a. Sounding database

The soundings evaluated here are contained in Rawinsonde Data for North America, 1946–1992 (Forecast Systems Laboratory and National Climatic Data Center 1993) and were all made at 0000 UTC nominal sounding time from the U.S. sites only. The year 1992 was chosen for this climatology in a completely arbitrary manner. The sounding data were subjected to two quality control checks only (beyond those performed in producing the CD-ROM dataset): hydrostatic checks and checks for missing wind data. Many soundings from 1992 have been examined using an interactive skew T–logp program, and no serious data problems have been encountered. Every sounding was evaluated for CAPE using the algorithm described below. If CAPE > 0, the sounding was further evaluated for a number of other parameters; 6793 soundings had nonzero CAPE and were utilized in this study.

b. Proximity–inflow method

An objective method has been devised to associate each meteorological event with a sounding. A meteorological event is defined as a cloud-to-ground lightning flash or a severe weather report. The method has been designed to find a reasonably nearby sounding that is in the “inflow sector” of the event and to reduce the likelihood that the sounding has been contaminated by convection. For example, the lower troposphere may have been stabilized by outflow, the upper troposphere warmed and moistened by anvils, and the wind structure altered radically. For a more thorough examination of the issues related to selecting “proximity soundings” see Brooks et al. (1994a). To accomplish the goal of establishing a sounding as an inflow sector sounding, the boundary layer mean wind vector was computed using the average of the u and υ wind components in the lowest 500 m. The sounding was assumed to be in the inflow sector of any meteorological event if it was within 400 km and the event fell within ±75° of the boundary layer mean wind vector. This is illustrated in Fig. 1, which shows soundings B and C meeting the inflow and range criteria.

If more than one sounding satisfied the inflow and range criteria, for simplicity the sounding with the largest CAPE was chosen as being “representative” of the event. This was done to alleviate two major problems:with some events, soundings taken in the warm sector, behind the dryline, and north of the warm front in a developing cyclone could all be considered as “inflow” soundings. Further, soundings meeting the inflow and range criteria but contaminated by convection likely have reduced CAPE and thus were more likely to be eliminated. The CAPE criterion sets this study apart from other similar studies and has important implications for the interpretation of the results herein. In any given case, it is quite possible that a sounding with nonzero CAPE that is in close proximity to the event is excluded in favor of a more distant sounding with greater CAPE. From a forecasting perspective, it means that the results herein should be applied in terms of the largest CAPE in a fairly large “inflow region” rather than the CAPE in the immediate storm inflow. Further, it means that the results herein may not be directly compared to results from similar studies; this point will be reiterated in later sections where appropriate.

Admittedly, the process described above may not be the ideal means of selecting a sounding representative of a meteorological event. A more appropriate method might be to choose only those routine or special soundings that truly were proximate to a given event [e.g., the method of Brooks et al. (1994a)]. Alternatively, one could perform objective analysis or utilize gridded numerical model data to determine the conditions proximate to an event. However, the chosen approach removes all questions about the subjective decisions made in including or excluding various soundings. The“rules” used to associate a sounding with each event are summarized below.

1. Step 1: Assemble list of all soundings that are within 400 km of the event.

2. Step 2: Assemble the subset of soundings that contain the event in a 150° sector centered on the boundary layer mean wind vector.

3. Step 3: Choose the sounding with the maximum CAPE.

c. Lightning database

Since the primary emphasis of this climatology is on convection, a method was needed to determine which soundings actually were associated with convection and which were not. This is a difficult problem with such a large dataset. The technique chosen was to determine if cloud-to-ground (hereafter CG) lightning flashes were associated with a given sounding. A minimum of 10 flashes was required before the sounding was assumed to be associated with convection.

The CG flash data are from the National Lightning Data Network operated by Geomet Data Services, Inc. All CGs that occurred between 2100 and 0600 UTC (i.e., −3 to +6 h from nominal sounding time) were treated as individual meteorological events, and an attempt was made to find a representative sounding for each one using the rules listed in section 2b. Out of a total of 5 711 187 flashes during the 9-h daily window in all of 1992, 3 748 833 individual CGs (∼⅔) were associated with soundings. Based on the rules listed in section 2b, it is apparent that many CGs occurred too far from nonzero CAPE soundings (e.g., far offshore), there were no soundings in the inflow sector of the CG, and, in some cases, there were no nonzero CAPE soundings. No attempt was made to quantify the reasons for CGs not being matched with soundings. Out of 6793 soundings with nonzero CAPE, 2767 were associated with 10 or more CG flashes (see Table 1).

