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Convective Initiation in an Idealized Model Using an Updraft Nudging Technique

JASON NAYLOR AND MATTHEW S. GILMORE Department of Atmospheric Sciences, University of North Dakota, Grand Forks, North Dakota

(Manuscript received 5 June 2012, in final form 7 August 2012)

ABSTRACT

Previous cloud modeling studies have noted difficulty in producing strong, sustained deep in environments with convective inhibition and/or midlevel dryness when the thermal bubble technique is used to initiate convection. This difficulty is also demonstrated herein, using 113 supercell proximity soundings— most of which contain capping inversions and some amount of convective inhibition. Instead, by using an updraft nudging initiation technique, substantially more supercells result and for a longer period. Addi- tionally, the number of supercell-producing cases is maximized when updraft nudging is applied for only the first 15 min of cloud time near the top of the boundary layer instead of longer/shorter periods or when nudging is applied near the surface.

1. Introduction used soundings for idealized supercells initiated using the bubble technique have capping inversions that Because the initial environment in most idealized have either been removed, were not resolved by the supercell simulations is devoid of horizontal gradients, vertical model grid spacing, or were absent by design. convective development must be initiated artificially. These are the 20 May 1977 Del City, Oklahoma, By far the most common method is the thermal per- sounding (e.g., Klemp et al. 1981; Grasso and Cotton turbation (or warm bubble) technique (Klemp and 1995; Gilmore and Wicker 1998; Adlerman et al. 1999; Wilhelmson 1978). With this method, a spheroid of Adlerman and Droegemeier 2005) and the Weisman positive potential perturbation is inserted and Klemp analytical sounding (e.g., Weisman and in the center of the domain at the initial time. In the Klemp 1982, 1984; Brooks and Wilhelmson 1993; Brooks appropriate environment, the positively buoyant air in et al. 1994; Wicker and Wilhelmson 1995; Richardson this spheroid will rise—creating convergence and addi- et al. 2007). tional vertical motion in its wake. Over time, a strong Ziegler et al. (1997) state that these two soundings are convective updraft develops. Although the warm bubble similar to the narrow convective initiation regions ob- technique is widely used, it is not without drawbacks. served along drylines but are not representative of the The vast majority of environments observed near mature storm environment. For instance, in the well- mature supercells have some amount of convective in- studied 22 May 1981 Binger, Oklahoma, supercell, the hibition (CIN; e.g., Thompson et al. 2003; Davies 2004). storm survived and was not tornadic until it moved However, several idealized simulation studies have re- into an area with larger values of convective inhibi- ported difficulty in using the warm bubble method to tion (Ziegler et al. 2010). Mun˜ oz (1994) emulated such initiate convection in environments containing capping environmental changes within an idealized cloud inversions (e.g., Chen and Orville 1980; Wicker et al. model by initializing the warm bubble in the uncapped 1997; Elmore et al. 2002; Letkewicz and Parker 2011) or sounding and progressively nudging a capping in- lacking deep moisture (e.g., McCaul and Cohen 2004). version into the model for a maturing supercell storm. Perhaps it is not surprising that the two most commonly Sustained convection would not initiate using only the capped environment. Corresponding author address: Jason Naylor, NorthWest Re- An alternative to using a warm bubble to initiate search Associates, 3380 Mitchell Ln., Boulder, CO 80301. convection is to apply a convergent field. Tripoli E-mail: [email protected] and Cotton (1980) and Loftus et al. (2008) both used

DOI: 10.1175/MWR-D-12-00163.1

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FIG. 1. Box and whisker plots of (a) mixed layer CAPE, (b) magnitude of mixed layer CIN, (c) CAPE/CIN ratio, and (d) 2–5-km average relative for the supercell-producing (SUP) and nonsupercell plus NULL producing simulations (NON 1 NULL) using warm bubble convective initiation. CAPE and CIN are calculated using a 500-m- thick parcel to represent the surface and . The whiskers represent 2.5 times the standard deviation from the mean.

