1. Introduction
High values of total lightning are a good indicator of the occurrence of severe weather, including cloud-to-ground (CG) lightning (e.g., Goodman and MacGorman 1986; Kane 1991; Smith et al. 2000; McCaul et al. 2004; Underwood. 2006; Schultz et al. 2009; Gatlin and Goodman 2010). Hence, the accurate prediction of lightning can be a useful indicator for the prediction of strong, and possibly severe, thunderstorms (Schultz et al. 2009)—a mortal hazard (e.g., Ashley and Gilson 2009).
Various diagnostic approaches have been developed to predict lightning in forecast models (e.g., McCaul et al. 2009; Dahl et al. 2011). Recently, Fierro et al. (2013) implemented a physics-based, explicit lightning scheme within the Weather Research and Forecasting (WRF) Model (Skamarock et al. 2008) that treats space charges as state variables and explicitly solves for the three components of the ambient electric field. Additionally, Lynn et al. (2012) developed a dynamic lightning model for forecasting CG and intracloud (IC) lightning in convection-allowing models. The dynamic lightning model is not an explicit approach as no electrical fields are calculated, nor is it a statistical approach (see, e.g., McCaul et al. 2009), wherein lightning values are calculated directly from the vertical velocity and hydrometeor masses. Rather, the dynamic lightning model uses vertical velocity and cloud hydrometeor fields to build up potential electric energy Ep as a four-dimensional variable. Akin to a charged particle (or charge), the Ep is advected from one grid to another, and dissipates when the potential energy exceeds threshold values, leading to CG (positive or negative) and/or IC lightning. The accuracy of all of these approaches has been found to be dependent upon the accuracy of the model forecast of convective and stratiform clouds.
One possible way to improve lightning forecasts is to use data assimilation, since data assimilation is currently widely employed in numerical weather prediction models to improve the forecast of high-impact weather events (e.g., Gao et al. 2004; Aksoy et al. 2009; Alexander et al. 2010; Sun et al. 2012). Fierro and Reisner (2011) and Fierro et al. (2012) proposed a simple, easy-to-implement assimilation technique that uses observed lightning (explained below). Fierro et al. (2012) compared observed versus model-derived radar data and showed that the assimilation of lightning improved the structure of simulated radar fields during the assimilation period compared to the control (without). Moreover, the improvement carried over quite prominently to the subsequent forecast hours. Also, Fierro et al. (2014) compared the same lightning assimilation scheme with a three-dimensional variational data assimilation (3DVAR) technique that assimilated radar reflectivity and radial velocity data. For the case of a severe continental derecho mesoscale convective system (MCS), they found that assimilating lightning produced a better forecast than did 3DVAR for the placement and intensity of this derecho wind and severe storm within a 6-h forecast. Fierro et al. (2014) also extended their findings for the 29 June 2012 derecho case to nocturnal MCSs in general [hundreds of real-time 4-km conterminous U.S. (CONUS) runs conducted during the NOAA Hazardous Weather Testbed spring experiment (Clark et al. 2012)].
One might also refer to the lightning assimilation method of Fierro et al. (2012) as “direct insertion” or nudging. The rationale is that the lightning assimilation does not impact other grid boxes through a spatial correlations approach. Instead, lightning assimilation involves modifying the forecast fields by locating lightning in individual grids at predetermined fixed-time intervals (here, 10 min). Adjustments to the humidity profile are made naturally and gradually at every time step after the update of the water vapor mass within the model (no adjustments to the wind or temperature field are made). This is in contrast to variational techniques that affect modifications to the atmosphere all at once with 3D radar data. Hence, compared to most traditional approaches, lightning nudging is simple to implement and inexpensive to compute.
Here, we used the Lynn et al. (2012) lightning forecast model to examine whether the assimilation of observed total lightning from the Earth Networks Total Lightning Network (ENTLN; Fierro et al. 2012, their Fig. 6) can lead to more accurate lightning forecasts of CG and total lightning (and by extension strong thunderstorms). The forecasts were compared to observed total lightning and CG lightning from the U.S. Precision Lightning Network (USPLN; USPLN is a product of WSI, a division of The Weather Company). Very fine grid spacing is liable to result in low-skill forecasts due to spatial and intensity errors at the level of individual grid elements. Hence, we adopted a neighborhood approach when calculating the equitable threat score (ETS) of the forecasts (Roberts and Lean 2008; Ebert 2009; Schwartz et al. 2009; Clark et al. 2010). The details of the lightning scheme and assimilation method are discussed in section 2. Results are presented in section 3. Statistical comparisons from multi-forecast days are described in section 4 (and the appendix). Section 5 offers a summary and our conclusions.
