1. Introduction
a. Background
Severe weather events are responsible for hundreds of fatalities and billions of dollars of damage annually in the United States alone. Therefore, there is considerable motivation to improve forecast skill for those events currently resolved by state-of-the-art numerical weather prediction (NWP) models. Toward this goal, it is proposed in the present work to assimilate total lightning data to provide an improved representation of the convection at the beginning of the forecasting period (i.e., analysis time). The rationale for conducting this modeling exercise arises from the existing well-known relationship between the occurrence of significant total lightning activity and deep convective updrafts and precipitation (e.g., MacGorman et al. 1989; Goodman et al. 1988; Wiens et al. 2005; Fierro et al. 2006), which allows for the development of lightning proxies within the aforementioned NWP models. For the case study presented herein (the tornado outbreak of 24 May 2011), the assimilation of total lightning data is strongly preferred relative to the assimilation of only cloud-to-ground (CG) flashes. This is because in contrast to CG flashes, intracloud (IC) flashes show an excellent correlation with updraft strength within deep continental storms and, consequently, with the timing of the convective development (MacGorman et al. 1989; Schultz et al. 2011). On the other hand, CG flashes in deep convective storms are generally better correlated with reflectivity core (~50 dBZ) descent and with the development of rainy downdrafts (e.g., Carey and Rutledge 1996).
The establishment of strong positive correlations between total lightning flash rate and deep convective intensity in the past decade has fostered interest in determining whether readily available, nearly continuous lightning data could be used in real time to improve convection forecast skill (e.g., Williams et al. 1999; Geernaert et al. 2010). Particular interest is focused on high-impact systems such as mesoscale convective systems, squall lines, or even supercell thunderstorms (e.g., MacGorman et al. 1989; Goodman and MacGorman 1986). Only a limited number of studies, however, have attempted to assimilate lightning into forecast models. The first study from Alexander et al. (1999) demonstrated an improvement of 12–24-h rainfall forecast when lightning data were assimilated into an extratropical cyclone. Similar results were found a few years later by Chang et al. (2001). A preliminary operational application of lightning data is the inclusion of rain rates as a proxy for lightning in the model’s initial conditions of the Rapid Update Cycle (RUC) model (Benjamin et al. 2004). Mansell et al. (2007) made use of the lightning data from the Oklahoma Lightning Mapping Array (LMA; Rison et al. 1999; MacGorman et al. 2008) and the National Lightning Detection Network (NLDN; Cummins and Murphy 2009; Biagi et al. 2007) by modifying the Kain–Fritsch (Kain and Fritsch 1993) convective parameterization scheme (CPS) to allow the lightning data to control the “trigger” function within this CPS scheme. The main idea behind this method was first proposed by Rogers et al. (2000) and used for assimilating radar data. Recently, Pessi and Businger (2009) assimilated Pacific Lightning Detection Network/Long-Range Lightning Detection Network (PacNet/LLDN) lightning data by adjusting the latent heating profile produced by the CPS for a Pacific storm case. They used the Tropical Rainfall Measuring Mission (TRMM) lightning and rainfall data to derive a lightning–rainfall relationship to convert PacNet/LLDN data to rainfall rates (following Jones and Macpherson 1997a,b; Alexander et al. 1999), which were then assimilated. Papadopoulos et al. (2005) utilized real-time CG flash-rate data from a long-range lightning detection network to force deep moist convection into a regional mesoscale model by nudging the simulated humidity profiles to empirical profiles representative of convective regimes from observed soundings during thunderstorm days. None of the aforementioned works, however, conducted assimilation of total lightning data at cloud-resolving scales (i.e., Δx ≤ 3 km), the latter objective being emphasized by the present study.
It is relevant to stress that the emphasis here is not directed on longer-term forecasts (6–24 h) but rather on demonstrating how assimilating total lightning data from the Geostationary Lightning Mapper (GLM) instrument aboard the upcoming Geostationary Operational Environmental Satellite “R” series (GOES-R; Gurka et al. 2006) into a convective-allowing model may improve the representation of the observed severe convection at the analysis time (i.e., just prior to the start of the forecast cycle) and conjointly 1 h into the forecast. In follow-on studies, those improved initial conditions via the assimilation of total lightning data could be used, for example, within a statistical ensemble Kalman filter (EnKF) to hopefully improve short-term forecasts of the high-impact weather, particularly where weather radar data are unavailable or sparse.
The first launch of the GOES-R series satellite is scheduled for 2015, and the GLM is modeled after the Lightning Imaging Sensor (LIS; Christian et al. 1999) that will map total lightning (CG + IC) with a nearly uniform resolution ranging between 8 and 12 km over the Americas continuously during day and night with >70% detection efficiency. Therefore, the present study makes use of pseudo GLM lightning data derived from the Earth Networks Total Lightning Network (ENTLN), whose main characteristics are given later in section 2b.
b. Brief description of the synoptic setup
On 24 May 2011, a significant outbreak of long-lived supercell thunderstorms struck central Oklahoma (OK). A total of 12 tornadoes were reported during the severe weather event and several tracked dangerously close to populated metropolitan areas (Fig. 1). Half of those were violent tornadoes rated EF-3 or greater on the enhanced Fujita scale (http://www.srh.noaa.gov/oun/?n=events-20110524-tornadotable).
