The Operational Meteorology

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NOAA TECHNICAL MEMORANDUM NWS NSSFC-5

NTIS Accession No. PB83-162321

THE OPERATIONAL METEOROLOGYOF CONVECTIVE WEATHER

VOLUME I: OPERATIONAL MESOANALYSIS

Charles A. Doswell III

National Severe Storms Forecast Center

Kansas City, Missouri

November 1982

UNITED STATES DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric AdministrationNational Weather Service

Electronic reprint produced by

Tim Vasquez

Weather Graphics Technologies / www.weathergraphics.com

March 2000


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I appreciate that Tim Vasquez is willing to make this available, since Icontinue to get requests for this material. There is a limited supply ofhard copy versions still available; I have the worlds supply of themand they can be had without charge by sending me a mailing address,as long as the supply holds up. I also have copies of the secondvolume in the two-volume series: Storm-Scale Analysis.

This first volume was written in 1982 and still contains material I amnot ashamed of, but a lot has happened since then to make the contentsomewhat obsolete. For example, Q-vector diagnostics, PotentialVorticity thinking, and the ideas associated with Moist SymmetricInstability and Slantwise Convection have all been developed after this

tech. memo. was finished. If I had it to do over, I think I could revisethe discussion of synoptic-scale vertical motion in a more useful waythan is currently given. In general, my ideas have not remained staticsince 1982, and Ive had to mull over occasional impulses towardrevising both of the tech. memos. since both of them are on the longslide to increasing obscelesence. However, Ive chosen not to do so.Rather, its my intention eventually to co-author a textbook (or two) thatwill incorporate a lot of what Ive learned since 1982. Note that in thesecond volume, I implied that there would be a third volume with lotsof examples of the methodology in action. Time and higher prioritieshave made it clear that this third volume simply will never get done,although I have some of the major components of it assembled (more or

less), so my intentions were good. Hopefully, all of this revision andinclusion of new material will be made manifest in the textbook I haveplanned to write.

At least some of this tech. memo. should remain relevant well into thenext century, so I hope that Tims making it available will be useful tothe readers. In the meantime, please visit my Websites at:

http://www.nssl.noaa.gov/~doswell/

http://webserv.chatsystems.com/~doswell/

where you can find a number of essays and other Web pages devotedto some of the issues covered in this old work of mine.

Chuck DoswellNorman, Oklahoma, Spring 2000

PREFACE

March 2000


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PREFACE TO

THE OPERATIONAL METEOROLOGY OF CONVECTIVE WEATHER

VOLUME I: OPERATIONAL MESOANALYSIS

Primary causes are unknown to us; but are subject to simple and constant laws, which may bediscovered by observation, the study of them being the object of natural philosophy.

Joseph Fourier, Theory of Heat

There is no other species on Earth that does science. It is, so far, entirely a human invention ... It has two

rules. First: there are no sacred truths; all assumptions must be critically examined; arguments fromauthority are worthless. Second: whatever is inconsistent with the facts must be discarded or revised ...The obvious is sometimes false; the unexpected is sometimes true.

L.F. Richardson was a British meteorologist interested in war. He wished to understand its causes. Thereare intellectual parallels between war and weather. Both are complex. Both exhibit regularities,implying that they are not implacable forces but natural systems that can be understood and controlled.To understand the global weather you must first collect a great body of meteorological data; you mustdiscover how weather actually behaves.

Carl Sagan, Cosmos

There is a growing accumulation of evidence to indicate that man has no direct contact with experienceper se but that there is an intervening set of patterns which channel his senses and his thoughts, causinghim to react one way when someone else with different underlying patterns will react as his experiencedictates.

It is time, however, that we began to realize that much of what passes for science today may have beenscientific yesterday but can no longer qualify because it does not make any additional meaningfulstatements about anything. It blindly adheres to procedures as a church adheres to its ritual.

E.T. Hall, The Silent Language

We can never have enough of nature. We must be refreshed by the sight of inexhaustible vigor, vast andtitanic features, the sea-coast with its wrecks, the wilderness with its living and its decaying trees, thethundercloud, and the rain which lasts three weeks and produces freshets. We need to witness our ownlimits transgressed, and some life pasturing freely where we never wander.

Henry David Thoreau, Walden


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These notes have been developed in an effort,however imperfect, to acquaint meteorologists inan operational environment with the basicconcepts of convective weather systems. It is asad fact of life that many of todays operationalmeteorologists have never been given a physicalinterpretation of the dynamics which are

understood to govern the atmosphere and, inparticular, convection. It is not my intent to becompletely exhaustive, although the length of thetext leads me to fear that it may be exhausting!

