A Study on the Relationship Between Cape, Storm-Relative Helicity and Tornadoes in Michigan

 

Michael S. Evans
National Weather Service Forecast Office
Detroit/Pontiac, Michigan
 
 

1. INTRODUCTION

It has long been known that tornadoes often develop in association with rotating supercell thunderstorms, in environments characterized by strong lower-tropospheric wind shear and extreme instability (Davies-Jones 1984). Wind shear results in thunderstorm rotation when horizontal vorticity associated with the shear is converted to vertical vorticity as it becomes ingested by the thunderstorm and tilted into the vertical. The vertical vorticity is then intensified as it becomes stretched by strong updrafts fueled by environmental instability.

If this process results in large enough values of vertical vorticity, a mesocyclone develops. Mesocyclones are defined from a doppler radar operator's perspective as a circulation exhibiting a persistent horizontal rotational velocity of approximately 25 knots or more across a distance of five miles or less through a depth of at least 10,000 feet (NWS 1995). The shear threshold gradually decreases with distance from the radar, due to decreased resolution of velocity data resulting from the widening radar beam. Approximately 90 percent of mesocyclones observed during the Joint Doppler Operational Project were associated with severe weather, and 50 percent produced tornadoes (Burgess and Lemon, 1990). Modeling and theoretical studies indicate those rotating thunderstorms are favorable for tornadogenesis because the resulting air motions within these storms tend to position low-level vertical vorticity near the storm updraft, where additional stretching can produce vorticity values sufficient for tornadogenesis (Rotunno and Klemp 1985, Davies-Jones and Brooks 1993, Brooks et al. 1993, Rotunno 1993).

One way to assess the potential for the development of mesocyclones and associated supercell thunderstorms is to examine environmental values of storm-relative helicity and convective available potential energy (CAPE). CAPE defines the vertically integrated positive buoyancy of an adiabatically rising parcel, and therefore provides a measure of thermodynamic instability. Storm-relative helicity is dependant on the magnitude of the component of horizontal vorticity in the direction of the storm-relative inflow (stream-wise horizontal vorticity) and the magnitude of the storm inflow vector. Therefore, storm-relative helicity can be considered one measure of the rotation potential that can be realized by a storm moving through a vertically sheared environment (Hart and Korotky 1991). It should be noted that horizontal vorticity in the direction perpendicular to the storm-relative inflow vector (crosswise horizontal vorticity) can also contribute to storm rotation through tilting and stretching. However, in that case the rotation initially occurs along the flanks of the updraft, instead of over the center (Rotunno 1993).

Figure 1 shows a plot of 0-2 km AGL storm-relative helicity vs. CAPE for 242 strong and violent (F2-F5) tornado cases (Johns et al 1993). The data indicates that the vast majority of these events occurred with either a CAPE > 1000 J/kg or a storm-relative helicity > 200 m2/s2. Also, for any given value of CAPE, there appears to be a range of helicity values that is most favorable for strong or violent tornado formation, with the values decreasing as CAPE increases.

Figure 1.A scatter diagram showing the combinations of convective available energy (CAPE J/kg) and 0-2 km AGL storm-relative helicity (m2/s2) for 242 strong-to-violent tornado cases (from Johns et al. 1993).

While strong or violent tornadoes often occur in association with supercell thunderstorms, it has been shown that tornadoes can form in thunderstorm environments that are not characterized by deep tropospheric rotation (i.e., Wakimoto and Wilson 1989, Forbes and Wakimoto 1983, Smith 1992). In these cases, it has been hypothesized that tornadoes form when pre-existing low-level vorticity is intensified by the updrafts or downdrafts associated with storms containing little or no deep mid-tropospheric rotation.

The purpose of this study is to examine the relationship between tornadoes, CAPE and storm-relative helicity in Michigan. The findings in this study will have implications regarding the percentage of tornadoes in Michigan that are associated with moderate or strong mesocyclones. In Section 2, a method for producing a graph for Michigan similar to the graph in Figure 1 will be described. Results will be presented in Section 3, a discussion in Section 4, and a summary in Section 5.