Map of tornado tracks over central Oklahoma from the National Weather Service with tornado ratings shown below each reported tornado (http://www.srh.noaa.gov/oun/?n=events-20110524-tornadotable).
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
Forecasts of this significant tornado outbreak were made available to the public up to days in advance, due to an exceptional congruence of environmental ingredients known to be associated with severe weather in the southern plains. On 24 May, a deepening low (995 hPa) associated with a negatively tilted shortwave trough emerging from the Rockies facilitated significant advection of moisture northward from the Gulf of Mexico ahead of a pronounced dryline in the Texas (TX) Panhandle (Fig. 2). Dewpoints ahead of the dryline were as high as 295 K (72°F) and were coincident with locally high static instability in the low to midtroposphere with mixed-layer convective available potential energy (CAPE) values exceeding 3000 J kg−1 (Fig. 3) over a broad area (Fig. 2). Extreme low-level directional and speed shear resulted in 0–3-km storm relative helicity values in excess of 250 m2 s−2 (Fig. 3), which is well above the 100 m2 s−2 threshold for the occurrence of significant tornadoes (i.e., EF-3 or greater; Davies-Jones et al. 1990; Droegemeier et al. 1993). Mixed-layer convective inhibition (CIN) ahead of the dryline was overall marginal (approximately −40–50 J kg−1; Fig. 3), which could assist in delaying the development of widespread convection there. Within this exceptional thermodynamic and dynamic environment, convective cells that initiated near 1900 UTC in northwestern OK quickly became severe and tornadic. A “particularly dangerous situation” (PDS) tornado watch was issued by the Storm Prediction Center over much of central OK at 1750 UTC, about 1 h prior to convection initiation (CI).
Sketch of the mesoscale discussion analysis (#925) at 1718 UTC from the Storm Prediction Center showing various key environmental factors of the 24 May 2011 tornado outbreak. The 50- and 65-kt wind speed contours (1 kt = 0.5144 m s−1) at 500 hPa are shown in blue and depict the midlevel jet streak. Similarly, the 70° and 72°F surface dewpoint contours are shown in green and the 1500 and 3000 J kg−1 contours for CAPE are highlighted in dark pink. The surface boundaries are represented by their usual symbols. Legends for contours are indicated on the map. States are indicted by their usual abbreviations with a black star showing the location of the Oklahoma City metro area for reference.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
Skew T–logp diagram at 1800 UTC 24 May for Norman, OK (OUN). The equilibrium level (EL; hPa), CAPE (J kg−1), convective inhibition (CIN; J kg−1), and lifting condensation level (LCL; hPa) are shown on the right of the figure. The CIN and CAPE were computed for mixed parcels from the 50-mb-deep layer based at the surface with appropriate virtual potential temperature correction made (Doswell and Rasmussen 1994). Sounding data courtesy of the University of Wyoming.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
2. Methodology
a. Model and simulation setup
The numerical model used in this study is the three-dimensional compressible nonhydrostatic Weather Research and Forecasting Model (WRF) with the Advanced Research WRF (ARW) dynamic solver (WRF-ARW, version 3.1.1) developed by the National Center of Atmospheric Research (Skamarock and Klemp 2007). For consistency, all the simulations herein make use of the same physics parameterizations, numerics, and domain parameters unless otherwise specified. The choice of the physics parameterizations and large-scale fields necessary for providing the initial and boundary conditions of the finescale simulation presented here were inspired by the National Severe Storms Laboratory (NSSL) daily forecast runs over the contiguous United States (CONUS) (Kain et al. 2011). The main physics choices are the WRF single-moment, 6-class bulk microphysics scheme (WSM6) from Hong and Lim (2006), the Mellor–Yamada–Janjic turbulence kinetic energy (TKE) scheme for the boundary layer (Janjic 1994) with Monin–Obukhov–Janjic similarity theory for the subgrid-scale turbulence processes (Chen et al. 1997), the unified Noah land surface model (Chen and Dudhia 2001; Ek et al. 2003), and the Dudhia (1989) shortwave and Rapid Radiative Transfer Model (RRTM) longwave radiation (Mlawer et al. 1997) schemes. Last, the initial and boundary conditions use the 6-hourly North American Mesoscale Model (NAM) 40-km reanalysis data for an entire 12-h period starting at 1200 UTC 24 May 2011.
The simulation domain (shown in Fig. 4) features two nested grids. The three domains have horizontal grid spacings of 9 km (D01), 3 km (D02), and 1 km (D03), with horizontal dimensions in grid points of (130 × 160), (262 × 361), and (604 × 802), respectively. With this configuration, the individual grids represent convection-resolving (1 km) and convection-allowing (3 km) as used in several experimental NWP models, and the scheduled GLM resolution over CONUS (9 km). The stretched vertical grid has 35 levels with model top at 50 hPa (~20 km). To facilitate independent comparisons of the results on each grid, neither one-way nor two-way nesting were employed. The fields on each nested grid were initialized by interpolating fields from the parent grid at the time the nested grid was spawned with the NAM-derived time dependent boundary conditions used every 6 h.
