A AVE-IV. Severe

Home , Atmospheric instability, Convective instability

NASA Technical ;x!' Novern ber 1982 \'

A I Stability Analysi)

I of AVE-IV. Severe

Weather Soundings..

Dale L. Johnson

runsn TECH LIBRARY KAFB. NY NASA Technical 00b7828 20Pager 5

1982 A Stability Analysis of AVE-IV Severe Weather Soundings

Dale L. Johnson George C. Marshall Space Flight Center Marshall Space Flight Center, Alabama

National Aeronautics and Space Administration Scientific and Technical Information Branch ACKNOWLEDGMENTS

The authorwishes to express his thanks to Dr. Robert E. Turner, Dr. Gregory S. Wilson,and Dr. William W. Vaughan of NASA-MSFC AtmosphericSciences Division, along with Dr. WalterFrost and Dr. Kenneth Kimble of the University of Tennessee Space Institute, for their assistance and suggestionsgiven throughout this study. Also, appreciation is expressed to Mrs.Jeannie Harper forher assistance and excellenttyping of this report.

ii .

TABLE OF CONTENTS

CHAPTER PAGE I. INTRODUCTION...... 1 I1. DEFINITIONS ...... 3 Introduction...... 3 Skew.T. Log-P Diagram ...... 3 StabilityIndex ...... 8 Stabi 1 ity ...... 10 I11. ATMOSPHERIC VARIABILITY EXPERIMENT IV DATADESCRIPTION ...... 15 Introduction...... 15 AVE-IV DataBackground ...... 15 SynopticSituation ...... 19 ManuallyDigitized RadarData ...... 24 Rawinsonde Data Grid ...... 24 AVE-IV Averaged Profiles ...... 29 AVE-IV AverageLag Profiles ...... 31 IV IV . INDICES USED IN STUDY ...... 40 Introduction...... 40 IndexSelection Criteria ...... 40 Indices Chosen ...... 41 Definitionof Indices ...... 41 Severeweather threat index ...... 41 Vertical-totalsindex ...... 47 Cross-totalsindex ...... 49

iii I I

CHAPTER PAGE IV . (continued) Total-totals index ...... 49 Theta-E methods ...... 50 Showalter stability index ...... 54 Rackcliff instability index ...... 57 Jefferson instability index ...... 59 Modified Jefferson instability index ...... 60 Boyden instability index ...... 61 K-index ...... 62 Bradbury potential stability index ...... 66 Energy index ...... 68 Martin index ...... 72 V . AVE-IV PROFILE ANALYSES ...... 75 Introduction ...... 75 AVG Profile Comparison ...... 76 Temperature/moisture ...... 76 Winds ...... 76 LAG Profile Comparison ...... 78 Temperature/moisture ...... 78 Winds ...... 78 AVG/LAG Profile Comparison ...... 80 Winds ...... 80 Temperature/moisture ...... 82 Theta-E AVG/LAG Comparison ...... 82

iV CHAPTER PAGE V . (continued) AVG/LAG Conclusions ...... 89 PossibleStability Index ...... 91 VI VI . AVE-IV STABILITY ANALYSES ...... 92 Introduction ...... 92 Temperature-Dependence ...... 92 StabilityIndex Results ...... 96 JohnsonLag Index ...... 99 VI1 . STABILITY CRITERIA APPLIED TO AVE.SESAME.1 ...... 104 Introduction ...... 104 SynopticSituation ...... 104 SoundingAnalyses ...... 106 Exceptionsto the Norm ...... 113 LagTesting ...... 114 VI11 . CONCLUSIONS ...... 116 BIBLIOGRAPHY ...... 118

V i'

LIST OF TABLES

TABLE PAGE 1. Rawinsonde Stations Participating in AVE-IV Experiment. .. 17 2. Manually Digitized Radar Data Code [8]...... 26 3. MDR Categories Used in the Present AVE-IV Analyses. .... 27

4. AVE-IV Average Profile Conditions for MDR = 0 (No Precipitation)...... 32

5. AVE-IV Average Profile Conditions for MDR > 0 (All Precipitation) ...... 33 6. AVE-IV Average Profile Conditions for MDR > 3 (All Thunderstorms) ...... 34

7. AVE-IV Average Profile Conditions for MDR > 7 (Severe Thunderstorms)...... 35

8. AVE-IV Average Lag Profile Conditions for MDR = 0 (No Precipitation)...... 36

9. AVE-IV Average Lag Profile Corditions for MDR > 0 (All Precipitation) ...... 37

10. AVE-IV Average Lag Profile Conditions for MDR > 3 (A1 1 Thunderstorms) ...... 38

11. AVE-IV Average Lag Profile Conditions for MDR > 7 (Severe Thunderstorms)...... 39 12. StabilityIndices ...... 42

13. Vertical-Totals Index Thunderstorm Threshold Values for Different Areas ...... 48 14. Delta Theta-E Upper and Lower Index Critical Values .... 53

vi TABLE PAGE 15 . K-Index Thunderstorm Threshold Values ...... 64 16 . K-Index Thunderstorm Probabilities ...... 65 17 . Energy Index Values Used in Convective Forecasting ..... 71

18 . Theta-E Differences (OK) Between Given Pressure Levels ... 88 19 . Stability Index Range Determined by Moist and Dry Adiabatic Lapse Rates ...... 94 20 . Stability Index Dependency as a Function of Temperature Change ...... 95 21 . Stability Index Values for LAG and AVG MDR Profiles .... 97 22 . JLI versus MDR Categories for LAG and AVG Conditions .... 102 23 . Abilene. Texas. AVE-SESAME-I Sounding Stability Index Values ...... 111

vii LIST OF FIGURES

F IGURE PAGE 1 . Coordinate System ofthe Skew.T. Log-P Diagram[3] ..... 5 2 . Skew.T. Log-PDiagram. withLifted Parcel Example [3] ...... 7 3 . Skew.T. Log-PDiagram. withHeating Parcel Example [3] ...... 9 4 . AtmosphericSounding Stability Classifications ...... 12 5 . LatentInstability Example ...... 12 6 . LayerPotential Instability ...... 14 7 . Locationof Rawinsonde Stationsfor AVE-IV [ll] ...... 16 8 . Surface Map for 0000 GMT. April 24. 1975 [9] ...... 20 9 . Surface Map for 0000 GMT. April 25. 1975 [9] ...... 22 10 . Surface Map for 1200 GMT. April 25. 1975 [l]...... 23 11 . ManuallyDigitized Radar (MDR) GridNetwork [8] ...... 25 12 . The 18x18Grid Used forNumerical Computations [8] ..... 28 13 . StepFunction Used in Computationof SWEAT Veering Term ...... 46 14 . GraphicalComputation of Equivalent Potential Temperature (eE) ...... 51

15 . ShowalterStabilityComputationIndex Method ...... 56 16 . RackcliffInstability Index Computation Method ...... 58 17 . BradburyPotential Stability Index Computation Method ... 67

18 Relationship Between and the BPI on . e W850 Thunderstorm Days [59] ...... 67

viii F I GURE PAGE 19. MartinStability Index Computation Methods...... 73 20. AVG Temperature and Dew-Point Profilesfor A and D MDR Conditions...... 77 21. AVG Wind Components for MDR A and D Conditions...... 79 22. WindComponents for AVG and LAG Type D MDR Conditions ... 81 23. Temperature and Dew-PointTemperature Profilesfor

AVG and LAG Conditionsof MDR = D ...... 83 24. AVG EquivalentPotential Temperature (BE) Vertical

Profilesfor Four MDR Categories...... 85 25. LAG EquivalentPotential Temperature (eE) Vertical Profilesfor Four MDR Categories...... 86

26. LAG and AVG EquivalentPotential Temperature (8 ) E VerticalProfiles for Type A and D MDR Categories .... 87

27. SevereWeather Occurrences Between 1200 GMT on April 10,

and 1200 GMT on April 11, 1979 inthe SouthCentral UnitedStates [68]...... 107

28. Abilene,Texas, Severe Weather Soundings for April 10, 1979...... 108 29. Abilene,Texas, Severe Weather Soundings for April 10-11,1979 ...... 109

I Ill LIST OF SYMBOLS

0 C Degreescentigrade

C Specificheat of air P Dew-pointtemperature at 900 meters De Staticenergy ES Totalenergy ET 9 Acceleration of gravity 0 K DegreesKelvin

L Latentheat

M Multiplication factor mb Mi 11 ibar pressure

P Pressure

Specifichumidity

Sineequation used in SWEAT index

Temperature

Dew -po in t temper at ure Td Wet-bulbtemperature Tw U Zonalwind component

V Meridionalwind component

W Scalarwind speed

W Mixing ratio w Saturationmixing ratio S Low-altitudescalar wind speed 'e WD Wind direction

2 A1 titude 8 Potentialtemperature e* Convective instability Equivalent potentialtemperature

'GE Geo-equivalent potentialtemperature % Wet-bulb potentialtemperature a Veering angle Dry adiabatic temperaturelapse rate Environmental temperaturelapse rate Saturated adiabatic temperaturelapse rate

xi CHAPTER I

INTRODUCTION

Thisstudy analyzes many of thestandard stability index conceptsused today inthe prediction of convective weather, includingsevere thunderstorms and tornadoes. These indicesare computed forthe National Aeronautics andSpace Administration

(NASA) AtmosphericVariability Experiment (AVE) mean atmospheric soundings(vertical profiles) taken during the AVE-IV project in

1975 [I]. The prof i1 es have been categorizedto correspond to the differingweather conditions that occurred by using the manually digitizedradar data (MDR) takenduring this time period as being representativeof the various weather categories that existed during

AVE-IV. The AVE proceduresare discussed in more detail in

Chapter111. It isthe purpose of this study to present and analyze thevertical weather profiles taken during AVE-IV, in termsof averaged(mean) weather profiles.

Thisinvestigation also compares severalstability indices calculatedfrom the AVE-IV mean profiles. The results and performance ofthe indices are discussed.

Also, it isthe intent of this study to determine if averaged weatherprofiles taken three hours prior to severe weather occurrence

1 Numbers in brackets refer to similarly numbered references inthe Bibliography. have forecast capability when based onlyon the AVE-IV three-hour lagdata soundings.

Finally,the results obtained from this stability index/

AVE-IV studyare applied to the independent AVE-SESAME-I [2] data setto see how wellthe conclusions based on the AVE-IV analysis applyto a setof independent, individual sounding profiles that dealwith a similarweather system.

2 "

CHAPTER I1

DEFINITIONS

A. Introduction

Thischapter presents a discussion of the Skew-T, Log-P thermodynamicdiagram which was used extensivelythroughout the study and inthe presentation of results. Secondly, a briefdis- cussiondefines the stability index. This is concluded by a section devoted to describing the different definitions of the stability of theatmosphere.

B. Skew-T, Log-P Diagram

Throughout thisinvestigation, stability indices, atmospheric processes, and atmosphericanalyses will involvethe use of a suit- ablemeteorological thermodynamic diagram. This will better illustrate and describeatmospheric processes, as wellas allow graphicalcomputations. This section presents a briefbut instructivediscussion of thethermodynamic diagram used in this study.

The Skew-T, Log-P diagram is employed inthis study because it is mostwidely used inthe United States. In particular, the

UnitedStates Air Force (USAF) Air Weather Service (AWS) uses this diagramexclusively. Its popularity is due tothe convenience and ease of use for mostatmospheric computations. The diagram will hereafter be referredto asthe "Skew-T." The Skew-T containsthe

3 same meteorologicalparametric lines as otherthermodynamic diagrams,

buttheir arrangement is different. Further discussion of the

advantagesobtained inusing the Skew-T diagram is given in

Reference [3].

The name ofthe diagram indicates how thepressure and

temperature 1 ines are presented. Constant pressure 1 ines ( isobars ) ,

expressedin millibars (mb), areplotted horizontally on a loga-

rithmicscale. Also, constant temperature lines (isotherms), in 0 C,

areplotted sloping from the lower-left to the upper-right (skewed)

on an approximate 45 degangle with respect to the horizontal

pressurelines. Figure 1 illustratesthe isobaric and isothermal

lines on a Skew-T diagram.

Alsoplotted on the Skew-T areslightly curved, dry

adiabaticlines (OC).They slopefrom lower-right to upper-left and

areindicated by two small and one largealternating dashed lines.

These linesindicate the rate of temperature changeencountered when

a parcelof unsaturated air risesor descends adiabatically(without

gainor loss of heat).

Saturationadiabats (or moist adiabats, 0 C) arethe large-

dashed, slightlycurved lines also sloping from lower-right to

upper-left. They begin more verticallyat lower levels on thechart

and become more parallelwith the dry adiabatic lines at higher

levels.Moist adiabatic lines represent the path along which a saturatedair parcel rises. Figure 1 shows theplacement of the dry

and saturatedadiabatic lines on the Skew-T diagram.

4 Figure 1. Coordinatesystem of the Skew-T, Log-P diagram [3]. Finally,saturation mixing-ratio (w ) linesare shown as S dashed, slightlycurved lines extending from lower-left to upper-

rightin Figure 1. The mixingratio of an air sample is a function

oftemperature and pressure. It isdefined as theratio of the mass

ofwater vapor to the mass ofdry air containing the vapor (gm/kg).

At a givenisobaric level, the intersection of the temperature line

withthe w linegives the saturation mixing ratio value of the air S at thattemperature and pressure. The dew-pointintersection with

the w linegives the actual mixing ratio value (w) ofthe air. S To illustratethe use ofthe Skew-T, an examplesounding profileof temperature (T) and dew-pointtemperature (Td) from the

1,000-mb level upward isplotted on theFigure 2 diagram. Dry adiabaticlifting of a surface air parcelis assumed totake place

inthis example.Beginning at theintersection of the Td and

1,000-mb pressureline and followingthe w line upward to where it S intersectsthe path of the dry adiabat extending upwardfrom the surfacevalue of T, introduces an intersectionpoint onthe Skew-T, calledthe lifting condensation level (LCL). At thispoint, saturationconditions exist. Traversing vertically from the LCL alongthe saturation adiabat until it intersectsthe environmental soundingof T definesthe level of free convection (LFC) location.

Above the LFC theparcel of air becomes warmer (lessdense) than the environmental air around it duringthis period of travel. Above thislevel the parcel will continueto rise at themoist adiabatic rateuntil it becomes coolerthan the environment. This, then, definesthe equilibrium level (EL). As can be seen inFigure 2,

6 Figure 2. Skew-T, LOCJ-P diagram,with lifted parcel example [3].

7 regions of negativekinetic energy which work against the vertical

motionof the cooler air parcel must beovercome. Likewise, positive

energyareas enhance the parcel's vertical motion.

A secondexample isillustrated in Figure 3. In this example

it is assumed that a parcelof surface air hasundergone thermal

convectionproduced from solar-ground heating. The parcelrises dry

adiabaticallyuntil reaching its convective condensation level (CCL) where it becomes saturated. The CCL isthe height of the cumuliform

cloudbases observed in the atmosphere. The CCL is obtainedby

proceedingupward from the surface Td value (1,000-mb level)along

the w lineuntil intersection with the environmental temperature S soundingoccurs. The equilibriumlevel (EL) is defined in the same manneras indicatedearlier.

C. Stability Index

At leastthree main factors are determined to benecessary forthe formation of convective weather: Instability of the atmosphere, sufficientmoisture, anda triggering mechanismwhich lifts and setsthe atmosphere inmotion [4]. Scoggins [4] concluded that verticalmotion is always required for thunderstorm development, regardlessof the degree of potential instability. The instability of the atmosphereover a locationcan be calculated by the use of upper airdata and a stabilitylinstabilityindex computation. With theadvent of the radiosonde and itsroutine use in obtaining upper air data, stability indices havebeen developed and used by man sincethe mid-1940's [5].

8 Figure 3. Skew-T, Log-P diagram,with. heating parcel example [3].

9 Temperature,pressure, moisture, and windscan be measured throughoutthe upper atmosphere. These data,together with the

large data processing ability of modern electroniccomputers, allow theresearcher to use thedata in testing and determiningwhich atmosphericparameters vary, and how much, when convectiveweather occurs.This type of parametric study would likely evolve into the establishmentof a stabilityindex. Generally, stability indices takethe form of a differencebetween parameters, such as temperature(T), dew-point temperature (Td), potential temperature (e), mixingratio (w),pressure (P), altitude (Z), etc., measured at twoheights or pressuresurfaces. The common, available pressurelevels generally used in index computations are the 1,000-,

850-, 700-, and 500-mb levels.