2. Method
a. Brief description of the WRF Model
The dynamic lightning model is embedded in the WRF Model. The WRF single-moment 6-class microphysics scheme (referred to as WSM6; Hong and Lim 2006) was used to represent cloud condensation processes on the convection-allowing grid [as in Fierro et al. (2012)]. WSM6 is a single-moment scheme that predicts changes in water vapor, cloud water and rainwater, ice, snow, and graupel mass content. The shortwave radiation scheme used was that of Dudhia (1989), while the longwave radiation scheme was that of Mlawer et al. (1997). The Rapid Update Cycle (RUC) land surface model (LSM) was used to simulate surface fluxes (Smirnova et al. 1997, 2000) in all the forecasts, except for the first case study, where the five-layer surface model was used. The Mellor–Yamada–Janjić boundary layer scheme (MYJ; Mellor and Yamada 1982; Janjić 2002) was used to predict boundary surface and boundary layer fluxes.
b. Dynamic lightning model
The dynamic lightning model for predicting CG (positive and negative) and IC lightning is described in Lynn et al. (2012). Separate Ep values are tracked (and advected) for each type and polarity of the lightning: positive cloud-to-ground (CG+), negative cloud-to-ground (CG−), and IC lightning. Each Ep was added to the WRF (Registry) and passed through the solver to the microphysical driver. Each is calculated within new subroutine algorithms, which are embedded within the physics directory, from the grid-scale value of vertical velocity and microphysical hydrometeor masses within specified temperature ranges.
The source of Ep is assumed to be the noninductive charge separation process involving the collisions of graupel and ice particles in the presence of supercooled liquid water (Takahashi 1978; Saunders 1993; Saunders and Peck 1998; Mansell et al. 2002; Saunders 2008; Emersic and Saunders 2010). In the dynamic lightning model, the maximum amount of energy is generated in the presence of strong updrafts, and for conditions in which graupel exists in equal ratios relative to snow, ice, and water. Each Ep is dissipated when it exceeds preassigned threshold values [similar to Marshall et al. (1995) where lightning initiation occurs when the electric field exceeds the “breakeven” field]. The number of lightning events of each type depends on the amount of energy dissipated. As noted in Lynn et al. (2012), the magnitude of the lightning is sensitive to the choice of microphysical schemes. Model sensitivity to changes in the threshold value is discussed in the appendix (see Table A1).
c. Forecast accuracy
USPLN and ENTLN were used to validate the simulated CG and total lightning, respectively. The data were provided as point data, and placed into the nearest grid box of the model domain. ENTLN detects IC lightning with an efficiency ranging between 40% and 75%. CG lightning from both ENTLN and USPLN is >95% over the CONUS. Hence, the observed CG was used to quantitatively assess the efficacy of lightning assimilation. Both the CG and total lightning results were used for qualitative comparisons between the lightning forecast and the observed lightning.
One would expect that the assimilation of lightning into the early part of a convective forecast would improve both the forecast intensity and the positioning of convective storms. Yet, the rapid growth of forecast errors on small scales in conjunction with preexisting errors on synoptic scales, combined with limitations in the representation of the modeled physics, creates the potential for forecast errors to occur in both position and intensity.
d. Lightning assimilation scheme
In Fierro et al. (2012), the number of total lightning events per grid element (from ENTLN) was interpolated onto a 9-km grid so as to mimic the expected (8–12 km) resolution of the Geostationary Lightning Mapper (GLM) instrument aboard the upcoming Geostationary Operational Environmental Satellite R series (GOES-R; Gurka et al. 2006) over the Americas. Mapping intervals of 10 min were chosen so as to reasonably resolve the movement of individual storms. In our experiments, total lightning observations (also from ENTLN) were interpolated onto a 4-km grid. For each assimilation cycle, lightning observations were also assimilated every 10 min for a 3-h (in one case, 4 h) period. The three constants in Eq. (3) were chosen to be very similar to those in Fierro et al. (2012), who also used a convection-allowing grid. Based on hundreds of quasi-operational runs during the 2013 warm season, the values of the coefficients are believed to remain valid over a wide variety of convective regimes when assimilating total lightning data. Note, following Fierro et al. (2012), that the assimilation scheme was only applied in the mixed-phase region and where forecast graupel and/or hail amounts in each atmospheric layer (or each grid element) were less than 3 g kg−1. This constraint is not as strong as the one used in Fierro et al. (2012), which (as noted above) may further reduce the potential wind mass imbalances that can occur upon the introduction of too much Qυ into the model.
The utility of the assimilation approach might be limited by biases in the initial or boundary conditions, but also because of the development of spurious convection. That is, the model forecast might produce convective storms at locations where lightning was observed, but also in areas where such convective storms were not observed. This could occur in response to biases in the mesoscale analyses of thermodynamic conditions (e.g., too little convective inhibition). In such situations, Fierro et al. (2012) note that spurious convection produced by the unconstrained model could be limited. They suggested a simple, yet untested approach whereby (for a certain threshold of observed radar reflectivity and/or flash rate at a given grid point) the model hydrometeor mass produced in convective storms could be limited by progressively nudging the hydrometeor mixing ratios toward smaller values. This would reduce the extent and magnitude of the convection in areas where no lightning was observed, in addition to eliminating spurious development of cold pools during the assimilation window.