Sketch of the WRF-ARW simulation 9-km parent domain (D01) with the 3-km (D02) and 1-km (D03) domains. States are indicated by their usual abbreviations and similar to Fig. 2; a black star shows the location of the Oklahoma City metro area for reference.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
The 3-km nested grid (D02) was introduced at 1400 UTC while the 1-km nested grid (D03) was spawned at 1600 UTC, thus allowing the respective parent grids a few hours of spinup prior to each nested grid initialization. Although the simulations reported in the current study span a 12-h period (until 0000 UTC 25 May), the analysis will focus on the period of frequent lightning activity accompanying the development of the first supercells along the dryline in OK between 1930 and 2130 UTC (Fig. 5). The computational dynamic time steps were set to 45, 15, and 5 s on the 9-, 3-, and 1-km grid, respectively.
(a)–(c) ENTLN flashes interpolated onto the WRF local 9-km grid (D01) for a 10-min period ending at the time shown on the upper right corner. The times shown include the formation of the first severe cells along the dryline near 1930 UTC until the full development of the storms along the dryline in central Oklahoma near 2130 UTC. (d)–(f) Radar reflectivity at 2 km MSL (in dBZ) obtained from the National Severe Storms Laboratory NMQ product projected onto the local 1-km (D03) domain.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
b. Brief description of the ENTLN lightning data and assimilation procedure
The ENTLN network consists of 500+ sensors worldwide with over 150 sensors deployed over CONUS alone (http://weather.weatherbug.com/weatherbug-professional/products/total-lightning-network). Each broadband sensor detects radio emissions spanning the 1- to 12-MHz frequency range, in principle allowing for the detection of both IC and CG flashes. The system then uses the differences in the times at which a given sferic arrives at four or more stations to compute the location and time at which the sferic was produced by a developing lightning channel [similar to, e.g., Rison et al. (1999)]. Over CONUS, the ENTLN geolocation accuracy varies from tens of meters in dense areas of the network to about 500 m (Fig. 6c), with a national average detection efficiency exceeding 95% for typical CG return strokes (~10 kA; Fig. 6a) and about 50% for typical IC flashes (~1 kA; Fig. 6b). Note that the detection efficiency for IC flashes over OK is larger than the national average, with values nearing 70% (Fig. 6b).
Maps showing the ENTLN detection efficiency over CONUS for (a) cloud-to-ground flashes, (b) intracloud flashes, and (c) geolocation error (in m). Figure used with permission by Earth Networks scientists and representatives (J. Anderson, S. Heckman, and S. Prinzivalli).
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
The ENTLN lightning data were gridded from latitude and longitude coordinates onto the local WRF Cartesian grid coordinates and parsed into 10-min intervals of accumulated lightning flash data that span the period beginning at 0000 UTC 24 May and ending at 0000 UTC 25 May. For the present study, the lightning data were first gridded onto a uniform 9-km grid and then projected onto the local coordinates of each of the three domains in Fig. 4. The projection of the lightning data from the 9-km resolution parent domain onto the inner nests simply assigns the value of the flash rate within a given 9 × 9 km2 grid cell onto all the grid cells of the finer-resolution nests (i.e., 1 × 1 km2 and 3 × 3 km2) that are encompassed in it. The motivation for this procedure is twofold: (i) the assimilation assumes a hypothetical scenario whereby GLM resolution lightning data are readily available and (ii) the resulting identical lightning fields (gridded flash rate) and lightning areal coverage for all grids allow for an equal amount of nudging to be performed on all the three grids. Note that the ENTLN sometimes locates more than one point per flash. Because the sparcity of the sample makes a distance criterion for defining flashes (e.g., MacGorman et al. 2005) problematic, this study did not attempt to define flashes, although for simplicity, this paper refers to mapped points as flashes.
Water vapor is added in the 0° to −20°C layer, which represents the mixed-phase graupel-rich region within convection and hence is most likely associated with electrification and lightning activity (MacGorman and Rust 1998) via the noninductive charging mechanism (e.g., Takahashi 1978; Saunders and Peck 1998). The local increase in water vapor [and hence relative humidity (RH)] is only applied if the RH at the time step within the corresponding grid point within the mixed-phase region is below 81%. In (1), the increase of RH that is applied within the mixed-phase layer is inversely proportional to the simulated graupel mixing ratio and hence is maximized when no graupel is present in the grid cell and minimized for mixing ratios greater or equal than 3 g kg−1. For graupel mixing ratios ranging between 0 and 3 g kg−1, RH increases as a function of gridded flash rate. For instance, if the simulated graupel mixing ratio at a grid point within the mixed-phase layer is 1 g kg−1 and the gridded flash rate at the grid location is 150 flashes per 10 minutes, then the local RH will be increased to ~89.5% provided that the simulated RH at the grid point is not already greater than or equal to 81% (Fig. 7). This overall mild RH slope (Fig. 7), combined with a marginal asymptotic value, was designed to increase the chances of generating isolated convection during the initial stages of the assimilation as observed in Figs. 5d–f and, concomitantly, to reduce the potential for outflow dominance of the forced storms (see section 3).
