Potential Temperature and Mixing Ratio--Contributions to Theta-e
on Elevated Terrain
Jonathan D. Finch

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Related items of interest

April 23  1960 Cheyenne Ridge Tornado

June 14-17  1965 Front Range Superstorm

May 7-8  1965 Front Range Tornado

Elevated Mixed Layer
Introduction

As experienced storm chasers are well aware, severe thunderstorms occur on the high plains with much lower surface dewpoint
temperatures than at low elevations. For example, supercell thunderstorms occur in spring and summer with dewpoints only from
3 to 15C(37 to 59F). Exactly why can we get by with lower dewpoints and still get explosive storms? The answer is twofold. In
answering this question I would like to correct a common misunderstanding concerning dewpoint temperature. I have often heard
something like, "wow Cheyenne has a 60F dewpoint, thats like a 80 dewpoint at our elevation". This is incorrect. The dewpoint
lapse rate is only about 1F /1000ft. This means that a 50F dewpoint at CYS has the same moisture as roughly a 56F dewpoint
at Houston. This corresponds to a mixing ratio of  9.6g/kg. In June, if the dewpoint at Houston is 56F, then the CAPE is
probably close to zero for any reasonable 500mb temperature. But at Cheyenne, if the wind is from the east or southeast and the
dewpoint is 50F(same amount of moisture), then interesting things can happen. Obviously it is not the high moisture content that
is responsible for a threat for storms at Cheyenne. To explain the importance of potential temperature we will consider the following
comparison between several stations.

Constraints: Mixing ratio, Potential Temperature and Theta-E are forced to be constant and SLP = 1000mb

 Elev(ft) Pressure(mb) T(F) Td(F) MR(g/kg) Theta(F) Theta-e(K) Laramie 7280 769 63.4 48.7 9.6 104 343.2 Cheyenne 6140 806 70.1 49.9 9.6 104 343.2 Limon 5360 823 73.4 50.6 9.6 104 343.2 Akron 4700 845 77.4 51.3 9.6 104 343.2 Dalhart 4000 869 82 52 9.6 104 343.2 Goodland 3700 878 83.4 52.3 9.6 104 343.2 Dodge City 2600 915 89.8 53.4 9.6 104 343.2 Wichita 1340 954 96.3 54.6 9.6 104 343.2 Coffeyville 750 975 99.9 55.2 9.6 104 343.2 Houston(HOU) 50 998 103.6 55.8 9.6 104 343.2

In the above example, if the MR(mixing ratio) is forced to be equal at differing elevations, then a  much higher surface temperature
is required at the lower elevation to achieve the same surface theta-e. Note that if the potential temperature and mixing ratio are
both forced to be the same at all elevations, then the theta-e will be the same at all elevations. Thus, it is the POTENTIAL
TEMPERATURE that is important in the generation of high theta-e and NOT strictly the temperature(note the "cool" temperature
of 70F at Cheyenne.

Constraints: Dewpoint Depression and Theta-e are forced to be constant and SLP = 1000mb

 Elev(ft) Pressure(mb) T(F) Td(F) MR(g/kg) Theta(F) Theta-e(K) Laramie 7280 769 66.6 46.6 8.9 107.6 343.2 Cheyenne 6140 806 70.1 49.9 9.6 104 343.2 Limon 5360 823 71.6 51.6 10 102 343.2 Akron 4700 845 73.5 53.5 10.5 99.7 343.2 Dalhart 4000 869 75.6 55.6 11.0 97.3 343.2 Goodland 3700 878 76.3 56.3 11.15 96.6 343.2 Dodge City 2600 915 78.8 58.8 11.8 93.5 343.2 Wichita 1340 954 82.1 62.1 12.7 89.4 343.2 Coffeyville 750 975 83.6 63.6 13.1 87.5 343.2 Houston(HOU) 50 998 85.2 65.2 13.5 85.5 343.2

In the above example, the theta-e remains constant with height despite lower mixing ratios due to elevated heating as shown on a
skewt chart. Thus, high theta-e air can be acheived on elevated terrain despite lower moisture content of the air. This helps explain
why storms generally weaken faster on the high plains after the loss of surface heating compared to the low-plains or southeast.
On the low-plains, storms are driven more by moisture which does not have a strong diurnal variation.

