On the Predictability of Supercell Thunderstorm Evolution

JULY 2013 C I N T I N E O A N D S T E N S R U D 1993

REBECCA M. CINTINEO Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/National Severe Storms Laboratory, Norman, Oklahoma

DAVID J. STENSRUD NOAA/National Severe Storms Laboratory, Norman, Oklahoma

(Manuscript received 12 June 2012, in ﬁnal form 10 January 2013)

ABSTRACT

Supercell thunderstorms produce a disproportionate amount of the severe weather in the United States, and accurate prediction of their movement and evolution is needed to warn the public of their hazards. This study explores the practical predictability of supercell thunderstorm forecasts in the presence of typical errors in the preconvective environmental conditions. The Advanced Research Weather Research and Forecasting model (ARW-WRF) is run at 1-km grid spacing and a control run of a supercell thunderstorm is produced using a horizontally homogeneous environment. Forecast errors from supercell environments derived from the 13-km Rapid Update Cycle (RUC) valid at 0000 UTC for forecast lead times up to 3 h are used to deﬁne the environmental errors, and 100 runs initialized with environmental perturbations characteristic of those errors are produced for each lead time. The simulations are analyzed to determine the spread and practical predictability of supercell thunderstorm forecasts from a storm-scale model, with the control used as truth. Most of the runs perturbed with the environmental forecast errors produce supercell thunderstorms; however, there is much less predictability for storm motion and structure. Results suggest that an upper bound to the practical predictability of storm location with the current environmental uncertainty for a 1-h environmental forecast is about 2 h, with the predictability of the storms decreasing to 1 h as lead time increases. Smaller-scale storm features, such as midlevel mesocyclones and regions of heavy rainfall, display much less predictability than storm location. Mesocyclone location is predictable out to 40 min or less, while heavy 5-min rainfall location is not predictable.

1. Introduction associated with supercells, the main feature that differen- tiates them from other thunderstorm modes is their deep, Although they account for only a small percentage of persistent, rotating updraft (Thompson 1998; Doswell thunderstorms, supercell thunderstorms have a large and Burgess 1993). societal impact since most of them are severe (Burgess Since the 1970s, the structure and evolution of super- and Lemon 1991) and they produce a disproportionate cells have been simulated and examined using convective- amount of the hazards associated with thunderstorms scale numerical weather prediction models to learn more (Duda and Gallus 2010). Those hazards include heavy about the physical processes that produce the various rain, large hail, damaging straight-line winds, and tor- storm features and the inﬂuence of varying the storm nadoes, with most strong or violent tornadoes associated environment (e.g., Weisman and Klemp 1982, 1984). The with supercell thunderstorms (Moller et al. 1994). These success of the convective models to qualitatively repro- long-lived, organized storms, ﬁrst termed ‘‘supercells’’ duce thunderstorm development and evolution has led to by Browning (1962), have been studied extensively using the recent implementation of convective-scale numerical radar observations and, while many characteristics are forecast systems that provide explicit forecasts of convection out to 12 h or longer. Increasing computing power and the decreasing grid spacing of numerical models Corresponding author address: Rebecca M. Cintineo, CIMSS, University of Wisconsin—Madison, 1225 W. Dayton St., Madison, has led to the possibility of utilizing storm-scale models WI 53706. in operational settings to forecast the development of E-mail: [email protected] thunderstorms and their associated hazards. With the