Plot of the water vapor nudging function for several values of graupel mixing ratios (in g kg−1) with legend shown in the top right corner.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
The various constant coefficients in (1) could be easily adapted to a given case study. In this simulation, A = 0.81, B = 0.2, C = 0.01, D = 0.25 and α = 2.2. The constant A controls the minimum RH in the grid column where (1) is applied. Coefficient B controls the amount of water vapor added to the minimum value set by A and therefore determines the asymptotic value (i.e., maximum RH) for each curve in Fig. 7. The coefficient C regulates the slope of the curves below the asymptotic value set by B and hence primarily controls the amount of water vapor added at lower flash rates, with larger C increasing the amount of water vapor and therefore RH. Finally, D sets the maximum Qg threshold value at which the local RH is not allowed to be nudged above the minimum value set by A. Additional tests revealed that this assimilation procedure is not sensitive to changes in A within ±5%.
Note that the RH nudging is carried out at each computational time step to prevent early demise of the forced convection. In other words, the lightning data are assimilated over a 10-min period using the lightning data from the 10-min lightning data file that corresponds to the current time in the simulation. After this 10-min period has been completed, the lightning assimilation switches to the subsequent 10-min period of lightning data, and so on until the final assimilation time (2130 UTC) is reached.
A nominal time interval of 10 min was selected for the lightning assimilation to resolve individual storm movements. For the present case study, time intervals greater than 20 min were deemed temporally too coarse to resolve storm motion, and hence intervals ranging between 5 and 20 min could have been easily considered. For instance, had a time interval of 5 min been selected to parse the ENTLN lightning data, the resulting lower gridded flash rates in the parsed lightning files could have been easily taken into account by increasing the constant C in (1) by a factor of about 2. Furthermore, for weakly electrified storms producing a lower gridded flash rate over a smaller area, the coefficient A could be increased from 81% herein to values ranging between, for example, 90% and 95% to increase the likelihood of the model in forcing convection. If needed, the remaining three constants (namely B, C, and D) described above could also be increased individually and/or simultaneously to further enhance the probability of the model in generating updrafts. For cases characterized by modest-to-high lightning flash rates over a broad area, it is recommended to opt for an overall gentle local introduction of water vapor during the assimilation cycle by using smaller values of C (mild slopes) and/or not too high thresholds of maximum supersaturation and minimum RH. This is because the introduction of too much water vapor into the model over a short time can result in the contamination of the solution by spurious gravity waves, leading ultimately to computational instability.
In summary, wherever lightning is observed, the nudging procedure for this case study guarantees that the minimum RH in the mixed-phase region remains at or above 81%. Several tests have been conducted using different Qg upper thresholds (here set to 3 g kg−1) as well as varying the lower and upper bounds of the RH increase (here set between 81% and 101%, respectively; Fig. 7). Those tests showed that the aforementioned values gave satisfactory results for the present case study and likely other case studies with similar high lightning flash rates. Locally increasing the water vapor mixing ratio (at constant temperature) in a layer is relatively easy to implement in a microphysical code and imposes minimal constraints in the model physics by locally increasing the perturbation virtual potential temperature, which leads to buoyancy acceleration and, ultimately, an updraft.
c. Observational data used to evaluate the model
The simulated radar reflectivity fields will be evaluated against observations from the three-dimensional National Mosaic and Multisensor Quantitative Precipitation Estimation (QPE)—referred to as NMQ—product from NSSL (as shown in Figs. 5d–f) interpolated onto the local grids. The algorithm behind NMQ takes base-level data from all available radars [e.g., Weather Surveillance Radar-1988 Doppler (WSR-88D), Canadian radars, terminal Doppler weather radar (TDWR), gap-filling radar, etc.] at any given time, performs quality control, and then combines reflectivity observations from individual radars onto a unified 3D Cartesian frame (Zhang et al. 2011).
Simulated key surface properties such as potential temperature, dewpoint, and horizontal wind fields will be evaluated against archive data from the Oklahoma Mesonet (http://www.mesonet.org/), which consists of 120 automated stations covering the state such that at least one Mesonet station is deployed within each of Oklahoma’s 77 counties. Each Mesonet station of this dense network is built around a 10-m-tall instrumental tower. The observations are transmitted every 5 min, 24 h per day year-round, and are made available to the public almost instantly.
The availability of this high spatial and temporal resolution data is one of the primary reason for selecting this case study over another in the United States to conduct this lightning assimilation experiment.
d. Simulations outline
Two simulations are sufficient for the objective of this study. In the first simulation, the control case (CTRL), the convection is allowed to evolve unforced (i.e., without assimilating any lightning data). The second simulation is the LIGHT case, which is the same as CTRL except that the ENTLN total lightning data are assimilated into the running model. Lightning is assimilated within a 2-h period spanning the initiation of the first severe convective cells along the dryline (near 1930 UTC; Fig. 5d) through full storm development along the dryline in OK (near 2130 UTC; Fig. 5f). Additional sensitivity tests with different lightning assimilation periods prior to 2130 UTC (not shown) revealed that a 2-h window was the minimum amount of time necessary to produce the desired improvement in the representation of the convection at the analysis time (2130 UTC). Starting the lightning assimilation at times earlier than 1930 UTC has little effect on the results obtained with the aforementioned time window (not shown). This was due to (i) the overall lack of observed deep convection (and thus also lack of lightning activity) in central OK between 1200 and 1900 UTC and (ii) the relatively much weaker lightning activity during the first 30 min of the storm lifetime (between 1900 and 1930 UTC; not shown).