Cases

On June 25, 1942 a tornado moved NW killing 2 people in a house 4 miles west of Wheatland, WY. At 1830 UTC
the T/Td were 75F/61F at Cheyenne, WY and 87F/73F at Tulsa, OK. The theta-e was higher at Cheyenne than
Tulsa even though the T/Td were both 12F higher at Tulsa. The weather calculator was down when I tried to
calculate the MR and theta so I approximated using a skewt.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Cheyenne 6140 808 1006.8 75 61 14.4 109 360.8 Tulsa 670 986 1009.5 87 73 17.3 89 358.3

On April 12, 1967 a tornado moved NE then north from SW of Veteran, Wyoming, causing considerable damage. Dewpoint
temperatures were only in the upper 30s to mid 40s. At Cheyenne, near the initiation point for the tornadic storm, the T/Td at
20 UTC were 59F/39F. Low-level upslope flow was occurring north of a warm front. The station pressure on the actual
observation form was 793mb. A 39F dewpoint temperature at Cheyenne has about the same moisture as a 45F dewpoint
at Topeka. Meanwhile, the T/TD at Topeka were 67F/60F, with a station pressure of 971mb. The elevation at Topeka is
881 ft compared to 6156 ft at Cheyenne. Despite the T/Td being 8F/21F higher at Topeka, the equivalent potential
temperature was actually the same at the two locations--328K! Even though the mixing ratio at Topeka was 80% higher
than at Cheyenne (11.5 versus 6.4 g/kg), the potential temperature at Cheyenne was 94.5F, compared to 71.4F at Topeka.
Thus, elevated heating overcame a huge moisture deficit at Cheyenne. Also, the 500mb temperature at Cheyenne was about
-18C, compared to -12C at Topeka(see 12Z  and 00Z 500mb charts), resulting in lifted indices of zero at Topeka and -6 at
Cheyenne(note the modified sounding). Also, notice the southerly mid-level flow that so often accompanies early season
tornado events on the front range.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Cheyenne 6140 793 990.6 59 39 6.4 94.5 328 Topeka 881 971 1003.3 67 60 11.5 71.4 328

On April 23, 1960, a tornado moved N and NW from 23 miles WSW of Cheyenne at elevations between 7400 and 7900 ft.
Surface dewpoints in the area of interest ranged from the lower 40s to lower 50sF, depending on elevation. Strong upslope
flow was occuring just north of a warm front. By 01 UTC, the dewpoint at Cheyenne jumped to 46F, with a temperature of
64F. The station pressure at Cheyenne at 01 UTC was 801 mb. Meanwhile, at Dallas, TX the temperature and dewpoint
were 80F/60F, with a station pressure of 995mb. But the surface theta-e was slightly higher at Cheyenne compared with
Dallas.  The potential temperature and mixing ratio at Dallas/Cheyenne were 80.8F/98.3F and 11.2 /8.3 g/kg respectively.
So despite the mixing ratio being 35% higher at Dallas and the temperature being 16F higher, the theta-e was actually higher
at Cheyenne(335.7K vs 333.5K). The best way to accomplish high theta-e on high terrain in April is to have deep,
southerly flow at and above 700mb, with upslope flow underneath. This helps steepen lapse rates with warm, moist low-levels
and cool upper levels.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Cheyenne 6140 801 999.6 64 46 8.3 98.3 335.7 Dallas 487 995 1011.9 80 60 11.2 80.8 333.4

On June 16, 1965 several tornadoes occurred along and west of the urban corridor in Colorado. The 20 UTC surface map
showed strong southeast winds advecting moisture onto the front range. The T/TD at Colorado Springs(elevation 6150 ft.)
were 64F/60F. At Dallas the dewpoint was 70F. But since a 60F dewpoint at COS has the same amount of moisture as a
66F dewpoint at Dallas, the mixing ratio at Fort Worth was only 16% higher than at COS. The surface temperature at
Dallas was 85F compared to 64F at Colorado Springs. However, the potential temperature was much higher at Colorado
Springs--96.9F versus 85.8F. Therefore, the surface theta-e was higher at COS(351.6K versus 350.8K). The 500mb charts at
12Z and 00Z showed southerly flow up and down the western high plains.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Colo. Springs 6184 808 1008.0 64 60 13.9 96.9 351.6 Dallas 487 994 1015.2 85 70 16.1 85.8 350.8