2. METHOD

During the period from 1991 through 1994, 51 tornadoes were verified in Michigan (source: Storm Data), intensities, using the Fujita scale (F-scale), were 22 F0s, 19 F1s, 9 F2s, and 1 F3. The tornadoes occurred on 29 different days. Radiosonde and surface data was collected from each day during which at least one tornado occurred, in order to create a data base of modified tornado proximity soundings.

For tornadoes that occurred within two hours of 00 UTC, 00 UTC sounding data from the nearest upper-air station were used to create the modified sounding. For most of lower Michigan the nearest upper-air station was located at Flint (FNT). However, data from Green Bay (GRB) and Sault Ste. Marie (Y62) was used for some events that occurred in northern Michigan. These soundings were modified by inserting surface data from reporting stations at locations and times nearest to the tornado. When winds or temperatures at the nearest station were clearly contaminated by thunderstorms or a change of airmass, the next closest observation was used. All modifications were performed using the Skew T-Hodograph Analysis and Research Program (SHARP) workstation (Hart and Korotky 1991).

For tornadoes that occurred at times more than two hours before or after 00 UTC, modified soundings were creating by using time-weighted values of temperature, dew point, wind speed and wind direction from the nearest 00 UTC and 12 UTC sounding. Time-weighted values of temperature and dew point were calculated at 850-mb, 700-mb and 500-mb, and were inserted into the 00 UTC sounding. Time-weighted values of wind direction and wind speed were calculated at 1500 m and 3000 m, and were inserted into the 00 UTC sounding. Again, surface data was taken from the nearest uncontaminated surface observation and inserted into the 00 UTC sounding. Some subjective smoothing of the data was done between the levels where the time-weighing calculations were performed.

On several of the 29 days, more than one tornado occurred. For those days, if the tornadoes all happened within a two-hour period and all nearest the same upper-air station, only one modified sounding was created, based on data taken from times and locations nearest to the strongest tornado. On two days when multiple tornadoes occurred with a time spacing greater than two hours, two modified soundings were created using data taken from times and locations nearest the strongest tornadoes separated by at least two hours.

A lack of data or bad wind data resulted in the removal of 3 days from the study. The final result was a total of 28 modified tornado proximity soundings. Calculations of 0-2 km AGL storm relative helicity and CAPE were then performed for each sounding, using the SHARP workstation.

3. RESULTS

Figure 2 shows a scatter diagram of 0-2 km AGL storm-relative helicities and CAPE for the 28 modified tornado soundings described in Section 2. The plotted values indicate the F-scale intensity of the strongest tornado associated with each modified sounding. The data in Figure 2 fell roughly into two regions. The soundings represented by the data plots in Region "A" were associated with values of storm-relative helicity and CAPE with roughly the same magnitude as the data shown in Figure 1. Frequently, storms that form in that kind of environment will exhibit supercell characteristics, with moderate to strong mesocyclones (Johns et al. 1993). As was the case in Figure 1, for each value of CAPE, there appears to have been a favored range of storm-relative helicity values, with the values decreasing as CAPE increased.

Figure 2. A scatter diagram of the 0-2 km AGL storm-relative helicity (m2s2) and convective available potential energy (CAPE J/kg) for the 28 modified soundings in the study. The plotted values indicate the F-scale intensity of the strongest tornado associated with each modified sounding. The "A" marks the region where tornadoes formed in environments that were favorable for mesocyclones. The "B" marks the region where tornadoes formed in unfavorable environments.