During the 2-h assimilation period, each severe cell was characterized by intense lightning activity, with several stronger cells exhibiting maximum flash rates exceeding 200 (10 min)−1 (81 km2)−1 during the interval considered (Figs. 5a–c). In operational forecasts, observations are routinely assimilated only up to the beginning of the forecast period. Again, the emphasis of this study is not to evaluate the skill of a single deterministic forecast after assimilation of the lightning data, but rather to improve the state of the convection at the analysis time (again, set here at 2130 UTC). It is expected that at least short-term (1–3 h) forecasts may be improved simply by starting with deep convection and corresponding cold pools at the correct locations (e.g., Mansell et al. 2007). Thus we will also examine how the subsequent 1-h forecast (2230 UTC) is improved by assimilating lightning data.
3. Results and discussion
a. CTRL simulation
To gauge the impact of the lightning data assimilation, the CTRL case is evaluated first. The resulting fields on the 3-km (D02) grid are emphasized because of the similarity of its resolution to that of current experimental NWP forecast models. Moreover, to facilitate the comparisons among all the three grids and to focus on the severe convection over OK (i.e., tornadic cell tracks shown in Fig. 1), all the results showing radar reflectivity are plotted with the geographical dimensions of the 1-km domain (i.e., D03). The surface potential temperature and dewpoint data from the model, however, are plotted on a slightly different domain whose dimensions are dictated by the spatial coverage of the Oklahoma Mesonet.
Before focusing on the convection, the evolution of basic surface properties such as surface potential temperature and horizontal wind is examined first. Figure 8 shows horizontal projection of the Oklahoma Mesonet surface wind vectors and potential temperature θ observations side by side with those of the CTRL run. The times of interest are 1930, 2030, and 2130 UTC, which span the lightning assimilation period. At 7 h 30 min into the simulation, the model does not capture the strong zonal θ gradient (or the dewpoint gradient; not shown) observed along the dryline during CI near 1930 UTC. However, simulated surface θ values far to the west (~313 K) and far to the east of the dryline (~303 K; Fig. 8) show overall good agreement with the Mesonet observations. Of importance also are the somewhat larger simulated θ values in central OK ahead of the dryline (~307 K) compared to the observations (~305 K). Simulated dewpoints to the east of the dryline are 2 K higher than observation, while to the west of the dryline they show overall good agreement with observations with values lower than 270 K (not shown).
(a)–(c) Oklahoma Mesonet observations of potential temperature (contours and shadings in K) and horizontal wind (in m s−1) at the same times as Fig. 5. (d)–(f) As in (a)–(c), but for the CTRL simulation on the 3-km nest (D02). Legends for colors and shadings are shown at the bottom of each corresponding row. Note that for convenience the same legends for contour and shading were used in the observations and the CTRL simulation.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
The wind speeds and wind direction outside the areas of active convection and well to the west and east of the dryline are in good agreement with the Oklahoma Mesonet observations near the time of CI. However, the model fails to reproduce the observed strong surface wind convergence across the dryline (e.g., cf. Figs. 8a and 8d). While admittedly the dewpoint, potential temperature, and wind fields to the west and east of the dryline are generally in good agreement with observations during CI, the lack of a sharp thermodynamic gradient coupled with weaker surface convergence across the dryline in the model explains why the simulated convection in Figs. 9a–c does not develop as consistently as in the observations (Figs. 9d–f). During the observed CI, the model has no convection over northwest OK (cf. Figs. 9a and 9d). An hour later, strong convective cells develop in northern TX and south central OK in agreement with observations. Conversely, at the same time in the Oklahoma City metro area near the EF-5 tornado track (Fig. 1), convection is still absent in the model (cf. Figs. 9b and 9e). The latter results still hold at 2230 UTC with a relative absence of simulated convection in north central and south central OK with the exception of an isolated southwest–northeast-oriented band of convection south of the Oklahoma City metro area (cf. Figs. 9c and 9f). The latter convective band is in broad agreement with observations (Figs. 9c,f). One could argue justifiably that a 3-km horizontal grid spacing might be too coarse for the convection to develop in a timely manner along the dryline (e.g., Ziegler et al. 1997). The convective evolution on the 1-km grid, however, shows similar results (not shown).