a sustained initiation technique to study convective This study has three main purposes: 1) to demonstrate development by nudging the model with a near- that a sustained updraft nudging initiation technique surface convergence field, but this was tested using is substantially more effective than the instantaneous environments without capping inversions. The hori- warm bubble technique at producing supercells in hori- zontal convergence produces a positive zontally homogeneous environments with capping in- anomaly, which drives an upward-directed pertur- versions; 2) determine which updraft nudging settings bation pressure force and resulting updraft to help produce the strongest, longest-lived supercells; and parcels reach their (LFC). 3) demonstrate that a sustained forcing technique is Alternatively, one may nudge an updraft within the most effective when elevated off of the surface. boundary layer (e.g., Ziegler et al. 2010). This is similar to the convergent wind technique, except that the horizontal wind field responds to the updraft instead of 2. Methodology vice versa. However, there is some question as to the a. Model setup time period and altitude that the low-level updraft nudging should be applied to overcome a typical cap- Simulations with 1-km horizontal grid spacing were ping inversion. Too low, and the air may slow or even performed using version 14 of the Bryan cloud model stop its vertical motion, causing the air to diverge (Bryan and Fritsch 2002). The model setup follows horizontally beneath the . Too high, Naylor et al. (2012), which includes a single moment, and the updraft may not be able to draw in air from bulk ice microphysics parameterization (Gilmore et al. below the capping inversion. 2004) with default parameters; a model grid that moves

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TABLE 1. Number of supercell-producing simulations and number of simulations that produce a supercell that exceeds specified durations for the various UN configurations. The boldface entries indicate the maximum for each column. The number in parentheses in the last column represents the longest possible supercell duration after UN is shut off for each 120-min simulation. None of the UN configurations produced NULL cases.

Total No. of Supercell Supercell Supercell duration supercells .60 min .75 min of simulation UN5min 91 52 43 0 (115 min) UN10min 99 61 52 33 (110 min) UN15min 102 61 53 33 (105 min) UN20min 102 56 49 35 (100 min) UN25min 98 48 42 31 (95 min) FIG. 2. Average supercell duration (black solid line) and average UN30min 98 51 44 36 (90 min) updraft helicity (gray dashed line) for all 113 cases as a function of UN35min 97 50 43 37 (85 min) updraft nudging duration. For comparison, the average supercell UN40min 97 48 42 40 (80 min) duration for the bubble technique is 4625 s and average updraft 2 UN45min 94 47 39 39 (75 min) helicity is 472 m2 s 2 (not plotted).

with the 0–6-km mean wind; and a simulation run time is not applied once the vertical velocity exceeds wmax. 21 21 of 2 h. Each idealized simulation, using a horizontally Here, a 5 0.5 s and wmax 5 10 m s . Nudging starts homogeneous environment, was initialized with 1 of at t 5 0 and lasts a specified duration. The durations 113 Rapid Update Cycle-2 (RUC-2) supercell proximity tested herein varied from 5 to 45 min at 5-min soundings from Thompson et al. (2003, 2007). increments—a total of nine UN tests for each sounding environment. b. Convective initiation c. Supercell detection Supercell simulations were initiated using two methods. First used was the traditional warm bubble method Supercell presence is determined based on threshold 2 (hereafter BUB) which is defined by a spheroid with values of 2–5-km updraft helicity (UH . 180 m2 s 2 10-km horizontal radius and 1.5-km vertical radius for 20 min; following Naylor et al. 2012). This method centered at z 5 1.5 km with a 4-K maximum potential is used to determine both supercell duration and su- perturbation. Brooks (1992) and McCaul and Cohen percell intensity (time average of domain maximum (2004) have shown that a 4-K perturbation can produce updraft helicity) based on model output available sustained convection in a wider range of environments every 60 s during the simulation. Naylor et al. (2012) (i.e., smaller CAPE and moisture content) than a 2-K showed that the UH technique has a small (roughly perturbation. 5%) false alarm rate from successive nonsupercell The second initiation method utilized updraft nudg- mesocyclones that jointly exceed the 20-min temporal ing (UN). A spheroid with the same dimensions and criteria. location as the warm bubble is used here except that the updraft at a particular time and grid point (wt)isde- termined by 3. Results and discussion 8 < p a. Simulations with the warm bubble technique w cos2 b ,if0# b # 1 w 5 max 2 , (1) Of the 113 simulations completed with BUB, only 35 mag : b . 0, if 1 (31%) had supercells detected at least once during the simulation (SUP). The average supercell duration in 5 1 3 a 3 2 wt wt21 dts max(wmag wt21, 0), (2) these cases was 4265 s. Of the 35 SUP cases, 18 (51%) produced supercells that lasted at least 1 h. Of the 78 where b is the distance from the center of the spheroid simulations without any supercell detection, 29 (37%) 2 normalized by its radius, a is the acceleration constant, produced a nonsupercell updraft exceeding 10 m s 1 dts is the small model time step (0.375 s in these simu- (NON) while 49 (63%) failed to produce any vertical 2 lations), and the maximum function insures that nudging motion greater than 10 m s 1 (NULL).

