling them such that their standard deviation at each level is a fraction (=0.025 in this study) of the base-state wind speed multiplied by exp(z/22), where z is the model-level height (km). Four ellipsoidal thermal bubbles having random sizes and magnitudes are inserted in each member at t = 0 to initiate storms. The bubbles are randomly positioned within a 40 km × 40 km × 1.5 km box centered on the location of the initiation bubble in the truth simulation. The ensemble members are then integrated 20 min forward to the beginning of the data assimilation period (t = 20 min). This allows physically realistic covariances to develop in the ensemble, thus maximizing the utility of radar data early in the assimilation period (e.g., Snyder and Zhang 2003; Dowell et al. 2004).
Prior to assimilation, observations are analyzed to a quasi-horizontal grid on each conical scan surface (e.g., Dowell et al. 2004; Dowell and Wicker 2009) using Cressman interpolation. Observations from the radars further from the storms (x ≥ 145 km; Fig. 4) are interpolated onto 2-km grids using a Cressman radius of 1.5 km. Observations from the radars closer to the storms are interpolated onto 1-km grids using a Cressman radius of 1.0 km. To account for storm motion between the times at which observations are valid and the times at which they are analyzed, the interpolated observations are shifted to locations determined by the estimated storm translational velocity components U and V. The U and V (=13 and 4 m s−1, respectively) are treated as constants in space and time and were determined by visually tracking features in the Zobs field. Observations are assimilated every 2 min using a 2-min window centered on t. As in many EnKF radar data assimilation studies, to reduce computational cost, the observation operator H trilinearly interpolates model fields to observational locations and, thus, makes no provision for the shape of, nor inhomogeneous reflectivity distribution within, the radar beam. [Thompson et al. (2012) showed these simplifications do not severely degrade EnKF analyses and subsequent forecasts.] Following Dowell and Wicker (2009), to save computational time, observations are not used to update π and Km since the impact of the observations on these variables is negligible. Observational error standard deviations of 2 m s−1 and 5 dBZ are assumed in the filter. As in Potvin and Wicker (2012), we used larger filter-assumed Zobs errors (5 dBZ) than were actually added to the Zobs (3 dBZ) to reduce the impact of errors in the forecast hydrometeor fields and Zobs operator. In experiments with both radars located roughly equidistantly from the storm, Zobs are assimilated only from radar 1 (Fig. 4) since Zobs from the second radar would contain little independent information.
A procedure similar to the additive noise method [Dowell and Wicker (2009); based on the ensemble initialization procedure of Caya et al. (2005)] is used to maintain ensemble spread consistent with the ensemble forecast error variance. Smoothed perturbations having horizontal and vertical length scales of 4 and 2 km, respectively, are added to u, υ, θ, and dewpoint temperature Td below z = 10 km wherever Zobs > 20 dBZ during the data assimilation process. Prior to being smoothed, the u, υ, θ, and Td perturbations have standard deviations of 2 m s−1, 2 m s−1, 1 K, and 1 K, respectively. Time–height plots of the Vobs consistency ratio and mean forecast innovation valid where Zobs > 10 dBZ (not shown) suggest sufficient ensemble spread was obtained in all of our experiments.
d. Forecast verification
Our evaluations of the LLM ensemble forecasts focus on estimates of the peak azimuthal-mean vortex-maximum tangential velocity averaged over the z = 0.5–1.5-km layer. This parameter, VT, is computed at each time within the evaluation period (t = 50–120 min) for both the truth simulations and the ensemble member forecasts using the following procedure:
vertically average ζ over z = 0.5–1.5 km, yielding
determine the location of the maximum
for each grid coordinate (x0, y0) within 3 km of (xmax, ymax), compute the circulation,
for each Γ, compute υt = |Γ/2πR|; and
VT = max(υt).