(a)–(c) Simulated radar reflectivity (in dBZ) for the CTRL run at 2030 (during assimilation period), 2130 (end of assimilation period or analysis time), and 2230 UTC (1-h forecast) for the D02 simulation, respectively. Note that in this and all subsequent plots, the domain boundaries of D02 were cropped to the size of the D03 domain to focus on the OK convection and to allow an easy comparison between all grids later on. (d)–(f) As in (a)–(c), but for interpolated radar reflectivity from the NMQ product onto the 3-km (D02) grid again using the same domain boundaries as D03. Legends for shadings are shown on the right.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
Coupling with the lack of surface convergence, strong zonal θ, and dewpoint temperature gradients across the dryline in the simulation, the delay or absence of convective development in the model may also be explained by the simulated thermodynamic environment in central OK being characterized by moderate CIN (approximately −45 J kg−1; Fig. 10), with marginally larger mixed-layer CIN magnitudes elsewhere in central OK (approximately −60 J kg−1; not shown), which is in good agreement with the observations from the OUN site in Norman, OK (Fig. 3). Under those prohibitive conditions for widespread convection, only strong forcing such as found near a sharp dryline with strong surface convergence, zonal θ, and dewpoint gradients with solenoidally forced secondary circulations could allow boundary layer parcels to overcome this layer of stable air and realize the CAPE aloft; simulated values from nearby OUN are about 33% larger than the observations (3100 J kg−1 in Fig. 3 compared to 4100 J kg−1 in Fig. 10).
Simulated sounding at 2000 UTC 24 May 2011 taken at the gridpoint coordinates (i, j) = (350, 400) on the 1-km nest (D03). This grid point is located in the south-central region of Oklahoma. As in Fig. 3, the CIN and CAPE (both in J kg−1) were computed for mixed parcels from the 50-mb-deep layer based at the surface with appropriate correction for virtual temperature made (Doswell and Rasmussen 1994). The parcel’s equilibrium level (EL; hPa), LCL (hPa), and the 0–3-km storm relative helicity (SREH; in m2 s−2) are also shown in the upper right corner.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
The assimilation of the total lightning data is not designed to remedy the aforementioned limitations in the simulated environment both prior and during CI, which likely arise from using relatively coarse 40-km reanalysis fields. On the other hand, it is shown in the next section that lightning data could assist in improving the analysis from which the forecast is derived by placing and evolving the observed convection at the right locations during the assimilation period.
b. Lightning assimilation experiment LIGHT
Figure 11 shows the same surface fields as Fig. 8 but for times shifted ahead by 1 h to show the 1-h forecast and the effects of the lightning data assimilation 1 h into the assimilation period. This is because the assimilation procedure increases RH between 0° and −20°C, and the formation and fallout of precipitation in the model requires a time scale of a few tens of minutes to see significant effects down to the surface.
As in Fig. 8, but for the LIGHT lightning assimilation run (on D02). The times shown are also the same as in Fig. 9.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
Several noticeable differences are worth mentioning in Fig. 11. An hour into the assimilation period, the lightning-induced convection in northwest OK produced a weak cold pool at the surface, which is still about ~6 K warmer than observations at the same time (Figs. 11a,d) for the reasons mentioned in the previous section. At 2130 UTC, however, the model shows a well-defined cold pool at the surface in north-central OK with temperatures near 299 K, which is in remarkably good agreement with the observations from the Oklahoma Mesonet (Figs. 11b,e). As the cold pools1 spread at the surface, they also assist in sharpening the θ gradient across the former dryline, which is now in better agreement with observation at analysis time (2130 UTC) in north central OK. Those results also hold at the 1-h forecast time (Figs. 11c,f).
While the assimilation of total lightning data clearly aids the model in forcing the convection at the right place as indicated by the presence of the cold pools (Fig. 11), the assimilation does not prevent the development of spurious convection as indicated by a second cold pool in central OK (e.g., Fig. 11b vs Fig. 11e and Fig. 11c vs Fig. 11f). This suggests that especially for case studies where thermodynamic conditions for strong convection are widespread, (e.g., low CIN below ~20 J kg−1 and moderate CAPE magnitudes in excess of ~1500 J kg−1), assimilating total lightning data might not have notable desired effects unless the spurious convection is limited during the lightning assimilation period. While this topic is certainly relevant for any case studies, it will be deferred to future work.
In addition to the results deduced solely by analyzing the surface cold pools, Fig. 12 shows clearly that the lightning assimilation results in a much improved representation of the convection at the analysis time (cf. Figs. 12b,e and 9b) and at the 1-h forecast (cf. Figs. 12c,f and 9c) with the assimilation starting to show some noticeable improvements of near-surface precipitation at 1 h into the assimilation (Figs. 12a,d). The improvements in the reflectivity field are best seen in north central OK and to some degree in northern TX (Figs. 12b,e).