There are numerous threads which can beused to sew up the package I am trying to deliver.In trying to unravel them, I have at times assumedthe reader knows things with which he/she maynot, in fact, be familiar. Conversely, I have attimes assumed the readers ignorance of somebasic ideas which I have felt important enough to

explain in detail and, in the process, may havebored more advanced readers. I hope that bothforms of exasperation never reach the breakingpoint.

In any work of this sort, it is easy to find thematerial one wrote a few months beforesomewhat less than satisfactory in light of newfindings, recent publications, or just plain furtherthought. One has to stop the process of revisionssomewhere, but I suspect we are at the start of anexciting new era in applied meteorology and hereI am trying to summarize the proverbial state ofthe art. Since I cannot hope to be completely up-to-date by the time this reaches the hands of thereaders, I have tried to give enough material tobring the interested reader to the point of a self-sustaining, self-education process. If the reader iscontent to absorb only what is in these notes, myeffort will not have succeeded.

While this preface is being written, Volumes IIand III are still embryonic. The reader will note

that there are many references to other parts of.the text within the body of these notes. Theseinternal references follow an outline-type ofstructure of the form I.III.A.3.b..., where theleading, underscored Roman numeral refers to thevolume number. This is omitted when thereference is within the given volume. The secondRoman numeral refers to the chapter in thevolume, the capital letter to the sub-heading, andso forth. Since the second and third volumes are

not yet finished, I can only promise that they willbe completed as rapidly as possible. Becausethese self-references generally concernamplifications or additional discussions of thereferenced topics, it should not he terriblydetrimental for them to be as yet unavailable. Ifthe material were essential, it would have been

included at that point in the notes.

The reader should also note that all footnotesin a given chapter will be collected at the end ofthat chapter. This is not the most convenientapproach, but it happens to solve a nasty problemin trying to fit these notes into a readable text. Myapologies for any inconvenience.

As in any large work, numerous contributorshave made these notes possible. The Chief of theTechniques Development Unit of NSSFC, Dr.

Joseph T. Schaefer, has perhaps been mostvaluable as an encourager (and occasionalpushes to complete this work are appreciated), asounding-board for many of the topics containedherein, an editor, and a respected colleague. Dr.Robert A. Maddox of NOAAs EnvironmentalResearch Laboratories, Office of WeatherResearch and Modification, has provided manyideas, inspiration, and the encouragement only akindred spirit can provide. The Deputy Directorof the National Weather Service Training Center,Mr. Larry Burns, gave me the initial support toundertake this effort and confirmed my perceptionof the need for it in the first place. Numerousindividuals have encouraged me by their interest,including Alan R. Moller (NWSFO, Fort Worth,Texas), Larry Wilson, Steve Weiss, Jim Henderson,and Mike Streib (all at NSSFC), as well as theusual host of those too numerous to mention.Valuable reviews were provided by Profs. Walter

J. Saucier, David A. Barber (North Carolina StateUniv.), and Richard J. Reed (Univ. of Washington).Naturally, any errors and misinterpretations are

my sole responsibility. Finally, Beverly Lamberthas suffered through the numerous revisions anddrafts and done an outstanding job with themanuscript preparation.

Charles A. Doswell III

Kansas City, Missouri

November, 1982


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Contents

I. Introduction ............................................................................................................................... 6

A. Preliminary Remarks .................................................................................................................. 6

B. Scaling Concepts ....................................................................................................................... 6

II. Upper-Air Data Analysis .......................................................................................................... 11A. General Remarks ..................................................................................................................... 11

B. Upper Air Char t Analysis .......................................................................................................... 111. Vertical Motion ........................................................................................................................................................... 12

2. Production of Unstable Thermodynamic Stratification ...................................................................................................... 17

3. Some Kinematic Considerations .................................................................................................................................... 21

C. Sounding Analysis and Interpretation ........................................................................................ 221. General Remarks ............................................................................................................. ............................................ 22

2. Sounding Thermodynamics ........................................................................................................................................... 23

3. Sounding Kinematics ................................................................................................................................................... 26

D. The Composite Char t ............................................................................................................... 30

III. Surface Data Analysis ........................................................................................................... 33

A. General Remarks ..................................................................................................................... 33