Meanwhile, half of the soundings were represented by the plot in Region "B". These soundings were characterized by relatively low values of CAPE and/or storm-relative helicity. The tornadoes associated with these events tended to be weaker than the tornadoes that occurred in Region "A". (The difference in the F-scale intensities of the tornadoes in the two groups was found to be statistically significant, based on a non-parametric Kruskal Wallace comparison test using a 0.10 significance level). That result corresponds to previous findings of non-mesocyclone tornadoes tend to be weaker than those associated with moderate to strong mesocyclones (i.e., Wakimoto and Wilson 1989). It should be noted however, that two of the tornadoes from Region "B" did reach F2 intensity. Wakimoto and Wilson (1989) also found that intensities as high as F2 were possible with a non-mesocyclone tornado, while Forbes and Wakimoto (1983) found that intensities as high as F3 were possible.

4. DISCUSSION

In order to explain the relatively large number of tornado events that occurred with soundings represented in Region "B", recall from Section 1 that thunderstorm rotation can sometimes occur due to tilting and stretching of cross-wise vorticity. In cases where thunderstorms develop in environments with large speed shear and little directional shear, large values of cross-wise vorticity can occur with small values of stream-wise vorticity, and correspondingly small values of storm-relative helicity. This horizontal vorticity can also be tilted into the vertical, along the flanks of the thunderstorm updraft, with the result being an increase in vertical vorticity. As a result, thunderstorm rotation can sometimes occur despite low values of environmental storm-relative helicity, when lower tropospheric speed shear is large. Johns et al. (1990) found that the relationship between CAPE and 0-2 km wind shear was similar to the relationship between CAPE and 0-2 km storm-relative helicity for environments that produced strong or violent tornadoes. In his study sample, all of the strong or violent tornado events occurred with 0-2 km shear values greater than 6 x 10-3s-1.

Another explanation for the large number of tornadoes that occurred in Region "B" may be that tornadoes can sometimes occur without significant thunderstorm rotation. Recall from Section 1 that non-mesocyclone tornadoes can sometimes form when pre-existing low-level vorticity becomes intensified by the updrafts of thunderstorms containing little or no deep mid-tropospheric rotation. The origin of the pre-existing low-level vorticity in these situations is not always clear (Doswell and Burgess 1993), but in many cases it appears to be associated with strong lower tropospheric wind shears. Wakimoto and Wilson (1989) described a case where tornadoes appeared to develop in response to updraft-induced intensification of low-level vorticity associated with horizontal wind shear along a lower-tropospheric convergence boundary. Forbes and Wakimoto (1983) examined a case of severe weather where several tornadoes appeared to develop in response to localized boundary-layer vorticity generation associated with horizontal and vertical wind shears near microbursts. Smith (1992), examined a tornado that formed in a weak large-scale shear/low CAPE environment, and also suggested that microbursts could have played a crucial role in generating the low-level vorticity associated with tornadogenesis. It was speculated that the advection of mid-tropospheric dry air into the area of tornadogenesis may have helped to produce microbursts. The combination of localized lower-tropospheric wind shears that developed in response to the microbursts, and convergence associated with a surface pressure trough may have provided enough low-level vertical vorticity for a tornado to develop.

Environments favorable for wet microbursts are typically characterized by dry air in the mid-troposphere, with a layer of relatively moist air near the surface (Figure 3). Atkins and Wakimoto (1991) found that the dry air at mid-levels is often advected into the area by mid-tropospheric wind. They also found that the decrease in equivalent potential temperature (e) with height can be a valuable predictor for wet microbursts, with a difference of at least 13C needed between the surface and the minimum e in the lowest 500-mb of the troposphere.

Figure 3. A schematic showing idealized thermodynamic soundings for a wet-microburst occurrence in a humid region (from Atkins and Wakimoto 1991).

Table 1 shows data for the 14 events that were characterized by relatively low values of storm-relative helicity and CAPE (located in Region "B" in Figure 2). The data in the column labeled "0-2 km sh" represents the 0-2 km wind shear values in the modified sounding for each event. The data in the column labeled e represents the difference between the e at the surface and the minimum e in the lowest 500-mb for the modified sounding for each event. Finally, the data in the column labeled Td represents the maximum difference between the 500-mb or 700-mb dew points from the observed (not modified) sounding nearest each tornado event, and the corresponding dew points from the nearest upstream sounding (positive values indicating drier air upstream). Data from the observed 12 UTC soundings are shown for tornado events that occurred at or before 00 UTC, and data from the observed 00 UTC soundings are shown for events that occurred after 00 UTC.