As in Fig. 9, but for the LIGHT lightning assimilation run.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
Despite this improvement, several shortcomings should be noted at the analysis time. First, the forced convection propagates farther to the north and east than the observations, as indicated by the eastward shift of the 30+-dBZ reflectivity contours relative to observations (Figs. 12b,e). Second, the assimilation does not capture well the convection over Kansas along the warm front, which is likely due to comparatively weak flash rates in those cells in the assimilation time considered (Figs. 5a–c). Figures 11 and 12 show that the lightning-induced convection exhibits a tendency of being outflow dominated in the later hours (2130 UTC and later) by showing traits of a fast-moving squall line (not shown). This tendency toward outflow dominance is exacerbated at finer grid spacing (D03), while being nonexistent at the coarsest grid spacing (D01) because of overall weaker convection and associated weaker downdrafts. Of greater fundamental importance, outflow dominance has been shown to be forced by excessively dry midlevel storm environment evident in Fig. 10 compared to Fig. 3 (Gilmore and Wicker 1998). Several tests with the current and other severe weather events showed similar issues, especially once the assimilation of the lightning data ceased (i.e., after the analysis time).
Figure 13 depicts simulated and observed reflectivities at 5 km MSL within the mixed-phase region where the lightning assimilation is applied. A more direct effect of the lightning assimilation is expected in this layer, as best illustrated in Fig. 13a. Of particular relevance, the model fails to reproduce the widespread areas of weak reflectivities (smaller than 25 dBZ) that are indicative of midlevel stratiform precipitation and anvils, downstream of the main convective cores (cf. Fig. 13b vs Fig. 13e, and Fig. 13c vs Fig. 13f). It is known that stratiform precipitation and anvil shadows have an overall cooling and stabilizing effect ahead of the storms as well as a moistening effect of the lower layers of the atmosphere, possibly in turn altering the evolution of the convection. Markowski et al. (1998) postulated that anvil shadows could generate baroclinic zones ahead of the storm, which in turn could enhance tornado potential once the storm updraft core moves over the area previously obscured by the anvil. The regions of weak reflectivities downstream of the main cores likely arise from the presence of falling low-density graupel and aggregates, neither of which is well represented in single-moment schemes such as WSM6. Thus, the use of single-moment bulk microphysics in the simulations could result in errors due to poor representation of stratiform precipitation regions.
As in Fig. 12, but at 5 km MSL.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
To explain why the simulated convection becomes outflow dominated in the model, Fig. 14 shows that the simulated dewpoints a few meters above the surface within the cold pools are lower by as much as 10 K than the observations (cf. Figs. 14b,e,h and Figs. 14c,f,i). Outflow-dominated storms are also seen on the 1-km mesh (not shown). Recall that the simulated θ values in the cold pools show overall much smaller departures from observations but translate to larger perturbation θ in the simulation. The areal coverage of the lower θ contour depicting the boundaries of the outflow region is also generally in reasonable agreement with observations for the forced convection (e.g., compare the 301-K contours in Figs. 11b and 11e). The much lower dewpoints suggest that the model is producing downdrafts that are too wide and too strong, which in turn accounts for the tendency of the assimilation-induced convection to become outflow dominated. The stronger than observed simulated downdrafts could likely be a consequence of the model sounding (Fig. 10) being much drier above the boundary layer (~1 km MSL) than the observations (Fig. 3). Moreover, the warmer boundary layer in the simulation (cf. Figs. 3 and 10) would enhance the penetration of midlevel downdrafts to the surface. Once the simulated strong downdrafts reach the surface, the larger temperature difference (and gradient) between the cold pool and the environment in the simulation (~10 K; Figs. 14e,f) compared to the observations (~4 K; Figs. 14b,c) would be conducive for the development of fast-moving squall lines rather than supercell thunderstorms. This highlights that the issue of outflow-dominated storms in the simulation does not arise from the assimilation procedure per se, but rather from the model environment near the storms in and above the boundary layer. Another possible factor could involve the lack of mixing of the downdraft air with the moist environment in its vicinity.
(a)–(c) Oklahoma Mesonet observations of dewpoint temperatures (in K) at 1.5 m above ground compared to the simulated dewpoint temperatures at 2 m above ground for the (d)–(f) CTRL run and (g)–(i) LIGHT lightning assimilation run. All times shown are, again, as in Fig. 9. Legend for color and shadings are shown at the bottom of each corresponding row.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
As alluded to earlier, it is possible to carry out direct comparisons of the results obtained on each grid separately since neither one-way nor two-way grid nesting were employed in the simulations. Figure 15 shows reflectivity fields at 2 km MSL at the same three selected times as in Fig. 12 on all three grids. As noted earlier, the forced convection on the outermost parent grid (9 km; D01) is weaker in terms of areal coverage and magnitude of radar reflectivity at all levels (e.g., cf. Figs. 15a,d,g). One of the reasons explaining the weaker response of the convection to the assimilation scheme (i.e., increase in grid RH) arises from using an explicit microphysics scheme on a coarse grid, whereas in operational mesoscale prediction models a CPS (e.g., Kain–Fritsch) might be used instead. In this study, however, explicit microphysics were intentionally chosen on all grids for two reasons: (i) to ensure consistency and enable meaningful comparisons across the grids and (ii) to keep the focus of the analysis on the finer meshes with priority given to the 3-km (D02) grid followed by the convection-resolving grid (1 km; D03).
Simulated radar reflectivity (in dBZ) at 2 km MSL for the same times as in Fig. 9 for (a)–(c) the 9-km parent domain (D01), (d)–(f) the 3-km nest (D02), and (g)–(i) the 1-km nest (D03). For convenience, again, all plots were cropped to the dimensions of the finest grid, namely D03.