DOI: 10.1175/JAS-D-12-0166.1

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‘‘Warn-on-Forecast’’ approach to issuing warnings based used assumed the turbulent flow to be continuous, which upon model ensemble forecasts of storm features being does not take into account the intermittency of storms in considered (Stensrud et al. 2009), instead of waiting for both time and space. Knowledge of the forcing of small- their detection, an investigation of the predictability scale phenomena could also impact the range of their of supercell thunderstorms from a practical operational predictability, with predictability lengthened in the pres- standpoint is warranted and is the focus of this study. The ence of weaker atmospheric instability or greater forcing confidence that a forecaster can place in the forecasts of by surface features (e.g., Anthes 1986). Interactions be- supercell thunderstorms using storm-scale models is in- tween storms also influence their evolution, and so errors vestigated, given the typical uncertainty of the environ- in the forecast of one storm would result in errors in mental forecast 1, 2, and 3 h prior to the initiation of the prediction of the development of other nearby sub- convection. sequent storms (Bluestein and Weisman 2000). Storms can Many studies have looked at the predictability of also modify their environments, further influencing their large-scale weather features, most frequently examining predictability (Brooks et al. 1994; Weisman et al. 1998). the error growth of the geopotential height forecasts at Therefore, there are many factors and limitations that a specified pressure level (e.g., Lorenz 1982; Dalcher would need to be taken into account in a comprehensive and Kalnay 1987; Molteni and Palmer 1993; Bengtsson study of supercell predictability. and Hodges 2006). Others have focused on the predict- The common approaches to exploring predictability, ability on the mesoscale (e.g., Warner et al. 1984; Anthes and even the definition of predictability, for large-scale et al. 1985; Zhang et al. 2003, 2006, 2007) and numerous atmospheric features may not necessarily be appropri- studies have also delved into the predictability of the cli- ate for the mesoscale because of the nature of the phe- mate and its features (e.g., Kirtman 2003; Chen and Cane nomena and operational application (Warner et al. 1984). 2008). However, few studies have been performed that The location and development of smaller-scale features is have investigated the predictability of the weather on the what is important on the mesoscale and thus a more op- storm scale, in which more complex, three-dimensional erationally practical perspective must be taken. Warner motions and turbulence become important. et al. (1984) suggest that the definition of predictability Lorenz (1969) used a turbulence-based approach to for the smaller scales should be changed to include the initially theorize that, while the predictability of larger, growth in error to where the forecast no longer provides synoptic-scale motions is around a few weeks, predict- predictive utility to forecasters. The same is true for ability decreases with decreasing horizontal scale to the the storm scale, and the present study seeks to provide point where it is on the order of only a couple hours for a more practical approach to predictability based upon storm-scale motions with 20-km wavelengths. However, specific storm features. This approach is similar to that that theoretical limit could be either increased or de- of previous studies that investigated the predictability creased in practice because of the inherent nature of of mesoscale convective systems (MCSs) (Stensrud and storm-scale atmospheric phenomena. Lilly (1986) pro- Wicker 2004; Wandishin et al. 2008, 2010). posed that the highly helical nature of supercell thun- The predictability investigated here is meant to pro- derstorms and their resulting high degree of organization vide an upper limit on the predictability of supercell as compared to other storms might likewise act to sup- thunderstorms, since the environment and storm ini- press the turbulent dissipation within storms, and there- tialization method used are highly idealized. The initial fore the energy cascade, enhancing their predictability. model environment is horizontally homogeneous and However, Lilly (1990) found that the actual helicity therefore not necessarily realistic since it leaves out the of supercells is only a fraction of what is theoretically effects of boundaries, surface topography, land use, and possible, and so its suppression of the energy cascade large-scale forcing, which could serve to either increase may be limited. A sensitivity study was performed by or decrease the predictability of the storms, depending Droegemeier and Levit (1993) to see if storms in low- or on the situation. Spatially varying vertical shear can also high-shear environments, which are conducive to multi- influence the evolution of storms, yet is not captured by cell or supercell storms, respectively, were more sensitive a horizontally homogeneous environment (Richardson to identical changes in initial conditions. They found that et al. 2007). Holding the environment constant through- more confidence could be placed in the forecast of the out the simulation is not a realistic depiction of what supercell than the forecast of a multicell storm, which is happens in the actual atmosphere, as shown by Ziegler consistent with the hypothesis of Lilly (1986). et al. (2010) and Bluestein (2009). The accuracy of the Droegemeier (1997) pointed out that Lorenz’s esti- initial conditions on the convective scale, such as when mate of the limit of storm-scale predictability may have radar data are assimilated into a model, can also affect the been too long since the turbulence-based approach he predictability of the storm (Snyder and Zhang 2003) but

Unauthenticated | Downloaded 10/01/21 01:58 AM UTC JULY 2013 C I N T I N E O A N D S T E N S R U D 1995 is not considered in this study. Convective initiation, accurate short-term forecasts (Benjamin et al. 2004). which has been found to be difficult to predict and to be For this study, the analysis time of 0000 UTC, which is a sensitive to small errors in the planetary boundary layer typical time for thunderstorm development in the United (Crook 1996; Brooks et al. 1993), is guaranteed in our States, is used as the best estimate of the atmospheric simulations and so only the predictability of the evolution state. RUC forecasts valid at 0000 UTC with 1-, 2-, and of the storm is investigated. It is assumed that the model 3-h lead times, which would be issued at 2300, 2200, and used is perfect and that any divergence in the solutions is 2100 UTC, respectively, are used to compute the forecast solely due to the errors in the initial atmospheric state. errors for the environment over a spatial domain limited While it is well known that model physics and parame- to a region encompassing most of the continental United terizations can affect storm simulations (Gilmore et al. States east of the Rocky Mountains, which is where most 2004; Cohen and McCaul 2006; Dawson et al. 2010), the supercell thunderstorms in the United States generally parameterizations are kept constant for all the model runs occur (Brooks et al. 2003a,b; Doswell et al. 2005). There in this study. are uncertainties in the RUC analysis itself, such that the Section 2 discusses the methodology used for this pre- errors computed here are estimates of the actual forecast dictability study, the computation of the typical environ- errors and likely provide a lower bound on these errors. mental forecast errors, the procedure chosen to perturb Within that domain, the supercell composite param- the control sounding with those errors, and the setup of eter (SCP) (Thompson et al. 2002) is used to define the the numerical model. The results of initializing and run- area in which to compute the forecast errors to ensure ning the model with the perturbed soundings are de- that the errors are computed only within environments scribed in section 3, and a discussion of those results is that have sufficient buoyancy and wind shear to support provided in section 4. supercell thunderstorms. The SCP definition used in- cludes normalized values of most unstable convective available potential energy (MUCAPE), the bulk 2. Methodology Richardson number shear (BRN shear), which is one This study seeks to determine the predictability of a measure of the deep layer shear, and 0–3-km storm- supercell thunderstorm with respect to errors in the relative helicity (SRH) and is calculated as initial storm environment. Environmental errors at 1-, 2-, and 3-h forecast lead times are computed for envi- 2 5 MUCAPE 3 0 3-km SRH SCP 2 2 ronments that are expected to produce supercell thun- 1000 J kg 1 150 m2 s 2 derstorms from an operational mesoscale model, and those errors are then used to construct 100 environ- 3 BRN shear 2 22 . mental perturbations on a control supercell sounding for 40 m s each of the forecast lead times. The homogeneous environment of a limited-area storm-scale model is defined The result is a dimensionless number for which values by the perturbed soundings and a storm is initiated using greater than or equal to 1 have been found to indicate an a warm bubble, similar to past studies (e.g., Crook 1996). environment that is expected to be supportive of super- The resulting storm simulations are analyzed for both cell thunderstorms (Thompson et al. 2002). their variability and the divergence from the storm ini- The dates for which the forecast errors are computed tialized using the control sounding, which is considered are the days on which the environment was known to to be the ‘‘truth.’’ Specific features of the storms are used have supported supercell thunderstorms for the period to quantify the variability as this gives more insight into of January–June 2010, selected using the archive of se- the practical predictability of the forecasts. vere thunderstorm events from the Storm Prediction Center (SPC; Storm Prediction Center 2012). This yields a. Computation of the environmental errors a total of 70 days from which to compute the environ- Data from the 13-km Rapid Update Cycle (RUC) are mental errors. Data for 4 and 5 June 2010 are left out of used to calculate environmental forecast errors from the analysis as RUC data for those 2 days were in- an operational mesoscale model in regions supportive complete on the National Oceanic and Atmospheric of supercells. RUC is an operational numerical weather Administration (NOAA) Operational Model Archive prediction model run by the National Centers for and Distribution System (NOMADS) website. Environmental Prediction (NCEP) that assimilates The root-mean-square errors (RMSE) for the temper- weather data and produces short-range forecasts out to ature, relative humidity, and u and y winds are computed 12 h with 1-h frequency. By assimilating weather obser- over all 70 days and all grid points within the regions de- vations to update its analyses, it is able to produce more fined by an SCP of at least 1. This gives a total of 349 546