B. Sur face Discontinuities ............................................................................................................ 351. Cold Fronts ................................................................................................................. ................................................ 37

2. Warm Fronts ............................................................................................................................................................... 39

3. Stationary Fronts ........................................................................................................... .............................................. 40

4. Occluded Fronts .......................................................................................................................................................... 41

5. Drylines ..................................................................................................................................................................... 42

6. Land/Sea Breeze Fronts ...................................................................................................... ......................................... 45

7. Thunderstorm Outflow Boundaries ................................................................................................................................. 46

C. Boundaries Not Involving Air Masses ....................................................................................... 531. Wind Shift Lines .......................................................................................................................................................... 53

2. Pressure Troughs ......................................................................................................................................................... 54

D. Pressure Change Analysis ........................................................................................................ 551. Applications to Synoptic Analysis .................................................................................................................................. 55

2. The Isallobaric Acceleration .......................................................................................................................................... 553. Mesoscale Isallobaric Analysis ..................................................................................................................................... 57

E. Thermal Analysis ......................................................................................................................60

F. Terrain Ef fects ..........................................................................................................................611. Mountain/Valley Circulations ........................................................................................................................................ 61

2. Upslope Flow ................................................................................................................ .............................................. 62

3. The Low-Level Jet ........................................................................................................................................................ 62

4. Mesoscale Eddies ....................................................................................................................................................... 67

5. Miscellaneous Examples .............................................................................................................................................. 68

G. Flash Floods and Severe Weather ............................................................................................ 71

IV. Objective Analysis Tools ........................................................................................................ 74

A. Moisture Convergence ............................................................................................................. 74

B. Sur face Geostrophic Winds ...................................................................................................... 76

C. Filtering by Objective Interpolation ............................................................................................ 78D. Upper-Level Divergence ........................................................................................................... 78

E. Kinematic Analyses and Trajectories ......................................................................................... 79

V. Interpretation of Numerical Guidance ......................................................................................84

A. General Remarks ..................................................................................................................... 84

B. Short and Long Term Error History ........................................................................................... 85

C. Initialization and Adjustment ....................................................................................................85

D. Statistical Convective Weather Guidance .................................................................................. 86

VI. Concluding Remarks on Mesoanalysis.................................................................................... 88

REFERENCES .............................................................................................................................. 90


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I. Introduction

process of mesoanalysis, but the reader is urged topursue these topics further by consulting thebibliographic references. Some generaldiscussions of mesoanalysis are contained inFujita et al. (1956), Magor (1959), Tepper (1959),and Fujita (1963 . Pieces of the materialconcerning practical mesoanalysis are containedin the references, but to the author's knowledge,these have not been collected in one place. Thepresentation in these notes is essentiallyqualitative and non-mathematical, since a

rigorous discussion is not necessary to thepracticing mesoanalyst. Many ideas are presentedwithout proof, but it is hoped that the referencematerial will be consulted when doubts arise.

B. Scaling Concepts

Under the general heading of OperationalMesoanalysis in these notes, a substantial varietyof phenomena and concepts is presented. It isworthwhile to discuss this in terms ofmeteorological scales at the outset. It should beemphasized that the notion of scaling is absolutelyessential to understanding current and futuremeteorological thinking. We shall attempt toreview current concepts on scales, from that ofthe extratropical cyclone (ETC) down to thosephenomena at the observation limits of the presentnetwork of routine surface reports. One exampleof a proposed ordering of meteorologicalphenomena by scales is shown in Fig. 1.1.

The large-scale limit to our discussion can begiven by some arbitrary order of magnitudeestimates for scaling lengths (say, horizontallengths of 103 km, vertical depths of 10 km, andtime scales of 105 s [about 1 day]. Note that thesethree values, suitably manipulated (as in Haltinerand Williams, 1980), can yield approximatevalues for most of the terms in the equationsgoverning large-scale flows. The suitability of the

A. Preliminary Remarks

Operational mesoanalysis is most oftenconsidered in the context of convective storms.Mesosystems significant to operational forecastingdo not only encompass deep convection, as thepatterns of heavy snowfall sometimes suggest, forexample. Also, it is not clear that the process ofmesoanalysis for convective storms can betransferred totally for application to, say, winter

storms, although good analysis techniques arerequired in both areas. In any case, these noteswill not address mesoanalysis associated withnon-convective weather.