Citation: Monthly Weather Review 140, 8; 10.1175/MWR-D-11-00299.1
As the grid spacing decreases, the convection forced by the introduction of water vapor in the lightning areas becomes more evident. As shown earlier, the convection on the 3-km grid (D02) exhibited the tendency to become progressively more outflow dominated, a trend that is further exacerbated at 1 km (Fig. 15i). Comparing Fig. 15i and Fig. 15f, the forced convection in north central OK on the 1-km mesh is shifted farther northeastward than the same forced convection at 3 km. On the 1-km grid, a well-defined leading convective line and developing trailing stratiform region are becoming more evident, especially at the 1-h forecast (Fig. 15i). The finest mesh tends to produce the strongest convective response in terms of local maximum updraft speed (not shown), low-level precipitation (Figs. 15g–i), and hence surface cooling and drying (not shown) compared to the two coarser grids, which has also been noted by earlier studies (e.g., Weisman et al. 1997; Bryan et al. 2003; Fierro et al. 2009).
4. Summary and conclusions
A simple lightning data assimilation scheme has been developed and tested in the convection-allowing WRF-ARW numerical prediction model. Near-saturation with respect to water is introduced within a confined layer in grid columns containing strong observed lightning flash rates. Incremental increases of vapor at constant temperature in lightning areas increase the local perturbation virtual potential temperature, which in turn leads to buoyancy accelerations and, ultimately, an updraft.
The lightning data assimilation showed value in improving the representation of the convection and cold pools at the analysis time. This improvement could be important in cases where the mesoscale environment is not well reproduced by the model either a few hours prior to or during CI. In the present case, the model failed to reproduce and maintain the observed strong surface convergence, zonal dewpoint, and θ gradient across the dryline, which most likely led to the delay or lack of convective activity ahead of the dryline in the CTRL simulation.
Despite this encouraging improvement from the lightning data assimilation, several shortcomings deserve particular attention. First, the convection that is forced by the lightning assimilation showed a tendency of becoming outflow dominated with time, especially during the forecast period. This occurred regardless of the amount of water vapor that was introduced during the assimilation period, provided that the local RH was sufficient to produce a storm. A closer analysis of the surface dewpoint temperature field revealed that the local midlevel environment within the simulated cold pools was much drier than observed, commonly with dewpoint departures of as much as 10 K. Analysis of the model thermodynamic soundings near the simulated storms revealed a much drier environment above the boundary layer coupled with a warmer boundary layer, which both promote strong downdrafts and storm acceleration due to enhanced surging cold pools (Gilmore and Wicker 1998; Ziegler et al. 2010). When the upper and lower bounds of the RH in the lightning nudging function (Fig. 7) are both reduced, the aforementioned tendency for outflow-dominated forced storms seen on the 1-km or 3-km grid was reduced but could not be completely eliminated. This study raises again the importance of the needs for further improvements of the mesoscale midlevel water vapor and potential temperature fields to promote a better depiction of cold pool evolution and potentially lead to more accurate analyses and forecasts of storm structure and evolution.
A relevant problem not seen here and likely limiting the effect of the lightning assimilation is when the areal coverage of the convection produced by the model is comparable to or several times that of the convection forced by the lightning. This could occur in response to biased mesoscale analyses of thermodynamic conditions (e.g., too little CIN). In such situations, the spurious convection produced by the unconstrained model needs to be limited. There is at least one way the latter could be achieved. Total lightning activity can appropriately provide information on where to effectively limit the effects of deep convection on the model environment. For example, below a certain threshold for observed radar reflectivity and/or flash rate at a given grid point, the convection at that grid point could be limited by nudging hydrometeor mixing ratios toward smaller values, thereby reducing the extent and magnitude of the spurious cold pools outside the lightning areas at analysis time. This procedure could be further improved by including observed radar reflectivity during the lightning assimilation period.
Where total lightning data are available, this relatively simple and inexpensive assimilation scheme could be readily incorporated into operational convection-allowing forecast models. The lightning assimilation would be most useful where weather radar data coverage is either sparse or nonexistent, as in the cases of mountainous areas and oceans, respectively.
Acknowledgments
Funding was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement NA08OAR4320904, U.S. Department of Commerce. This work was supported by the NESDIS program, which is under the auspices of the National Oceanic and Atmospheric Administration of the U.S. Department of Commerce under Grant NOAA-NESDIS-OAR- NA08OAR4320904. Computer resources were provided both by the Oklahoma Supercomputing Center for Education and Research (OSCER) hosted at the University of Oklahoma. The authors thank Scott Dembek for providing the 40-km NAM data and Ami Arthur for providing the NSSL three-dimensional NMQ radar mosaic data. Thanks also go out to Steve Prinzivalli, Stan Heckman, and Jim Anderson from Earth Networks for providing the total lightning data for this case study. Finally, the authors would like to express their gratitude for the helpful suggestions provided by the anonymous reviewers on an earlier version of the manuscript.
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The surface dryline is effectively undercut and elevated above the spreading cold pool.