The degree to which each forecast replicates the timing and intensity of the true LLR is assessed by comparing time series of the ensemble probability of VT exceeding prescribed thresholds in the forecast supercell to time series of VT in the “true” supercell (Figs. 3d–f). The skill with which each forecast replicates the path of the maximum LLR is evaluated by comparing 3 × 3 point neighborhood ensemble probabilities (Schwartz et al. 2010) of the forecast-period-maximum VT exceeding a threshold to the region where the forecast-period-maximum true VT exceeds the same threshold. These temporal and spatial ensemble probabilities are labeled Pt and Pxy, respectively. While care must be taken not to overgeneralize the limited number of experiments performed, the results do permit useful conclusions to be drawn.
3. Experiments
a. Both radars distant from storm
Within the WSR-88D network, supercells are often >100 km from the nearest radars. In such cases, echoes in the planetary boundary layer, which is dynamically critical to supercell evolution, are largely unobserved. In addition, the resolution of radar observations is substantially reduced at such long ranges. To explore whether useful ensemble forecasts of potentially tornadic supercells can be achieved in such suboptimal circumstances, we performed experiments (far_G-CBA_supA, far_G-CBA_supB, and far_G-CBA_supC; experiment nomenclature described in section 2b) with both emulated radars positioned > 100 km from the low-level updraft throughout the data assimilation period (Fig. 4). At these distances, the lowest (0.5°) beam from each radar is centered > 1.5 km above the ground. Thus, the development of accurate ensemble covariances between the model state variables above and below the data cutoff is critical to retrieving the low-level storm fields during the data assimilation. Favorable CBAs of roughly 60°–90° are obtained during the assimilation period for all three supercells; the impact of poor CBAs on forecasts of supA is examined in section 3c.
The Pt and Pxy provide mixed, but overall positive, support to the ability of a WoF system to predict low-level rotation in a supercell located within a gap in the low-level domain of the WSR-88D network. We first evaluate the supA forecast initialized at t = 50 min (far_G-CBA_supA_50min-DA). Consistent with the brief LLM that occurs just after t = 60 min in the truth simulation (Fig. 3d), roughly 40% of the ensemble members contain VT > 10 m s−1 shortly after initialization (Fig. 5a). The forecast LLMs, however, generally form 5–10 min too early (a possible reason for this is given in the next subsection) and, due partly to their premature development, are displaced southwest of the true LLM (Fig. 6a). The timing of the onset of sustained strong low-level rotation, on the other hand, is well forecast, with Pt(VT > 10 m s−1) rapidly increasing beginning near t = 75 min, roughly coincident with the true VT exceeding the same threshold. During the period of maximum true VT, t ≈ 90–100 min, Pt(VT > 10 m s−1) and Pt(VT > 15 m s−1) average near 75% and 30%, respectively. The Pt values for both thresholds decrease after t ≈ 105 min, consistent with, though slightly delayed from, the decline in true VT after t ≈ 100 min. The Pt(VT > 10 m s−1) remains high, generally > 60%, through the end of the forecast period, consistent with the maintenance of VT > 10 m s−1 in the true supercell.
The Pt of VT > 5 m s−1 (black), 10 m s−1 (red), and 15 m s−1 (blue) for forecasts initialized at t = 50 min (solid) and t = 70 min (dashed): (a) far_G-CBA_supA, (b) far_G-CBA_supB, (c) far_G-CBA_supC, (d) near_G-CBA_supA, (e) near_G-CBA_supB, and (f) 50km_G-CBA_supC. Shading denotes periods of true VT of 5–10 m s−1 (gray), 10–15 m s−1 (red), and > 15 m s−1 (blue). Darker shades indicate larger values within each range. Note that Pt(VT > 15 m s−1) = 0 at all times in (b) and (e).