In order best to accomplish operationalmesoanalysis, one should have a thoroughunderstanding of synoptic-scale meteorology.Further, one should be familiar with convectivestorms and their dynamics. This is easy to say, butdifficult to satisfy. No one person has a completeunderstanding of either one of these areas,

especially the latter. Much remains to be learnedabout convective storm dynamics. Regrettably,there seems to have been a trend away fromsynoptic meteorology, both in the universities andwithin the operational arena as well (Doswell etal., 1981). Increasing dependence on numericalmodels has led to an overall decline in the skillsof the synoptic meteorologist (Snellman, 1977).Additional evidence for this decline can be seenin the frequent reference here to texts and journalarticles published in the 1950s. If more recent

references were available, they would have beenused, but the lack of interest in relating dynamicto synoptic meteorology (and vice versa) over thelast two decades has led to the paucity of morerecent references.

Realistically, these notes cannot provide aworking knowledge of both synoptic meteorologyand the dynamics of convective storms. Materialin these areas will be covered, as it relates to the


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manipulation hinges, in large measure, onknowing the answers we want before we begin.In other words, a formal scale analysis isessentially a way of justifying makingmathematical assumptions to describetheoretically a problem for which we alreadyhave observed the answer! In the process, we cangain insights which may have not been previouslyobvious, and considerable physical understandingcan be gained. Perhaps the most successfulapplication of scale analysis is in the problem ofour large-scale limit, the extratropical cyclone.

However, such a formal approach may not be theeasiest to understand from an operationalviewpoint and it suffers from a major deficiency:

namely, on our lower scale limit, we do not haveas clear a picture of the desired answer to beobtained. Instead, we consider a more physically-motivated way of establishing the scale ofphenomena which draws heavily from thediscussions by Emanuel (1980). By doing so, it ishoped that the reader can relate the discussion toobserved daily weather events and will thereforebe encouraged to pursue the topic as moreformally developed in the references (Holton,1979; Palmen and Newton, 1969; Haltiner andWilliams, 1980).

It is convenient that our upper scale limit is theextratropical cyclone, since that weather systemis probably the best understood. Without going

Fig. 1.1. Scale definitions and different meteorological phenomena with characteristic temporal and

horizontal spatial scales (after Orlanski, 1975).


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into details, the essential physical mechanismdriving the extratropical cyclone is known asbaroclinic instability. The phenomenon itself (theETC) was first described qualitatively by the so-called Bergen School (Bjerknes, 1919; Bjerknesand Solberg, 1921, 1922) via the Polar FrontModel. This is summarized in Fig. 1.2, which

shows the basic structure and evolution of anextratropical cyclone. A variety of explanationswere put forward to explain the underlyingprocess during the ensuing decades, but the lackof adequate upper-air data prevented anysatisfactory explanation for nearly 30 years. Then,the insights of Rossby (1940) and Charney (1947)provided the long-sought answer in quantitativeterms which have come to be known asbaroclinic instability.

This instability theory can be fairly easily

summarized without mathematics. We begin withthe fact that the north-south variation in solarheating results in a north-south temperaturegradient. With the observation that this gradient isnot uniformly distributed, but is concentrated inmid-latitudes, forming the so-called polar front,physical reasoning can be used to show that overthe front the westerly winds must increase withheight (with the increase being proportional to thestrength of the temperature gradient).1 Thisincreasing westerly wind with height, or verticalshear, intensifies as the unequal heating

continues. The extratropical cyclone forms as theprimary process by which this strong gradient isalleviated. In essence, the unequal heating storesup potential energy and when enough is stored upto trigger baroclinic instability, the developingcyclone draws on this reservoir of potentialenergy to drive the circulation (thus producing

kinetic energy). When the reservoir drops belowsome critical level, the system then begins todecay and the circulation slowly winds down.Along the way, the storm has moved warm airupward and northward, while cold air hastravelled downward and southward. Therefore,the flow has acted to relieve the strongtemperature gradients which initiated the system.

Fig. 1.2. Life cycle of extratropical cyclone (after J. Bjerknes, from Godske et al., 1957). In middlefigures, thin lines are sea-level isobars. Top and bottom figures show schematic clouds, frontal surfacesand tropopause along lines n, a little north and south of ETC center. The times from stages a to c andfrom c to e are roughly one day in each case.

Fig. 1.3. The balance of forces for geostrophic

equilibrium (after Holton, 1979). The pressure

gradient force is denoted by P and the Coriolis

force by Co,

while the resultant geostrophic wind is

Vg.