We followed the suggestion of Fierro et al. (2012) and removed spurious convection based on a comparison of observed versus forecast lightning during each 10-min interval of the assimilation period. In one of our case studies, we performed the lightning assimilation without removing spurious convection. We then reran the assimilation and compared the forecast lightning to the observed lightning in each grid box and at each 10-min interval. Wherever there was forecast lightning but no observed lightning during each 10-min window, the hydrometeor mass values were progressively nudged to zero. The result is that excess moisture was transferred to water or ice and removed, while the latent heat of condensation (and/or fusion) was vertically advected and eventually stabilized the atmospheric column in locations where lightning (i.e., convection) was forecast in error. Immediately removing hydrometeor mass upon formation also limits the subsequent rate of diffusional growth (and generation of spurious heating) because large particles (of which there are fewer) condense more water vapor than small particles. This also reduces collision-related cloud growth. Finally, this minimizes secondary feedbacks such as cold-pool triggering of gust fronts (in error) from spurious convection. We will show that this is an effective way to improve the efficacy of the assimilation approach. Results from additional forecasts simulations with filtering applied are also discussed in the appendix.
e. Forecast simulations
Four reforecasts were initialized with Rapid Refresh (RAP) forecast data obtained from the National Oceanic and Atmospheric Administration’s (NOAA) Earth Systems Research Laboratory (ESRL). These data are available at 13-km grid spacing, and were used at hourly time intervals during the assimilation period on a 4-km grid with 31 vertical levels. Each geographical domain is shown along with its respective grid domain size in Fig. 1. In each forecast, RAP data were used during the 3-h assimilation period (set to 3 h unless otherwise specified) to nudge the boundary layer and atmospheric temperature, humidity, and wind fields. When data assimilation was performed, lightning data were used to nudge the humidity during the same assimilation period.
The following domains are used in the experimental cases studies: (a) 500 × 500, (b) 700 × 600, (c) 447 × 447, and (d) 499 × 499 grid elements. The domain labeled “March 19” was also used in the set of eight forecasts experiments from 19 to 21 Mar 2012.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
In each case study, one experiment was produced with lightning assimilation (hereafter referred to as ASML) and one experiment was produced without lightning assimilation (hereafter referred to as CNTL). The first case study (Fig. 1a) was a forecast with severe weather in Texas, in which an MCS developed from the merger of two isolated convective areas. Two 6-h forecasts were made, and each began with a 3-h assimilation period from 2100 UTC 1 May to 0000 UTC 2 May 2013. This was followed by a 6-h forecast until 0600 UTC 2 May 2013 without any nudging, wherein the boundary conditions were updated every 3 h.
The second study (Fig. 1b) covered the period from 1800 UTC 19 March to 0600 UTC 20 March 2012, and was characterized by a convective line ahead of a cold front. The convective line initially extended from Texas, Oklahoma, Missouri, and Iowa, and moved eastward by about 200 km during this time period. Lightning assimilation ended at 2100 UTC 19 March.
The third case study (Fig. 1c) was a wintertime convective case associated with a strong, midlevel trough. Large-scale dynamic processes forced a broad area of convection, which stretched from Texas into Arkansas and had a few stronger cells embedded within (over southeastern Texas). This area moved southeastward into Louisiana and Arkansas. The simulation began at 0300 UTC 4 February 2012 and ended at 1200 UTC of that day, and used RAP forecast lateral boundary conditions every 3 h in both CNTL and ASML. Lightning assimilation ended at 0600 UTC in the ASML experiment.
The fourth case study (Fig. 1d) was a squall line that developed over Indiana and Kentucky, and then moved eastward across Ohio. The simulation covered the period from 1500 UTC 10 July to 0000 UTC 11 July 2013, and nudging of the atmospheric fields with RAP data and humidity with lightning continued until 1900 UTC (referred to as ASML19). (The rationale for selecting a 4-h assimilation period instead of a 3-h period is provided below.) This experiment was also performed with filtering during the assimilation period. Filtering of spurious convection was done for this case study (but not the others) because lightning assimilation without filtering produced many areas of spurious convection that detrimentally impacted the forecasts of the squall line. To investigate the impact of the duration of assimilation and filtering on the forecast results, additional assimilations were produced: the first is referred to as ASML18, wherein assimilation and filtering were done for the first 3 h, while the second is referred to as ASML17, and assimilation and filtering were done for the first 2 h. Two additional experiments are described in the appendix, where we imposed various constraints on the model during the assimilation/nudging procedure dependent upon the graupel mass content.
It is of interest to evaluate over what time scale forecasts of convection (and by extension lightning) might be improved through lightning assimilation. For these purposes, we conducted eight retrospective forecasts from 0900 UTC March 19 to 0300 UTC 21 March 2012, each 6 h apart. The grid covers the same area shown in Fig. 1b. Each forecast period was 18 h, preceded by 3 h of assimilation time.