The data in Table 1 shows that 0-2 km wind shear values of greater than 6x10-3s-1 were present in 4 of the 14 modified soundings represented in Region "B". That result implies that significant amounts of cross-wise horizontal vorticity may have been present in the storm environment during those 4 events, which could have contributed to thunderstorm rotation, despite low values of storm-relative helicity.

The data in Table 1 also shows that the decrease in e with height was greater than the Atkins and Wakimoto wet microburst threshold of 13C for 12 of the 14 soundings. In the case of the two soundings where the difference was less than 13C, the data in Table 1 indicates that there was relatively dry mid-tropospheric air upstream from the soundings, indicating the potential for advection of drier air into the area of interest at about the time of tornado occurrence.

A check of the synoptic-scale conditions associated with the 14 events represented in Table 1 indicates that a synoptic-scale cold front or warm front passed through the area of interest near the time when tornadoes occurred for 12 of the 14 events. Recall from Section 1 that considerable pre-existing low-level vorticity must exist for tornadoes to form, especially in a non-supercell environment. In these cases, some of the low-level vorticity was probably generated by the convergence and wind shears associated with these large-scale fronts. (It is probable that mesoscale boundaries also generated significant amounts of low-level vorticity in many of these cases as well).

 

Table 1
Date Time In County
Cape
J/kg
0-2 Sh
x10m-3s-1
0-2 Hel m/s2
e
C
Td
C
7/18/94 00z F0 Misaukee 541 3.5 40 14 3
6/20/94 21z F0 Lenawee 870 5.3 69 14 5
9/03/93 22z F0 Wayne 755 3.6 -18 25 18
7/28/93 18z F0 Delta 429 4.9 106 16 -5
7/09/93 03z F1 Allegan 685 6.1 60 29 2
6/20/93 18z F0 Macomb 1691 3.0 42 21 16
6/19/93 20z F1 Genesee 1553 4.8 52 16 7
9/21/92 21z F1 Ingham 1091 6.6 89 14 12
7/14/92 02z F2 Cass 0 11.9 106 8 16
6/17/92 23z F1 Huron 1723 3.0 36 18 4
6/17/92 21z F1 Kent 1721 4.3 34 18 4
7/07/91 20z F2 Oakland 1908 2.7 65 26 -2
5/31/91 00z F1 Ottawa 860 7.8 86 17 2
4/23/91 22z F0 Branch 206 3.4 12 6 17

 

Data from the 14 modified soundings plotted in Region "B" in Figure 2. The data in the column labeled 0-2 km shear represents the 0-2 km wind shear values (s-1) in the modified sounding for each event. The data in the column labeled e represents the difference between the e at the surface (degrees C) and the lowest e (degrees C) from the surface through 500-mb for each modified sounding. The data in the column labeled Td represents the maximum difference in degrees C between the 500-mb and 700-mb dew points at the observed sounding nearest each tornado event, and the corresponding dew points from the nearest upstream observed sounding.

5. SUMMARY

The results summarized in Figure 2 indicate that half of the tornado events in Michigan, during the period from 1991 through 1994. occurred with values of storm-relative helicity and/or CAPE lower than what is typically associated with moderate to strong mesocyclones in supercell thunderstorms. The F-scale intensities associated with those tornadoes tended to be lower than the F-scale intensities of the tornadoes that occurred with higher storm-relative helicities and CAPEs.