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One of the observationally verifiable notionswhich has allowed treatment of baroclinicinstability from a theoretical viewpoint is the basicvalidity of geostrophic balance on the scale of theextratropical cyclone. That is, the observed windsare pretty close to geostrophic, except perhapsnear the surface. This observation has been

incorporated in the analysis of extratropicalstorms under the general heading ofquasigeostrophic theory (see e.g., Holton, 1979,Chap. 6 and also II.B.1). Basically, the geostrophicwind is parallel to the isobars (or the contours, inpressure coordinates), with low pressure (heights)on its left, and with speed proportional to themagnitude of the pressure (or height) gradient (Fig.1.3).

However, one might easily be led to ask somepotentially embarrassing questions about this state

of balance. For example, if the geostrophic windis so good at approximating the true wind, how dopressure systems deepen (or fill)? If the windspeed happens to be non-geostrophic (i.e.,ageostrophic) for some reason, how do the windsand/or pressures re-adjust to geostrophy? Sincethe geostrophic wind is not divergent,2 can wesay then that vertical motion is unimportant forbaroclinic instability?

We shall not explore the answers to all thesequestions in these notes, but once again refer the

reader to the references. However, the subject ofhow the winds and pressure field come to adjustthemselves to a state of near-geostrophic balancehappens to be relevant to the issue of scale. Themanner in which the adjustment occurs dependson the scale of the pressure system (Rossby, 1938).Specifically, on the small scale, the pressure fieldchanges to fit the winds while on the largescale,the winds adjust the pressure field. But howsmall is small and how large is large? It turnsout that we can define a length scale called theRossby radius of deformation, lambda, which is

related to the problem of geostrophic adjustment.Physically, the adjustment is accomplished bygravity waves which travel at relatively fastspeeds. If we take this gravity wave speed anddivide it by the Coriolis parameter3 (the reciprocalof the Coriolis parameter defines a time scaleappropriate to geostrophic balance), we obtainthe Rossby radius of deformation. This can beinterpreted as the influence radius of the gravity

waves which accomplish the adjustment. Forlength scales much less than lambda, the gravitywaves have time to reach any point in the systemand they act to adjust the pressure field. Forlength scales much greater than lambda, gravitywaves can not penetrate the entire system and thewinds have time to adjust to the pressure.

Just how large is lambda ? It happens that lambdais about 1500 km, which is a length of the sameorder as that of the ETC. Since these disturbancesare neither much larger nor much smaller thanlambda , we can conclude that synoptic-scalesystems adjust both their wind and their pressurefields to maintain a state of near-geostrophicbalance. Such a conclusion should be readilyapparent to those who deal with the weatheroperationally. The Rossby radius of deformationalso provides a useful clue to the behavior of the

short wave troughs in the atmosphere, and thesmaller-scale features in the jet stream. Sincethese smaller features have lengths perhaps assmall as 300 km, one expects their pressure fieldsto react to non-geostrophic winds rather thanvice-versa. Again, operational experiencesupports this conclusion.

We have established our large-scale limit as theRossby radius of deformation. In doing so, wehave made a somewhat less arbitrary choice thanis often made, since it is based on well-accepted

theory and observational experience. That is,baroclinic instability (which is widely accepted asthe dominant physical mechanism in extratropicalcyclones) requires both wind and pressureperturbations to operate, limiting the scales ofthese weather systems to near the Rossby radiusof deformation.

Can we motivate a definition similarly for whatwe call mesoscale i.e., our lower limit ofconsideration in this section? The main issue indeveloping a physical-dynamical definition of

mesoscale is whether or not there exists adominant, scale-dependent instability whichforces mesoscale systems. Emanuel (1980) hassuggested the so-called symmetric instability forthis purpose, but he also leaves open thepossibility that other processes may exist and bephysically significant. His basic definition ofmesoscale is that on such a scale, both Coriolisaccelerations and ageostrophic advection areimportant.4 This approach seems entirely


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reasonable, and symmetric instabilities do,indeed, operate on such length scales (about 100km). Further, this scale definition turns out to lie atabout the resolution limit of operational surfacedata. Hence, this is probably the best choice forour lower scale limit, even if the dominantphysical process is not as clearly established as

on the larger scale.

It does seem clear that on scales below 100 km,the Coriolis acceleration becomes moredynamically irrelevant, while on scales muchlarger than 100 km, the ageostrophic contributionto advection becomes decreasingly significant.Quantitatively, this is accounted for by the RossbyNumber (R

o) the ratio of the actual to the

Coriolis acceleration. Thus, Ro

is small for lengthscales of 1000 km or more, and large for scalesbelow 100 km. Around 100 km, R

o~1, which says

that the Coriolis and actual accelerations areabout the same.