3. Results
a. 1 May 2013
Three sets of maps are shown in Fig. 2. Figures 2a–c show the total lightning from the second simulation hour (referred to as A02), while Figs. 2d–f show the forecast lightning from the fifth simulation hour (F02; 2 h after the end of assimilation). Figures 2g–i refer to the seventh simulation hour (F05). Each set of maps shows forecast convection in different stages of development.
Observed and forecast total (hourly) lightning for the case study of 1 May 2013. The hour, day, month, and year are shown above for (a),(d),(g) observations; (b),(e),(h) ASML; and (c),(f),(i) CNTL.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
As seen on Next Generation Weather Radar (NEXRAD) imagery (not shown), this severe weather event began with a convective storm that developed between 2100 and 2200 UTC near Lawton, Oklahoma. This storm continued moving eastward while another convective storm formed near San Angelo, Texas, during the same time period. The ASML experiment correctly simulated the total lightning associated with these developing convective storms at A02, whereas CNTL did not predict these storms (cf. the observations shown in Fig. 2a with Fig. 2b and Fig. 2a with Fig. 2c). Assimilation was continued, as noted, for another hour, to provide continued forcing support to these developing convective cells. At F02, the ASML experiment correctly predicted the position and intensity of the observed lightning (cf. Fig. 2d with Fig. 2e), but CNTL did not (Figs. 2d–f). The observations at F05 (Fig. 2g) show a meridionally oriented mesoscale convective system, which is well reproduced in the ASML experiment (Fig. 2h). The CNTL predicted, in obvious error, a west–east area of convection, with a small convective cell to its north (Fig. 2i).
b. 19 March 2012
Figure 3 shows observed and forecast CG lightning. Lightning assimilation positively impacts forecasts of CG lightning (and total lightning; not shown). To “spin up” the development of the squall line along the eastward-moving cold front, 3 h was sufficient time. At the end of the first 3-h forecast period [F03; a similar construct was used to indicate the end of the first 6-h (F06) and 9-h (F09) forecast periods] both the position and the north–south extent of the lightning associated with the squall line from Texas to Iowa is better depicted in the ASML forecast than in CNTL (cf. Figs. 3a,b with Fig. 3c). The ASML forecast at F06 reproduced the observed curvature and north–south extent of the lightning field within Texas better than the CNTL (Figs. 3d–f). At F09, the ASML simulation results (Fig. 3h) were most notable for their better positioning of the forecast lightning versus observed lightning (Fig. 3g), as compared to the faster CNTL (Fig. 3i), whose MCS propagated more rapidly toward the east.
As in Fig. 2, but for 3-hourly CG lightning for the case study starting at 1800 UTC 19 Mar 2012.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
c. 4 February 2012
Figures 4a, 4d, and 4g show observed total lightning from the wintertime convective case. At the end of the assimilation period (0600 UTC), the map of observed lightning (Fig. 4a) indicates that there were strong convective cells over southeast Texas, with a leaflike extension through the southeast corner of Oklahoma, continuing into Arkansas, which was more realistically simulated in the ASML (Fig. 4b) than in the CNTL (Fig. 4c) experiments. As the convective storm and lightning leaf progressed eastward (Fig. 4d), the ASML experiment better forecast (Fig. 4e) the intensity of the total lightning than did CNTL (Fig. 4f) at F03. At F06, Figs. 4g–i show that ASML (Fig. 4h) and CNTL (Fig. 4i) produced similar intensities of total lightning, but that the ASML forecast lightning was, for the most part, more accurately positioned compared to the observations (Fig. 4g).
As in Fig. 2, but for 3-hourly total lightening for the case study starting at 0300 UTC 4 Feb 2012.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
d. 10 July 2013
As noted, three forecasts were made, ASML17, ASML18, and ASML19, where the number delimiter indicates the hour (from 1500 UTC) through which both lightning assimilation and filtering were applied.
Lightning forecasts are shown in Fig. 5, for each experiment, as well as observations. For forecasts valid at 1900 UTC, simultaneously assimilating lightning and filtering through 1800 UTC removed spurious convection simulated in ASML17 in central Ohio (cf. Figs. 5a,b with Fig. 5c). Assimilating and filtering through 1900 UTC (Fig. 5d) was necessary to forecast (shown in Fig. 5h) the observed forked lightning (Fig. 5e) associated with convection in northern Kentucky [not seen in ASML18 (Fig. 5g) or ASML17 (Fig. 5f)]. Moreover, the intensity of the total lightning in ASML19 was closer to the observed lightning. The 10-min analysis of radar reflectivity (not shown) indicated that the separate north–south convective areas shown in Fig. 5a merged to form the squall line shown at 2000 UTC in Fig. 5e. Only ASML19 was able to reproduce this merger.