On June 6, 1990, an  elevated mixed layer covered the western plains with 700mb temps from 15 to 19C. However, strong
upslope flow and elevated heating, along with convergence on the Palmer Divide, helped initiate convection. The T/TD at
Limon, CO(elevation 5300ft) were 78F/56F. The T/TD were much higher at Dallas(95F/67F). However, the theta-e was
only slightly higher at Dallas(351.2K versus 353.6K). This is because the potential temperature at Limon was actually
much higher than at Dallas(106.7F versus 96.7F). The mixing ratio at Dallas was 25% higher than at Limon.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Limon 5300 833 1007.2 78 56 11.6 106.7 351.2 Dallas 487 989 1008.7 95 67 14.5 96.7 353.6

On June 9, 1990, tornadoes occurred in Weld county Colorado, which is just south of Cheyenne, Wyoming. At 22 UTC the
T/TD's were: CYS(77F/57F), Fort Worth(94F/64F), Topeka(85F/60F), and Chanute, KS(85F/70F). Out of these 4 stations,
the theta-e was highest at Cheyenne(355.7K) compared to Fort Worth(348.8K), Topeka(338.5K) and Chanute(353.6K).
Mixing ratios were as follows: Cheyenne(12.4g/kg), Fort Worth(13.1g/kg), Topeka(11.4g/kg), and Chanute(16.3g/kg).
Note that the mixing ratio was higher at Cheyenne than Topeka despite a lower dewpoint. Also note that the potential
temperature was 110F at Cheyenne, compared to 94.2F at Fort Worth, 88F at Topeka and 88F at Chanute.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Cheyenne 6140 810 1011 77 57 12.4 110.1 355.7 Topeka 881 981 1018 85 60 11.4 88 338.5 Chanute 1020 978 1017 85 70 16.3 88 353.6 Fort Worth 700 987 1016 94 64 13.1 96.1 348.8

On July 16, 1979, an F4 tornado struck Cheyenne, Wyoming. There was likely a strong moisture gradient across the city of
Cheyenne. The T/TD at Cheyenne airport were 80F/51F at 20 UTC, compared to 82F/70F at Topeka and 97F/64F at
Fort Worth. The mixing ratios were 9.5g/kg at Cheyenne, 16.2g/kg at Topeka and 12.8g/kg at Fort Worth. Despite the
mixing ratio being 70% higher at Topeka than Cheyenne and the tempertaure being about the same, the theta-e was nearly
the same at the three locations--348.5K at Cheyenne vs 349.9K at Topeka and 349.4 at DFW. This is because the potential
temperature was much higher at Cheyenne(113.1F), compared to 83.9F at Topeka. The 500mb chart showed NW flow
across the plains.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Cheyenne 6140 817 1019.0 81 50 9.5 113.1 348.5 Topeka 881 988 1023.6 82 70 16.2 83.9 349.9 Dallas(DFW) 660 996 1019.2 97 64 13.0 97.6 349.4

On April 11, 1977, a F2 tornado hit near Colorado Springs(COS). The T/TD at 20 UTC were 58F/41F at Colorado Springs,
with strong upslope surface winds at 20kts, 81F/40F at Topeka, 83F/45F at Omaha, and 81F/55F at Fort Worth. Despite
dewpoints being nearly identical at Topeka and COS(40F vs 41F), the mixing ratio was 28% higher at COS compared to
Topeka (5.3 vs 6.8g/kg). Despite the low temperature of 58F at Colorado Springs, the potential temperature was 90F, compared
to 83F at Topeka, 86F at Omaha and 81.5F at Fort Worth. The theta-e was higher at Colo. Springs than Topeka or Omaha.
The theta-e was only slightly higher at DFW(328.4K) than COS(326.2K). The 500mb chart showed a deep upper trough over
the southern rockies with meridional flow up the high plains.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Colo. Springs 6140 810 1008 58 41 6.8 90 326.2 Topeka 881 987 1021.6 81 40 5.3 83 317.8 Omaha 980 981 1017.4 83 45 6.5 86 323 Dallas(DFW) 660 997 1022.6 81 55 9.2 81.5 328.4

On June 13, 1984, a tornado struck near Lance Creek in east-central Wyoming. Theta-e values were fairly uniform across
eastern Wyoming at 22 UTC, despite differing T/TD values. For example, the dewpoint was only 52F at Laramie, 58F at
Cheyenne and 60F at Douglas. But note that the potential temperature was much higher at Laramie, which made up for the lack of
moisture. Also note that the theta-e was higher at Laramie than Little Rock, despite the T/Td being 23F/13F lower.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Laramie 7240 780 1011.3 72 52 10.7 111.1 351.1 Cheyenne 6140 816 1013.7 69 58 12.8 100.6 350.7 Douglas 4970 845 1010.7 73 60 13.3 99.2 351.3 Dodge City 2600 927 1016.1 82 64 13.9 93.8 349.9 Little Rock 262 1009 1017.6 95 65 13.2 93.6 347.7