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FIG. 1. Root-mean-square errors (RMSE) of the (a) relative humidity (%), (b) temperature 2 (K), and the (c) u and (d) y components of the wind (m s 1) calculated at 0000 UTC from 1-, 2-, and 3-h 13-km RUC forecasts. Calculations only made in regions with SCP $ 1 over a 70-day period. grid points used in the calculations of the RMSE and from demonstrate a similar vertical structure to the errors which random errors could be chosen to perturb the found by Benjamin et al. (2004) when the 20-km RUC control sounding. If the horizontal spatial correlations of forecasts were veriﬁed against rawinsonde observations. the errors were computed, they would likely show that The 1-, 2-, and 3-h forecast errors display similar trends, there are fewer unique grid points for computing the er- though with the values increasing with increasing lead rors, and so fewer degrees of freedom. The errors were time, as expected. computed at all 37 vertical levels available from the RUC, b. The control sounding and its perturbation which are isobaric levels every 25 hPa from 1000 hPa at the lowest level up to 100 hPa at the highest atmo- The control sounding used in this study is an idealized spheric level (Fig. 1). The calculated RMSE proﬁles supercell sounding, compliments of George Bryan (2010,

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The vertical pressure difference at which the correlation drops to near zero is approximately 200 hPa but varies somewhat depending on the environmental variable. The spacing deemed appropriate for each variable, shown in Table 1, is used to apply a new random variable to the control sounding. A random draw from the RUC errors at the pressure levels given in Table 1 for each variable is used to construct the perturbations to the control sounding. A poly- nomial spline is used to interpolate the perturbations to model levels between the assigned levels and generate a complete perturbation profile to add to the control sounding. To keep the soundings physical, supersatura- tion is avoided by limiting the relative humidity through- out the sounding to 100%. Initial testing indicated that a sounding with a saturated layer or a lapse rate that is dry adiabatic or greater than dry adiabatic above the lifting condensation level would cause the model to generate convection over the entire domain, which is unphysical, so soundings with these characteristics are discarded and FIG. 2. Idealized sounding used as the control sounding. The replaced by other randomly perturbed soundings. In this black line shows the temperature and the gray line shows the way, 100 different perturbed soundings to initialize the dewpoint temperature. storm-scale weather prediction model are created for each of the three forecast lead times. The vertical correlations that were computed for the perturbations applied to the personal communication; Fig. 2). It has surface-based con- soundings resemble those of the RUC errors (not shown), 2 vective available potential energy (CAPE) of 2315 J kg 1, giving confidence in the method used. 2 convective inhibition (CIN) of 244 J kg 1, and a lifted The vertical profiles of the RMSE of the relative hu- condensation level (LCL) of 880 hPa, which corresponds midity, temperature, and u- and y-wind perturbations to a height above ground level of 741 m. The winds veer that were applied to the sounding have general shapes with height, producing a 0–6-km vector wind difference, and magnitudes similar to the profiles of the RMSE 2 referred to hereafter as wind shear, of 22 m s 1 and calculated from the entire RUC dataset. When the mean 2 a clockwise hodograph with 171 m2 s 2 of 0–3-km storm- perturbed soundings are plotted, they match up quite relative helicity. The large amount of CAPE and the wind well with the control sounding (not shown). Since we shear create a sounding that is typical of environments applied perturbations to both temperature and relative supportive of supercell thunderstorms, with an SCP value humidity, the resulting error distributions for mixing of 2.3. Since the shear is at the lower end of the spectrum ratio are slightly larger in the sounding perturbations for supercell environments, a sounding with a greater than suggested by the RUC dataset with the differences amount of shear may lead to differing results given the decreasing with height. The soundings that resulted from same environmental errors as used in this study. the perturbation of the control sounding display quite a Perturbations are added to the control sounding based range of variability, especially with regard to CAPE upon the RUC model errors for the three forecast times. (Fig. 4). For the 1-h forecast errors, the soundings have Since the errors do not have a Gaussian distribution—so surface-based CAPE (SBCAPE) that varies from 780 up to 2 2 normality cannot be assumed—errors are randomly 5907 J kg 1. The mean is 2408 J kg 1, which is fairly close to 2 drawn from the RUC error dataset for specified pressure the value of 2315 J kg 1 for the control run, and the inter- 2 levels. Errors in between these pressure levels are in- quartile range (IQR) is 954 J kg 1. Thompson et al. (2003) 2 terpolated. The pressure levels for which errors are found a similar IQR of about 900 J kg 1 for the 1-h drawn are chosen through examination of the vertical SBCAPE errors from the 40-km RUC-2. The SBCAPE error correlations and determining the depths over from the 1-h-lead-time RUC data used in this study had 2 which the correlations decrease to zero. The Pearson a larger IQR at 1625 J kg 1, while the mean was a lower at 2 correlation coefficient is computed for temperature, 1409 J kg 1. When considering only RUC SBCAPE values 2 2 relative humidity, and wind errors every 100 hPa to de- greater than 250 J kg 1, the IQR decreased to 1396 J kg 1 2 termine the vertical correlation of the errors (Fig. 3). and the mean increased to 1737 J kg 1.Themean