(a),(e),(i) Total lightning for the case study starting at 1500 UTC 10 Jul 2013 from observations. Lighting was assimilated up to (b),(f),(j) 1700 UTC (ASML17); (c),(g),(k) 1800 UTC (ASML18); and (d),(h),(l) 1900 UTC (ASML19). Forecasts included filtering of spurious convection, and the filtering occurred during the specified time period as the lightning assimilation.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
An hour later, the forecasts at 2100 UTC (Figs. 5i–l) show that ASML19 (Fig. 5l) produced the best lightning forecast, although the lightning intensity in Kentucky is not as strong as observed. Comparing these forecasts to those without any filtering (see the appendix Figs. A1b,f,h) showed that assimilating and filtering for even 2 h produced a better forecast than assimilating lightning (without filtering) for 4 h (from 1500 to 1900 UTC). Moreover, the eastward progression of the squall line was forecast more realistically, and this carried over through the end of the forecast simulation (not shown).
Figure 6 shows the observed and simulated composite radar reflectivity for the same times as in Fig. 5. None of the forecasts were able to reproduce the finescale structure shown in the radar, or the extent of the indicated stratiform precipitation. This is most likely because the forecasts were made with a single-moment scheme and at convection-allowing rather than cloud-resolving grid resolution. Otherwise, the radar confirms the importance of extended assimilation and filtering for the initial development of the squall line (Figs. 6a–d), the placement of the strongest convection (echoes) within the squall line (Figs. 6e–g), and the more correct eastward progression of the squall line (Figs. 6i–l). Radar also confirms that the convection in Kentucky was underforecast, regardless of the assimilation or filtering time.
Radar composite reflectivity for observations and forecasts ASML17, ASML18, and ASML19. Assimilation and filtering were used as described in Fig. 5.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
To illustrate the impact of filtering on the forecast results, Fig. 7 compares first-layer model temperature perturbations T′ for ASML17 and ASML19 at 2000 UTC—3 h after the forecast began in ASML17 and 1 h after the forecast began in ASML19. At this time, the squall line was located on a diagonal from northeast through southwest Ohio (as shown). There are large differences in the forecast perturbation temperatures. For instance, ASML17 produced much larger and colder (negative) values of T′ than ASML19 behind the squall line, as well into Virginia and southwestward into Kentucky and North Carolina. In contrast, ASML19 produced colder T′ just south of the Indiana border, associated with the more correctly forecast forked convection in this area. Ahead of the squall line, the ASML19 T′ map also shows a continuous area of warm and potentially more unstable area of (positive) T′, while ASML17 produced patches of cold, negative T′ within the same area. The negative T′ values were associated with spurious convection occurring ahead of the main (squall line) convective area. Moreover, the excessively strong cold pool behind the convection in ASML17 was most likely the reason its forecast squall line propagated too quickly eastward compared to the observations.
First-layer model temperature perturbations in forecasts with lighting assimilation and filtering (a) from 1500 to 1700 UTC (ASML17) and (b) from 1500 to 1900 UTC (ASML19). The diagonal black line indicates the approximate location of the squall line.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
Figure 8 shows west–east vertical cross sections of perturbation temperature, relative humidity (RH), vertical velocity, and total hydrometeor mass for ASML17 at 1800 UTC. The cross section is through the center of the forecast domain and the squall line was located at about 85.5°W. Figure 8a shows that the cold pool behind the squall line extended up to about 0.7 km, with minimum values between −2.5° and −3.5°C. At this time, small positive (warm) magnitude variations within the relatively large warm area ahead of the squall line are shown above what is probably the cloud-base level (located at about 1 km). These perturbations extend to about 5 km in height, or about the height of the tallest convective cells preceding the squall line where cloud-top heights reach more than 12 km. Multiple regions of drying (adjacent to areas of likely spurious convection) are seen within the relative humidity field (Fig. 8b) ahead of the squall line, with relatively dry air (40% ≤ RH < 60%) shown over a deep layer behind the squall line. There are also regions with higher humidity above the cloud layer, associated with the convective cells themselves, as seen in the vertical cross section of vertical velocity (Fig. 8c), and the total hydrometeor mass field (Fig. 8d).
West–east vertical cross sections through the midpoint of the simulation domain of (a) perturbation temperature (°C), (b) RH (%), (c) vertical velocity (m s−1), and (d) total hydrometeor mass (g m−3) with lightning assimilation but without filtering, valid at 1800 UTC 10 Jul 2013.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
In contrast, Fig. 9 shows a single convective cell forecast, ASML19, with a relatively small and weak (from 0° to −0.5°C) cold pool (Fig. 9a). Heterogeneity in temperature and humidity fields (Fig. 9b) ahead of the squall line is much less pronounced than in Figs. 8a and 8b, respectively, and the humidity behind the squall line (in the weak cold pool) was >75%, comparatively moister than in ASML17. The maximum vertical velocity in the main convective cell (Fig. 9c) was between 2.5 and 5 m s−1 compared to between 5 and 10 m s−1 in ASML17 (Fig. 8c). Hence, the initial convective cell was weaker in ASML19 than in ASML17. Correspondingly, the maximum of the total cloud mass (Fig. 9d) in the main convective cell was between 0.5 and 1 g m−3 compared to between 3 and 4 g m−3 in ASML17 (Fig. 8d). Moreover, the area of total hydrometeor mass covered a much smaller area of the cross section than in ASML17. In ASML19, the area of apparent stratiform mass was particularly small compared to that shown in the ASML17 forecast. Each of these examples illustrates how filtering dampens spurious convection.