d. Severe weather reports and classification

The goal of this work is to utilize available data, suitable for a large climatology, to ascertain the association of sounding-derived parameters with severe weather related to supercells. Severe weather reports were taken from Severe Local Storms Unit log for 1992 and were filtered as follows. Tornado reports were filtered into significant (F2 or greater) versus other tornadoes because of the well-known reporting vagaries (e.g., Doswell and Burgess 1988). Only hail larger than or equal to 5.1 cm (2.0 in.) was considered under the assumption that it is associated with supercells when it occurs. Wind reports were not considered in this study because of the difficulty in determining if the severe wind was due to a supercell or not. Only events occurring within −3 to +6 h of 0000 UTC were considered. These events were matched with soundings using the proximity rules described above.

Three categories of soundings were defined as summarized in Table 1. The categories were designed with the intent to identify soundings associated with tornadic supercells, nontornadic supercells, and nonsupercell storms. Because there is no climatological record of the supercell character of storms, this must be inferred through the available reported phenomena. This requires certain caveats regarding the interpretations and limitations of these categories as described in the following.

TOR: This category was designed to identify soundings associated with tornadic supercells. While some of the reports of tornadoes of F2 and greater damage intensity in 1992 possibly were associated with nonsupercell tornadoes, nothing in the database of severe weather reports allows nonsupercell to be distinguished from supercell tornadoes. The justification for the exclusion of F0 and F1 tornadoes in TOR was to generally exclude nonsupercell tornadoes, as well as to filter some of the myriad of erroneous tornado reports (Doswell and Burgess 1988) that generally are given the F0 or F1 rating. The label TOR is used here mainly for convenience; the strict interpretation of the category is soundings associated with tornadoes rated F2 or greater.

SUP: For comparison to the TOR category, information from the climatological database was sought to identify supercells without significant tornadoes. The only information readily available is reports of large hail in the absence of significant tornadoes. Further research is required to quantify the actual association of large hail with supercells versus nonsupercells, although Cotton and Anthes (1989) state that supercell storms“generally produce the largest hailstones.” It may be determined that the occurrence of large hail is a poor indicator of supercell structure invalidating the present supercell classification. Further, it is likely that many, if not a majority, of supercells do not produce hail of the required size and were excluded. The label SUP is used for convenience; the strict interpretation of the category is soundings associated with storms that produce large hail but not significant tornadoes, in itself an important category of storms in operational meteorology regardless of the supercell characteristics.

ORD: This category was designed to exclude supercells. This was done by including soundings associated with a modest amount of cloud-to-ground lightning, but excluding soundings associated with damaging wind, large hail, or any tornado. This exclusion is based on the idea that most supercells produce some severe weather at the surface (Burgess 1976; Moller et al. 1994).

e. Computation of storm motion

In all computations, the assumed storm motion is that computed based on the limited climatology of Rasmussen and Straka (1998). The hodographs for representative soundings for 45 supercell cases were translated so that the 0–500 m above ground level (AGL) (assumed boundary layer, hereafter BL) mean wind was at the origin and rotated so that the BL–4 km AGL shear vector was aligned with the +u axis. The storm motions were plotted. It was found that for LP (low precipitation updraft region, based on subjective visual classification) and classic supercells, the motion was always within 4 m s⁻¹ of a point found as follows: 8.6 m s⁻¹ orthogonal to the right of the tip of the 0.6S vector, where S is the BL–4 km shear vector (Fig. 2). It is this storm motion vector that is used in the present study and has been tested for several years in the National Center for Atmospheric Research (NCAR) operational version of the Mesoscale Model, version 5, forecast model (J. Bresch 1998, personal communication). Recently, Bunkers et al. (1998) have derived a very similar formula for predicting supercell motion using a sample of 125 supercells based on a technique proposed by M. Weisman (1998, personal communication). Note that unlike the common methods based on angular deviation from deep mean wind vectors, the present method is Galilean invariant. A hodograph produces the same hodograph-relative motion regardless of where it falls relative to the origin. In the limited climatology, high precipitation (HP) supercells generally deviated much more than 4 m s⁻¹ from the “predicted” motion and did not seem to be strongly related to the shear in the lower half of the troposphere. Supercell motion forecasting derived from the above technique, based largely on the work of Rotunno and Klemp (1982), is the subject of an ongoing investigation.