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
The Pxy(VT > 10 m s−1; shading) for forecasts initialized at t = (left) 50 and (right) 70 min: (a),(b) far_G-CBA_supA and (c),(d) near_G-CBA_supA. The red contours enclose the regions where the true VT > 10 m s−1 during the forecast period.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
The peaks in Pxy(VT > 10 m s−1) are generally displaced several kilometers south of the true LLM track, but these errors are relatively small given the long forecast lead times. The swath of peak Pxy is generally centered within the envelope of LLM tracks, which is ≤30 km wide (along the direction perpendicular to the storm motion) through the forecast period. Given that current tornado warning boxes are generally ~20–30 km wide at 30-min lead times, a tornado-warning polygon constructed to encompass the envelope of Pxy > 0 (a conservative approach) in this case would comfortably include the true LLM (and potential tornado) track at 0–70-min lead times without being unduly large. Computations of Pxy(VT > 10 m s−1) for 10-min subintervals of the forecast period (Fig. 7a) show that the forecast LLM trajectory is reasonably accurate in time as well as in space. This suggests that WoF ensembles will ultimately permit greater temporal resolution in tornado warnings.
The Pxy valid over 10-min subintervals (shading) of (a) VT > 10 m s−1 in far_G-CBA_supA_50min-DA and (b) VT > 5 m s−1 in far_G-CBA_supB_50min-DA. The black contours enclose regions of true VT (a) >10 and (b) >5 m s−1 during each subinterval.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
As implied by the large width of the Pxy > 0 envelope relative to the true path of VT > 10 m s−1, large variance exists among the individual low-level rotation forecasts (Fig. 8a). The differences between the forecasts are striking given the qualitative similarities between the member initial conditions (shown at low levels in Fig. 8b), and serve to underscore the chaotic nature of the phenomena being predicted. The large errors that occur in many of the individual member forecasts highlight the advantage of using an ensemble, rather than deterministic, forecast approach.
(a) Forecast-period-maximum VT (shading) for a representative subset of the far_G-CBA_supA_50min-DA member forecasts. The black contours enclose the regions of true VT > 10 m s−1 during the forecast period. (b) Initial conditions (t = 50 min) of the member forecasts in (a): surface θ′ (shading), surface convergence (green contours: −0.015, −0.010, −0.005, 0.005, 0.01, and 0.015 s−1), and 1 km AGL reflectivity (black contours; 20, 40, and 60 dBZ).
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
The far_G-CBA_supA_70min-DA forecast is superior to the far_G-CBA_supA_50min-DA forecast, an expected result of the larger number of radar volumes assimilated and the shorter forecast lead times. The Pxy swath is considerably narrower at later times than for far_G-CBA_supA_50min-DA, and the maximum Pxy are substantially larger (cf. Figs. 6a and 6b). The Pt also improve; for example, the timing of the onset of VT > 15 m s−1 is slightly better captured, as is the decrease in VT after t = 100 min (Fig. 5a). While the significance of the relatively small changes in Pt is questionable, the combination of the Pt and (more substantial) Pxy improvements supports the expectation that WoF ensemble output will be valuable not just to issuing tornado warnings, but also to refining existing warnings as newer forecasts become available.
We now turn to evaluating the far_G-CBA_supB forecasts (recall that supB is the left-moving counterpart to supA; see section 2a). Consistent with the lower VT in supB (cf. Figs. 3a and 5b), the Pt are much smaller than for the supA forecasts (cf. Figs. 5a and 5b). The rapid increase in the true VT to above 5 m s−1 is reasonably well captured by the Pt(VT > 5 m s−1) in both far_G-CBA_supB_50min-DA and (especially) far_G-CBA_supB_70min-DA. The decrease in VT after t = 100 min, however, is not reflected in either forecast.