As in Fig. 8, but for a forecast at 1800 UTC with filtering.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
At 2000 UTC, the forecast ASML17 produced a very large and extensive cold pool (Fig. 10a) behind the squall line (located at about 83°W). The minimum values were as low as from −5.5° to −6.5°C. The cold pool is associated with very high humidity values, but there was also midlevel warming and drying behind the squall line associated with strong subsidence in the upper and midtroposphere (Fig. 10c), which was set back somewhat westward from the convective cells. The maximum values of vertical velocity in the squall line were between 5 and 10 m s−1, while the hydrometeor mass cross section (Fig. 10d) shows maximum values of 6–8 g m−3. There are multiple regions of comparative drying in the humidity field ahead of the squall line, but also two vertical columns of high humidity extending as high as the main convective area (>12 km; Fig. 10b). These columns of moisture are associated with two strong convective clouds preceding the main convective area, as suggested by the vertical velocity and cloud hydrometeor mass cross sections.
As in Fig. 8, but for a forecast at 2000 UTC without filtering.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
In contrast, Fig. 11a shows that ASML19 (at 2000 UTC) produced a relatively weak cold pool behind the squall line, which was located at about 84°W (farther west than in the forecast ASML17). There was also much less midlevel drying (Fig. 11b) and warming behind the squall line than was shown in Figs. 10a and 10b. In contrast to the strong upper- and midlevel subsidence produced in ASML17, the strongest subsidence was located in the lower troposphere. The T′ and the humidity fields remain relatively unperturbed ahead of the developing squall line (more conducive to continued development along the squall line), while the maximum vertical velocity was between 30 and 40 m s−1 (Fig. 11c), compared to less than 10 m s−1 in the forecast without filtering (Fig. 10c). In contrast to the multiple deep convective cells shown in the hydrometeor mass field of Fig. 10d, the hydrometeor field in Fig. 11d shows two upright and adjacent convective cells, with the rightward cell in the couplet developing immediately just ahead of a small low-level cooling area associated with the rearward cell. The maximum hydrometeor was 6–8 g m−3, the same as in the ASML17 forecast.
As in Fig. 8, but for a forecast at 2000 UTC with filtering.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
4. Statistical evaluation of forecasts
The ETS for CG lightning was calculated for 3-h forecast periods from eight 18-h forecasts initialized every 6 h between 0900 UTC 19 March and 0300 UTC 21 March 2012 (note that nudging with RAP forecast data and lightning was done for 3 h preceding each forecast). The forecasts were compared to 3-hourly observed values of CG. Figure 12 shows ETS values for a neighborhood radius of 96 km. In the first 3 h, the ASML forecasts produced very strong [50 (3 h−1)] and extreme [100 (3 h−1)] lightning values with higher ETS values than did CNTL; however, only the ASML forecasts for the extreme events produced significant differences (for α = 0.05). In the next two 3-h periods, ASML forecasts of strong [25 (3 h−1)], very strong, and extreme lightning events were better than in CNTL; all differences in ETS were significant. (The CNTL ETS values for extreme events were all zero or below.)
ETS values for a neighborhood radius of 96 km for strong, very strong, and extreme lightning events. In the first 3 h, only the extreme events produced significant differences (i.e., ASML was significantly better than CNTL). In the other 3-h periods, all differences were found to be significant (α = 0.05). The CNTL ETS values for extreme events were all zero.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
The ETSs were also calculated for other radii. Tables 1–3 only show scores for significant ETS values for very strong (Table 1), extremely strong (Table 2), and strong (Table 3) events. For very strong storms (Table 1), lightning assimilation led to significantly better forecasts than did the CNTL forecasts. During the first 3-h period, the forecasts were significantly better at all radii. During the next 3-h period, the ASML forecasts were significantly better than the CNTL forecasts for all neighborhood radii but 12 km. The forecasts for hours 6–9 were significantly better for radii of 72 km and greater. Significant differences in ETS (Table 2) for extreme events were obtained in each of the first three, 3-hour periods, although the ETS values for extreme events were zero (no skill) for radii <48 km. The largest ETS values for the extreme events were obtained during forecast hours 3–6, suggesting that the spinup of storms with extreme lightning values take longer than, for instance, storms with only strong lightning values.
ETS values for different neighborhood radii (km) per 3-h period for ASML/CNTL. Only numbers that have significant differences (α = 0.05) are shown. The threshold is 50 CG events per 3 h (very strong events). The forecasts were for 18 h (3-h periods with no significant differences are not shown).
Many of the higher ETS values were also significant in forecasting storms with strong lightning values (Table 3). The ASML forecasts were significantly better than the CNTL forecasts from the second through fifth 3-h periods, for almost all neighborhood radii. The fact that the first period did not produce significantly better forecasts indicates that the control experiments were able to produce the location of 25 3-h events as accurately as the forecasts with assimilation. The higher ETS values that occurred in subsequent periods were in part associated with the greater forecast accuracy for the very strong, and extreme, lightning events.