Stabilityindices act only as an aid in the forecasting of convectiveweather, by alerting the forecaster to areas of the map orsoundings which should be examined more closely by other methods.

D. Stabi 1 ity

Atmosphericinstability is usually defined in terms of conditionalinstability, latent instability, and potentialinstability.

The definitionsare not inclusive, however.

Conditionalinstability is defined [6] as, "thestate of a column of air in the atmosphere when itslapse rate of temperature isless than the dry-adiabatic lapse rate, but greater than the saturation-adiabaticlapse rate. With reference to the vertical

10 displacementof an airparcel, the air will be unstable if saturated,

and stable if unsaturated."This isillustrated in Figure 4.

To explainFigure 4, assume parceltheory [3]. When the

environmentaltemperature lapse rate (re) lies to the left (PQ) of thedry adiabat (rd) through point P, theatmosphere is said to have absoluteinstability within the vertical region between PQ. If an

airparcel, originally unsaturated, ascendsupward along the dry

adiabat, it will bewarmer (atQ') than the surrounding environment

(atQ); thereby, the parcel will tendto continue to rise.

The reversesituation, indicating absolute stability with

respectto saturation, is true if theenvironmental lapse rate is

locatedto the right (PR) ofthe saturated adiabat (rs) PR'. The parceltemperature (at R') would then be colder than the environment

temperature(at R), allowingthe parcel to sink andbe stable. The

region between thedry and saturatedadiabats indicates the region

ofconditional instability. This means thatthe parcel is stable if

notsaturated, or unstable if saturated.

The parcelmethod mentioned here involves simply an

unsaturatedparcel of air whichmust be forced to ascend vertically

along a dryadiabat (r ) untilsaturated at the lifting condensation d level. It is thenforced to ascend along a saturated(or moist) adiabat (I',) from this point upwardthrough the level of free convection, and thereafteris accelerated along rs by a positive buoyancy and need not be forced.Figure 5 shows thisprocess, with thearrows indicating the parcel's path.

11 "...... _.. -

ABSOLUTE

ABSOLUTE INSTABILITY

T- Figure 4. Atmospheric sounding stabilityclassifications.

\ +\\

P 1

T- Figure 5. Latent instabi 1 i ty example.

12 Latentinstability is defined [6] as, "thestate of that portion of a conditionally unstable air column lying above the level offree convection." The negativeregion (on Figure 5) shown below the LFC isthe area in which the environment is warmer thanthe parcel.Therefore, if theparcel is initially given an impulsewith sufficient kinetic energy to carry it throughthe negative region, then above the LFC liesthe positive region which signifies the latent instability needed toaccelerate the parcel, since the parcel will now bewarmer thanthe environment.

Potentialinstability (or convective instability) is the lastatmospheric instability category to beconsidered here. It is defined [6] as, "thestate of an unsaturatedlayer or column of air inthe atmosphere whose wet-bulbpotential temperature (Ow), or equivalentpotential temperature (eE), decreaseswith altitude. If such a column islifted bodily until completely saturated, it will become unstable"(i.e., r >r ). Inthis definition one is layer s consideringthe stability of a wholelayer of air (not a small parcel) which is lifted entirely by either frontal activity or flow over a mountain. As shown inFigure 6, thebottom of this layer

(AB) may saturate,via dry/moist adiabatic processes (at A), before thetop of the layer does (at 9). Thisresults in the layer lapse rate(between AB) becoming, in time, an unstablelayer lapse rate

(between A'B'). Potentialinstability (or stability) is strictly a

"lifted-layer"-typeof approach to stability.

13 B'

LAYER AFTER LIFTING P 1 LAYER BEFORE LIFTING

Figure 6. Layer potentialinstability.

I CHAPTER II I

ATMOSPHERIC VARIABILITY EXPERIMENT IV

DATA DESCRIPTION

A. Introduction

Presentedin this chapter is the description of the Atmos- phericVariability Experiment IV (AVE-IV).This includes background informationfor the experiment, the synoptic situation present, the datasoundings obtained, the corresponding available radar data, and thedata reduction technique used. Finally,averaged AVE-IV profiles pertainingto pre-storm and stormenvironments are presented for differentseverities of radar-measured weather conditions.

B. AVE-IV Data Background

The NASA AVE-IV project [l]took place between 0000 GMT,

April 24 and 1200 GMT, April 25, 1975. Forty-two AVE network rawinsondestations participated in this 1.5-day mesoscale experiment in whichatmospheric soundings, from the surface to 25 mb, were takenat each site every three hours (with some exceptions).

Releaseswere taken nine times at most sites:April 24 at 0000,

0600, 1200,1500, 1800, and2100 GMT, andon April 25 at 0000, 0600, and 1200 GMT. Figure 7 shows a map ofrawinsonde stations, east of theRocky Mountains, thatparticipated in the AVE-IV experiment.

Table 1 lists eachstation. Because ofthe small temporal and spatialresolution of these sounding data, it isbelieved that

15 ‘4% 1-I

Figure 7. Location of rawinsonde stations for AVE

I Table1. Rawinsonde Stations Participating in AVE-IV Experiment

Stat ion Number Location

208 (CHS) Charleston,South Carolina 21 1 (TPA) Tampa, Florida 213(AYS) Waycross,Georgia 220 (VPS) Apalachicola,Florida 226 ( CEN) Centervi 1 le, A1 abama 232(BVE) Boothville,Louisiana 235(JAN) Jackson, Mississippi 240(LCH) LakeCharles, Louisiana 248 (SHV) Shreveport,Louisiana 255(VCT) Victoria, Texas 260(SEP) Stephenville, Texas 261 (DRT) DelRio, Texas 265 (MAF) Midland, Texas 304 ( HAT) Hatteras,North Carolina 311 (AHN) Athens, Georg ia 317 (GSO) Greensboro,North Carolina 327(BNA) Nashville, Tennessee 340 (LIT) Little Rock, Arkansas 349 (UMN) Monette,Missouri 363 (AMA) Amari 1 lo, Texas 402 (WAL) WallopsIsland, Virginia 405(IAD) Sterling,Virginia (Dulles Airport) 425 ( HTS ) Huntington, West Virginia 429 (DAY) Dayton, Oh io 433(SLO) Salem, Illinois 451 (DDC) Dodge City, Kansas

77 Table 1. (continued)

~ ~~~ ~~~~~ . "

Station Number " .~.. Location.~ . . ..

(TOP ) Topeka, Kansas456Topeka, (TOP) 48 6 (JFK)486 FortTotten, New (KennedyYork Airport) 51 8 (ALB) Albany,(ALB) 518 New York 520Pittsburg,Pennsylvania (PIT) 528 (BUF) 528 Buffalo, New York 5 32 (PIA) Peoria, IllinoisPeoria, (PIA) 532 (OMA) Omaha,553 (OMA) Nebraska 56 2 (LBF) North Platte, NebraskaPlatte,North (LBF) 562 606 (PWM) MainePortland, 637 (FNT) 637 MichiganFlint, 645 (GRB ) Bay,Green Wisconsin 654 (HUR) DakotaSouthHuron, 655 (STC) 655 St. MinnesotaCloud, 662 (RAP) Rapid City, DakotaSouth 11001 (MFS) Marshall Space FlightCenter, Alabama 22002Fort (FSI) Sill, Oklahoma

.. ~~ . , ~. ~~ .. . . .""

18 smallermeteorological scale (mesoscale) can be studied in terms of

thevariability of atmospheric parameters, than havebeen studiedin

thepast, in application to stability analyses. Normally, across theUnited States, rawinsonde releases take place with a 12-hour

separation and over a significantlywider spatial network of

stations. The datareduction and processingprocedures, together withfurther project information and thedata itself (with 25-mb

spacing),are presented in Reference [l].

C. SynopticSituation

The surfacesynoptic weather map forthe beginning of the

AVE-IV experiment (0000 GMT, April 24, 1975) is presented inFigure 8.

The generalweather situation throughout the AVE-IV experimentcon- sisted of a coldpolar air mass movingslowly across the northern

UnitedStates with warm, moist air fromthe Gulf of Mexico flowing overthe southern and easternstates. This movement was due to circulation around a high-pressurecell located off the coast of the

Carolinas. At thestart of the experiment, these two differing air masses wereseparated by a pseudo-stationaryfront extending from a

low-pressurecell over lower Michigan into a secondarylow located overKansas. From there,the front trailed into west Texas,as shown inFigure 8. Throughoutthe AVE-IV period,the primary low moved intothe Gulf of St. Lawrence, whilethe secondary low had moved intoKentucky by the end of theexperiment.

The upperatmospheric flow pattern remained basically zonal throughoutthe experiment, with the exception of two short wave

I I I I I I I I1 I I I Ill1 1111 IIIII I Figure 8. Surface map for 0000 GMT, April 24, 1975 [9].

20 passageswhich moved throughthe network. This wave activity

resultedin the formation of two squall lines which produced severe

we at her.

The first short wave disturbance was alreadylocated in the

Midwestat the beginning of AVE-IV and producedthe squall line,

from Kansas throughIllinois, as shown inFigure 8 (at 0000 GMT,

April 24, 1975). The squall 1 inethen moved easterly, ahead ofthe

front, and produced maximum thunderstormactivity between 0300 and

0600 GMT. All thunderstorm,hail, and tornadicactivity produced by

thissystem hadended by 0000 @IT on April 25, 1975.

The second short wave passageproduced the squall line situ-

atedthrough Oklahoma at 0000 GMT, April 25, 1975,as shown in

Figure 9.Most ofthe tornadic and severeweather throughout AVE-IV

resultedfrom this second squall line as it moved eastward.This

second squallline formed initially sometime after 2100 GMT on

April 24, stretchingfrom Missouri into Texas.Storms and convective

developmentcontinued until 0600 GMT, April 25, 1975, whenmaximum

squalldevelopment occurred, producing large hail, strong winds, and

tornadoes.This activity included the Neosho, Missouri,tornado at

0040 GMT, April 25.The line was movingeastward and was still

strongby the end of the experiment, although the thunderstorm

activity had lessened. The finalsurface weather map of AVE-IV for

1200 GMT, April 25, 1975, is shown inFigure 10.

The AVE-IV datacollection and analyseshave been carried

outby several investigators. Complete AVE-IV information and

analysescan be found in References [l]and [7 through 221.

21 p Figure 9. Surface map for 0000 GMT, April 25, 1975 [9].

22 Figure 10. Surface map for 1200 GMT, April25, 1975 [l].

23 D. ManuallyDigitized RadarData

In order to correlate the stability analyses with the radar

measurements ofprecipitation which developed during AVE-IVY the

manuallydigitized radar (MDR) data,from the National Oceanic and

AtmosphericAdministration (NOAA) TechniquesDevelopment Laboratory,

wereused. These data had been obtained and correlatedpreviously

forother AVE-IV investigationsbefore use in the present study.

The MDR gridnetwork of squares (83 km on a side)is shown in

Figure 11. Arealcoverage and echo intensityof rainfall within

eachsquare, forevery hour, determined the MDR code(from 0 to 9)

assignedto each square. The codeused isdescribed by Foster and

Reap [23] and isgiven in Table 2. Radar datafor each square were

thencompiled, with the maximum hourly radar intensity value over a

three-hourperiod being used. The MDR timeperiod was centered on each ofthe nine AVE-IV rawinsondeobservation times in order to

compare thetwo sets directly. However, forthis study, instead of

usingall nine categories of MDR precipitation codes,only four compositecategories of MDR precipitationintensitylcoverage classifications wereused. These MDR definitions weretaken from Reap [24] and Wilson [17] and arepresented in Table 3.

E. RawinsondeData Grid

The AVE-IV 25-mb spacedrawinsonde profile data were interpolatedfor each of the nine time periods using an 18x18 grid, with 160-km spacingbetween grid points, as shown inFigure 12.

24 Figure 11. Manually digitizedradar (MDR) grid network [8].

i Table 2. ManuallyDigitized RadarData Code [8]

Intensity, Coverage , Max imum Percentof VIP Maximum Code Observed Coverage Rainfall Intensity No. VIPaValues In Box Rate ( in h-l) ~~ . ~ ~. . Category 0 No Echoes 1 1 Any VIP1 <0.1 Weak 2 2 550% of VIP2 0.1 to 0.5 Moderate 3 2 > 50% of VIP2 0.5 to 1.0 Moderate 4 3 550% of VIP3 1.0 to 2.0 Strong 5 3 >50% of VIP3 1.0 to 2.0 Strong 6 4 550% of VIP3 1.0 to 2.0 VeryStrong and 4 7 4 >50% of VIP3 1.0 to 2.0 VeryStrong and 4 8 5 or 6 250% of VIP3, >2.0 Intenseor 4, 5, and 6 Ex treme 9 5 or 6 >50% of VIP3, >2.0 Intenseor 4, 5, and 6 Extreme

a VideoIntegrator Processor (intensity of returned radarsignal, gated).

26 Tab1 e 3. MDR CategoriesUsed inthe Present AVE-IV Analyses

Category . MDR ~~ Value ~ ConvectiveActivity

A 0 No precipitation B >O All precipitation C >3 All thunderstormactivity

D >7 Allthunderstorm severeactivity

~~ ~ ~ ~~

I1 I1 I1I1 Ill Ill1 IIIII Ill1 Ill IlIll1lllll1l1lll1lll

t++t+-+++++? +Q+& + + +y;.y4-+ t++ i- t + + + + +-4- + -+*'+.+

Figure 12. The 18x18 grid used for numericalcomputations [8].

28 I

Thisproduced a workablefield of measured data at all grid points.

Accordingto Barr et al. [25], thisgrid spacing produces the maximum

resolutionpossible given a sample of randomlyspaced rawinsonde

stations. More detailconcerning numerical computation criteria in

usingthe AVE grid is given in the 1976 reportof Wilson and

Scogg ins [ 261.

F. AVE-IV Averaged Profiles

A number of stability analyses havebeen carried out for

storm and severestorm environments where stability indices were

calculated.Most analyses involved the computation of only one or

maybe twoindices. However, there havebeen only a fewstudies in

which a number of stability indices havebeen computed withidentical

data and compared. Some ofthese studies are reported in References

[26through 311. Most ofthese studies involved comparisons of the

differentstation indices computedthroughout convective development

of a movingstorm system. Also, four reports on stability analyses

duringthe AVE-IV project havebeen published [7, 9, 11,181.

However,as indicatedin the Introduction, a differenttype

ofatmospheric stability analysis will beexamined here; that is,

one involvingarithmetically averaged soundings which relate to

different AVE-IV weathercriteria, ranging from noweather tosevere

weather. It was suggestedthat if mean atmosphericprofiles repre-

senting a certainconvective atmospheric environment were compared

withsoundings representing, say, IIa moresevere environment," then

an examinationof all parameter profile averages might indicate a

29 structuraltrend within these profiles that would be related directly

to the degree of convection just prior to or duringoccurrence of

severeweather. A forecasttool might result from these trends if

examined.This average profile study may uncoversomething unique

when appliedto a convectivesituation, not observable from an indi-

vidualstation's vertical sounding. It is suggestedthat atmospheric

stabilitythrough a stabilityindex procedure is one way to do an

analysison averaged profile soundings. This averaged-profile method

isnot new. Wilson and Scoggins [ZO] in 1978 presented a quick-look

at AVE-IV averagesounding analyses involving temperature, dew point,

and vectorwind, along with a fewcalculated parameters. The present

studyextends the work ofWilson and Scoggins [ZO] in termsof a

detailed study of just the thermodynamic stability of the AVE-IV

atmosphere.

The AVE-IV profiledata, related to a grid,can now be linked tothe MDR griddata. This computational linking had previously beendone by objectivetechniques [Zl] for use in other AVE-IV studies.This resulted in producing the six averaged (mean) vertical profilesof temperature, dew-point temperature, mixing ratio, zonal

(east-west) and meridional(north-south) wind speed,and pressure levelheight for the 17 pressurelevels of data from 900 to 100 mb, with 50-mb spacingfor the nine AVE-IV timeperiods. The procedure t.0 obtainthese average profiles versus weather category is described byexample inthe following paragraph.