Plots of Pxy(VT > 5 m s−1) indicate that, as in the supA forecasts, the supB forecast LLM tracks are generally displaced ~5 km or less from the true LLM track (Figs. 9a and 9b). Moreover, the envelope of Pxy > 0 again encompasses the true LLM path. While the Pxy > 0 envelope is substantially wider than in the far_G-CBA_supA forecasts, using a slightly less conservative criterion, such as Pxy > 0.1, defines a much narrower tornado risk area that still includes the true LLM path. Thus, both the supA and supB forecasts effectively outline the region of greatest tornado risk. Moreover, as with far_G-CBA_supA_50min-DA, far_G-CBA_supB_50min-DA accurately predicts the timing in addition to the path of the LLM (Fig. 7b), further suggesting that WoF ensemble output may permit enhanced temporal information in warnings. Also consistent with the far_G-CBA_supA forecasts, far_G-CBA_supB_70min-DA is substantially better than far_G-CBA_supB_50min-DA (Fig. 5b; cf. Figs. 9a and 9b).
The Pxy(VT > 5 m s−1; shading) for forecasts initialized at t = (left) 50 and (right) 70 min: (a),(b) far_G-CBA_supB and (c),(d) near_G-CBA_supB. The red contours enclose regions where the true VT > 5 m s−1 during the forecast period. The black contours enclose regions where Pxy(VT > 5 m s−1) > 0.1.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
In the supC simulation, intense low-level rotation is absent for most of the forecast period, with VT generally remaining well below 10 m s−1 (except near t = 70 min; Figs. 3c and 3f). This is therefore a suitable null case test for our ensemble system. Interestingly, the peak Pt(VT > 10 m s−1) is substantially higher in far_G-CBA_supC_50min-DA than in far_G-CBA_supB_50min-DA (cf. Figs. 5b and 5c) despite supB exhibiting stronger low-level rotation and supC never actually exceeding the VT = 10 m s−1 threshold (Fig. 3f). In addition, while the true VT generally remains below 5 m s−1 after t = 80 min, the far_G-CBA_supC_50min-DA Pt(VT > 5 m s−1) ranges between 60% and 80% during the same period. Thus, based solely on the Pt, supC would be regarded as a greater tornado threat than supB, despite supC never developing a mature LLM. The overprediction of the low-level rotation in supC is also starkly reflected in the Pxy(VT > 5 m s−1) and Pxy(VT > 10 m s−1) plots (Figs. 10a and 10e). These results raise concerns about the reliability of WoF low-level rotation guidance in null cases, particularly with respect to false alarms. These concerns are enhanced by the fact that the results of our idealized forecasts are likely more accurate than would typically be obtained in practice for similar cases (section 1). On the other hand, while the Pt(VT > 5 m s−1) and Pxy(VT > 5 m s−1) do not improve in the t = 70 min forecast (Fig. 5c; cf. Figs. 10a and 10b), the Pt(VT > 10 m s−1) and Pxy(VT > 10 m s−1) substantially decrease (Fig. 5c; cf. Figs. 10e and 10f). This again highlights the potential value of regularly restarting ensemble forecasts as new radar data become available.
The Pxy(VT > 5 m s−1; shading) for forecasts initialized at t = (left) 50 and (right) 70 min: (a),(b) far_G-CBA_supC and (c),(d) 50km_G-CBA_supC. The red contours enclose the regions where the true VT > 5 m s−1 during the forecast period. (e)–(h) As in (a)–(d), but for VT > 10 m s−1 (note that the true VT never exceeds 10 m s−1).
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
b. One radar close to storm, one distant from storm
The analyses and subsequent forecasts in the above experiments are hindered by the absence of radar data over the lowest 1.5 km of the storms and the relatively coarse resolution of the assimilated observations, both of which result from the large distances between the supercells and both radars. While that scenario is common, the WSR-88D network is sufficiently dense that storms are often located relatively close to one radar. A set of experiments was therefore performed (near_G-CBA_supA, near_G-CBA_supB, and near_G-CBA_supC) in which radar 2 was relocated to within ~30–50 km of the supercells during the data assimilation period (Fig. 4).