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FIG. 3. Vertical correlations between the 1-h forecast errors at heights every 100 hPa for (a) relative humidity, (b) temperature, (c) u-wind component, and (d) y-wind component.

SBCAPE for the perturbed soundings decreases to 2190 93%, and 89% of the 1-, 2-, and 3-h environmental er- 2 and 2253 J kg 1 for the 2- and 3-h errors, respectively, but rors, respectively. the spread increases as the lead time increases such that 2 c. Numerical model the IQRs are 1116 and 1154 J kg 1,respectively. The mean 0–6-km wind-shear values for all 100 per- The control and perturbed soundings are used to ini- turbed soundings are close to the value from the control tialize idealized runs of the Advanced Research Weather sounding, though they increase slightly with increasing Research and Forecasting model (ARW-WRF), ver- 2 forecast lead time to 22.6, 22.9, and 23.3 m s 1 for the sion 3.2.1 (Skamarock et al. 2008), used as a three- 1-, 2-, and 3-h errors, respectively. There is a greater dimensional, nonhydrostatic storm-scale model with amount of spread with time as the standard deviations 1-km horizontal grid spacing. Bryan et al. (2003) dis- also increase with increasing lead time to 2.0, 2.4, and cuss the potential need for higher resolution for sim- 2 3.1 m s 1. The wind proﬁles of the perturbed runs are ulating deep moist convection, but for the present shown in Fig. 5. The SCP values are greater than 1, in- purpose, 1-km horizontal grid spacing should be suf- dicating environments favorable for supercells, for 92%, ﬁcient while remaining computationally affordable.

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TABLE 1. Pressure levels (hPa) at which new random errors were initialize the model is integrated out to 2 h of simulation applied to the sounding. time, with the model output available every 5 min of sim- Relative humidity Temperature u y ulation time, and is the ‘‘truth’’ against which the model runs initialized with the perturbed soundings are com- 100 100 100 100 300 200 200 200 pared. All simulations have the same model setup, yielding 500 400 400 400 ensembles of 100 different 2-h simulations for each of the 700 600 600 600 three lead times. 800 800 800 800 900 900 1000 1000 d. Supercell definition 1000 1000 The one characteristic that has been used to un- ambiguously differentiate supercells from other thunderstorms is a quasi-steady rotating updraft that persists The horizontal domain is 150 km 3 150 km, chosen to for tens of minutes (Thompson 1998; Doswell and be large enough to keep the 2-h storm simulation Burgess 1993). Therefore, having a storm with a large, within the domain. We use 55 stretched vertical levels, persistent, rotating updraft is the basic dynamical def- allowing for a higher density of layers in the boundary inition of a supercell. It has been suggested that the layer, with about 30-m vertical spacing between the convective time scale, over which a parcel travels through lowest levels increasing to about 570-m spacing at a storm’s updraft, is 20–30 min (Doswell and Burgess the top of the atmosphere, located at 20 km AGL. The 1993; Doswell 2001; Markowski and Richardson 2010), microphysics option used is the Lin–Farley–Orville and so that length of time is used as a minimum lifetime (LFO) microphysics scheme (Lin et al. 1983). Since the for a supercell mesocyclone. simulation is idealized and cloud-resolving, the radia- Updraft helicity (UH) is a useful parameter for the tion, surface, and boundary layer physics are turned off detection of mesocyclones and is described by Kain et al. and there is no cumulus parameterization. A 1.5-order (2008) as the product of vertical velocity and vertical three-dimensional turbulent kinetic energy closure vorticity integrated over a depth of the atmosphere. It is schemeisusedforsubgrid-scalemixingandthereisno given by the equation upper-level damping applied. A sixth-order horizontal ð z advection scheme and a third-order vertical advection t UH 5 wz dz, scheme are used with open boundary conditions on the z domain edges. 0 2 A single input sounding is used to create a horizon- where w is the vertical velocity (m s 1)andz is the 2 tally homogeneous atmosphere with which to start the vertical vorticity (s 1). For looking at midlevel rota- model simulation. The convection within the model is tion in a storm, the integral is taken over the layer from initiated by introducing an artificial 4-K thermal bubble z0 5 2000 m to zt 5 5000 m AGL. Kain et al. (2008) find 2 with a horizontal radius of 10 km into the initial atmo- a UH value of at least 50 m2 s 2 to be a good indicator sphere just above the surface, which ensures convective of rotating updrafts, so that threshold is used to define initiation. The simulation run using the control sounding to a mesocyclone in this study.