As an example,consider the most severe thunderstorm cases

(MDR>7). The followingprocedure was used tocreate average

30 soundingsfor the six measuredparameters described inthe preceding

paragraph. All valuesof the parameters at grid points within -80 km

of a three-hourcomposite MDR value >7 wereaveraged for the total

AVE-IV timeperiod. This procedure was alsocarried out for the

otherthree MDR categoriesdefined in Table 3, page 27. The

resultingfour tables of averaged (mean) profilesare presented in

Tables 4 through 7.

G. AVE-IV AverageLag Profiles

As a finaltask using the AVE-IV data,average lag profiles werecomputed. Lag here isdefined as thetime difference between

thesounding and theoccurrence of severe weather, three hours later.

Examinationof lag profiles promises a certainforecast capability throughdetermination of the average environment three hours prior to severeweather occurrence.

The three-hourcomposite MDR data had previouslybeen cate-

gorizedaccording to the four weather types given in Table 3.

To createthe average lag profile, all soundings three hours prior 1 tothe occurrence of each MDR convectivecategory were extracted fromthe data set for each parameter. Thesewere then averaged to obtainthe average lag profile for the four MDR cases. The results arepresented in Tables 8 through 11.

1 If three-hoursounding separation was notavailable, the soundingtaken six hours prior was used.

31 Table 4. AVE-IV Average Profile Conditions for MDR = 0 (No Precipitation)

Press. Ht. Temp. Dew Pt. U Wind V Wind Mix. Ratio Wind Sp. Wind Dir. mb m OC OC m/s m/s gm/k 9 m/ s Deg . 900 1,010 13.8 8.0 2 .o 4.74.3 8.0 205 850 1,490 12.4 2.9 4 .O 4.0 6.3 5.7 225 800 2,000 10.1 -2.6 2395.7 6.63.4 4.7 750 2,530 7.6 -10.5 249 7.4 7.92.8 3.1 700 3,100 4.4 -15.5 8.9 2.5 2.2254 9.2 650 3,700 0.5 -17.9 10.4 2.4 1.9 10.7 257 600 4,330 -4.1 -22.6 11.9 2.1 1.5 12.1 260 550 5,010 -9 .o -26.8 13.6 2 .o 1.2262 13.8 500 5,740 -14.2 -31.8 15.4 2.5 0.8 26 15.6 1 450 6,530 -19.8 -39.3 17.4 3.0 0.5 17.7 260 400 7,400 -26.4 -44.4 19.7 3.3 0.3 20 .o 260 350 8,350 -33.7 -50.4 22.8 3.9 0.2 23.1 260 300 9,410 -42.0 26.2 4.9 "- 259 26.7 250 10,600 -51.1 30.1 5.7 -" 259 30.6 200 12,000 -59.5 32.2 5.1 "- 26 32.6 1 150 13,800 -59.5 "- 28.2 5.0 "- 260 28.6 100 16,400 -62.2 "- 19.1 4.7 -" 256 19.7

Note: Number of soundings = 1,053. Table 5. AVE-IV Average ProfileConditions for MDR > 0 (AllPrecipitation)

Press. Ht. Temp. Dew Pt. U Wind V Wind Mix. Ratio Wind Sp. Wind Dir. mb m OC OC m/s m/s gmlkg m/s Deg . 900 998 13.7 9.8 5.1 7.6 8.8 9.2 214 850 1, 480 11.3 6.4 8.1 7.2 7.6 10.8 228 800 1,980 8.8 3.1 10.2 6.4 6.4 12.0 238 750 2,520 5.9 -2.4 11.6 6.0 5.0 13.1 243 700 3,080 2.6 -8.0 12.8 6.2 3.6 14.2 244 650 3,670 -1.1 -1 1.8 14.4 6.6 2.9 15.8 245 w w 600 4,310 -5.3 -17.0 16.1 6.8 2.2 17.5 24 7 550 4,990 -9.9 -22.2 18.0 6.7 1.7 19.2 250 500 5,710 -14.7 -28.1 19.7 6.9 1.2 20.9 251 4 50 6 ,500 -20.2 -34.9 20.9 7.4 0.7 22.2 251 4 00 7,370 -26.5 -40.9 22.6 8.0 0.4 24.0 251 350 8,320 -33.8 -47.2 24.9 8.5 0.2 26.3 251 300 9 ,380 -42.1 "- 27.5 9.6 "- 29.1 25 1 250 10,600 -51.5 "- 30.5 10.5 "- 32.3 25 1 200 12,000 -60.6 "- 32.5 9.2 "- 33.8 254 7 50 13,800 -59.5 "_ 28.9 6.7 "- 29.7 25 7 100 16,300 -60.2 "- 20.2 4.5 "- 20.7 257

Note: Number ofsoundings = 567. Table 6. AVE-IV Average ProfileConditions for MDR > 3(All Thunderstorms)

Press. Ht. Temp. Dew Pt. U Wind V Wind Mix. Ratio WindSp. Wind Dir. mb m OC OC mls m/s gmlkg mls Deg . 900 987 15.9 11.2 5.4 6.7 8.6 9.6 21 9 850 1,470 13.3 7.7 8.6 6.6 8.2 10.8 233 800 1,980 10.5 4.4 10.8 6 .O 7.1 12.4 24 1 7 50 2 ,520 7.3 -0.1 12.3 13.65.7 5.7 245 700 3 ,080 3.9 -7.5 14.0 15.36.2 3.8 246 650 3,680 -0.1 -12.1 15.8 17.57.4 2.9 245 600 4,310 -4.5 -17.1 17.9 8.1 2.1 19.7 246 P 550 4 ,990 -9.4 -22.5 19.9 8.5 1.6 21.6 247 500 5 ,720 -14.3 -29.1 21.4 8.8 1.1 23.1 248 450 6,510 -19.7 -35.5 22.5 9.3 0.7248 24.4 400 7,380 -26.1 -40.6 24 .O 10 .o 0.4 26 .O 247 350 8,330 -33.5 -46.6 25.8 10.4 0.3 27.8 248 300 9,390 -41.7 "- 27.8 11.4 -" 30.1 248 250 10,600 -51.1 "- 30.0 12.0 "- 32.3 248 200 12,000 -60.5 "- 32.1 10.9 -" 33.9 25 1 150 13,800 -60.0 29.3 8.6 "_ 30.5 254 100 16,300 -60.7 20.7 6.7 "- 21.8 252

Note: Number of soundings = 189. Table 7. AVE-IV Average ProfileConditions for MDR > 7 (SevereThunderstorms)

Press. Ht . Temp. Dew Pt. U Wind V Wind Mix. Ratio Wind Sp. Wind Dir. mb m OC OC m/s m/s gmlkg m/s Deg . 900 978 18.8 11.6 4.3 6.2 9.9 6.2 4.3 11.6 18.8 978 900 7.6 21 5 850 1 8.2 850 15.6 ,470 230 9.9 7.58.5 6.4 800 1 800 12.5 ,980 238 10.5 7.3 5 .O5.6 8.9 0.7 10.2 4.6 5.9 11.2 246 2,520 11.2 7 50 5.9 4.6 8.610.2 0.7 700 3 -7.8 700 4.8 246 ,090 13.3 3.6 5.4 12.1 650 3 65016.0 2.8, 680 7.0 0.5 14.4 -11.8 244 -4.4 -17.2 17.4 8.0 2.0 19.2 2.0 8.0 60017.4 4,320-17.2 -4.4 245 50 5 5 50 ,000 -23.5 -9.4 19.5 2458.9 21.4 1.4 730 -13.9 -29.9 20.5 9.5 1 9.5 5 20.5 500 -29.9 -13.9 ,730 .o 245 22.6 -19.4 -35.9 22.3 10.0 0.6 24.4 0.6 10.0 450 22.3 6,520-35.9 -19.4 246 390 -25.9 -40.4 24.3 10.8 24.3 -40.4400 -25.9 7 ,390 246 26.6 0.4 350 8,340-45.9 -33.4 10.9 26.7248 28.8 0.3 300 9,410 -41.5 9,410 300 "- 29.4 11.8 248"- 31.7 250 10,600 250 -51 .O "- 12.6 32.8 -" 35.1 24 9 200 12,000 -60.2 -" 35.3 12.0 "- 37.3 25 1 150 13,800 -60.7 13,800 150 -" 10.1 31.1 252"- 32.7 100 16,300 -61 .O -" 21.8 7.8 250-" 23.2

Note: Number of soundings = 66. Table 8. AVE-IV AverageLag ProfileConditions for MDR = 0 (No Precipitation)

Press. Ht . Temp. Dew Pt. U Wind V Wind Mix.Ratio Wind Sp. Wind Dir. mb m OC OC mls m/s gm/kg m/s Deg . 900 1,010 14.3 8.2 8.1 2.1 4.4 206 4.9 850 1,490 12.5 3.6 4.2 4.1 6.5 5.9 226 800 2 ,000 10.1 -1.7 5.0 6 .O 3.5 240 7.0 7 50 2 ,530 7.5 -9 .o 3.4 7.7 2.9 249 8.2 700 3,100 4.3 -14.4 2.3 9.2 2.7 254 9.6 650 3 ,700 0.4 -16.7 10.7 2.7 2.0 11 .o 256 600 4,330 -4.1 -21.3 1.6 12.4 2.4 12.6 259 5 50 5,010 -9.0 -25.3 1.3 14.1 2.2 14.3 26 1 500 5 ,740 -14.1 -30.4 0.9 15.9 2.6 16.1 26 1 450 6 ,540 -19.7 -37.7 17.7 3.2 0.5260 18.0 400 7 ,400 -26.2 -43.3 0.3 19.9 3.7 20.2 259 3 50 8 ,350 -33.5 -49.5 0.2 22.7 4.5 259 23.1 300 9,410 -41.9 26 .O 5.6 "- 26.6 258 250 10,600 -51.1 29.7 6.6 "- 30.4 257 200 12,000 -59.4 32 .O 6.1 "- 259 32.6 150 13,800 -59.3 28.3 5.5 -" 259 28.8 100 16,400 -62.2 19.4 4.7 "- 20.0 256

Note: Number of soundings = 956. Table9. AVE-IV AverageLag ProfileConditions for MDR > 0 (AllPrecipitation)

Press. Ht. Temp. Dew Pt. U Wind V Wind Mix. Ratio Wind Sp. Wind Dir. rnb rn OC OC m/s rn/S gm/k g rn/S Deg . 900 999 900 13.5 9.9 5.3 8.5 8.8 10.0 21 2 850 1 ,480 11.3 6.1 7.6 8.3 7.9 11.5 226 800 1 ,980 8.8 2.7 10.4 6.9 6.3 12.5 236 750 2,520 6.1 -3 .O 11.7 6.4 4.9 13.3 24 1 700 3,080 2.7 -8.4 13.1 6.4 3.6244 14.6 650 3,670 -1 .o -12.5 14.8 6.7 2.8 16.3 246 w U 600 4,310 -5.2 -18.1 2.1 16.4 6.9 17.8 247 5 50 450 5 ,990 -10.0 -22.5 1.6 18.2 6.8 250 19.4 500 5,710 -14.8 -28.2 20.1 7 .O 1.1 21.3 25 1 450 6 ,500 -20.2 -35.5 21.4 7.6 0.7250 22.7 400 7 ,370 -26.6 -41.3 0.4 22.9 7.8 24.2 25 1 350 8,320 -33.9 -48 .O 25.4 8.1 0.2 26.7 252 300 9 ,380 -42.3 "- 28.0 9 .o "- 252 29.4 250 10,600 -51.8 "- 31.1 9.6 "- 32.6 253 200 12, 000 -60.6 "- 32.7 8.4 "- 256 33.8

150 13,800 -59.4 "- 29.4 6.9 "- 30.2 257 100 16,300 -60.0 "- 20.4 4.7 "- 20.9 25 7

Note: Number ofsoundings = 484.

I I Table 10. AVE-IV AverageLag ProfileConditions for MDR > 3 (All Thunderstorms)

Press. Ht . Temp. Dew Pt. U Wind V Wind Mix. Ratio Wind Sp. Wind Dir. mb m OC OC m/s m/s 9 gm/k m/s Deg . 900 994 15.9 11.5 9.7 5.7 9.2 10.8 212 850 1,480 850 13.3 8.0 8.4 8.9 8.5 12.3 226 800 1 ,990 10.5 4.6 11.3 7.3 7.1 13.5 237 750 2,520 7.7 -1.1 5.412.9 6.8 14.6 2 24 7 00 3,090 4.3 -8.8 14.5 7.1 3.5 16.1 244 650 3,690 0.5 -14.6 2.6 16.6 7.9 18.4 245 600 4,330 -4.0 -19.6 18.4 8.6 1.8 20.3 245 550 5,010 -9.0 -23.9 20.3 8.6 1.4 22.1 24 7 500 5 ,740 -14.0 -30.1 22.4 8.8 0.9 24.1 249 450 6 ,530 -19.5 -37.6 0.523.4 9.4 25.2 248 400 7 ,390 -26.0 -42.8 0.324.5 9.4 26.2 249 350 8,350 -33.3 -49.4 0.226.5 9.3 28.1 25 1

300 9,410 -41.8 ”- 28 .O 10.3 -” 29.8 250

250 10,600 -51.1 “- 30.3 10.4 -” 32 .O 25 1

200 12,000 -60.2 ”- 32.4 9.7 -“ 33.8 253

150 13,800 -59.9 ”- 30.3 8.8 ”- 31.6 254

100 16,400 -60.9 ”- 20.9 6.2 ”- 21.8 253

Number of soundings = 164. Table 11. AVE-IV AverageLag ProfileConditions for MDR > 7 (SevereThunderstorms)

Press. Ht . Temp. Dew Pt. U Wind V Wind Mi x. Ratio Wind Sp. Wind Dir. mb m OC OC mls Deg m/s m/s gm/kg . 900 992 18.5 13.1 4.6 8.9 10.7 10.0 207 850 1,480 15.8 8.9 7.8 8.2 8.9224 11.3 800 1 ,990 12.7 4.7 10.1 6.3 7.2238 11.9 7 50 2,530 9.4 -0.6 11.3 5.4 5.4 12.5 244 700 3,100 5.9 -7.7 12.9 6.2 3.5244 14.3 650 3,700 1.8 -12.6 15.1 7.7 2.5243 17.0 c3 m 600 4,340 -3.3 -18.4 17.5 9.1 1.8243 19.7 550 5 ,030 -8.6 -22.8 20 .o 9.3 1.3 22.1 245 500 5 ,760 -13.6 -28.0 23.1 9.7 1 .O 25.1 24 7 450 6 ,550 -19.1 -36.8 25.1 10.0 0.5 27 .O 248 400 7,420 -25.7 -41.2 26.8 10.0 0.4250 28.6 350 8,370 -33.1 -46.1 29.5 9.8 0.2252 31.1 300 9 ,430 -41.6 "_ 32.4 10.0 253-" 33.9 250 10,600 -50.7 35.3 10.1 254"- 36.7 200 12,100 -59.9 37 .O 10.9 254-" 38.6 150 13,900 -60.7 32.6 10.2 "- 253 34.2 100 , 16,400 -61.4 22.5 6.9 253"- 23.5

~~ ~ ~~~~ ~

Note: Number of soundings = 51. CHAPTER IV

INDICES USED IN STUDY

A. Introduction

Thischapter presents the criteria used in the selection of

stability indices that werechosen foranalyses in the present study.

The indicesare then presented, with a detaileddescription given

for each.

B. IndexSelection Criteria

The stability indices used in this study wereselected to

utilizethe available AVE-IV datadescribed in Chapter 111. Indices

werechosen based on ease ofcomputation. Computations involving

differences,additions, multiplications, and divisions among the

availableatmospheric parameters at orbetween vertical pressure

levels were, in general,selected.

Mean profile data for AVE-IV does notextend below the 900-mb

level and therefore,all atmospheric stability indices which use the

surfaceor data levels up to 900 mb wereeliminated from this study.

Indiceswhich require complex computation with the available data

were alsoeliminated (i-e., indices which require forecasted tempera-

tureor moisture parameters at thesurface or aloft). Finally,

sincethe computer was used in computingindex values for this study, most indicesinvolving a thermodynamicdiagram computation were not

used.