On February 7, 1980 a tornado moved from Farewell, TX(near the New Mexico state line) to just south of Dimmitt, TX. A
tornado was also reported near Melrose, NM. At 22 UTC the T/Td at Clovis, NM was 59F/45F. The T/TD were 63F/59F at
Victoria, TX and 65F/60F at San Antonio, TX. Despite the much lower T/Td at Clovis, the theta-e was actually higher at Clovis
than Victoria, and only slighly lower than San Antonio. This is despite a much lower mixing ratio. But note the much higher potential
temperature at Clovis.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Clovis 4295 854 1002 59 45 7.5 82.9 324 San Antonio 809 982 1010.1 65 60 11.4 67.7 325.6 Victoria 130 1008.4 1012.8 63 59 10.7 61.8 319.9

On June 17, 1965 several tornadoes occured along the front range in Colorado. The T/TD at Pueblo was 72F/66F at  18 UTC.
This is about as high as the dewpoint ever gets at 4700ft. In fact, a 66F dewpoint at Pueblo has nearly the same mixing ratio as a 71F
dewpoint at Dallas, TX. The T/Td at Dallas and Victoria were 83F/71F and 90/74 respectively. The theta-e was higher at Pueblo
than Dallas and about the same as Victoria. This is despite the T/TD being 18F/8F higher at Victoria.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Pueblo 4726 856.7 1013.6 72 66 16.2 96 358.2 Victoria 130 1012.1 1016.5 90 74 18.1 88.1 358.6 Dallas 487 1002.9 1020.1 83 71 16.5 82.6 350.0

On June 24, 1979, a tornado moved SE down Williams Canyon on the east side of Pikes Peak to Manitou Springs. A convenient
store and gas station were demolished. At 20 UTC the T/Td were nearly identical at Colorado Springs(COS) and Omaha. The 500mb
temperature were also similar at Omaha and Denver(-12C to -13C). But the theta-e was 351K at COS and only 326.7K at Omaha.
So the lifted index was -1 at Omaha and -9 at Colorado Springs. Even though the dewpoint was higher by 1F at Omaha, the
mixing ratio was actually 17% higher at Colorado Springs. Even though the temperature was the same, the potential temperature
was 30F higher at Colorado Springs.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Colo. Springs 6180 814 1014 73 56 11.9 105.2 351 Omaha 984 987 1023.7 73 57 10.2 75 326.7

On March 27, 1992, a tornado moved NE from near Farewell, TX to south of Bovina. At 22 UTC, the T/TD at Clovis were
60F/58F. The T/Td at Brownsville, TX were 76F/67F. Despite the much higher T/Td values at Brownsville, the sites had nearly
identical  theta-e values.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Clovis 4295 858 1006.8 60 58 12.2 83.2 337.6 Brownsville 10 1011.7 1012.0 76 67 14.2 74.2 337.7

On April 25, 1984, upslope flow developed north of a warm front on the central high plains. As in most early season severe
weather cases on the front range, the mid to upper level flow was fairly meridional, with cold mid level temps(-19C at Denver at
500mb). At 20 UTC the T/Td at Akron, CO(elev. 4700ft) were 64F/46F. The mixing ratio was 15% higher at Mcalester than
Akron, but the potential temperature was higher at Akron(91.6F vs 85.9F). So the theta-e was about the same at the two
locations.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Akron, CO 4700 835 986.4 64 46 8 91.6 330.7 Mcalester, OK 771 975 1002.1 82 54 9.2 85.9 330.8

On April 21, 1957,  a stationary  or warm front was located just south of Lubbock. The T/TD was 67/64 at Lubbock at 0030 UTC.
Meanwhile the T/TD was 74F/72F at Galveston along the gulf coast.  The 2230 UTC surface map is similar. Even though the
dewpoint was 8F higher at Galveston(mixing ratio 17% higher) and despite the temperature being 7F higher, the theta-e was similar
at the two stations. This is because the potential temperature was 11.2 F higher at Lubbock.

 Elev(ft) Pres.(mb) SLP(mb) T(F) Td(F) MR(g/kg) theta(F) theta-e(K) Lubbock 3280 902 1009.5 67 64 14.3 82.7 343.7 Galveston 0 1017 1017.6 74 72 16.8 71.5 343.5