In the case of supA, the Pt(VT > 10 m s−1) and Pt(VT > 15 m s−1) are larger than in the original forecasts during the peak in the true VT, and the subsequent decline in VT is better captured (Figs. 3d and 11a,d). The impact of the closer proximity of radar 2 on the Pt is not uniformly desirable, however. For example, during t ≈ 70–80 min, the Pt(VT > 15 m s−1) in near_G-CBA_supA_50min-DA is much higher than that in far_G-CBA_supA_50min-DA, whereas the true VT < 15 m s−1 (Fig. 11a). The Pxy swaths, on the other hand, are more generally improved. Much of the southward bias in the LLM track disappears, and the Pxy(VT > 10 m s−1) increases relative to the original forecasts throughout most of the region where the true maximum VT > 10 m s−1 (cf. Figs. 6a and 6c and Figs. 6b and 6d).
The Pt of VT > 5 m s−1 (black), 10 m s−1 (red), and 15 m s−1 (blue) for forecasts initialized at t = (left) 50 and (right) 70 min: (a),(d) far_G-CBA_supA (solid) and near_G-CBA_supA (dashed), (b),(e) far_G-CBA_supB (solid) and near_G-CBA_supB (dashed), and (c),(f) far_G-CBA_supC (solid) and 50km_G-CBA_supC (dashed). Shading denotes periods of true VT of 5–10 m s−1 (gray), 10–15 m s−1 (red), and >15 m s−1 (blue). Darker shades indicate larger values within each range.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
Comparisons of surface θ′, surface divergence, and 1 km AGL reflectivity fields from the EnKF mean analyses (Fig. 12a) and individual ensemble members (not shown) from far_G-CBA_supA and near_G-CBA_supA reveal that all the fields are generally slightly better retrieved in the latter analysis. Perhaps the most important difference between the far_G-CBA_supA and near_G-CBA_supA analyses is that the analyzed surface RFD gust front (RFDGF), and thus the leading edge of the storm cold pool, is generally too far east and too meridionally oriented in many of the far_G-CBA_supA member analyses. This bias was also found 1 and 2 km AGL, but not at higher altitudes where observations were available (not shown). We speculate that the premature development of low-level rotation in many of the far_G-CBA_supA_50min-DA member forecasts (section 3a) resulted from the analyzed RFDGF and associated regions of baroclinic (horizontal) vorticity generation and barotropic (vertical) vorticity generation and stretching having advanced too close to the low-level updraft (within which horizontal vorticity is tilted into the vertical and vertical vorticity is stretched) by the initialization time.
Surface θ′ (shading), surface convergence (green contours: −0.015, −0.010, −0.005, 0.005, 0.01, and 0.015 s−1), and 1 km AGL reflectivity (black contours: 20, 40, and 60 dBZ) for (a) supA and (b) supB ensemble mean analyses at t = 50 min: (top) truth, (middle) far_G-CBA_supA_50min-DA and far_G-CBA_supB_50min-DA analyses, and (bottom) near_G-CBA_supA_50min-DA and near_G-CBA_supB_50min-DA analyses.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
Moving radar 2 closer to the storms has a more varied impact on the supB forecasts than on the supA forecasts (Figs. 9 and 11b,e). On one hand, the Pt and Pxy for the near_G-CBA_supB forecasts are higher than in the original (far_G-CBA_supB) forecasts when and where the true VT is highest. On the other hand, the rapid increase in Pt is delayed by ~5–10 min relative to the original forecasts and to the truth simulation, and in near_G-CBA_supB_50min-DA, the maximum Pxy is generally displaced eastward of the maximum true VT (the maximum Pxy in far_G-CBA_supB_50min-DA was roughly collocated with the maximum true VT). As a result, the Pxy(VT > 5 m s−1) envelope in near_G-CBA_supB_50min-DA excludes part of the region of true VT > 5 m s−1. These results are somewhat surprising given that the near_G-CBA_supB_50min-DA initialization appears mildly better than the far_G-CBA_supB_50min-DA initialization (Fig. 12b). The Pxy (cf. Figs. 9c and 9d) are improved in near_G-CBA_supB_70min-DA relative to near_G-CBA_supB_50min-DA. Overall, however, neither the t = 50 nor 70 min forecasts benefit substantially from the greater proximity of radar 2.