5. Summary and conclusions
Dynamic lightning forecasts were produced on a convection-allowing forecast grid with 4-km grid spacing with (ASML) and without (CNTL) assimilation of total lightning. Four case studies were analyzed, each representative of a different type of convective regime. A qualitative comparison between lightning forecasts demonstrated improvements in CG and total lightning forecasts when lightning assimilation was used, even exhibiting in one case different modes of convective development. Equitable threat scores were used to evaluate experiments consisting of eight 18-h forecasts. The analysis suggested that using lightning assimilation to initialize convection led to significantly better forecasts of convective storms associated with strong [25 (3 h−1)], very strong [50 (3 h−1)], and extreme (100 (3 h−1)] CG lightning events. Improvements in the forecasts of very strong and extreme events occurred out to 9 h of forecast time. The forecasting of strong events showed improvement out to 15 h, but the better forecasts beyond 9 h were most likely associated with better forecasts made for storms with strong and extreme events during the prior 3-h time period.
A method of removing spurious convection was implemented in one of the case studies. This method compares the forecast lightning during the assimilation period to the observed lightning to filter out areas of spurious convection during a restart of the forecast. The use of this method for the forecast on 10 July 2013 greatly improved the timing and intensity of the squall line and associated total lightning. As described in the appendix, applying filtering for the forecasts between 19 and 21 March 2012 produced mixed results. Using the lightning to filter spurious convection during the assimilation period increased the number of hits while reducing the number of misses during the first 6 h, but forecasts worsened thereafter.
Kain et al. (2014) note that “future work on the [convective initiation] forecasting problem should be couched in terms of convection-event prediction rather than detection and prediction of individual convection cells.” This is because convection is inherently unpredictable, as convective processes are small scale and associated with rapid, nonlinear error growth. Thus, in theory, even a perfect model would quickly diverge from reality because of small errors in the initial conditions. Both filtering and ensemble forecasts could extend the time range over which the intensity of individual cells or mesoscale systems could be better predicted, with less spatial error.
Acknowledgments
We heartily thank the reviewers for their extraordinary efforts and incisive comments. We also thank the editor, Dr. Paul Markowski, for his encouragement. We thank Eric James of NOAA for providing us with backforecasts from the RAP for the case studies and forecast evaluation. We thank Alexandre Fierro for advice on how to use and implement his assimilation scheme in WRF. We also used RAP forecast data from NCEP and NCDC. Earth Networks provided the total lightning data, while cloud-to-ground lightning data were provided by WSI (USPLN). Computer resources and computer software/scripts, including meteorological simulation data were used with permission of Weather It Is, LTD.
APPENDIX
Sensitivity of Forecast Results to Magnitude of the Charging Parameter
Table A1 shows forecast CG lightning amounts from three different forecasts started at 1500 UTC 19 March 2012 (these forecasts included a prior 3-h assimilation period, starting at 1200 UTC). CG lightning values are shown from observations and from forecasts with different values of the charging parameter Q [i.e., the number of coulombs (C) assumed transferred during 1 s]. The forecasts of CG lightning with the previously published values of Q were closest to the observed values. When Q was reduced by half, the forecast CG values were from one-third to less than one-half those initially forecast, while when Q was doubled, forecast CG values were more than 2 and as much as 3 times larger than with the original charging values. A statistical lightning forecast would have produced values one-half or twice the originally forecast values, respectively.
Number of CG lightning strokes observed and for different values of Q [i.e., the number of coulombs (C) transferred during 1 s]. The forecast period was from 1500 UTC 19 Mar to 0900 UTC 20 Mar 2012. There was a 3-h spinup period prior to the forecasts shown.
Sensitivity to Nudging Formulation and Filtering
(a),(e),(i) Observations and forecasts for the case study day of 10 Jul 2013. Each forecast has lightning assimilation through 1900 UTC, but (b),(f),(j) NOQG was based on Eq. (3) (Qυ only calculated when graupel mass was less than 3 g kg−1), while (c),(g),(k) QG reduces the calculated humidity changes forced by lightning by taking into account graupel concentration [Eq. (A1)]. (d),(h),(l) NOQGT has no constraints at all, that is, no graupel threshold.
Citation: Weather and Forecasting 30, 2; 10.1175/WAF-D-13-00028.1
At 1900 UTC, forecasts are shown just prior to the formation of the squall line (Figs. A1a–d). Each of the forecasts reproduced the general structure of the forecast squall line, with the NOQGT forecast producing the highest total lightning values. In fact, the intense convection produced in NOQGT appears to have suppressed spurious convection ahead of the developing squall line. Otherwise, NOQG and QG produced very similar lightning forecasts.
By 2000 UTC, the squall line has formed. The NOQG (Fig. A1f) and QG (Fig. A1g) forecasts were again very similar to each other, but the NOQGT forecast (Fig. A1h) was most similar to the observations (Fig. A1e).