40 C. Indices Chosen

Fourteenatmospheric stability indices were chosen for

testingwith the AVE-IV mean profiledata. They arelisted in

Table 12 and aredescribed in detail in Section D.

D. Definitionof Indices

Thissection defines and giveshistorical information con- cerningeach stability index used in the study. In order for the

readerto follow various thermodynamic procedures involved in atmos- phericprocesses used in the index computation, a simplified Skew-T diagram(as described in Chapter 11) is given whenever possibleto

helpdescribe and visualizethe steps taken during the index compu-

tation.

SevereWeather Threat Index

The SevereWeather Threat (SWEAT) index was developedby the

UnitedStates Air ForceGlobal Weather Central (AFGWC) and presented

in 1970[32, 33, 341 foruse in forecasting potentially critical

convectiveweather (i-e., severe thunderstorms and tornadoes). It

is a computer-preparedindex based on weighted, empirical parameters

at the 850- and 500-mb levels. The Air Forcehas revised the SWEAT

indextwice thus far, and allrevisions to date will be presentedin

thissection.

The initial SWEAT index (SWEAT1) fromReference [32] was

derivedsubjectively from a study of 328 sev,erestorm vertical

soundings and is written as:

41 Table 12. Stability Indices

Index Name Symbo Name Index 1 .. ~ ". SWEAT Index SWEAT Vertical Totals Index VT I Cross Totals Index CTI Total Totals Index TT I Theta E e; Showal ter Index SI Rackcliff Index RI Jefferson Index JI Modified Jefferson Index MJI Boyden Index BI Bradbury Potential Stability Index BPI K-Index KI Energy Index E1 Modified Martin Index MI

42 where,

= dew-pointtemperature at the 850-mb level Td850 (OC) (pos iti ve Td850 values only are used;

i 0, thenset Td850 = 0) 9 if Td850 0 TTI = total-totalsindex ( C) TTI = (T + Td)850 - 2 T500

(if TTI < 49, set TTI = 49; thesecond term

thendrops out of Eq. (1)) ,

= 850-mb wind speed (knots) '850 ,

= 500-mb wind speed (knots) 500 .

The SWEAT index is alwayspositive. No individualterm may everbe negative. Based on empiricaldata, the SWEAT indexthreshold valuefor tornado cases is -350, whilefor severe thunderstorms it is -250. Miller[35] refers to thisinitial SWEAT index as the "Soft SWEAT" index . The SWEAT index was furthermodified [32] toinclude the

500-mb/850-mb levelwind directional shear term. This shear term is also basedupon directionalwind shears observed during severe weathercases and changes the SWEAT index (SWEAT2) equationto read:

SWEAT2 = 12 Td850 + 20(TTI - 49) +2W850 + W500 + 125(S+0.2) , (2)

I I1 I II 1111 I1 where,

S = sin(WD500 - WD850) , and

WD = winddirection (degrees) .

If the 850-mb wind isnot within the range 130 and 250 deg,

or if the 500-mb wind is not between210 and 310deg, or if the

expression WD500 - WD850 < 0, set. S = -0.2 todrop the shear term.

The addition of theshear term to the SWEAT indexraises the severe

thunderstormthreshold to -300, and thatfor tornadoes to -400 to 425.

The SWEAT indexis not a toolfor forecasting ordinary

thunderstorms. It is designed toindicate the potential of severe

thunderstorms(with gusts at least 50 ktsand/or hail at least

0.75 in.diameter) or tornadoes.

Lastly,in the SWEAT equation,Miller [35] replaced the

850-mb levelwith the 900-meter level(except in the TTI and shear calculations) and changed thewind directional shear procedure. The revised SWEAT equation (SWEAT3) thusreads:

44 where, 1 = lowlevel dew point atthe 900-meterlevel, De (OC) 2 = lowlevel wind speed (kts)at the 900-meterlevel, We 4 f(a) = a stepfunction3 of the veering angle We to '500

The term f (a) is set to 0 if both We and W500 are not 21 5 kts. The 850- and 500-mb levelwind directions must alsofall withi n earl ier

statedranges (see Figure 13). All otherterms are defined exactly

as before. The useof 900-meter level parameters in the calculation

ofthe SWEAT index isreferred to as "BLM SWEAT" since it is the

equationused in the AFGWC Fine Mesh and BoundaryLayer Models (BLM)

forecastmodel.

The soft SWEAT indexplots can be computer-calculatedwithin

1.5 hours of the 00 GMT or 12 GMT soundingtime. The BLM SWEAT

calculationstake up tofour hours of computertime. Both SWEAT

indexmethods are currently being used and 12-, 24-,and 36-hour

SWEAT indexprognostic maps aregenerally output.

Recently,Miller and hisassociates [35, 361 have noticed

that many timessevere weather has formed within overlapping areas

'Use 850-mb dew point in soft SWEAT.

'Use 850-mb windspeed in soft SWEAT.

3Use ofthe sine function was discontinuedfor soft or BLM SWEAT because it was notrepresentative from 30 to 120deg.

4Veering isdefined as a change inwind direction versus altitude,in a clockwisesense.

45 1.0

I-

O. 8

0.6

0.4

0.2

0.0

0 <20 460440 ~. a = VeeringAngle (degrees)

Figure 13. Stepfunction used in computation of SWEAT veeringterm.

e I ofhigh SWEAT and high SPOT (SurfacePotential index [37]) values.

Therefore,these two statistically derived indices can beused

together as an aidto accurately identify short-term (three to six

hours),small-scale potential severe storm areas. The falsealarm

rate within the SWEAT/SPOT forecastoverlap area is much smaller

thanthat of eitherindex used separately.

The second SWEAT equation (Eq. (2)) hasbeen programmed and is used inthe present study as the SWEAT index.

Vertical -Totals Index ____ ""_ In 1967, Miller[38] introduced the term "vertical totals"

inrelation to potential thunderstorm development. The vertical-

totalsindex (VTI) represents the stability of the atmosphere

(temperaturelapse rate) between 850 and 500 mb with nomoisture

parametersinvolved. It isdefined as the 500-mb temperaturesub-

tractedfrom the 850-mb temperature;that is,

Vertical-totalsvalues give a measure of instability.

Generally,values 226 representthunderstorm development without

regardto moisture. Specific areas and theirapproximate critical

VTI thunderstormthreshold values are listed in Table 13.

A1 thoughthe VTI canbe used alone, it is also valuable when

added tothe cross-totals moisture index (CTI). Combination of VTI

and CTI resultsin a total-totalsindex (TTI) is described later.

47 t Table 13. Vertical-Totals Index Thunderstorm Threshold Values for Different Areas

Area Critical Area ~. ~ VTI Gulf Coast Gulf 226 British Isles British 222 Western Europe Western 228 West of the Rockies the of West 129 Pacific Coastal Areas 130 AreasCoastal Pacific Great Lakes 230 Lakes Great

.~. .. ..

48 Cross-TotalsIndex

Also in 1967, Miller[38] introduced the cross-totals index

(CTI) as the 500-mb temperaturesubtracted from the 850-mb dew-point

temperature;that is,

= Td850 - T500 (OC)

Thus, a low-levelmoisture parameter is introduced intothe index calculation. The CTI hasbeen used toindicate thunderstorm

potential,with the cross-totals thunderstorm threshold usually

about 18. However, alongthe Gulf Coast a CTI of 16 (with VTI 223)

generallyproduces a thunderstorm. The cross-totalsindex is also

an initialindex used inthe calculation of thetotal-totals

stabilityindex explained in the next section.

Total -Totals~ Index

In 1967, Miller[38] introduced the concept of thetotal-

totalsindex (TTI) as being a measure ofatmospheric instability

betweenthe 850- and 500-mb level. The TTI is defined as the

arithmetic sum of thevertical-totals index and thecross-totals

index;that is,

TTI = VTI + CTI (OC) , or

The VTI thunderstormthreshold of 26 and the CTI of 18pro- duces a minimum thresholdof 44 forthe total-totals index. Total- totalsindex values $50 generallyindicate the potential of numerous

49 P and severethunderstorm/tornadic activity if an adequatelow-level

moisturesupply and a trigger mechanism areboth present. The TTI

proved to bemore accurate inforecasting of thunderstorms, in all

places and seasons, thandid either the VTI or CTI alone.

Theta-EMethods

The use ofequivalent potential temperature (0,) canbe used

insynoptic meteorological practice as a measure of atmospheric

stability [39]. The quantity BE is quasi-invariant(conservative)

withrespect to both dry and moistadiabatic processes, and is

invariant(does not change) with respect to evaporation of falling

rain [40, 41, 421.Equivalent potential temperature is a single

parameterwhich takes into account both temperature and moisture

content.Theta-E cannot be measured directly since it issimply a

concept. It isdefined as follows: A parcelof air at tempera-

ture To, dew-pointtemperature Tdo, andany pressurelevel P rises 0 verticallyby a dry-adiabaticprocess until saturated (at LCL) and

thenfollows the moist-adiabat until all moisture precipitates out.

At thispoint, the moist-adiabat is parallel with the dry-adiabat on

the Skew-T diagram. If theair parcel is now compresseddry-

adiabatically down to a pressure of 1,000 mb, it will have a tempera-

turedefined as theequivalent potential temperature expressed in

degreesabsolute. Figure 14 illustratesthis process.

Theta-E is also a measure of potential stability in that it

gives a measure of the effect lifting will haveon a column of

air [39].Theta-E can becomputed attwo vertical levels on a

L P 1

Figure14. Graphical computation of equivalentpotential temperature (eE).

51 sounding, and if it decreaseswith height between the two levels

(i.e., AOE/AZ or A€JE/AP < 0), this layer is absolutely unstable if

liftedto the saturation level [26, 311. On theother hand, the

layerremains stable if liftedto the saturation level when eE

increaseswith height. Reference [43] reports that computed 700-mb

Theta-Echarts were being transmitted via the facsimile network to

aidin the forecasting of thunderstorm activity as early as1950.

The 700-mb Theta-E critical value of -327'K togetherwith the 6 g/kg

mixingratio line was generally used tooutline areas likely to

experienceheat-type thunderstorms. Values of BE -321°K and

w-4 g/kgindicated the potential of a lifting-typethunderstorm.

DeltaTheta-E (ABE) values have also been used inthunder-

stormforecasting [44], which expressed the change in BE versus

pressure-altitude (AOE/AP), as indicatedearlier. The differencein

Theta-Ebetween 850 and 700 mb forms a lowerindex, and that between

700 and 500 mb an upperindex; that is,

- "EL - 'E850 - 'E700 '

- "EU - 'E700 - 'E500 *

Criticalvalues for eachindex are presented in Table 14, with

positivedifferences indicating instability.

Recently,Alaka et al.[31] haveused and tested a simple 'E

differenceequation of the form: 'ESfc -+ eE850 '* = 'E700 2 9

2 Table 14. DeltaTheta-E Upper andLower IndexCritical Values

Index StabiIndex 1 ity

Lower Uns t ab1 e Upper

Lower Questionably Unstable > -5 Upper < -2 Lower Stable < -5 Upper

53 where 8* definesconvective instability, if 8* < 0 ataltitudes between 700 mb and closeto the ground (surface and 850mb). This differenceis similar to the lower index of the Delta Theta-Emethod mentionedpreviously. The 8 indexselected for this study is that E ofAlaka, with Eq. (10)being modified by replacing eESfc with 'E900, sincethe 900-mb levelis the lowest level of averaged data available.

Thisindex will be referredto as 0* Also, allequivalent E' potentialtemperature (8 ) computations made inthis study are E derivedfrom the approximate form (0 ) from Eq. (21 ), as explained GE later on inthe EnergyIndex section of this chapter.

Showal ter Stabil itv Index

The ShowalterStability Index (SI) was developedby

A. K. Showalterof the United States WeatherBureau in 1946and documentedmore widelyin 1953 [5]. It is a thermodynamic static indexwhich can provide a quick,simple estimate of possible thunderstormsbased on thepotential (convective) instability concept.

Thisindex was designedfor initial use inthe southwestern United

States,but has been used extensively all aroundthe world. It was believed that areas of instability are not generally altered signifi- cantlyat 850 mb andabove. Therefore, a stability-index map based on thislevel andabove can be derived and thestability movement prognosticatedfor 12 and up to 24 hours.

The SI is computedas follows:Dew-point temperature (Td) and temperature (T) values(in 0 C) areobtained at the 850-mb level

(the assumed topof the moisture 1 ayer),together with the temperaturevalue (in OC) at 500 mb. Showalterindicated that mountain

54 sitescan use T and T valuesfrom the 700-mb levelinstead of the d 850-mb levelin their SI computations. The 850-mb parcelis now lifteddry-adiabatically to the saturation level (LCL) and then liftedmoist-adiabatically to 500 mb. The lifted 500-mb temperature isthen subtracted from the observed 500-mb temperature;that is,,

SI=T -T (in OC) . OBS LIFTED 500 500

The procedure isdepicted graphically in Figure 15. Showalter

Stability Indexvalues of +3 deg orless generally indicate probable showers and some thunderstorms in thearea; SI valuesfrom +1 to

-2 deg indicateincreasing probability of thunderstorms; SI values from -3 to -5 deg (orless) indicate possible severe thunderstorms;

SI valuesfrom -6 deg or less indicate suspect cond itions for tornadoes.

The Showalterindex has been used extensive ly overthe years indifferent capacities. It hasbeen directlycorrelated with hail [45,461 and withstorm radar echoes [47 through 491. It has beenused inthe forecasting of generalshowers resulting from surfaceheating as well as fromlifting [3]. Thisindex has also beenused inheating calculations because, besidesbeing a functionof the BE or Bw lapserates, it isalso partly a functionof the ordinary temperature lapse rate and is, therefore, indicativeof stability for use insurface-parcel heating applications.This index is a measure ofconvective stability when the indexvalue isgreater than +6, and convectiveinstability when

55 TL500 \ Tcnn 1 500 rnb P \ I 4\\ LCL k \

Figure 15. Showalter stability indexcomputation method.

56 valuesare less than zero. Also, theindex is a firstapproximation

inestimating latent instability, becausenegative index values do

indicatethat a positivearea (energy) does exist above the LFC.

The Showalterindex islimited for use in mountainareas,

and will not work well if theair is extremely dry, or if critica.1

instabilityexists higher than the 850-mb level. This is because

theindex uses only the one lowerpoint at 850 mb as beingrepre-

sentativeof low-level moisture and temperature.

-Rackcl iff Instabil ity Index

In 1962, Rackcliff[50] introduced a simplelatent insta-

bility index,patterned after the lifted-index [51], for use in

regi ona 1 forecastingof air-mass-type summer thunderstorms inthe

British Isles and WesternEurope.

Whilethe lifted-index uses a forecasted maximum afternoon

temperature inits calculation, Rackcliff used a computedtempera-

turein the calculation of his index. The900-mb wet-bulbpotential

temperature(ewgoo) was thelow-level temperature parameter selected

byRackcliff. It isobtained by taking the 900-mb wet-bulb

temperature and descendingmoist-adiabatically to the 1,000-mb level,

as shown inFigure 16. The 8 valueis believed to be repre- w900 sentativeof the air at low levels and is also only slightly

affectedat night by outgoing terrestrial, radiation. The environ-

mentaltemperature at 500 mb (T500) isagain used as theindicator of middle-tropospherictemperature. The Rackcliffindex (RI) is

thendefined as thealgebraic difference of the 500-mb temperature fromthe 900-mb wet-bulbpotential temperature; that is,

57 t I I'

900 rnb SURFACE -Td - -T 1000 rnb 4v900

Figure 16. Rackcliffinstability indexcomputation method. where positivevalues represent latent instability. Rackcliff determined the following thunderstorm/no thunderstorm criteria:

1. RI < 25 (stablecondition).

2. RI > 25 (showerspossible).

3. RI > 30(thunderstorms possible).

4. RI > 35 (heavythunderstorms possible).

The valueof 30 is a thunderstormthreshold value used in fore- castingnonfrontal thunderstorm activity in the British Isles.