21 FIG. 4. Histograms showing the distributions of the surface-based CAPE (J kg ) for the soundings perturbed with the (a) 1-, (b) 2-, and (c) 3-h forecast errors.

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FIG. 5. Hodographs showing the wind proﬁles for the soundings perturbed with the (a) 1-, (b) 2-, and (c) 3-h forecast errors, with the control sounding wind proﬁle overlaid in black.

The definition employed in this study is that a super- whereas in other runs the convection is much more cell exists in the model when there is a rotating updraft, widespread. Predictability is investigated by looking at 2 defined by UH values of at least 50 m2 s 2, that lasts for how quickly the features of the storms in the ensembles at least 25 min. Similar to Hocker and Basara (2008), the of perturbed runs diverge from one another and from storm cell is said to have initiated with the first occur- the features in the control simulation. The time length of rence of a 40-dBZ echo and ended when there is no the practical predictability for various storm features longer a mesocyclone. refers to the time since model initialization, even though supercell characteristics may not appear during the first 20 min of simulation. 3. Results a. Supercell success rate The model run initiated with the control sounding produces deep convection that splits into a persistent According to the criteria for a supercell described right-moving supercell and less-organized convection previously, 97% of the 1-h forecast error–perturbed that moves off to the left (Fig. 6). The first 40-dBZ radar runs, 98% of the 2-h forecast error runs, and 92% of the signature is produced at 1 km AGL at 20 min into the 3-h forecast error runs produce a supercell with a me- simulation, the same time at which the precipitation socyclone that lasts for at least 25 min (Fig. 8). With downdraft reaches the ground and the updraft at 4 km fewer storms becoming supercells in the 3-h error runs, begins to split. By 30 min, there are two completely there are also fewer that remain supercells over the re- distinct updrafts at 4 km (not shown). At the time of the mainder of the simulation time. By the end of the 2-h storm split, the rainfall accumulation drops off and the simulation, 81% of the 1-h error runs, 82% of the 2-h updraft speed decreases, consistent with previous stud- error runs, and 74% of the 3-h error runs still have a right- ies (e.g., Klemp et al. 1981; Rotunno and Klemp 1985). moving supercell storm. The mean lifetime of a supercell The rainfall and updraft increase again after the storm is roughly constant in the 1- and 2-h error runs at 92 min splits. The left-moving storm develops into a region of but is several minutes shorter at 86 min as the forecast less-organized, multicellular convection and additional lead time increases to 3 h. Thus, the convective mode convection develops on the edge of the cold pool. The forecasts for supercells are very predictable in the pres- right-moving storm, which is the focus of this study, ence of typical 1–3-h environmental forecast errors. maintains its supercell characteristics for the remainder of the 2-h simulation, giving it a lifetime of 100 min by b. Storm evolution and movement the end of the simulation, which would have been longer 1) FREQUENCY OF 40-DBZ SIMULATED had the simulation been allowed to run further. REFLECTIVITY The variation among the simulations in the ensemble gives an idea of the confidence that can be placed in The evolution and movement of the storm during the a forecast. An example of some of that variation is seen simulation can give insight into how far out the forecast of when looking at the simulated reflectivity at the end of a storm’s position is useful to a forecaster and how rapid several of the perturbed simulations (Fig. 7). In some storm location errors grow. One measure of the pre- runs, the right-moving supercell dissipates by 120 min, dictability of storm placement is the amount of overlap

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21 FIG. 6. Simulated reflectivity (dBZ) and storm-relative winds (m s ) at 1 km AGL at (a) 30, (b) 60, (c) 90, and (d) 120 min into the simulation for the control run. between the storms in the perturbed runs (Fig. 9). At for the perturbed runs is plotted (Fig. 10), with the 30 min, there appears to be good agreement in the place- 40-dBZ contour of the control run overlaid. Once again, ment of the storms, as judged by the 40-dBZ contours. By the 1-h error runs are shown, but the 2- and 3-h error runs 60 min, the placement is still reasonable, but by 90 min depict a similar spatial pattern, though with lower fre- and later there is a lot of spread between the runs. At quencies overall. At 30 min, there is overlap between 120 min, the main, right-moving storm in the control run about 90% of the runs. By 60 min, the number of runs that appears to lag behind a majority of storms in the per- have overlapping reflectivity of at least 40 dBZ is still turbed runs and the locations of the storms in the per- around 85% to 90% and the 50% density contour matches turbed runs often do not overlap the control run. Similar up fairly well with the control contour. The control su- results are found for the 2- and 3-h error runs. percell starts to lag behind the area of higher frequency The picture of what is happening becomes clearer when around 80 min into the simulation, and there is a maximum the frequency of simulated 40-dBZ or greater reflectivity overlap of only about 55% of the runs for the right-moving

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21 FIG. 7. Simulated reflectivity (dBZ) and storm-relative winds (m s ) at 1 km AGL at 120 min from four different simulations. storms by the end of the 2 h. The convection to the north, first 40-dBZ contour at the same time overlap at that which was a result of the left-moving supercell that split off time, which seems to be due to the area of the storms at and additional convection on the edge of the cold pool, 1 km not becoming large enough for a majority of them displays a higher frequency since the convection in that to overlap until about 30 min into the simulations. The area was more persistent and widespread and thus more greatest frequency of at least 40 dBZ is around 40 min, likely to have overlap. The right-moving storms cover which is not long after most of the storms split, and it a smaller area and are more isolated, so the overlap of their decreases after that. For a 1-h lead time, which shows the 40-dBZ reflectivity falls off faster over time. greatest amount of predictability, there is 80% or greater Analyses of the domain-maximum frequency of at overlap between 30 min to just a little over 1 h. The least 40-dBZ simulated reflectivity for all three forecast overlap then drops off steadily, reaching just over 60% lead times show that at no time do all the simulations by the end of the 2-h simulation. The other two forecast overlap, even for the 1-h forecast lead time errors lead times show similar trends, but the domain-maximum (Fig. 11). Not all of the storms that initialize with their frequencies decrease as the lead time increases.