At 2100 UTC, the lightning observations (Fig. A1i) show that the squall line has moved eastward, bisecting Ohio. However, without any filtering applied, the lightning forecasts in both NOQG (Fig. A1j) and QG (Fig. A1k) suggest that the forecast squall line has weakened dramatically. This is most likely because of the spurious convection produced in the forecasts without filtering (as noted in the results section above). In contrast, the NOQGT forecast (Fig. A1l) shows a well-defined squall line.
The improvement obtained in the forecast without any graupel threshold was a bit surprising, especially knowing that the introduction of too much moisture into the model forecast could produce unrealistic moisture–mass balances. However, in this experiment the lack of secondary convection seemed to be more important than any mass imbalances introduced.
To examine the impact of the graupel threshold on forecast accuracy, NOQGT forecasts were made for the 19–21 March 2012 events and compared against the set of NOQG forecasts (section 3b). Here, it was found that ETS values produced with NOQGT were much lower than those obtained with NOQG for strong, very strong, and extreme lightning events (not shown). Hence, eliminating the graupel threshold worsened the forecasts.
Forecasts were produced for the 19–21 March 2012 events using Eq. (A1) to add moisture to the grid column (eight QG experiments). Table A2 compares the total lightning produced during the assimilation period of each forecast for the NOQG and QG experiments. The total number of grid elements with total lightning values of at least one event or more was quite similar. However, the experiments with NOQG produced on average 50% more lightning than those from QG, and about 50% more than was observed (yet, we know that the observed total lightning varies between 40% and 70% of the actual, so there is probably less of an overestimation in reality than appears in Table A2). Table A3 shows the ETS values for a radius of 96 km for very strong storms. The NOQG forecasts produced higher ETS values except for the forecast period of 9–12 h. Hence, using the ETS as a measure of forecast accuracy suggests that modifying the Qυ forcing depending on graupel amounts worsened the forecast.
Simulated results from eight sequential QG forecasts (left column) from 0600 UTC 19 Mar to 0000 UTC 21 Mar 2012, every 6 h. The results pertain to the 3-h assimilation period of each forecast (e.g., from 0600 UTC to 0900 UTC 19 Mar). The middle column shows (i) the number of grid points with observed (OBS) lightning, (ii) the ratio of the number of NOQG lightning forecast elements divided by the number of observed elements (%; %-NOQG), and (iii) the ratio of QG forecast elements divided by the number of observed elements (%; %-QG), where QG refers to calculating changes in humidity forcing while taking into account graupel concentrations as expressed in Eq. (A1). The right column is the same as middle column but for total observed lightning values.
Comparison of ETS values from forecasts NOQG/QG. The forecasts simulated were the same as in Tables 1–3. The threshold was 50 CG events per 3 h.
Yet, Table A4 shows that QG produced more hits and fewer misses than the NOQG forecasts. The reason that the QG forecasts produced lower ETS values was because QG produced almost 25% more false alarms than NOQG. It appears that weaker forcing of observed convection (again) leads to the possible development of more spurious convection, even though introducing less moisture mass produced a higher number of hits and a smaller number of misses.
Top three rows show the sum of contingency values from all eight experiments (19–21 Mar 2012) for a threshold of 50 (3 h)−1, for hits, misses, and false alarms. The QG (filt) row shows the QG forecasts but with the lightning filter applied during the assimilation period. The following rows show the sums following the forecasts hours shown. Values are also shown for a threshold of 25 (3 h)−1.
The 8 March QG forecasts were simulated with the lightning filter [referred to as QG (filt)]. Here, the filter was applied whenever there was forecast lightning, but there was no observed lightning within two grid points of the forecast lightning or ±10 min from the current 10-min interval (this is a “relaxation” of the approach presented in the results section). The value of ETS in QG (filt) was better (0.56) than that of QG (0.51) for a radius of 96 km, but only in the first 3 h. Afterward, the values were worse. To examine this further, the numbers of hits, misses, and false alarms for very strong storms were summed over the six 3-h periods for the QG and QG (filt) forecasts. The QG forecasts had more hits, fewer misses, and fewer false alarms (Table A4) than did the QG (filt) forecasts.
The data are also presented in Table A4 as sums from one 3-h period to the next (for the 96-km neighborhood radius). Here, an advantage to filtering was obtained. The forecasts with filtering produced substantially more hits and fewer misses, while producing slightly more false alarms during the first 6 h (but not thereafter). Forecasts of lightning with strong storms produced more hits and fewer misses, but slightly more false alarms through the first 6 h of the forecasts. However, there were more hits through the first 9 h.
The goal of filtering is to reduce the number of false alarms. For these forecasts, it appears that the utility of filtering was to remove competing areas of convection, allowing the convection most closely correlated with the observed convection to initially propagate downstream more closely to the observed convection. Yet, overall the application of this technique did not improve these forecasts over the full forecast period. Hence, further investigations are ongoing and use lightning forecast rates as a tool in filtering spurious convection.
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