Jefferson Instabi 1 ity Index

A modificationof Rackcliff's index wasmade byJefferson [52] in 1963 so thatthe instability index could be used in summertime air-massthunderstorm forecasting at the London Airport.Jefferson determinedthat Rackcliff's index makes no allowancefor the fact that instability in a layer depends notonly on the temperature differenceacross the layer, but also on its mean temperature.Since thevalue of 8 variesbetween 10 and 20°C overnorthwest Europe in W summertimethunderstorm situations, this would give a- variable

Rackcliffindex value between 36and 29. Therefore,Jefferson amended Rackcliff'sformula with an empiricalstudy and obtained an instabilityindex value independent of temperature, but with the same thresholdvalue of 30 forthunderstorms. This was truefor a widerange of temperatures. This modified index can now beused in widerareas and for a1 1 seasons. The Jeffersoninstability index(JI) is expressedas:

I I1 I I I I I ll11l1ll1 JI = 1.6 ewgo0 - T5-0 - 11 , (13) where ewgo0 is the 900-mb wet-bulbpotential temperature (OC) and isthe observed 500-mb temperature Positiveindex values T500 (OC). representinstability.

ModifiedJefferson Instability Index

In 1963, Jefferson[53] published a second modificationto theRackcliff index, or simply, a modifiedJefferson index (MJI).

Whileusing the Jefferson index at the London Airport, it was determinedempirically that the index was forecastingthunderstorms

(i.e., JI valuesexceeded 30) inthe Mediterranean area, but many times no thunderstormsformed. This was foundto be causedby very dry air existing above900 and 500 mb overthe Mediterranean area.

Sincethe base ofthunderclouds over the Mediterranean is generally quitehigh (-700 mb), theidea of introducing a 700-mb moisture parameter seemed logical, as long as theindex continued to work for north-central Europe.This modified Jefferson index (MJI) is written as:

where,

e = 900-mb wet-bulbpotential temperature (OC) , w900

= 500-mb observedtemperature (OC) , T500

60 The factor1/2 ATd700 was introducedto avoid overweighting by the

parameter. ATd700

Boyden Instabi 1 ity Index"

Just prior to the 1963 publicationof the modified Jefferson index, Boyden [54] alsointroduced an instabilityindex to be used inthe forecasting of thunderstorms and heavy rainover southeast

Englandduring the months of May to September. Boyden assumed that thedevelopment of heavyshowers and thunderstormsover land on a summer afternoondepends on the mean temperaturelapse rate only up to 700 mb. Forneutral static stability conditions (i.e., dry-bulb temperaturesalong a moistadiabat), Boyden determinedthat the

1,000- to 700-mb thickness(in decameters) minus the 700-mb temperature (OC)was an approximateconstant (-294) for all summer- timeatmospheric conditions measured over Crawley, England.

Instability is thenmeasured by the amount thisdifference exceeds theconstant. Therefore, instability exists if the 700-mb temperature is a low(cold) value as compared tothe 1,000- to 700-mb thicknessvalue. Boyden's index (BI) is expressed as:

- 200 , B1 = Az(l,OOO to700) - T700 where,

AZ = 1,000- to 700-mb thickness(decameters) ,

T700 = 700-mb temperature (Oc) .

The unitsconflict in the BI expression.Only the numerical value should beused. The value 200 is used to remove thelarge unwanted

61 number generatedby this index. It allowsthe BI totake ona value

around 90.

The BI is strictly a measure ofthe mean stability in the entirelayer below 700 mb. The Boyden index isnot intended to r forecastslight or moderate showers. The diurnalvariation of BI was foundto be low, allowing a 12-hourforecasting of the index to be made. It was determinedthat Boyden indexisopleths (drawn in

intervalsof two units) move with the 700-mb wind.

Forboth frontal and non-frontal summer days, it was found thatthere was, indeed, a markedincrease inthunderstorm/h eavy rain occurrence when BI reachedvalues of 94 and higher.Since hum idi ty was foundto be veryloosely related to the development of thunderstorms, it was notincluded with the Boyden index. The mai n advantageclaimed for the Boyden index isits usefulness at mobile sitesduring frontal or non-frontal weather.

Forthe present study, the Boyden index was modified,since

1,000-mb heightsare not obtainable from the averaged soundings.

Therefore,the 900-mb height was used inplace of the 1,000-mb height.

K-Index

The K-index(KI) was developedby Whiting and documentedby

George (bothof Eastern Air Lines)in 1960 [55]. Thissimply derived stabilityindex is used inthe forecasting of inland air mass thunder- stormswith weak winds and withoutapparent frontal or cyclonic influence. It is preparedfrom the 1200 GMT soundings and is generallyissued on an areal map (with KI intervalsevery five units).

62 The Whiting-GeorgeK-index measures air mass thunderstormpotential bydirect indication of the vertical temperature lapse rate

(T850 - T500), loweratmospheric moisture (Td850), and veryindirect indications of the vertical extent of the moist layer (700-mb dew- pointspread). The K-index is expressedas:

whereK-values versus thunderstorm occurrence frequencies generally fallwithin the categories given in Table 15.

The K-index map usedconcurrently with a subjectiveanalysis of convergence and relative vorticity hasbeen proven by George to be a valuableair mass thunderstormforecasting tool. Areas of confluence,determined by constructing 850- plus 700-mb heightareal charts,are used to represent convergent flow conditions between thesetwo levels. Confluence areas below 700 mb, withwinds

<20 knots,generally require an adjustment tothe next higher categoryof K-values. If thewinds are >20 knots,adjust upwardtwo categories.Positi ve vorticity lsoincreases the chance of thunder- stormdevelopment.

Bryan[56] and Hambr idge [57]have tested the K-index versus I thunderstormactivi ty over the m d-South and WesternUnited States, respectively;they found a highcorrelation. Hambridge suggested theassignment of thunderstorm probabilities versus K-value given in

Table16.

In 1971[58], theK-index chart was added tothe lifted indexpanel of the composite moisture index chart. This chart is

63 Table 15. K-IndexThunderstorm Threshold Values

K-Index Value ThunderstormValueFrequency K-Index

20 None K < 20

20 < K < 25 Isolated

25 < K < 30 WidelyScattered

30< Kc 35 Scattered

35< K Numerous

h Table 16. K-Index Thunderstorm Probabilities

K- IndexValue Thunderstorm Probability < 15 0% to 20 15 to < 20% 21 to 25 20 to 40% 26 to 30 40 to 60% 31 to 35 60 to 80% 36 to 40 80 to 90% > 40 Near 100%

65 distributedvia the NWS NAFAX (NationalWeather Service National

FacsimileNetwork) system to all meteorologistsacross the United

States .

Bradbury Potential Stabi 1 ity Index

In 1977, Bradburypublished an article [59] dealing w ith the use ofwet-bulb potential temperature ) chartsin weather (eW analysis and forecasting. One conclusion he reached was that many summer thunderstormsbroke out over Europe when low-levelsoutherly windsadvected air with 8 > 16OC. Bradburythen developed a W850 - potentialstability index (BPI), since the e valuesalone failed W850 toidentify occasions of thunderstorm development in a relatively coolair mass. Thisindex, similar in structure to Rackcliff's and

Jefferson'sindex, is defined by subtracting the value of Ow at

850 mb fromthe value at 500 mb. A negativevalue of this difference indicatesthat the air betweenthe two levels ispotentially unstable.

Inequation form, the BPI is expressedas:

One can obtainthe BPI from a thermodynamicdiagram procedure as illustratedin Figure 17.

Bradburyalso found that the BPI varied as a functionof

, when used inthe forecasting of thunderstormsduring the 'W850 year.This is illustrated in Figure 18, where 5%, 50%, and Limit representthe cumulative percentage frequency of BPI versus for 544 thunderstormday soundings from 1973 to 1976. The graph

66 \ \

1000 mb ew500 0,850

Figure 17. Bradbury potential s tabi I i ty i ndex computation method.

OC +6 I I I I 1 I I 1 I I 1

‘W850 mb Figure 18. Relationship between 8 and the BPI onthunderstorm days [&?!

67 merelyindicates a rangeof conditions that existed when thunder-

stormsoccurred. Thunderstorms would be unlikely outside the range given. One shouldnot use the BPI asa strictthunderstorm fore- castingrule, but rather, asa guidealong with routine surface and upper-aircharts.

EnergyIndex

A unique and reliable substitute for the widely usedthermo- dynamicindices, used inthe forecasting of convective storms, is thetotal energy index (EI). It was introducedby Darkow [60] in

1967 and dealswith the total energy (ET) of a unit mass of air.

The specificenthalpy (c T), potentialenergy (gZ), latent P 2 energy(Lq), and kineticenergy (W /2) ofthe unit mass of air is comb ined as :

2 -1 ET = c T + gZ + Lq + W /2 (cal gm ) , P where ,

-1 0 -1 c = specificheat of air (0.24 cal gm K ) , P 0 T = temperature ( K) -2 g = accelerationof gravity (980 cm sec ) ,

Z = altitude (km)

L = latentheat (cal gm-’) ,

q = specifichumidity (gm kg-’) ,

w = scalarvelocity (cm sec-l) .

68 I

Sincethe kinetic energy term is two orders of magnitudesmaller

thanthe other three terms, it canbe neglected,resulting in the

energyformula being called static energy (ES); that is,

2 ET 2 c T + gZ + Low , P where,

L =: Lo = 600 cal gm-’ , -1 q z w = mixingratio (gm kg ) ;

therefore,

Staticor total energy is conservedwith respect to both

typesof adiabatic processes and isrelated to the pseudo-equivalent

potentialtemperature (eE) and wet-bulbpotential temperature (e,). Thisfact can beseen bydividing E by c whichproduces a geo- T P’ equivalentpotential temperature ), which is a conservative (eGE (invariant)property in regard to adiabaticprocesses. The term eGE

differsjust slightly in definition from 8 E and is expressedas:

t = = T + 9.8 Z + 2.5 w (OK) . ‘GE 2cp

Totalenergy or geo-equivalent potential temperature can

both becomputed easily for use inthe forecasting of convective

activity.This total energy concept can beused inboth ascent and

descentair parcel theory convective calculations, and the amount of

potentialconvective instability of theair column isindicated by

69 thedecrease of total energy with increasing altitude. This defines

the Darkow totalenergy index (EI). It is expressedas the algebraic

differencebetween the atmospheric total energy at the 500- and

850-mb levels;that is,

= ET500 - ET850 (cal gm-’ ) . (22 1

Empiricaltesting of the index produced the ranges given in Table 17

forforecasting severe weather. The totalenergy index horizontal

map patternturns out to be verysimilar in structure to the

Showalterindex pattern. This is due inpart becauselow-level

totalenergy is usuallygreater than mid-tropospheric values.

The totalenergy index combines temperature, moisture, and heightfields. Darkow [60] indicatesthat this gives it a possible advantageover the Showalter and liftedindices since it isthe only one totake into account the possible contribution of descending, potentiallycold, mid-tropospheric air on thetotal energy release ofconvective storms. Most indices involve only the process of ascending warm air.

Darkow took an additionalstep by suggesting that a modified energyindex can be developed which takes into account the mean mixingratio of the lowest 100-mb layer(or of the first kilometer altitude) above theground. This may bemore representative of lowerlevel moisture than using just the 850-mb valueof mixing ratio.

A number ofatmospheric studies haveused t heDarkow energy index and totalenergy concept. Some ofthese stud iesare presented

70 Table 17. Energy Index Values Used in Convective Forecasting

0.0 to -1.0 Non-severe thunderstorms possible. -1.0 to -2.0 Isolated severe thunderstorms possible. < -2.0 Severe thunderstorms and tornado activity possible.

a If a trigger mechanism is available to release potential instability, otherwise, convective activity may not take place.

I I I I I 111111111l111111l1l1 in References[61 through 641. Eagleman [61]used Darkow's index

separately and also combined with a windshear index to aid in fore-

castingtornadoes. Darkowhas alsoapplied the static energy concept

tosurface analysis in detecting areas of high static energy related

tothunderstorm and severestorm occurrences [65, 661.

MartinIndex

Wright-Patterson Air Force Base, Ohio,published a stability

indexconstructed by D. 0. Martin [67] saidto be more sensitiveto

low-levelmoisture than the Showalter index, since it usesthe

maximum valueof low-level moisture.

The procedurein computing the Martin index (MI) (see

Figure19) is as follows: From the 500-mb temprature(A), descend

moist-adiabaticallyto the intersection (B) of this line and the

mixingratio line that passesthrough the point (C) of maximum

mixingratio. From thisintersection, move dry-adiabaticallyto the

850-mb level (D). The MI is defined as thedifference betweenthe

observedsounding temperature and calculatedtemperature at 850 mb;

thatis,

MI = T 850 - T850 (OC) - Calc. Obs.

The onlyexception to this procedure occurs whenever a marked low-levelturbulence or subsidence inversion (non-surface, non- radiation)is established below 850 mb. Then thepoint (D) is obtainedat the pressure level where theinversion base is located.

The normal and theexception cases are illustrated in Figure 19.

72 U w

/ 1 850 mb I -/\D 850 mb / / SURFACE C KTc SURFACE

1 EXCEPTIONNORf4AL CASE CASE

Figure 19. Martinstability index computation methods. Sincethis study involves the 900-mb level as beingthe closestlevel to the surface, the index will bereferred to as the modifiedMartin index (MI).

74 CHAPTER V

AVE-IV PROFILE ANALYSES

A. Introduction

Beforestability indices canbe constructed, used, or evalu- ated,the atmospheric parametric profiles themselves need to be examined and understood.Ther,?fore, this section presents a discussionof the AVE-IV average and lagsoundings as they are compared withthe four MDR precipitationcategories, andas theyare compared witheach other. Tabular values of these profile parameters have beenpresented in Chapter 111, Tables 4 through 11, pages 32 through 39.

Forclarity, and toavoid confusion, the average profiles whichpertain to precipitation conditions occurring at the time of thesounding observation will hereafter be referredto as AVG. Also, theaveraged lag profiles, which represent the environmental obser- vationsthree hours prior to a precipitationcategory occurrence, will hereafterbe referred to as LAG profiles.

Throughout thissection, more attention will be givento the parametricaverage profile differences which exist between precipitationcategories A and D (definedin Table 3, page 27).

Categories B and C parameterdifferences havebeen compared butare notalways presented here because they either do not represent any drasticenvironmental change, orsince they do have inherent category D information,they could present a bias.In most all casesthese two intermediate precipitation categories merely link

75 categories A and D. The averageprofiles of LAG and AVG temperature,

potentialtemperature, and windsare presented and compared forthe

stormcategories A and D. Differencesare noted for possible

inclusionin a forecast-typeof storm index.

B. AVG Profile Comparison

TemDerature/Moisture

The verticaltemperature profile differences noted between A

(non-precipitation) and D (severestorm) conditions for the AVE-IV

average (AVG) profilesare shown in Figure 20. Althoughthe two

temperatureprofiles are almost ident ica'l above 700 mb, the D profile

temperaturesincrease 5OC warmer than the A conditions betweenthe

700- and 900-mb levels.

The dew-pointtemperature profile for D conditions is

2 to 10deg warmer (more moist)than for A conditions at all altitudes,as shown inFigure 20. Most ofthe difference (6 to 10°C) occursbetween the 600- and 800-mb levels.

Winds

As one wouldexpect, for all altitudes,winds are higher when goingfrom precipitation categories A to D usingthe AVG wind profileinformation. Wilson and Scoggins [20] alsoconfirmed this.

Thisincrease pertains to both meridional and zonalwind components.

The category D meridionalwind component exhibitedthe most difference(-8 m sec-' ) overcategory A conditions.Zonal (and scalar)wind differences between A and D categoriesgenerally range

76 I 1 I I 1 I I I I I I I I

400 t A 1

-50 -40 -30 -20 -1 0 0 10 20 TEMPERATURE (OC)

Figure 20. AVG temperature and dew-pointprofiles for A and D MDR conditions. between 2 and 6 m sec-’(see Figure 21). All windcomponents calcu-

latedare positive (i.e., zonal winds being westerly and meridional

windssoutherly) for all AVG and LAG conditionspresented. Zonal westerlywinds dominate in magnitude.

C. LAG Profile Comparison

To determine if a forecast scheme can be realized based on

AVE-IV data,this stability study will involvethe analysis of LAG

,profiles and how their averageconditions differ from the AVG profilesrepresenting storm activity.