a. Boundary layer to 6-km shear

In this section, the magnitude of the shear vector between the 0–500 m AGL mean wind and 6 km AGL wind (hereafter BL–6-km shear) is examined. Figure 3 shows the frequency of occurrence of various magnitudes of BL–6-km shear as a function of category. The gray boxes contain the middle 50% of the events, with the median shown with a horizontal black line. The vertical black bar contains the middle 80% of the events. Graphs of this type can be used to gain an understanding of the overall distribution of a parameter, but more importantly they can be used to gauge the relative value of a parameter in distinguishing among categories. It can be seen that BL–6-km shear has value for distinguishing between the populations of soundings associated with the TOR and SUP categories, and that associated with the ORD category. In the case of ORD soundings, BL–6-km shear is between five and 15 m s⁻¹ in half of the cases, while for TOR–SUP the equivalent range is 11–21 m s⁻¹. From Fig. 3 it can also be seen that BL–6-km shear has no utility for distinguishing between the SUP and TOR categories.

b. Storm-relative helicity

SRH (Davies-Jones et al. 1990) is defined as

View Expanded

where V is horizontal velocity, c is the storm motion vector, and h is the depth over which the integration is performed (3 km herein). SRH shows considerably greater utility for distinguishing among the categories than BL–6-km shear (Fig. 4). Most ORD have small SRH (75% with SRH <100 m² s⁻²). Half of the SUP soundings have SRH between 64 and 208 m² s⁻². Soundings in the TOR category are quite distinct from the ORD soundings, with no overlap in SRH among the central 50% of cases. The mean value of SRH in TOR soundings is almost 200 m² s⁻². However, it is not true that large SRH implies that a particular sounding will be associated with a significant tornado. The 23% of ORD soundings with SRH between 100 and 168 m² s⁻² represent over 600 cases, which is more than the total number of soundings in the TOR and SUP categories combined. This “false alarm” problem occurs with all the parameters investigated and will be discussed in section 8.

c. Mean shear

Mean shear (Rasmussen and Wilhelmson 1983) is defined as

View Expanded

which is the length of the hodograph divided by the depth over which the hodograph was measured (4 km here). The box-and-whiskers diagram for mean shear is given in Fig. 5. As with SRH, but to a much smaller degree, mean shear does distinguish between the three categories. For example, half of ORD soundings have mean shear <0.053 s⁻¹, while only 15% of SUP soundings have values that small. Mean shear, as well as SRH, becomes a stronger predictor of supercells and tornadoes when paired with CAPE, as discussed in section 5c. The fact that SRH better discriminates between the categories suggests that it is the streamwise component of horizontal vorticity that dominates the production of rotating updrafts in supercells as described by Davies-Jones (1984).

d. Storm-relative upper-tropospheric wind speed

Recently, Rasmussen and Straka (1998) have evaluated a small (45 case) sample of supercells and concluded that isolated HP supercells (Doswell and Burgess 1993) generally have anvil-level storm-relative wind speeds <18 m s⁻¹, isolated classic supercells have wind speeds between 18 and 28 m s⁻¹, and low precipitation (LP) storms are characterized by storm-relative wind speeds >28 m s⁻¹ [see Rasmussen and Straka (1998) and references therein for a more complete discussion of these supercell types and the climatological analysis]. Here, we evaluate the storm-relative winds for the 2-km-deep layer centered at the −40°C level in the sounding (Fig. 6). Average upper-tropospheric flow strength is greater in the SUP sounding population than in the ORD. This may indicate that the strong low-level shear favoring supercells continues through the depth of the sounding, or it may be an indication that supercells do indeed require a certain amount of storm-relative upper-tropospheric flow to evacuate the water mass that diverges from the updraft summit. The Rasmussen and Straka (1998) finding that isolated HP supercells exist in environments with upper-tropospheric storm-relative wind speeds <18 m s⁻¹ would suggest that at least half of all supercells should be HP based on the data shown in Fig. 6. Because the Rasmussen and Straka analysis is for supercells that are isolated from “seeding” effects of nearby storms it can be inferred that the typical occurrence of nearby storms implies that even more supercells should be HP than the ∼½ implied above. Therefore this climatology, combined with the notion that many supercells are driven toward the HP end of the spectrum by seeding, is consistent with the observation that a majority of supercells are indeed HP storms (Moller et al. 1994).