These results imply that tornado occurrence cannot be dismissed in Michigan just because the environment does not appear favorable for the formation of supercell thunderstorms, based on calculations of storm-relative helicity and CAPE. On days when those calculations imply that the environment is not favorable for the formation of supercell thunderstorms, 0-2 km wind shear values should also be considered to check for the possibility of cross-wise vorticity contributing to thunderstorm rotation.

In addition, the forecaster should consider that non-mesocyclone tornadoes can form in response to intense boundary-layer vorticity generation. The results of this and other studies indicate that such tornadoes can form near synoptic-scale or mesoscale surface boundaries, near microbursts. Typically, tornadoes that form in this fashion will be weak (F1 or F0), but occasionally an F2 tornado may occur. Some indicators for forecasting wet microbursts include:

6. REFERENCES

Atkins, N.T., and R.M. Wakimoto, 1991: Wet Microburst Activity over the Southeastern United States: Implications for Forecasting. Wea. Forecasting, 6, 470-482.

Brooks, H.E., C.A. Doswell, and R. Davies-Jones, 1993: Environmental Helicity and the Maintenance and Evolution of Low-Level Mesocyclones, The Tornado: It's Structure, Dynamics, Prediction and Hazards, American Geophysical Union, Washington, D.C., 97-104.

Burgess, D.W., and L.R. Lemon, 1990: Severe thunderstorm detection by radar, in Radar in Meteorology, American Meteorological Society, Boston, 619-647.

DOC. NOAA, NWS, 1995: WSR-88D Operators Guide to Mesocyclone Recognition and Diagnosis. WSR-88D Operational Support Facility, Operations Training Branch, Norman, OK.

____________, 1991-1994: Storm Data, National Climatic Data Center, Asheville, NC.

Davies-Jones, R.P., 1984: Streamwise Vorticity: The Origin of Updraft Rotation in Supercell Storms. J. Atmos. Sci., 41, 2991-3006.

____________, and H. Brooks, 1993: Mesocyclogenesis from a Theoretical Perspective, in The Tornado: it's Structure, Dynamics, Prediction, and Hazards, American Geophysical Union, Washington, D.C., 105-114.

Doswell, C.A., and D.W. Burgess, 1993: Tornadoes and Tornadic Storms: A Review of Conceptual Models. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, American Geophysical Union, Washington, D.C., 161-172.

Forbes, G.S., and R.M. Wakimoto, 1983: A concentrated Outbreak of Tornadoes, Downbursts and Microbursts, and Implications Regarding Vortex Classification. Mon. Wea. Rev., 111, 220-235.

Gibbons, J.D., 1976: Nonparametric Methods for Quantitative Analysis. Holt, Rinehart and Winston, 463pp.

Hart, J.A., and J. Korotky, 1991: The Sharp Workstation v 1.50. A Skew-T Hodograph Analysis Research Program for the IBM and Compatible P.C. DOC/NOAA/NWS Charleston, WV, 30 pp.

Johns, R.H., J.M. Davies, and P.W. Leftwich, 1993: Some Wind and Instability Parameters Associated with Strong and Violent Tornadoes: 2. Variations in the Combinations of Wind and Instability Parameters, in The Tornado: It's Structure, Dynamics, Prediction, and Hazards, American Geophysical Union, Washington D.C., 583-590.

Rotunno, R., and J.B. Klemp, 1985: On the Rotation and Propagation of Simulated Supercell Thunderstorms, J. Atmos. Sci., 42 271-292.

____________, 1993: Supercell Thunderstorm Modeling and Theory, in The Tornado: Its Structure, Dynamics, Prediction, and Hazards, American Geophysical Union, Washington, D.C., 57-73.

Smith, B.B., 1995: Weak Tornado Development From Shallow Convection Over South Central Lower Michigan: September 21, 1992, in Postprints, First Symposium on Michigan Weather and Forecasting, Southeast Michigan Chapter of the American Meteorological Society, 7pp.

Wakimoto, R.M., and J.W. Wilson, 1989: Non-supercell Tornadoes. Mon. Wea. Rev., 117, 1113-1140.

 


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