Temperature/Moisture

LAG thermodynamic profileconditions for the four precipitationcategories are very similar in appearance to the four respective AVG profiles.Temperatures of category D are warmer by a similarmagnitude than category A, as was thecase for the AVG profiles.This effect extends higher, however, from 900 to 650 mb. The category D dew-pointprofile also remains warmer by a similar moisturedifferential spread, aswas thecase with the AVG dew-point data.

Winds

LAG windsagain invoked a patternsimilar to that of AVG winds,with both D windcomponents exhibitingstronger flow than

A wind component conditions.Category D LAG winddirections between

7 and 13 km altitudeare slightly westerly, so as to resemble category B LAG winddirections over this altitude range. This is

78 2o r '* 1AVG A-V AVG D-V AVG A-U AVG D-U 16 I I 14 I I c. E i \ A 12 cc \ W \ / 2 10 i 1 k 58 a 6

4 AVG D 2 /\\ \' 01 Y+i I I I I I I I 0 5 10 15 20 25 30 35 40' WIND SPEED (m/s)

Figure 21 . AVG wind components for MDR A and D conditions. completelyunlike the AVG D, AVE-IV stormwind directions, which are

farthest away from the west of all four precipitation categories.

Thisdirectional change will bediscussed further in Section D.

D. AVG/LAG Prof i1 e Compar ison

Winds

Differencesbetween the AVE-IV average LAG (threeto six

hoursprior to storm occurrence) and AVG (time of stormoccurrence)

windprofiles are, again, generally small. However, thelargest

differencesdo occur between the category D (severestorm) wind profiles of each . Therefore,only category D comparisons will be discussedhere.

From Tab les 7 and 11, pages 35 and 39, respectively,

scalarwind speeds andU-component (zonal ) speedsare -2 m sec-'

strongerfor the LAG averagethan for the AVG average,between

6- and 12-km altitude. Wind magnitudedifferences were less than

thisvalue above12-km altitude(see Figure 22).

Magnitudes ofthe V-component wind(meridional) give slightly

stronger ("2 m sec-l)southerly winds at AVG timethan LAG time,

between8- and 12-km altitude.This stronger AVG V-component effect

coupledwith the weaker AVG U-component results in the AVG wind

direction between8- and 12-km altitudebeing -5 degmore from the

south(248 deg) than the LAG average(253 deg). Meaning, on the

average,winds during the LAG periodare 1 to 2 m sec-'stronger and from a more westerlydirection than conditions existing during severe stormoccurrence.

80 *O18 [I 16 -

14 -

12 -

10 - a-

" ~ ~~ 0 5 10 15 20 25 30 35 40 WIND SPEED (mh)

Figure 22. Wind components for AVG and LAG type D MDR conditions, Temperature/Moisture

The thermodynamicstructure between AVG and LAG category D

profiles,in terms of temperature and dew point, is shown in

Figure 23. Averageconditions for each respective parameter are,

indeed,very similar. The unusualfeature is the -1.5OC temperature

differencethat exists around 650 mb, withequal or lesser differ- encesindicated between the 800- and 500-mb levels, and with LAG temperaturesbeing slightly warmer.Also, the layer between 500 and 650 mb is more unstablethree hours prior to storm activity. The temperaturelapse rate of the LAG soundingbetween these two levels

is 15.4OC/150 mb; whereas, only 14.4'C/150 mb (difference = l.O°C) existedduring AVG stormtime. This slightly more unstablelayer is noticedat a loweraltitude between 800 and 650 mb atstorm time.

It thenhas a temperaturegradient of l2.OoC/150 mb ascompared to

10.9°C/150 mb (difference = l.l°C)for this layer on theprior LAG profile.

Threehours prior to storm activity, the dew-point temperature at 900 mb is -1OC higherthan at the time of storm activity. By the

850-mb level,this difference vanishes and neither AVG nor LAG dew- pointtemperatures dominate above thislevel.

E. Theta-E AVG/LAG Comparison

Beforethe stability index results are presented and discussed, it isdesirable to select an indexor procedure involving equivalentpotential temperature (0 ) asan instability measure(see E

82 I I I 1 I I I I I I I I 1

300

400

In ccE 500 aw w3 E 600

700

800

900

-40 -30 -20 -10 0 10 20 TEMPERATURE (OC)

Temperature and dew-point temperature profiles for AVG and LAG conditions of MDR = D. Chapter IV discussionof BE). Thisis an importantdecision to make

because of the manynumber of ways in which BE canrepresent atmos-

phericinstability.

AVG 8 profilesare presented for the four MDR conditionsin E Figure 24. Similar LAG profilesare given in Figure 25. The two 8 E figurespresent similar results and show highervalues of OE for more

severeweather activity. The comparisonbetween LAG and AVG profiles

of 8 aregiven in Figure 26 forcategories A and D MDR conditions. E The LAG profilesexhibit slightly greater 8 (ortotal energy) than E do the AVG profiles. The altitudeof minimum BE occursat -700 mb

forthe two profiles with no MDR activity.(category A), while it

occurshigher (“600 mb) forboth the MDR>7 (category D) profiles.

One itemof significance is the more stable 8 gradientobserved E between850 and 800 mb onthe AVG-D profilethan the LAG profile

indicates. The AVG-D BE profilealso indicates a slightly more

unstableregion between 750 and700 mb, as compared to LAG-D

conditions.

Resultsfrom the convective stability equation of

Alakaet al. [31] and the BE differencesbetween 800 to 850-,

800 to 900-, and 700 to 750-mb levels, as suggestedby observing the

BE LAG and AVG verticalprofiles, are presented in Table 18. It

should be notedthat Alaka’s equation (Eq. (10))is similar in

structureto the Delta Theta-E equation (Eq. (8)), as discussed earl ier in Chapter IV.

Whilethe 8* equation of Alaka (Eq. (10)) is represent ati ve ofthe entire lower atmospher ic instability when app lied to

84 300

400

c5 500 n vE u1 K 3 600 3w CT a

700

800

900

I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 315 320 325 320 310 315 330 Figure 24. AVG equivalentpotential temperature (BE) verticalprofiles for four MDR categories. I

400 -

n E Y 500 - w a cn2 LLI K a. 600 -

700 -

800 -

900 - 1 I 1 I 1 I I 1 I I 1 1 I I 1 I I 1 I 1 I

310 315 320 e,( OK) 325 330 Figure 25. LAG equivalentpotential temperature (0,) verticalprofiles for four IIDR categories. 300

400

MDR-A AVG "-"" CI MDR-A LAG -*-*"- Y2- w MDR-D AVG a 3 MDR-D LAG v) """- v) 600 0.

700

800

900

310 Figure 26. Table 18. Theta-E Differences (OK) Between Given Pressure Levels

Percent Difference Between LAG AV G AVG-D 8~ Pressure Level MDR Conditions MOR Cond iti ons and Difference Cateqory A B C D A B C D LAG-D 03os 1. Alaka 8; (700 tosurf.) -3.47 -3.17 -6.02 -8.73 -2.95 -3.36 -5.31 -8.12 -7

2. A~E(800 to 850) -1.15-0.85 -1.05 -2.35 -1.30 -0.60 -0.55 -1.10 -53 3. A~E(800 to 900) -2.25-1.34 -2.14 -4.77-2.25 -1.28 -1.92 -2.98 -38 4. A~E(700 to 750) -0.36-1.17 -2.57 -2.66 t0.14 -1 -32 -2.67-3.97 +49 . .. ”

individualsoundings, it is not when appliedto averaged soundings, asshown in Table18. The layer between thesurface and 700 mb appears to be toolarge. to note meaningful differences (only 7%) between LAG-D and AVG-D conditions.

Values of ABE overnarrower layers are presented in Table 18, usingtwo lower atmospheric levels (items 2 and3 of Table18) and one upperatmospheric level (item 4). The significantpoint to noticeis that pre-storm conditions (LAG-D) have a stronger

8 lapserate between 800 mb and below,as compared tostorm con- E ditions (AVG-D); the AVG being 38and 53% lowerthan LAG conditions.

The oppositeis true when the 700 to 750-mb BE gradients,for both

D. MDR conditions,are compared.Here, AVG-D gradientsare 49% higher than LAG-D conditions.

The resultspresented in Table 18 do indicatethat possibly a stabilityindex could be arrived at byusing one or two A0 E parameters in its computation.This would make theindex a function of both a temperature and moistureinput over a 50- to 100-mb spacing inthe atmosphere.

F. AVG/LAG Conclusions

A fewgeneral conclusions can be made regardingthe atmos- phericenvironment three hours prior to severe storm development and duringthe occurrence of the severe storm. They are as follows:

1.The LAG profileexhibits a moreunstable temperature

gradient (15.4OC/150 mb) inthe upperatmosphere between

650 and 500 mb threehours before severe storm activity.

89 By thetime of severe storm occurrence, this unstable

layer has fallen 150 mb and islocated between 650 and

800 mb with a12.OoC/150 mb gradient.

2. Dew-pointtemperatures are warmer(more humid) from 900

to 850 mb by 1OC three hours prior to severe weather.

3. Scalarwind and zonalwind speeds are stronger by -I ?2 111 sec threehours prior to storms. At storm

occurrencetime the 2 m sec-'stronger, southerly, AVG

meridionalwind component, locatedbetween 8 and 12 km

altitude(400 to 200 mb), resultsin producing a more

southerlydirection (248 deg) than three hours prior

(253 deg).

4. Equivalentpotential temperature (0,) differences

between 800 and 850 mb arethe most unstable three hours

priorto convective weather; whereas, e differences E between 700 and 750 mb aremore unstable at the time of

severeweather occurrence.

The resultsobtained here could be used inthe construction of a typeof three-hour lead time severe storm index. However, thesechanges noticed in the atmospheric structure are, indeed, all verysmall changes. It shouldbe noted that they are small due to thefact that they are basedon theaverage of many pre-storm soundingstaken during only one independentmajor storm system development/movement. It may alsoturn out that these AVE-IV conclusions may or may not apply to a differentstorm sounding history

90 for a station. One purposeof the present study is to test this theory,thereby affecting current understanding of the severe storm environment.

G. PossibleStability Index

At thispoint, a stability-typeof index could be constructed consisting of a temperaturedifference (AT), or an equivalent potentialtemperature difference (A0 ), betweentwo levels. A low- E leveldew-point indicator (ATd), and possibly a windmagnitude term

(AW) and directionalterm (AWD) could be included. The combination ofthese terms, with the appropriate multiplication weighting factors (M), couldresult in a meaningfulsevere storms lag index

(SSL). A possibleform of the equation is:

SSL = Ml(AT) + M2(ATd) t M3(AW) t M4(AWD) + M5(ABE) . (24 1

All oronly a coupleof the terms expressed in Eq. (24) may prove useful as an indexparameter when compared toits respective severe stormthreshold value. Considering the broad scale in which these fiveterms were expressed, only general inferences may proveuseful.

Terms fromthis type of equation will be used and testedin

Chapter VI.

91 CHAPTER VI

AVE-IV STABILITY ANALYSES

A. Introduction

Thischapter will dealwith the AVG and LAG AVE-IV profiles as theyare applicable to the current standard stability indices of thunderstorms and severeweather reported in Chapter IV. The profile indices will be compared and the ability of each toforecast/measure severeconvective weather will bedetermined. Temperature- dependency for eachindex will alsobe included, as wellas the introductionof a new lagindex.

B. Temperature-Dependence

It isgenerally desirable to know if a stabilityindex changes withthe changing temperature of an air column. The index issaid to betemperature-dependent if thisis the case. An index with a verylarge temperature-dependency isundesirable for use in representingthe stability over a largegeographical area in which differingair masses may reside. The changing aircharacteristics wouldaffect the threshold value of an index,as reported by

McPherson [ 291.

McPherson[29] suggested a method todetermine the temperature-dependency of an index.His method isthe approximate procedureused inthe present investigation. A rangeof stability conditionsfor each index is determined first. The selection of two

92 hypotheticalvertical temperature profiles, which represent (a) near normal stability and (b)less stable conditions, is accomplished by assumingmoist-adiabatic and dry-adiabaticvertical temperature lapserate conditions, respectively. Thesetwo conditionsare chosenbecause they separate the area for conditional stability, and alsogive index values on either side of the threshold values

(Chapter IV) whichare representative of thunderstorm/severe thunder- stormconditions as used in this study. For both adiabatic conditions,the temperature at 700 mb was assumed fixedat O°C, and thedew-point depression at all levels was assumed to be 10°C.The resultingrange for all indices is presented in Table 19.

Indexvalues were next obtained given five different cases ofmoist-adiabatic lapse rate conditions from 900 to 500 mb, with

8 valuesof 0, 6, 12, 18, and 24OC, assumingsaturation at all W levels. These indexresults are presented in Table 20, which now gives a relationship betweenindex value and temperaturechanges.

The range of indexvalues obtained from the five different temperature (0 ) cases is presentedin the next-to-last column of Table 20. W The right-mostcolumn of Table 20 presents a percentagechange of therange of each index with respect to the index's total range, as givenin Table 19 forthe five temperature categories.

From thesecalculations it is shown thatthe Showalter and

Bradburyindices have small or notemperature-dependence since they involveconservative moist-adiabatic procedures (eN) in their computation. The Jefferson,Modified-Jefferson, e:, Energy, and Modified-

Martinindices are only moderately (-1 to 10%) temperature-dependent.

93 Table 19. StabilityIndex Range Determinedby Moist and Dry AdiabaticLapse Rates

Norma 1 Lesser Stability Stability Range Moist- Dry- of Inde x AdiabaticIndex Adiabatic Va 1ues

SWEAT 8 549 54 1

VerticalTotals 26 41 15

Cross Tota 1s 16 31 15

TotalTotals 41 72 31 e; -14 3 17 Showal ter 7 -10 17

Rackcl iff 28 44 16

Jefferson 34 55 21

Mod. Jefferson 21 42 21

Boyden 2.5 2.5 Oa

Bradbury 3 -7 10 K- Index 14 37 23

Energy 2 -4 6

Mod. Martin 10 - 20 30

aIndefining the 700-mb temperature asa constanthere for both adiabatic processes, the Boyden index will result in a constantvalue. McPherson[29] concludes thatthe Boyden indexis verytemperature-dependent.

...... Table 20. StabilityIndex Dependencyas a Functionof Temperature Change

Range Rangea as eW Percentof of Index 24OCoo c18OC 12OC 6OC 19ValuesTable Range

SWEAT -76.6 123.444.2-36.2-71.0 200 37% ## VerticalTotals 32.6 30.7 26.2 23.9 20.6 12 80% ## CrossTotals 22.6 20.7 16.2 13.9 10.6 12 80% ## TotalTotals 55.2 51.4 42.4 37.8 31.2 24 77% ## e* 2.8 3.0 2.7 3.2 3.6 0.9 5% # E W Showal ter 0 0 0 0 0 0 0% * cn Rackcliff 41.4 38.7 33.3 30.3 26.4 15 94% ## Jefferson 41.4 42.3 40.5 41.1 40.8 1.8 9% # Mod. Jefferson 28.4 29.3 27.5 28.1 27.8 1.8 9% # b Boyden 22.7 14.9 6.9 -1.0 -8.6 31 ## Bradbury 0 0 0 0 0 0 0% * K- I ndex 3.8 8.7 11.1 15.5 18.8 15 65% ## Energy 1.21 1.28 1.80 1.60 1.55 0.59 10% # Mod. Martin -1.2 -1.6 -2.0 -2.4 -2.6 1.4 5% #

a Temperature-dependencycode: * = None orsmall; # = Moderate; ## = High. b McPherson[29] concludes that the Boyden index isvery temperature- dependent.

i Finally,the SWEAT, K, threeTotals, Boyden,and Rackcliffindices areall highly dependent upontemperature changes. Since 0; was derivedby using the BGE approximateequation for BE, theresulting moderatetemperature-dependency actually would have been less had thisequation not beenused.

Temperature-dependencyon an averagedprofile, ascompared to an individualprovile, may appearunimportant since only averaged

(AVG or LAG) severestorm thermodynamic profiles and indicesare developed. However, when otherindividual vertical soundings (and their computed stabilityindices) are compared tothose of the averaged profile, temperature-dependent indices may giveunrealist ic results. A1 so , theresults of the AVE-IV soundingsbeing averaged springtimesoundings, over two independent days for the east/central

UnitedStates, may notapply accurately for a different season

(temperatureregime) or location, if temperature-dependentindices areused. Therefore, in the evaluation of index performance, it is wellto know in advancewhich indices are temperature-dependent and whichare not.