In the case of supC, the decreased distance to radar 2 substantially degrades the t = 50 min forecast (Figs. 10 and 11c). While the Pt(VT > 5 m s−1) and Pxy(VT > 5 m s−1) are now much larger within the spatiotemporal window of true VT > 5 m s−1, they are also much larger at subsequent times/locations along the storm path. Moreover, the Pt(VT > 10 m s−1) and Pxy(VT > 10 m s−1) are substantially increased, despite the fact that the true VT < 10 m s−1 at all times.
Visual comparison of the EnKF means and individual member fields at t = 50 min (not shown) reveals the RFDGF is analyzed slightly too far east in far_G-CBA_supC, and slightly too far west in near_G-CBA_supC. Perhaps as a consequence of this, many of the near_G-CBA_supC_50min-DA member forecasts, but not the far_G-CBA_supC_50min-DA forecasts, erroneously delay the undercutting of the updraft by the cold pool (not shown). As a result, the period of vertical vorticity generation is erroneously prolonged in the near_G-CBA_supC_50min-DA forecast, presumably explaining the overprediction of VT. It is not clear why assimilating observations nearer the ground failed to improve the initialization of the RFDGF in near_G-CBA_supC.
The t = 70 min supC forecast is not degraded overall by the greater proximity of radar 2 (cf. Fig. 11f; cf. Figs. 10b and 10d; cf. Figs. 10f and 10h). As a result, near_G-CBA_supC_70min-DA improves upon near_G-CBA_supC_50min-DA. As was the case with supB, however, forecasts of supC do not appear to generally benefit from decreasing the distance to radar 2, despite the additional information content of the assimilated observations. Our limited number of experiments precludes any general conclusions other than that assimilating additional observational information does not necessarily improve the ensemble forecasts.
c. Impact of poor radar cross-beam angles
The far_G-CBA_supA and near_G-CBA_supA experiments (section 3a) were repeated with the second radar relocated so as to maintain roughly the same distance from the storm while effecting much poorer CBAs (Fig. 4). In far_P-CBA_supA, the CBA over the low-level updraft varies between ~20° and ~30° during the t = 20–70 min period. In near_P-CBA_supA, the CBAs are particularly poor, varying from 30° to as low as 0° (in which case the wind component perpendicular to the radar baseline is totally unsampled). The Pt and Pxy for the ensemble forecasts initialized at t = 50 and 70 min are presented in Figs. 13 and 14, respectively.
The Pt of VT > 5 m s−1 (black), 10 m s−1 (red), and 15 m s−1 (blue) for forecasts initialized at t = (left) 50 and (right) 70 min: (a),(b) far_G-CBA_supA (solid) and far_P-CBA_supA (dashed) and (c),(d) near_G-CBA_supA (solid) and near_P-CBA_supA (dashed). Shading denotes periods of true VT of 5–10 m s−1 (gray), 10–15 m s−1 (red), and >15 m s−1 (blue). Darker shades indicate larger values within each range.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
The Pxy(VT > 10 m s−1; shading) for forecasts initialized at t = (left) 50 and (right) 70 min: (a),(b) far_P-CBA_supA and (c),(d) near_P-CBA_supA. The red contours enclose the regions where the true VT > 10 m s−1 during the forecast period.
Citation: Weather and Forecasting 28, 4; 10.1175/WAF-D-12-00122.1
The impact of the poorer CBAs, rather than being consistently undesirable as might be expected, is mixed. Only minor differences occur between far_P-CBA_supA_50min-DA and far_G-CBA_supA_50min-DA (Fig. 13a; cf. Figs. 14a and 6a). From t = 80 to 95, the far_P-CBA_supA_70min-DA Pt are higher than in far_G-CBA_supA_70min-DA (Fig. 13b), a desirable result given the true VT > 15 m s−1 during that period (Fig. 3d). On the other hand, the subsequent rapid decrease in the far_P-CBA_supA_70min-DA Pt(VT > 15 m s−1) occurs too early, while that of far_G-CBA_supA_70min-DA comports well with the true VT falling below 15 m s−1 around t = 105 min.