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FIG. 3. Time series of domain maximum updraft (a) for a specific RUC-2 sounding using the bubble (BUB) convective initiation method and (b) various durations of updraft nudging. Maximum updraft is plotted at all times for BUB and only at times when a supercell was present for UN cases. The bubble method did not produce a supercell at any time in the simulation.

The relationship between CAPE, CIN, and whether BUB, none are NULL. Although average supercell BUB was able to produce a supercell is striking but duration2 is largest for the 10-min UN configuration perhaps not surprising. For the SUP cases, mixed layer (Fig. 2), the 15-min UN configuration (hereafter UN15) CAPE1 is larger (on average; Fig. 1a), mixed layer is able to produce supercells in more environments 2 jCINj is significantly smaller (median of 18 J kg 1; (Table 1) and those supercells are strongest, on average, Fig. 1b), and the ratio between CAPE/jCINj (Fig. 1c) is with a substantial drop-off in supercell strength when larger (75 or greater) than in the NON 1 NULL cases. UN is applied for longer or shorter periods (Fig. 2). In In fact, Fig. 1c shows almost no overlap in the upper addition, Table 1 shows that the UN15 configuration quartile of CAPE to jCINj ratio between the SUP and also produced the most supercells both lasting longer NON 1 NULL categories. In other words, although the than 60 min and lasting longer than 75 min.3 proximity soundings are all associated with supercells To illustrate one reason why supercells are stronger in nature, the capping inversion was usually too strong and longer lived for UN15, a few sounding cases with for BUB to initiate sustained convection in the model. substantially longer-lived supercells for UN15 com- Furthermore, midlevel relative humidity, averaged paredtoUN45wereexaminedinmoredetail(not from 2–5 km (RH25; Fig. 1d) is larger in the SUP cases shown). The longer UN duration produces supercells and smaller in the NON 1 NULL cases—consistent with greater mixing ratio aloft and faster- with the results of McCaul and Cohen (2004) who found propagating gust fronts that surge ahead of the midlevel that simulated storm lifetime was short in environments updraft once the heavier precipitation reaches the sur- with small relative humidity. These results demonstrate face: a well-known mechanism for supercell demise the limited supercell environments in which BUB is (McPherson and Droegemeier 1991). Because the mi- effective. crophysics is ‘‘switched on’’ the entire UN time, it is logical that longer UN times would produce more preci- b. Updraft nudging simulations pitation and future work should explore this sensitivity, All UN configurations result in about three times as many SUP simulations than BUB (Table 1), and unlike 2 Supercell duration is likely underestimated since approxi- mately 35% of supercell-producing simulations still contained a supercell when the simulations ended at t 5 2h. 1 Thermodynamic indices were calculated using a 500-m mixed 3 Supercell duration is calculated only after UN is turned layer parcel and the virtual temperature method discussed by off. Thus, 75 min is the longest possible duration for the UN45 Doswell and Rasmussen (1994). simulations.

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FIG. 4. As in Fig. 1, but for UN15 simulations. Note that NULL 5 0 for all UN configurations so NON 1 NULL is really equal to the number of NON. including tests where precipitation is delayed during the method is not strongly affected by the amount of CIN UN period. Conversely, if the UN duration is too short, and RH25 in the initial environment. the nudging ends before a cold pool is established. Thus, c. Sensitivity to UN spheroid placement when nudging is turned off, the low-level updraft could weaken because it is not aided by convergence along the To demonstrate the importance of spheroid place- gust front. ment, the UN15 simulations were repeated with the These mechanisms of supercell demise are illustrated same settings as before, except with a spheroid having for one case in a capped environment (Fig. 3a). Figure a vertical radius of 500 m centered at z 5 500 m (hereby 3b shows that a long nudging duration (UN45) produces referred to as the UNsfc simulations). These simulations a supercell that weakens earlier than those in simula- are meant to emulate a ‘‘surface based’’ forcing tech- tions using a shorter UN duration while nudging that is nique similar to that of Loftus et al. (2008). Tests have too brief produces only a short-lived supercell (UN5 in shown that the near-surface convergence response to Fig. 3b). In contrast, the UN15–UN35 configurations all the UNsfc settings is approximately 6–8 times stronger produce a long-lived, quasi-steady supercell (Fig. 3b). than the maximum surface convergence specified by Note that the bubble technique failed to produce a su- Loftus et al. (2008). Compared to the original UN15 percell in this case (BUB in Fig. 3b). simulations with the spheroid centered at 1.5 km AGL, For the UN15 technique, jCINj is a poor discriminator the UNsfc simulations produced fewer SUP cases (28 vs (Fig. 4b) between the SUP and NON cases. CAPE to 102), fewer supercells lasting longer than 1 h (14 vs 61), 2 jCINj ratio values in the UN15 SUP cases are about half and smaller average updraft helicity (524 m2 s 2 vs 2 those of the BUB SUP cases (Fig. 4c). In addition, the 744 m2 s 2). Further analysis of the UNsfc simulations UN15 results show a small difference in RH25 between revealed that the SUP cases were only possible for the NON 1 NULL and SUP cases (Fig. 4d). Thus, in smaller environmental jCINj (Fig. 5) as compared to the contrast to the BUB results, the effectiveness of the UN original UN15 runs. Thus, Unsfc is less able to overcome