C. StabilityIndex Results

Thissection presents the stability index results, based on the LAG and AVG profiles. The 14 stabilityindices described in

Chapter IV wereused inconjunction with the MDR LAG and AVG averagedatmospheric profiles. These resultsare presented in

Table 21.

96 Table 21. Stability Index Values for LAG and AVG MDR Profiles

Approximate Threshold MDR-LAG MDR-AVG Index Index A B C Da A B C Da Va 1ue SWEAT 194 237 271 @ 186 233 249 290 250 to 350 Vertical Totals 26.6 26.1 27.3 29.4 26.6 26.0 27.6 a 26 Cross Totals 17.7 20.9 22.0 17.1 21.1 22.0 22.1 18 Total Totals 44.3 47 .O 49.3 a 43.7 47.1 49.6 51.6 44 to 50 0;C -3.5 -3.2 -6.0 a -2.9 -3.4 -5.3 -8.1 -" Showa 1terC 4.1 1.9 0.0 -1.2 3.6 1.7 -0.6 -3 to -6 Rackcl iff 29.1 30.4 31.3 a 28.8 30.2 31.3 32.0 30 to 35 Jefferson 38.1 39.8 41.7 @ 37.6 39.5 41.5 42.9 30 Mod. Jefferson 20.8 26.2 27.1 a 19.6 26.2 27.8 28.6 28 to 29 Boyden' 6.8 6.4 5.8 5.2 6.7 6.5 5.2 a Bradbury' 0.8 -0.1 -2.0 a 0.7 -0.4 -1.5 -2.4 "- K- Index 11.5 21'.1 22.2 24.7 9.6 21.8 23.9 30 to 35 Energy' 0.20 -0.27 -1.08 a 0.26 -0.18 -0.94 -1.61 <-2 Mod. Mart i nc 2.2 0.7 -3.4 @J 2.6 0.3 -3.8 -4.8

~~~~ ~~ ~ a Circled "D" category values indicate the largest unstable index value. b C Potential Lag index. Indices in which instability is negative (-). As canbe seen from Table 21, thecategory D profiles pro-

ducedthe largest instability index values, as onewould expect.

Sincecategory D conditionsare the main items of interest in the

presentinvestigation, emphasis will beplaced on them. The circled

category D LAG and AVG stabilityindices indicate the index with the

largestD-category index value. Two indices,in particular, show a

much greater LAG instability than their AVG counterpartindex value.

The SWEAT and modified-Martinindices both indicate a LAG-REG

differencegreater than 7%, as a functionof the index range. These

twoindices would be potential LAG stabilityindex forecast indi-

cators when used priorto the occurrence of severe weather.

To establishconcrete threshold values for all theindices

usedhere is difficult, since eachindex may offer a thresholdindex

valuefor only a selectedtype of thunderstorm condition (i.e.,

scatteredthunderstorms rather than numeroussevere thunderstorms).

However, an attempthas been made toinclude approximate threshold

indexvalues for severe-type thunderstorms (see last column of

Table21).

Note that mostindices equal or exceed the threshold values

indicated,with the exception of perhaps the K-index. However, the

K-indexhas been designed for routine, non-severe thunderstorm prediction.

Therefore, allindices presented in Table 21 appear to be potentiallyequal by thisanalytical comparison between prior and

actualsevere storm averaged conditions. This supposition will have to beconsidered in Chapter VII, when an actual,independent set of

98 severestorm soundings is presented and analyzedwith respect to

atmosphericstability.

D. JohnsonLag Index

As contemplatedin Chapter V, Section G, it isbelieved that

thedevelopment of a forecast-typeprocedure or index should be

attemptedthat is based entirely upon thedifferences noted in the

averaged AVG and LAG profiles. If theenvironment three to six

hoursprior to severe weather shows anytype of parametric structure

differencefrom that at thetime of severe weather, a stability

index/procedureshould be developed to model this phenomenon. Since

winddifferences are small between LAG and AVG profiles, and the

individualwind profiles are so variable, it was feltthat for the

initialattempt, w indsshould not be used--onlythe use of signifi-

cantthermodynamic parameterchanges versus altitude to keep the

indexsimple.

As explainedearlier, the major differences observed in the

temperaturestructure between LAG and AVG profilesoccur throughout

the800- to 650-mb and 650- to 500-mb levels. The maindiffer-

encesnoted occur between the 900- to 800-mb and 750- to 700-mb

levels. The LAG and AVG temperature and equivalentpotential

temperaturelapse rates that exist between these pressure levels werethen calculated. A gradienthalfway between the LAG and AVG

gradients was selected as being a mostrepresentative standard of

atmosphericconditions between three hours prior to storms and storm occurrenceitself. Lapse rates onone sideof this standard gradient

99 wouldrepresent conditions of the LAG, whilegradients observed on

theother side of this standard would represent AVG conditions.

The fourthermodynamic termsmentioned earlier were therefore

se 1ec ted as potentialforecast terms: Two terms to represent

temperature gradientsin lower and upperatmospheric areas, and two

BE gradient terms torepresent thelow- and middle-atmospheretemper-

ature and moisturestructure. The fourterms were thencombined so

as to maximizethe negative value of the index in representing

.extreme instabilityonly during LAG-D time(three to six hours before

storms).Since this gradient procedure, or index, is maximized a

fewhours before storm occurrence, the application of theindex

duringperiods of severe weather (AVG-D conditions)should result in

a positivevalue. This new JohnsonLag Index (JLI)is expressed as:

where,

- T650-800 - T650 - T800 '

- T500-650 - T500 - T650 ' - 'E 800-900 - 'E 800 - 'E 900 '

- 'E 700-750 - 'E 700 - 'E 750 ' 0 (T and BE Unitsin C or OK) .

100

c The fourterms of Eq. (25) wereweighted by applying multi- plicationfactors of 1, 2, 2, and1/3, respectively.This was done to offset the effect of the category A (non-precipitation)small temperature and potentialtemperature gradients, which tended to allowthe unweighted JLI equation to produce an unstablenegative

JLIvalue close in magnitude to LAG-D JLIconditions. Thus, this weighting will helpeliminate the occurrence of false alarms when- evercategory A, non-precipitationareas are encountered. The weightingfactors were determined from a subjective,trial-and-error procedureinvolving different combinations of weighting, in order to arrive at a largeJLI difference between A and D precipitation conditions.

The JLIvalues calculated for LAG-D conditionsequaled -4.35.

Likewise,JLI values computed for AVG-D conditionsresulted in a value of +2.76. The theory,then, isthat if atmosphericconditions from an individualsounding produce a negativeJLI of similaror greatermagnitude, one shouldexpect severe weather to occur within thenext three to six hours. This conclusion has yet to beproven, and isonly stated at this time. In Chapter VI1 the theory will be tested as to its performancealong with the other stability indices.

The completeJLI values versus MDR categoriesof LAG and AVG profiles aregiven in Table 22.

Again, it shouldbe realized that the very small parametric differencesnoted in these averaged profiles havebeen used inthe constructionof the JLI; whereas, in reality, individual atmospheric

101 Table 22. JLI versus MDR Categories for LAG and AVG Conditions

MDR LAG AVG Category JL I JL I A 0.52 -0.15 B 4.11 4.78 1.78 3.45 C 1.78 D -4.35 2.76

102 .. , , .. .. . , .”

soundings do, indeed, have a much greater range of variability in the vertical. The question is, how well will the JLI model the real atmosphere?

103

I IIIII Ill1 Ill l1l1l111llIll I I CHAPTER VI I

STABILITY CRITERIA APPLIED TO AVE-SESAME-I

A. Introduction

Thischapter will present an analysiswhich will use the stabilityindices defined in the previous chapters. These are appliedto a different and independentset of individualdata soundingstaken during severe weather situations. The

AVE-SESAME-I [2] datacase of April 10-11,1979 was selectedfor the presentstudy as thecomparison data set against which to run all of theindices.

The synopticsituation for AVE-SESAME-I will bepresented alongwith the individual soundings. Stability indices will be computed forall soundingsprior to, during, and aftersevere storm occurrence. The computed indices will becompared inhelping determine how eachindex varies throughout this data set, and how eachindex might be used as a short-termpredictor of severe weather.

B. SynopticSituation

The AVE-SESAME-I timeperiod was chosen for the stability indexevaluation case because the AVE-IV and AVE-SESAME-I projects involvedApril storm cases in which similar synoptic weather situ- ationsdeveloped.

A low-pressuresystem located north of western Texas with associatedfrontal positions existed, allowing a moistGulf flow to

104 persistover the southeastern and southernbniddleplains areas of theUnited States. This situation, coupled with the advancing cold front, causedextensive convective and severeweather to form, with thedevelopment of two pre-frontal squall lines, during both AVE cases. The destructiveWichita Falls, Texas,tornado that occurred during AVE-SESAME-I was only one of morethan 40 tornadooccurrences.

Abilene,Texas, was thesounding station chosen to analyze during AVE-SESAME-I because it was theclosest station during most ofthe tornado and severeweather occurrences inthe north-Texas and southern-Oklahomaareas. A preliminaryweather summary for

AVE-SESAME-I hasbeen publishedby Wi lliams [68], and theindiv idual upper-airsounding data are available inthe Gerhard et al. [2] document.

Sincethe Abilene sounding data were selected for analysis inthis study, the time and location of thesevere weather/tornado occurrencearound Abilene during April 10-11,1979 will bediscussed at thistime. Generally speaking, there were threeseparate severe weatherpatterns which occurred near Abilene during the afternoon of

April 10, 1979 and extendedthrough the early morning hours of

April 11 , 1979.

The firstsevere weather event consisted of hail damage between 125and 150 milesnorth and northeastof Abilene, between

1730-1800 GMT on April 10. The second verysevere weather outbreak occurredbetween 2050-0100 GMT, withtornado and hailoccurrence from 75 to 150 milesnorth and thennorth-northeast of Abilene.

Thisincluded the Wichita Falls tornado. Finally, a squallline

105 developedaround 0245 GMT (April11) from Abilene and extended

-75 milessouth-southwest to San Angelo,Texas. For the next six

hours(until 0817 GMT), thissquall line moved eastwardproducing

hail and some tornadoesfrom 35 to beyond125 miles of Abilene. The

severeweather occurred at Abilene and then moved southof, southeast

of,east of, and finally,northeast of the city. Figure 27 indicates

thesevere weather pattern which occurred around Abilene (ABI) from

1200 GMT onApril 10 to 1200 GMT onApril 11, 1979.

C. SoundingAnalyses

Forthe Abilene site, eight atmos,pheric soundings were taken

between1200 GMT on April 10, 1979and 1200 GMT on April 11, 1979.

Onlythe 0600 GMT soundingof April 11 was missing due totracking

problems,with no second release as backup.

Fiveof the eight critical Abilene severe weather soundings

arepresented in Skew-T formin Figures 28and 29. Givenare the

April 10, 1979soundings for 1442,1740, 2034, and2333 GMT, together withthe one for 0226 GMT on April 11, 1979. The progressionof

thesesoundings intime indicates that low-level moisture was con-

finedby a cappinginversion to levels under 800 mb prior to 1442 GMT.

From theseprofiles, extremely dry air can beseen above thislevel.

After 1500 GMT, thecapping inversion lifted and, withstorm development,allowed moist air topenetrate upward to beyond 600 mb by

2034 GMT. The April 11,1979 Abilenesounding for 2333 GMT shows thatduring this time period, while severe weather was currently affectingthe Wichita Falls area, the dry- line beh indthis system

106 I C +' I I - 0 HRO OFYV

e 10 FSM

" ; OHOT

oTX K

OELD I -,

0"O" OTYR &GG OSHV o MAF

LEGEND v :TORNADOES SPOTTED BY GROUND OBSERVERS :TORNADOES IDENTIFIED SOLELY BY RADAR OBSERVATIONS :HAIL REPORTS WITH DIAMETER IN INCHES L6:STRONG THUNDERSTORM SURFACEWIND 0 :SEVERE THUNDERSTORM IDENTIFIED SOLELY BY RADAR

Figure 27. Severeweather occurences between 1200 GMT on April10, and 1200 GMT on Apri 1 11 , 1979 in the southcentral United States [68].

1 07 200

300

400 E b

W 'CY 3 v, 500 cf n

600

700

800

900

1000

I TEMPERATURE ("C) Figure 28. Abilene, Texas, severeweather soundings forApril 10, 1979. 0 W I I I I I1 I 1111 I1 I1 I I

had now moved intothe Abilene area. This condition was relatively

short-livedbecause a second squallline was formingnear Abilene

and startedinflicting severe weather there and eastwardby 0245 GMT.

The 0226 GMT soundingof Figure 29 shows an abruptincrease in moisture up to 350 mb, where thedata terminate. Sometime after

0600 GMT on April 11, 1979, thecold front began enteringthe

Abilenearea, bringing dry air close to the surface while still leaving a pocketof moisture above thefront between 550and 750 mb.

Sincestability is the item of interest in the present investigation,the 15 stabilityindices used earlier werecomputed for eachAbilene sounding. These stabilityindex results are presented in Table 23, togetherwith the exact time of radiosonde release.Listed below the index values in this table is a severe weathertimeline applicable to the north-central Texasarea, within

150 milesof Abilene. This separation of sounding site and areaof severeweather occurrence is, indeed,too large to be completely applicableto the Abilene data. Therefore, one shouldkeep in mind thatthe Abilene timeline needs to beshortened somewhat. Also on

Table 23, thehighest three unstable index values for each index havebeen circledfor easy reference. The mostunstable value has also beenmarked with a superscript 'Ia."

As can beseen in Table 23, there seems to begood general agreement that most allindices appear toperform adequately in the evaluationof atmospheric instability during the passage of the two squallsystems near Abilene. Profiles 4 and 6 werethe two soundings takenat Abilene just prior to the severe weather which occurred

110 Table 23. Abilene, Texas, AVE-SESAME-I Sounding.Stability Index Values

10, 1979April 10, April 11, 1979 Sounding No. Time (GMT) Index

SWEAT 221 69 292 -33 -37 VerticalTotals 28.5 27.8 27.9 "- 26.6 26.3 CrossTotals 16.1 3.1 15.0 9.3 6.3 TotalTotals 44.6 36 .O 50.0 "- 35.9 32.6 -11.3 -8.1 -6.0 11.2 14.0 E Showal terC -1.1 7 .O a 0.8 8.9 10.3 Rackcl iff 32.2 32.6 31.4 26.0 26.1 Jefferson 43 .O 44.3 a 42.4 33.1 32.6 Mod. Jefferson 19.9 20.8 10.5 21.9 22.9 Boyden' -3.2 -3.9 -7.3 -7.1 -6.9 Bradbury' -0.7 1.7 @ -1.8 2.8 3.8 K-Index 0.2 -10.0 -10.8 "_ 15.3 13.9 Energy' -0.2 1 .o a -1.1 1.9 2.3 Mod. Martin' -7.3 -9.4 -1.2 13.5 13.8 JL~ @J -I7 -10 1 12 "- 6 AbileneSevereAreaWeather n Time1 ine GMT:7 1730-081 20500245- 0100 - 1800 Description: (No Convective(Tornadoes(Hail) (Hai (Storms1 and ,Move Activity) Eastward)Tornadoes) and Hail)

a Circledvalues indicate the highest three unstable index values for eachindex. b C Mostunstable stability index value. Indices in which instability is negative (-1. near and aroundthe city. Stability index values from Table 23

indicatethat most indices peak (withinstability) using soundings 4

and 6 data; 10 of the 15 indices peak usingsounding 6, whilethree

peak usingsounding 4. This means that 13 ofthe 15 peakedduring

theoccurrence of upper-levelmoisture buildup, just prior to the

onsetof the Abilene storms. Only two indices (0; and JLI) peaked

attimes prior to this. Sounding 6 is more unstablethan sounding 4

becausethe storms developed very close to the sounding site, and

themoisture aloft haddeveloped more extensively than during

sounding 4. The dry-line passage atAbilene between 2200-0000 GMT

can readily beseen bythe sudden increase in stability in most all

ofthe indices during sounding 5 (2333 GMT). Whileweather activity

existedeastward of Abilene during sounding 8 (0806 GMT, April ll),

allindices showa generalincrease in stability as the cold front

arrives.

Table 23 alsohints that soundings taken when stormsare not