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for every 10% drop. This 2-h predictability time is longer than the range of values suggested in real data cases by Stensrud and Gao (2010), Aksoy et al. (2010), and Dawson et al. (2012), as would be expected from a perfect model experiment. The differences in predictability limits derived from perfect model and real data cases can provide an estimate of the role of model error.

2) 5-MIN RAINFALL ACCUMULATIONS UP TO 2 MM The domain-maximum frequency is likewise found for the rainfall accumulations for each 5-min interval over the simulation time for rainfall accumulation thresholds FIG. 8. Supercell success rate vs simulation time (min) for 1-, 2-, and from 1 to 10 mm (Fig. 12). The areal extents of the 1- and 3-h environmental error runs. 2-mm rainfall accumulations tend to match or slightly While individual users may have greater or lesser fall inside the region of 40-dBZ reflectivity (not shown). tolerance for position error, an accurate storm location Thus, it is not surprising that the domain-maximum prediction is critical to issuing hazardous weather warn- frequencies for these thresholds mimic that found for ings. A subjective comparison of the spaghetti (Fig. 9) 40-dBZ reflectivity, with the frequencies increasing to and the domain-maximum frequency plots (Fig. 11) al- a maximum around 40 min before decreasing with the lows us to estimate a frequency value for which the use- storm split. These results suggest a predictability length fulness of the forecasts is lost. Storm locations from the for the 1-mm rainfall region of 120 min for the 1-h error 100 simulations show reasonably good overlap through runs, decreasing to 85 min for the 3-h error runs. The 60 min and arguably out to 90 min (Figs. 9a–c). The num- frequencies for the higher accumulation thresholds will ber of perturbation runs that have overlap with the right- be discussed further when looking at the smaller-scale moving control storm based on the 40-dBZ threshold is features within the storms. found and, for the 1-h error runs, an increasing number of 3) COLD POOL AREA runs have distinct separation from the control beginning at 70 min (not shown). However, a large fraction of the Precipitation falling from the storm enhances the storms at 120 min are spatially far enough apart that it storm’s downdraft through evaporative cooling as the becomes difficult to conclude that they are the same storm precipitation falls through subsaturated air and evapo- from 90 min earlier without additional information. Out of rates. When the downdraft reaches the ground, the air, the 100 runs, 40% have no overlap with the control storm which is cooler than the surrounding air at the surface, and so have completely lost their association with it. Thus, spreads beneath the storm to form a cold pool, which is we relate the 60% domain-maximum frequency value a broad-scale feature of the storm. The edge of the cold with the loss of useful storm location information for pool, also termed the gust front, is defined by the 218C warning operations and that value is chosen as a rea- perturbation potential temperature isotherm at 100 m sonable threshold for the loss of practical predictability AGL. The total area of the cold pool is calculated and for storm feature location. Depending on the user, compared (Fig. 13). By the end of the 2-h simulation, the other frequency threshold values can be chosen, such as mean maximum cold-pool size for the runs perturbed with 85% if overlap between all of the storms is required or the 1-h errors is 2689 km2, for the 2-h errors is 2475 km2, 70% if having no overlap between 20 of the 100 runs and for the 3-h errors is 2293 km2,whichareallmuch can be tolerated. larger than the control run’s cold-pool size of 1164 m2.This If the 60% domain-maximum frequency value is decrease in mean cold-pool area with increasing forecast chosen as an indicator for when practical predictability lead time is likely due to fewer supercells being maintained is lost, then the 1-h error runs provide useful information within the ensemble of runs for the longer lead times. on storm location out to 2 h. However, practical pre- These results indicate that predictions of cold-pool area dictability is lost for the 2-h error runs at 85 min and is are very sensitive to the initial environmental errors. lost for the 3-h error runs at roughly 60 min. This suggests that with characteristic short-term environmental c. Storm structure errors, useful storm location forecasts can extend out to 1) MESOCYCLONE PATH between 1 and 2 h. Since the maximum frequencies decrease roughly linearly with time, decreasing the thresh- Smaller-scale features within supercell thunderstorms old value increases the predictability by roughly 20 min are likely more difficult to predict accurately than the