Turning to the forecasts with radar 2 positioned closer to the storm, the maintenance of true VT > 10 m s−1 after t = 100 min is much better signaled in near_P-CBA_supA_50min-DA than in near_G-CBA_supA_50min-DA (Fig. 13c; cf. Figs. 14c and 6c), as is the timing of the onset of VT > 15 m s−1 (Fig. 13c). The decline of VT below 15 m s−1, however, is better reflected in near_G-CBA_supA_50min-DA (Fig. 13c). The near_P-CBA_supA_70min-DA forecast is the only one that is substantially degraded by the poor CBAs. The Pt(VT > 10 m s−1) and Pxy(VT > 10 m s−1) are substantially lower in near_P-CBA_supA_70min-DA than in near_G-CBA_supA_70min-DA after t = 80 min (Fig. 13d; cf. Figs. 14d and 6d), during which the true VT > 10 m s−1. The Pt(VT > 15 m s−1) is also greatly reduced during this period, which is a desirable result after t = 105 min (when VT falls below 15 m s−1; Fig. 3d), but is inconsistent with the true VT > 15 m s−1 during 80 min < t < 105 min.
Despite the varied impacts of reducing the CBAs, two tentative conclusions can be drawn from the results. As exemplified in near_P-CBA_supA_70min-DA, very poor radar CBAs can substantially limit the accuracy of the LLM forecasts. On the other hand, the results of the remaining three forecasts suggest that slightly less narrow CBAs (20°–30°) do not necessarily introduce large errors. The latter conclusion is encouraging given that such CBAs are common within the WSR-88D network.
4. Summary and conclusions
The OSSEs presented above provide tentative support to one of the primary hypotheses of the warn-on-forecast vision (Stensrud et al. 2009): that storm-scale ensemble forecast systems achievable in the near future will enable mean tornado-warning lead times of 30 min or more. The most encouraging results were obtained in experiments where both emulated WSR-88D radars were positioned > 100 km (during the data assimilation period) from a pair of supercells (supA and supB) that later developed distinct LLMs. Despite the relatively coarse radar resolution and the absence of observations over the lowest 1.5 km of the atmosphere, the EnKF data assimilation system retrieved the boundary layer well enough for ensuing ensemble forecasts to effectively predict the development and evolution of the LLMs. Supercell supA was correctly forecast to develop a stronger LLM than supB, and the timing of the onset of significant LLR was predicted fairly well in both cases. In addition, the trajectories of both storms' LLMs were captured reasonably well. These results suggest that even in the common scenario where a supercell exists within a low-level gap in the WSR-88D domain, operationally useful probabilistic guidance can be obtained on the timing, path, and magnitude of tornado risk. Moreover, additional experiments with supA indicated that while extremely narrow radar cross-beam angles may substantially degrade LLM forecasts (though not enough to render them useless), cross-beam angles as low as 20°–30° may not be unduly detrimental. The latter result is broadly consistent with the OSSEs of Potvin and Wicker (2012), in which decreasing radar cross-beam angles from ~90° to ~30° had a relatively minor impact on EnKF analyses of a supercell wind field, while analyses from assimilating only single-radar data contained large dynamical errors. The results of the present study suggest the frequently suboptimal radar–storm geometry within the WSR-88D network does not preclude useful numerical prediction of LLMs.
Forecasts of a supercell that failed to develop strong LLR (supC) were less successful than forecasts of supA and supB. The magnitude of LLR was overpredicted during much of the forecast period; in fact, more ensemble members predicted the development of strong LLR in supC than in supB. This result implies that mitigating the tornado-warning false alarm rate may continue to be a significant challenge under the warn-on-forecast paradigm.