a. CAPE

CAPE (Moncrieff and Miller 1976) is in common use as a forecast tool for supercells. It is included here as a guide to aid forecasters in understanding what constitutes large or “extreme” CAPE as often quoted in National Weather Service forecast discussions. In this investigation, the virtual temperature correction has been included (Doswell and Rasmussen 1994), and the parcel has the uniformly mixed equivalent potential temperature of the lowest 1000 m of the atmosphere. If one assumes that extreme refers to those ORD soundings composing the upper 10% of the distribution, then CAPE ≳1820 J kg⁻¹ is extreme in this sample. Fifty percent of the ORD soundings have CAPE ≳530 J kg⁻¹ (Fig. 7). Interestingly, CAPE is significantly different between ORD and SUP soundings, as well as between ORD and TOR soundings, suggesting that CAPE alone has some value as a supercell predictor, even when not paired with a measure of shear (although combined measures are much better, as discussed below). The reader is urged to remember that the CAPE values may be biased upward compared to actual proximity values owing to the use of the sounding with the largest CAPE when more than one meets the inflow sector criterion.

b. CAPE immediately above the LFC

Consistent with the idea that large low-level stretching is required for low-level mesocyclone intensification and perhaps tornadogenesis, several researchers have explored the idea that the distribution of CAPE with height is important and large low-level accelerations are favorable for tornadic supercells (McCaul 1991). Figure 8 depicts the distribution of the CAPE that accrues in the soundings in the lowest 3 km above the level of free convection (LFC). It appears that the ORD category has somewhat less CAPE in the lowest 3 km of buoyancy than the two supercell categories, consistent with the previous finding that this category has less CAPE in general. Very little difference can be seen between the TOR and SUP categories, contradicting the idea that increased low-level stretching, perhaps associated with significant tornadoes, owes to low-level CAPE. Instead, the required stretching probably can be attributed to dynamic pressure effects from the interaction of low-level shear and the updraft.

c. Downdraft CAPE

Owing to the apparent association of the rear-flank downdraft (RFD) with tornadogenesis (Lemon and Doswell 1979), and more recent work by Gilmore and Wicker (1998) on the role of midlevel dryness in supercell downdraft production, downdraft CAPE (dCAPE) was investigated. Downdraft sources at levels spaced 1 km apart beginning at 1 km AGL were examined. None of these showed any clear differences between the categories in terms of the frequency distributions. There are various possible causes for this null finding. It is possible that the RFD is not driven primarily by negative buoyancy, but is instead caused by accelerations associated with nonhydrostatic vertical pressure gradient forces [e.g., the “occlusion downdraft” of Klemp and Rotunno (1983) or downward forcing associated with pressure increases in the midlevel stagnation region upwind of the updraft]. Further, it is possible, as suggested by Gilmore and Wicker (1998) that the appropriate parameter space for forecasting RFD intensity includes low-level shear as well as dCAPE. The association of the RFD with sounding-derived parameters is discussed further in section 8.

a. Bulk Richardson number

The bulk Richardson number (BRN) has been used as a supercell predictor ever since it was investigated using numerical simulations (Weisman and Klemp 1982). Weisman and Klemp determined that environments with BRN <50 favored supercells, while BRN >50 favored multicellular events. The parameter space of CAPE and BL–6-km shear is shown in Fig. 9. Supercells (TOR and SUP; all circles) are generally found at larger CAPE and BL–6-km shear than nonsupercells (ORD; dots). The frequency density contours were computed by gridding the parameter space and dividing the number of soundings in each grid cell by the total number of soundings of that category. The heavy black contour representing higher probabilities of SUP is considerably displaced toward larger CAPE and shear than the equivalent probability of ORD. This implies that the“correct” combination of CAPE and shear for discriminating between SUP and ORD is of the form CAPE^x times shear^y, where x and y are both positive, rather than 1.0 and −0.5 as in the BRN.

Combining these two parameters into a form of the BRN yields the distributions shown in Fig. 10. The range of BRN suggested by Weisman and Klemp for supercells does appear to be validated by this climatology with over 75% of the SUP soundings having BRN <17. However, over 50% of ORD soundings have these values as well, meaning that BRN is a poor discriminator (compared to EHI and VGP below) between supercell and nonsupercell sounding populations. It was found that the BRN as formulated by Weisman and Klemp (1982), using the density-weighted mean wind from the surface to 6 km instead of the 6-km wind itself, has similar capability to discriminate among the categories.

b. Energy–helicity index

The energy–helicity index (EHI) (Hart and Korotky 1991; Davies 1993) is defined as