inprogress in the general area result in slightly greater insta-

bility than when stormshave formed inthe area during the radiosonde release.This mayseem toindicate that the instablity (stored potentialenergy) which can build up priorto storm occurrence can berelieved (made more stable)through the release of thunderstorm kineticenergy activity.

112 D. Exceptionsto the Norm

Thereare a few stabilityindices which peak at an earlier

soundingthan the rest. It was decidedto look at eachindex that fellinto this category.

Sincethe 8; indexpeaked out during sounding 3, thecause was sought. The index is basedon a BE differencebetween 700 mb

and thesurface level. Since sounding 3 indicatedthat the atmos- pheredried out very quickly between 750 and 700 mb, this wouldalso produce a verydramatic 8 dropbetween the same two levels, E resulting in a veryunstable 6; indexvalue.

The modifiedMartin index indicated a slightinstability peak usingsounding 2. Thisindex uses the 850-mb level as the comparisonaltitude. At thistime interval there existed a large cappingtemperature inversion top located at 850 mb. Thislarge temperaturevalue would produce a higherindex value than if this cap inversiontop were located at a differentlevel.

The Energyindex peaking during soundings 3 and 4 is believedto bedue to the ampleabundance ofmoisture at 850 mb duringthese two sampling times, which would strengthen the 850-mb

E value.Sine the JLI was designedto peak outduring time periods T priorto storm development, this early peaking of the JLI index duringsoundings 1and 2 is expected and desirable.

113 E. Lag Testing

In Chapter VI it was indicated that, based on the AVE-IVLAG profile as it related to the AVG profile, three indices appeared to be potentia 1 lag indices. These three indices were: SWEAT, modified Martin, and the JLI. According to the AVE-SESAME-I sounding data (Table 23, page lll), all of these indices, with the exceptionof the JLI, fail to qualify asa lag index, since the peak index out- liers which occur before storm development have been explained away. The JLI does give large negative values (-29 and -18) during the non-storm time period represented by soundings 1 and 2. When distant storms occur, Abilene sounding 3 records a JLI = -7. Just prior to the first major outbreakof storms closer to Abilene, sound ing 4 gives a JLI = -10. The dry-line passage, during sound ing 5, produces a JLI = +l. Sounding 6, released 19 minutes pr i or to hail occurrence near Abilene (51 minutes prior to first tornado report) gave a JLI = -28. This large negative index value was surprising, since the sounding represents squall line-produced activity. However, the JLI could still be sensing the intense, unstable, pre-squall line environment which appears not to have passed the release site at this time. Overall, the JLI has functioned well and it gives large positive values (+6 and +12) when the cold front moved into the area. This indicates that no more storms were due to follow.

114 II

Basedon only onesevere storm case, it appearsthat of 15 stabilityindices tested as a pre-stormlag index, only the JLI appears togive satisfactory results thus far. However, sincethe

JLI is a new index,representing low- and middle-leveltemperature and moisture, it will have to be testedfurther, and possibly be adjusted,before it can quality as a lag/forecastindex for severe storms.

115 CHAPTER VI II

CONCLUSIONS

The followingproject goals and conclusionswere accomplished and presentedin this study:

1. Averaged AVE-IV environmentalthermodynamic/wind profiles

havebeen presented for different MDR severestorm

periods (AVG), and forperiods three to six hours prior

tosevere storm occurrence (LAG).

2. The AVE-IV AVG and LAG profiles wereanalyzed paramet-

rically and with 14 common atmosphericstability indices

to determine if a severestorm forecast index or pro-

cedurecould be developed based on theseaveraged severe

storm profiles.

3. A thermodynamiclag index, called the JohnsonLag

Index(JLI), was developed,based upon low- and middle-

troposphericlevel temperature and moisturestructure

usingthe AVE-IV averagedprofiles. The JLI was designed

to have short-termedforecasting ability.

4.Based on theaveraged AVE-IV profiles, twoother

stabilityindices (SWEAT and modifiedMartin) had some

potential as forecastlag indices.

5. All 14 stabilityindices and the JohnsonLag Index were

testedby employing an independentsevere storm case

studyusing the AVE-SESAME-I individualdata soundings

from one station.

116 6. All AVE-SESAME-I stabilityindices tested appeared to

recognizethe severe weather environment with unstable

values, as well as presentingstable values when severe

weatherhad passed.

7. All AVE-SESAME-I stabilityindices tested as a pre-storm,

three-hourlag forecast index performed unsatis-

factorily.Only the JLI appeared to show promise in

termsof forecasting severe weather three to six hours

priorto occurrence. However,more testingof this

indexwith case study data is needed.

117 BIBLIOGRAPHY

118 BIBLIOGRAPHY

1. Fucik, Nancy F., and Robert E. Turner. "Data for NASA's AVE-IV Experiment: 25-mb Sounding Data and Synoptic Charts," National Aeronautics and Space Administration TMX-64952, George C. Marshall Space Flight Center, Marshall Space Flight Center, Alabama, August, 1975. 2. Gerhard, Myron L., Henry E. Fuelberg, Steven F. Williams, and Robert E. Turner. "AVE-SESAME I: 25-mb Sounding Data," National Aeronautics and Space Administration TM-78256, George C. Marshall Space Flight Center, Marshall Space Flight Center, Alabama, December, 1979. 3. Use of the Skew-T, Log P Diagram in Analysis and Forecasting. AWSM"105-T~.~~ottAirForce Base, Illinois: United States Air Force, Air Weather Service, Headquarters Air Weather Service (MAC), July, 1969 (reprint October 1971). 4. Scoggins, James R., and James E. Wood. "Factors in the For- mation and Prediction of Convective Clouds and Thunder- storms." Paper presented at American Meteorological Society Seventh Severe Local Storms Conference, Kansas City, Missouri, October 5-7, 1971. 5. Showalter, A. K. "A Stability Index for Thunderstorm Fore- casting," Bulletin of the- American Meteorological Society, 34:250-252-7Jiine, 1953.- 6. Huschke, Ralph E. Glossary of Meteorology. Boston: American Meteorological Society, 1959. 7. Connell, James R., and Lillian Ey. "Wind Shear and Wet and Dry Thermodynamic Indices as Predictors of Thunderstorm Motion and Severity and Applications to the AVE-IV Experimental Data," National Aeronautics and Space Administration CR-150220, George C. Marshall Space Flight Center, Marshall Space Flight Center, Alabama, March, 1977. 8. Scott, Robert W., and James R. Scoggins. "The Moisture Budget in Relation to Convection," National Aeronautics and Space Administration CR-2817, George C. Marshall Space Flight Center, Marshall Space Flight Center, Alabama, March, 1977. 9. Read, William L., and James R. Scoggins. "Vorticity Imbalance and Stability in Relation to Convection," National Aero- nautics and Space Administration CR-2819, George C. Marshall Space Flight Center, Marshall Space Flight Center, Alabama, March, 1977.

119

I I I I1 l1111ll111l1ll1l1 10. Fuelberg,Henry E. "AtmosphericEnergetics in Regions of IntenseConvective Activity," National Aeronautics andSpace Administration CR-2826, George C. Marshall Space Flight Center,Marshall Space FlightCenter, Alabama,March, 1977.

11.Dupuis, Leonard R., and James R. Scoggins."Differences BetweenMeasured and LinearlyInterpolated Synoptic Variables Over a 12-hPeriod During AVE-IVY" NationalAero- nautics andSpace Administration CR-3150, George C. Marshall Space FlightCenter, Marshall Space FlightCenter, Alabama, June,1979.

12. Turner,Robert E. "TheMechanics of AtmosphericSystems DerivedThrough Vertical and HorizontalAnalysis of Para- metricData," National Aeronautics andSpace Administration TP-1072, George C. Marshall Space FlightCenter, Marshall Space FlightCenter, Alabama,November, 1977.

13. Fuelberg,Henry E., and James R. Scoggins."Relationship Between theKinetic Energy Budget and Intensityof Con- vection."Paper presented at the. American Meteorological SocietyTenth Conference on SevereLocal Storms, Omaha, Nebraska,October 18-21, 1977.

14. Turner,Robert E., and Kelly Hill. "Skew-T,Log P Diagramsfor NASA's AVE-IV Experiment,"National Aeronautics andSpace Administration NASA/MSFC-ES-84-1, George C. Marshall Space FlightCenter, Marshall Space FlightCenter, Alabama, March,1977.

15. Maddox, R. A. "The Evolutionof Middle andUpper Tropospheric FeaturesDuring a Periodof Intense Convective Storms." Paperpresented at the American Meteorological Society EleventhConference on Severe Local Storms, Kansas City, Missouri,October 2-5,1979.

16.Wilson, Gregory S. "Relationships BetweenConvective Storms and TheirEnvironment in AVE-IV Determinedfrom a Three- DimensionalSubsynoptic-scale, Trajectory Model." Paper presentedat the American Meteorological Society Tenth Con- ferenceon Severe Local Storms, Omaha, Nebraska, October 18-21,1977.

17.Wilson, Gregory S. "Large-scaleVertical Motion Calculations in the AVE-IV Experiment--ofAtmospheric Wind Velocity," GeophysicalResearch Letters, NO. 12):735-738, December, 1976.

120 18. Davis, James G., and James R. Scoggins."The Development of Con- vectiveInstability, WindShear, and VerticalMotion in Relationto Convective Activity and Synoptic Systems in AVE-IV," NationalAeronautics andSpace Administration CR-3386, George €.Marshall Space FlightCenter, Marshall Space FlightCenter, Alabama, February,1981.

19. Fucik, Nancy F.,and Robert E. Turner."Data for NASA's AVE-IV Experiment: 25-mb SoundingData and SynopticCharts," NationalAeronautics andSpace Administration TND-8161, George C. Marshall Space Flight.Center,Marshall Space Flight Center, Alabama,March, 1976.

20. Wilson,Gregory S., and James R. Scoggins."Environmental ConditionsAssociated with the Development of Severe Thunder- storms as Determinedfrom 3-h AVE Data."Paper presented atthe America1 Meteorological SocietylAmerican Institute of Aeronautics and AstronauticsConference on Atmospheric Environmentof Aerospace Systems and AppliedMeteorology, New York, New York, November 14-16,1978.

21. Wilson,Gregory S. "Thunderstorm-EnvironmentInteractions Determinedwith Three-Dimensional Trajectories," National Aeronautics andSpace Administration RP-1054, George C. Marshall Space FlightCenter, Marshall Space FlightCenter, Alabama, January,1980.

22. McCown, Milton S., and James R. Scoggins."Gradients of MeteorologicalParameters in Convective and Non-convective Areas,"National Aeronautics and Space Administration CR-2818, George C. Marshall Space FlightCenter, Marshall Space FlightCenter, Alabama,March, 1977.

23. Foster, D. S., and R. M. Reap. "Archivingof Manually- Digitized RadarData," Techniques Development Laboratory OfficeNote 73-6, National WeatherService, Silver Springs, Maryland,1973.

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121 26. Wilson,Gregory S., and James R. Scoggins."Atmospheric Structure and Variability in Areas ofConvective Storms Determinedfrom 3-h Rawinsonde Data," National Aeronautics andSpace Administration CR-2678, George C. Marshall Space FlightCenter, Alabama, April, 1976.

27. Booth,David M. "A Study of StabilityIndices and Vertical Motionin Relation to Convective Clouds Over Texas." UnpublishedMaster's thesis, Texas A&M UniversityGraduate College,College Station, Texas, January, 1970.

28. Whitehead,Dare11 R. "A Comparison ofObjective Convective ActivityIndices," University of OklahomaResearch Insti- tuteReport OURI-1828-71-1,Atmospheric Research Laboratory, Department of Meteorology, Norman, Oklahoma,November, 1971.

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32. Miller, R. C., and A. Bidner. "The Use of ComputerProducts in Severe-WeatherForecasting," Automated Weather Support Proceedingsof the Sixth AWS TechnicalExchange Conference, U. S. Naval Academy, 21-24September, 1970. Technical Report242. Ln.p.J: Air WeatherServiFeF(MAC), United States Air Force,April, 1971. Pp. 224-228.

33. Bidner, A. "The Air ForceGlobal Weather Central Severe Weather Threat (SWEAT) Index(A Preliminary Report) ,I' Automated WeatherSupport Proceedings ofthe Sixth AWS Technical ExchangeConference, U. S. NavalAcaTmy, 21-24 September, -Technical[-. j: Air WeatherService (MAC), UnitedStates Air Force,April, 1971. Pp. 229-231.

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125 I I

68. Williams, Steven F. "A Preliminary Look at AVE-SESAME-I Con- ducted on April 10-11, 1979," National Aeronautics and Space Administration TM-78262, George C. Marshall Space Flight Center, Marshall Space Flight Center, Alabama, February, 1980.

126 ~ ~ ". .- . . - .. . . - 1. REPORT 1. NO. 2. GOVERNMENTACCESSION NO. 3. RECIPIENT'SCATALOG NO. NASA TP-2045

.. ~~ 4. TITLE AND SUBTITLE 5. REPORTDATE November 19 82 A Stabi 1 i tyAnalysis of AVE-IV Severe Weather Soundings . 6. PER~O~MINGORGANIZATION CC,OE

~ - .~.~ 7. AUTHORfS) . 8. PERFORMING oRCANlZATlON-REP0R.r Dale L. Johnson ~~ ~ ". .~ ." 9. PERFORMINGORGANIZATION NAME AND ADDRESS 10. WORK UNIT,NO. George C. MarshallSpace Flight Center "384 MarshallSpace FlightCenter, Alabama 35812 1 1.CONTRACT OR GRANT NO. - 13.TYPE OF REPOR-; 8r PERIOD COVERE 12.SPONSORING AGENCY NAME AND ADDRESS Technical Paper NationalAeronautics and Space Administration Washington, D.C. 20546

" " I ~~~~ . . -. .- 15. SUPPLEMENTARYNOTES

Prepared by Space SciencesLaboratory, Science and EngineeringDirectorate

. . ~ ___~~. . . _" ..- 16, ABSTR AnCT investigation wasmade to determinewhether the stability and verticalstruc- ture of an averagesevere storm sounding, consisting of both thermodynamic and wind verticalprofiles, could be distinguished from an average lag soundingtaken 3 to 6 hours prior to severeweather occurrence. The term"average" is definedhere to indi- catethe arithmetic mean of a parameter, as a functionof altitude, determined from a large number of availableobservations taken either close to severeweather occurrence or else more than 3 hoursbefore it occurs. The investigativecomputations were also done to helpdetermine if a severestorm forecast scheme or indexcould possibly be used or developed. The studypresents these mean verticalprofiles of thermodynamic and wind parameters as a functionof severity of theweather, determined from manually digitized rad: (MDR) categoriesobserved during theNational Aeronautics and Space Administration (NASA) Atmospheric Variability Experiment IV (AVE-IV) which took place on April24-25, 1975. Profiledifferences and stability index differencesare presented along with the developmentof the Johnson Lag Index (JLI) which is determined entirely upon environmental verticalparameter differences between conditions 3 hours prior to severeweather, and severeweather itself. All ofthe stability indices tested were then used on a separate and independent data sample (AVE-SESAME-I) consisting of individualsoundings taken during April 10-11 1979. TheAVE-SESAME-I data profilesare presented along with stability index compu- tationsfor each. Allof thestability indices tested appeared to do a reasonable job in indicating both thesevere weather as well as thenonsevere weather environment. As a pre-severeweather lag (3 to 6 hours) index , onlythe JLIappears to show promise as a potentialforecast index. More testing of this index, however, is needed " . __~~__.~. - 17. KEY WORDS 18.DISTRIBUTION STATEMENT

Stabilityindices Unclassified - Unlimited Thermodynamic quantities Severeweather soundings Subject Category 47

I I ~~ ~ 19.SECt RlTY CLASSIF. (of thlm repat) 20. SECURITYCLASkIF. (or tht. Unclassified UnclassifiedUnclassified 1 38

~ ~ "~~~~ ~- For sale by National Technical Information Service. Springfield, Virginia 2 2 16 1

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