In experiments in which one of the radars was relocated to within 30–50 km of the storms, supA forecasts generally benefited from the higher-resolution observations and data availability nearer the ground. This result is consistent with previous studies (e.g., Dong et al. 2011; Schenkman et al. 2011; Snook et al. 2012) and motivates the installation of gap-filling (e.g., Collaborative Adaptive Sensing of the Atmosphere; McLaughlin et al. 2009) radars within the current WSR-88D network. The supB forecasts, however, generally did not improve when the radar was moved closer to the storm. Worse, the supC forecast initialized at t = 50 min was substantially degraded, with low-level rotation being even more overpredicted than in the forecast with both radars > 100 km away. These results indicate that assimilating additional observational information may not necessarily improve ensemble forecasts of supercells. The limited number of experiments, however, prevents us from determining whether such behavior may be common. Whether the unexpectedly poor forecasts arose from a deficiency in the data assimilation system, compensating model and initial condition errors in the far-radar experiments, a pathology in the model solution space surrounding the truth simulation trajectory (such that some solutions that are initialized further from the truth trajectory end up nearer the latter than solutions initialized closer to the truth trajectory), or some other factor is an important question that the authors may investigate in future OSSEs.
Forecasts of all three supercells were substantially improved in all but one case (near_P-CBA_supA) when initialized at t = 70 rather than 50 min, presumably due to both the better initial conditions (owing to the additional 20 min of data assimilation) and the shorter forecast lead times. In instances where forecasts initialized at t = 50 min were degraded from moving one of the radars closer to the storm, initializing the forecasts at t = 70 min significantly mitigated those errors. To the extent that the improvements in the t = 70 min forecasts resulted from improved initial conditions, it is possible that methods for reducing the ensemble spinup time [e.g., “running in place,” or RIP; Kalnay and Yang (2010)] or assimilating phased-array radar data (Yussouf and Stensrud 2010) could substantially improve the t = 50 min forecasts. This would soften the trade-off between increased forecast accuracy (later initialization) and increased forecast lead time (earlier initialization).
As explained in the introduction, the forecast results presented in these idealized experiments provide an estimate of the best-case scenario achievable in practice. It is plausible that if the above experiments with supA and supB were repeated for real storms in similar scenarios (i.e., comparable radar–storm geometries and storm environments), larger model errors could increase the spread and/or bias in the LLM path forecasts enough that a reasonably sized tornado-warning polygon based on that guidance would fail to encompass the true LLM path. Perhaps more concerning is the possibility that supercells that do not develop strong low-level rotation (as with supC) may pose an even greater false alarm risk than our idealized experiments suggest. To explore these possibilities, the OSSE framework presented herein should be extended to examine the impact of various model errors (including in the initial storm environment) on LLM forecasts. The results of those experiments would further clarify expectations for the performance of near-future warn-on-forecast systems and, potentially, identify additional scenarios where numerical forecasts of low-level rotation may fare poorly. It would also be valuable to explore how much the forecast accuracy suffers under more unpredictable scenarios, such as when the supercell is strongly interacting with nearby storms or traversing a highly heterogeneous, poorly sampled environment. Finally, forecast improvements from recent EnKF innovations, including asynchronous filters (Sakov et al. 2010; Wang et al. 2012) and the RIP method mentioned above, should be examined. The authors plan to pursue at least some of these lines of research in future work, with particular emphasis on the impact of microphysical parameterization and background state errors.
Acknowledgments
The first author was supported by a National Research Council Research Associateship Award at the NOAA/National Severe Storms Laboratory. We thank David Stensrud and Thomas Jones for their helpful suggestions on a preliminary version of this paper. We are also grateful for the thoughtful critiques of Jim Marquis, David Dowell, and an anonymous reviewer.
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