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2) was able to produce supercells in environments 2 with larger median jCINj than BUB (38 J kg 1 vs 2 18 J kg 1); 3) usually resulted in stronger and longer-lived super- cells than for longer UN; and 4) was more effective at producing supercells than whentheUNspheroidwasmovedfromthelowest 3kmtothelowest1km. Thus, perhaps the sustained UN convective initiation technique—with settings that maximize supercell lon- gevity and intensity—should be considered for studying future idealized simulations of mature supercells oc- curring in environments with capping inversions. Al- though this current study only investigated supercells, FIG. 5. As in Fig. 4b, but for simulations using an updraft nudging these tests could be expanded to study the initiation spheroid with a vertical radius of 500 m and centered at z 5 500 m. sensitivity to other modes of convection. Future work could also investigate the sensitivity of the UN method to grid spacing, grid motion, spheroid size, and pre- larger jCINj compared to when UN is placed at 1.5 km cipitation development during the UN period. AGL, suggesting that the UN method is more effective when the spheroid extends higher than the area Acknowledgments. This work was supported by NSF of convective inhibition and above (or close to) the Grant AGS-0843269. Computational resources were LFC—similar to the warm bubble results of Brooks provided by the National Center for Supercomputing Ap- (1992). plications through Teragrid allocation TG-MCA94P023 d. Additional UN simulations and Texas Advanced Computing Center through XSEDE allocation TG-ATM100048. We thank Richard Additional simulations were performed to test the Thompson and Roger Edwards for providing the RUC-2 sensitivity to the updraft nudging parameters a and soundings, Jerry Straka for suggesting a nudging tech- wmax. When simulations in section 3b were repeated 2 nique for capped soundings, and Justin Weber for with a 5 0.1 s 1, 15 min is again the optimal UN dura- assisting with the simulations. Russ Schumacher and two tion. However, there were fewer SUP cases (88 vs 102), anonymous reviewers provided helpful suggestions to fewer SUP exceeding 1 h (47 vs 61), and the average UH 2 2 improve this work. was less (628 m2 s 2 vs 744 m2 s 2) than the UN15 sim- ulations (not shown). The authors have also experi- 21 mented with decreasing wmax from 10 to 5 m s ,but REFERENCES doing so consistently decreased supercell duration and Adlerman, E. J., and K. K. Droegemeier, 2005: The dependence of intensity no matter what environmental sounding was numerically simulated cyclic mesocyclogenesis upon envi- used (not shown). ronmental vertical . Mon. Wea. Rev., 133, 3595– 3623. ——, ——, and R. Davies-Jones, 1999: A numerical simulation of cyclic mesocyclogenesis. J. Atmos. Sci., 56, 2045–2069. 4. Summary and conclusions Brooks, H. E., 1992: Operational implications of the sensitivity of RUC-2 supercell proximity soundings were used modelled to thermal perturbations. Preprints, Fourth AES/CMOS Workshop on Operational , within an idealized cloud model with 1-km horizontal Whistler, British Columbia, Canada, Atmospheric and Envi- grid spacing to test the sensitivity of supercell intensity/ ronmental Service and Canadian Meteorological and Ocean- longevity to two different convective initiation methods: ographic Society, 398–407. the traditional warm bubble technique (BUB) and a ——, and R. B. Wilhelmson, 1993: Hodograph curvature and up- sustained updraft nudging (UN) technique. The UN draft intensity in numerically modeled supercells. J. Atmos. Sci., 50, 1824–1850. initiation technique, applied for the first 15 min of sim- ——,C.A.DoswellIII,andJ.Cooper,1994:Ontheenviron- ulation over the lowest 3 km, ments of tornadic and nontornadic mesocyclones. Wea. Forecasting, 9, 606–618. 1) was more effective at producing supercells (102 cases; Bryan, G. H., and M. Fritsch, 2002: A benchmark simulation for 61 lasting longer than 1 h) than BUB (35 cases; 18 moist nonhydrostatic numerical models. Mon. Wea. Rev., 130, lasting longer than 1 h); 2917–2928.

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