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FIG. 9. Spaghetti plots of the 40-dBZ-reﬂectivity contour from all 100 simulations for the 1-h error runs at (a) 30, (b) 60, (c) 90, and (d) 120 min with the control run 40-dBZ contour overlaid in black. location of the storm as a whole. However, knowing the to 25 min for the 3-h error runs. This 35-min pre- location of those features is important to forecasting dictability limit is roughly consistent with the results the path of severe weather, such as knowing the path of from Dawson et al. (2012), who examined simulations a mesocyclone to predict the possible track of a tornado. of the Greensburg, Kansas, tornadic supercell thun- A time series of the domain-maximum frequency for UH derstorm. 2 of at least 50 m2 s 2 indicates that for most of the simula- To investigate the variability and predictability of the tion time there is much less overlap between the runs, and direction and length of the right-moving storm’s track, so less predictability, for the location of the mesocyclone the path of the maximum positive UH within the right- than for the storm as a whole (Fig. 14). The frequency moving storm is examined. The length of the control peaks around 20 min and then falls off dramatically. simulation’s UH path from the starting point to the end- By the end of the simulation, there is less than 20% ing point is 61.8 km in a direction of 298 with respect to the overlap between the storm mesocyclones for all three x axis (Fig. 15). The mean UH pathlengths for the per- lead times. If we again use the 60% domain-maximum turbed runs are somewhat longer than that of the control frequency threshold to deﬁne the limit of practical run for all three forecast lead times, with lengths of 64.5, predictability, then mesocyclone location is predictable 64.9, and 62.3 km, respectively. As may be expected, the out to roughly 35 min for the 1-h error runs decreasing variability of the pathlengths increases with increasing

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FIG. 10. Frequency (scaled 0–100) of at least 40-dBZ reflectivity calculated at each grid point for the 1-h error runs at (a) 30, (b) 60, (c) 90, and (d) 120 min with the control run 40-dBZ-reflectivity contour overlaid in black. lead time, with a standard deviation of 14.01 km at a 1-h The control run and many perturbed runs show a clear lead time increasing to 23.3 km at a 3-h lead time. The transitiontoamorerightward-movingstormduring 2 control storm moves at a mean speed of about 10.9 m s 1 the first hour of the simulation. The different environ- over its lifetime, while the mean speeds for the perturbed ments not only change the mean wind in the cloud 2 2 runs are faster at 12.2 m s 1 for the 1-h errors, 12.8 m s 1 layer, but also influence the amount of turning once the 2 for the 2-h errors, and 12.5 m s 1 for the 3-h errors, with storm becomes supercellular. The directions of the UH 2 standard deviations of 1.4, 1.8, and 2.6 m s 1, respectively. paths with respect to the positive x axis have a range of The longer mesocyclone pathlengths and faster speeds of 708 for the 1-h error runs, 658 for the 2-h error runs, and the perturbed storms are consistent with the lag in the 868 for the 3-h error runs. The wider range in the 3-h location of the control run when overlaid on the fre- error run directions is primarily due to one rogue model quency of 40 dBZ or greater simulated reflectivity seen run that has the main storm taking a much sharper right previously. turn than the rest of the storms among all of the

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FIG. 11. Time series of the domain-maximum frequency of at least 40-dBZ reflectivity for all 100 runs perturbed with the 1-, 2-, and 3-h environmental forecast errors. simulations. While the path of that storm is atypical, it still should be kept in mind that the track of that par- ticular simulation is a possibility given the environmental errors. When the paths are smoothed using kernel density estimation (KDE) (Wilks 2006), a clearer picture of storm behavior emerges (Fig. 16). KDE is a method for smoothing data by combining probability density func- tions for individual data points. A larger fraction of the storms in the 2- and 3-h error runs than the 1-h error runs take a sharper right turn, yielding mean path directions that are displaced to the right of the control run by 0.888 and 1.318, respectively. The supercell mode with small FIG. 12. Time series of domain-maximum frequency of 5-min rightward turns are still present in the 2- and 3-h error accumulated rainfall at thresholds from 1 to 10 mm for the (a) 1-, runs but are not as prevalent as seen in the 1-h error (b) 2-, and (c) 3-h error runs. runs. The combination of the differences in the lengths and directions of the UH paths leads to large differences in UH location among the runs for all three lead times higher than the initial one. Using a 60% domain-maximum and explains the rapid decrease in practical predictability frequency to determine when practical predictability is of the mesocyclone location. lost suggests that all 5-min accumulated rainfall totals above 5 mm are unpredictable in terms of location. For 2) 5-MIN RAINFALL ACCUMULATIONS ABOVE the 3-h error runs, all accumulated rainfall totals above 2 MM 2 mm are unpredictable. Thus, the locations with the The lower predictability of the smaller-scale features highest 5-min rainfall are less predictable than the me- within the storm is also seen when looking at the frequency socyclone location. values for the 5-min rainfall accumulation thresholds 3) DOMAIN-MAXIMUM UPDRAFT VELOCITY above 2 mm, at which point the finer-scale features of the storm’s rainfall become more apparent (Fig. 12). The fre- In addition to the spatial variability of the storm quency values decrease as the rainfall rate threshold is features given the environmental forecast errors, the increased, which makes sense as the lighter rain rates cover variability in the strength of the storm is investigated by broader areas and are therefore more likely to have looking at the updraft speed. Similar to the storm in the overlap among the perturbed simulations. Most of the control run, many of the storms reach their peak updraft rainfall thresholds have an initial frequency peak around speeds within the first half hour of the perturbed sim- 40 min followed by a second peak 20–30 min later. At ulations. As the storm splits, the updraft speed de- higher rainfall thresholds, the secondary peak is actually creases and does not increase again to its original value