View Expanded

This index is used operationally for supercell and tornado forecasting, with values larger than 1.0 indicating a potential for supercells, and EHI >2.0 indicating a large probability of supercells. The EHI parameter space of CAPE and SRH for this climatology is shown in Fig. 11. As with BRN, but to a greater degree, it can be seen that TOR and SUP soundings occupy a different portion of the parameter space than ORD soundings, with the primary differences being that the former have larger SRH. Further, it appears that EHI has some value in discriminating between TOR and SUP soundings. Although further research is required, this is in contrast to the finding by Brooks et al. (1994a) that combinations of CAPE and shear do not discriminate between tornadic and nontornadic supercells (significant differences in the sizes of the datasets and the methodology may account for this disagreement). In fact, the likelihood of significant tornadoes does increase with increasing EHI, as shown in Fig. 12. Based on this climatology, it appears that EHI is a good discriminator between all three populations of soundings (see additional discussion in section 9). For ORD soundings, 90% have EHI <0.77, while only about 60% of SUP soundings have EHI <0.77, and less than ⅓ of TOR soundings have values less than 0.77. TOR soundings are very strongly distinguished in the neighborhood of EHI = 1.5, where ∼50% of TOR supercells have values greater than 1.5 and only 10% of SUP soundings have values larger than 1.5.

c. Vorticity generation parameter

The vorticity generation parameter (VGP) is derived from an examination of the parameter space investigated in Rasmussen and Wilhelmson (1983) and the physical concept of tilting of vorticity. The rate of conversion of horizontal to vertical vorticity through tilting is

View Expanded

where ζ is the vertical component of vorticity, η is the horizontal vorticity vector, and w is the vertical component of velocity. Here, VGP = [S(CAPE)^1/2], where S is mean shear (or hodograph length divided by depth [Eq. (2)]. To the extent that mean shear is proportional to η, w is proportional to CAPE^1/2, and storm updrafts are all of roughly the same horizontal scale, VGP is roughly proportional to the tilting rate in Eq. (4). Figure 13 illustrates the CAPE and mean shear parameter space. As with EHI, in general the SUP and TOR soundings occupy a different part of the parameter space than ORD soundings. These differences are further illustrated by examining the box-and-whiskers diagram of VGP (Fig. 14). Like EHI (but to a slightly lesser degree), the mean values of VGP are significantly different between all three categories of soundings. Further, as with EHI, TOR soundings have an obviously different frequency distribution than SUP soundings.

In summary, the combination of CAPE and shear in VGP and EHI substantially improves the use of soundings in discriminating among the three categories compared to the various measures of shear or CAPE alone. BL–6-km shear distinguishes the population of supercell soundings from nonsupercells. However, it would appear that low-level shear, especially the streamwise component of horizontal vorticity paired with CAPE, plays a more important role in the production of significant tornadoes.

a. Lifting condensation level

The lifting condensation level (LCL) was investigated in this climatology because the authors have observed on a number of occasions that supercells on hot days, with adequate CAPE and shear, failed to produce tornadoes and seemed to be characterized by too much outflow. This was found to occur even in the presence of CAPE >4000 J kg⁻¹. It is hypothesized that relatively low values of boundary layer relative humidity support more low-level cooling through the evaporation of rain, leading to stronger outflow. Relatively dry boundary layers are characterized by higher LCLs. The distributions in Fig. 15 are consistent with the subjective storm intercept observations. In fact, it can be seen that the LCL on TOR soundings is significantly lower than that for SUP soundings, and even somewhat lower than that for nonsupercells (ORD). Half of the TOR soundings have LCLs below 800 m, while half of the SUP soundings have LCLs above 1200 m. It should be noted that with the LCL, as with most of the parameters explored herein, major variation occurs on small time- and space scales (e.g., Markowski et al. 1998b) that are not well sampled with network soundings. Actual LCL heights near tornadic supercells may be considerably lower than found here.

b. Convective inhibition

There are at least two plausible reasons why convective inhibition (CIN; Colby 1984) might be related to the occurrence of supercells and tornadoes. First, the presence of large CIN in soundings associated with thunderstorms would tend to indicate that the thunderstorms are being strongly forced by local low-level convergence (e.g., by a cold front, outflow). Local strong forcing could imply that storms would tend to be organized into larger-scale convective systems rather than isolated supercells that are more favorable for tornadoes. Second, supercells occurring with large CIN could be“elevated” storms (Colman 1990) that draw inflow from a potentially buoyant layer above the boundary layer; these storms are thought to be relatively less likely to produce tornadoes. Because the occurrence of elevated storms in this climatology is unknown, the association of these events with the large CIN soundings is also unknown.

In this analysis, three-fourths of soundings associated with significant tornadoes occur with CIN <21 J kg⁻¹, whereas over 60% of SUP soundings had CIN larger than this value (Fig. 16). This topic merits further research before it can be considered for operational application; the findings herein should be considered preliminary and the explanations speculative.