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FIG. 13. Area of the cold pool as defined by the 21-K perturbation potential temperature contour at 100 m AGL for the (a) 1-, (b) 2-, and (c) 3-h forecast errors. The solid black line shows the values for the control run and the dotted black lines show the 5th and 95th percentiles of the areas from the perturbed runs. for most of the model runs. The mean peak updraft based upon environmental forecasts (Grams et al. 2012). 2 velocity for the 1-h error runs is 62 m s 1, the same as However, not all of the runs produced convection that 2 the control run, with a standard deviation of 12 m s 1. lasted long enough to be classified as a supercell, high- The 2-h error runs are similar, having a mean maximum lighting limits to storm predictability. For all three 2 updraft speed of 61 m s 1 and a standard deviation of forecast lead times, about 80% of the runs that produce 2 13 m s 1. The mean maximum updraft speed decreases a supercell maintain the storm for the remainder of the 2 to 57 m s 1 for the 3-h error runs, while the stan- simulation. 2 dard deviation increases to 17 m s 1. Those differences The practical predictability of the storm features de- among the runs at the three lead times are consistent creases with the size of the feature, assuming the defi- with what is seen visually when the updraft velocities of nition of predictability used herein. Storm location all the runs for each lead time are plotted as a time se- and the region of lightest rainfall are the most predict- ries (not shown). The variation of the evolution of the able, with domain-maximum frequencies suggesting domain-maximum updraft speeds over the simulation useful location forecasts are possible out to about 2 h. time between the model runs does not appear to change Given the 1-h-lead-time environmental errors, 90% of much between the 1- and 2-h lead time ensembles, the storm locations defined by reflectivity above 40 dBZ but several of the 3-h error runs have the updraft ve- overlap with the control run at 70 min into the simula- locity fall off dramatically because of storm dissipation. tion. By 15 min later, however, only 60% of the locations While maximum updraft speeds are highly irregular overlap with the control storm. By the end of the full 2 h, over the course of each individual run, the predict- 2 ability of updraft speed exceeding 20 m s 1 is very high. Predictability decreases as updraft speed increases. The irregularity of the updraft speeds causes the updraft helicity values to also be highly irregular over each run (not shown).

4. Discussion and conclusions Almost all of the of the 1- and 2-h forecast error model runs produce storms that ﬁt the criteria for a supercell, while 92% of the 3-h-lead-time error runs produce supercells. That means that there can be a high level of conﬁdence placed in the forecast of a supercell given the uncertainty in the forecast environment with up to 3 h of lead time. This result underlies FIG. 14. Time series of the domain-maximum frequency of UH $ 2 current severe weather forecast practices that outline 50 m2 s 2 for all 100 runs perturbed with the 1-, 2-, and 3-h envi- regions where supercells are likely days in advance ronmental forecast errors.

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FIG. 15. UH paths for the right-moving storm from the runs with the (a) 1-, (b) 2-, and (c) 3-h environmental forecast errors, with the path from the control run overlaid in black. only 55% of the perturbed run locations have overlap of at the storm’s initialization time that could affect the the right-moving storms. The location of the midlevel storm’s subsequent evolution through their outflow mesocyclone is much less predictable than the storm boundaries or interaction between the storms them- location, with useful forecasts out to no more than selves. A storm may either strengthen or deteriorate as 40 min for 1-h environmental errors decreasing to 25 min it rides along or crosses over a boundary (Maddox et al. for 3-h errors. The predictability decreases even further 1980; Atkins and Weisman 1999; Wilson and Megenhardt when examining the locations of heaviest 5-min accu- 1997; Rasmussen et al. 2000; Bunkers et al. 2006). mulated rainfall totals, with the locations unpredictable Ziegler et al. (2010) found that when a storm moved into for accumulations above 5 mm. The predictions of cold- a more stable environment, it was able to persist longer, pool areal extent clearly show the difficulties in predicting suggesting that the exact effects of crossing boundaries are that field accurately in the presence of environmental not completely known. errors. Another limitation is the use of a thermal bubble One limitation of this study and its applicability to inserted into the initially homogeneous atmosphere to the real-world environment is that the initial environ- artificially initiate a storm since simulations may be sen- ment is initialized with a single point sounding and sitive to the magnitude and size of the initial thermal is therefore horizontally homogeneous. The real atmo- bubble (Lilly 1990; McPherson and Droegemeier 1991; sphere contains inhomogeneities, such as airmass bound- McPherson 1991; Brooks 1992). In operational use, the aries and influences from topographic features, and initial fields of the storm could be obtained with radar and other storms may already be within the environment inserted into the cloud-scale model to initiate the storm,

FIG. 16. The UH paths from Fig. 13 smoothed using kernel density estimation from the runs with (a) 1-, (b), 2-, and (c) 3-h environmental forecast errors. Probability isolines every 0.0004, beginning at 0.0001. The path from the control run is indicated by the dotted line.

Unauthenticated | Downloaded 10/01/21 01:58 AM UTC JULY 2013 C I N T I N E O A N D S T E N S R U D 2009 which can also introduce additional error into a simula- Bengtsson, L., and K. I. Hodges, 2006: A note on atmospheric tion (Snyder and Zhang 2003). A similar approach was predictability. Tellus, 58A, 154–157. tested in the initial phase of this study by taking the winds Benjamin, S. G., and Coauthors, 2004: An hourly assimilation– forecast cycle: The RUC. Mon. Wea. Rev., 132, 495–518. and thermal profile of the control storm once it had Bluestein, H. B., 2009: The formation and early evolution of the formed in the simulation and inserting them into the Greensburg, Kansas, tornadic supercell on 4 May 2007. Wea. model at the initial time, but the results were largely Forecasting, 24, 899–920. unchanged. The idealized environment and the assump- ——, and M. L. 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