Theory suggests that for these intermediate scales,a wide variety of instabilities are possible and theactually occurring combination of parametersmay determine which process is most unstable ina given situation. This variety of theoreticalinstabilities is plausible when we realize that amuch greater range of phenomena is seen to existon the mesoscale than on larger scales. The ETCis by far the dominant form of weather system

operating at scales near the Rossby radius (at mid-latitudes), whereas we shall see that a lot offundamentally different phenomena occur in themesoscale range.

Further, it is not clear on this scale what sort ofdominant force balances exist, if any, analogousto geostrophic balance on the large scale.Hopefully, future research will provide someinsight into mesoscale instabilities and allow aclearer picture to emerge of what mesoscalereally implies about the dynamics of systems. At

this time, it seems plausible to suggest that frictionand latent heat are likely to have larger roles thanthey play in baroclinic instability. Since these twofactors have proven difficult to treat in theoreticalmodels, considerable time may elapse before wecan treat mesoscale processes on the same levelas we now deal with the ETC.

Finally, the density and frequency of upper airdata may well prove to be the barrier to our

mesoscale understanding that they once were onthe large scale. It is difficult for meteorologists toattempt an explanation of phenomena they havenot routinely observed, since the mathematics ofatmospheric flow allow a bewildering variety ofsolutions. Only by careful comparison withobservations can plausible theories be selected

from the vast array of candidates. Sincemesoscale observations are still not routinelyavailable, only limited conclusions can beredrawn from the limited mesoscale data.

CHAPTER I FOOTNOTES

1 I.B: This physical reasoning is based on theconcept of the thermal wind (see e.g., Holton,1979, p. 68ff and also II.8.2), which is in turn anapplication of the geostrophic wind law, validonly for large-scale flow.

2 I.B: This is not exactly true, as wc shall see inIV.B.

3 I.B: The Coriolis Parameter (often denoted byf) can be thought of as the vorticity of the earthabout the local vertical. Thus, at the north pole,

where the local vertical is also the earths rotationaxis, f is simply the earths vorticity (twice itsrotation rate, or 1.4584 x 10-4 s-1). Since the localvertical increases its departure from the earthsrotation axis as one moves away from the poles,the Coriolis parameter decreases with latitude,and vanishes at the Equator. The rate of decreasein f is slow at high latitudes (f is 1.0313 x 10 -4 s-1 at45 deg N), but increases rapidly, reaching itsmaximum at the equator itself. Coriolis parameterchanges signs upon crossing into the SouthernHemisphere so, for example, the Southern

Hemisphere geostrophic wind blows with lowpressure on its right.

4 I.B: In the case of large-scale motions justdescribed, the advection of atmosphericproperties is dominated by the geostrophiccontribution. In fact, this is a cornerstone ofquasigeostrophic theory.


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II. Upper-Air Data Analysis

satellite imagery to the synoptic scale analysisproblem.

A 4-dimensional understanding is possible, evenwith limited time constraints, using centrallyanalyzed charts at the standard upper levels. Asdetailed by Maddox (1979b), these upper air andsurface maps can and should be enhanced toemphasize features of importance to convectivestorm forecasting. At SELS, analysis of upper levelcharts is done by hand, as well. Althoughsubjective analysis has numerous drawbacks froma theoretical and aesthetic viewpoint, it is anexcellent way of accomplishing severalworthwhile goals. These include: (1) all of thedata are subjected to examination, thuspinpointing erroneous observations, convection-contaminated soundings, and so forth; (2) theprocess of redrawing lines forces an awarenessof the significant upper-air features; and (3) ananalysis of upper-air maps can be accomplishedwhich is oriented toward mesoanalysis i.e., theheavy smoothing necessary for large-scalemodelling purposes can be avoided. Many textsexist to help guide the process of synoptic-scale

analysis (e.g., Saucier, 1955; Petterssen, 1956a;Godske et al., 1957).

The forecast day generally begins with themorning (1200 GMT) soundings. The data at thattime are relatively free of convectivecontamination. This is somewhat less true in thelate spring and summer, when convection maycontinue through the night and on into the nextday (note the discussion by by Maddox, 1980b).Nevertheless, the morning analysis should allowthe forecaster to develop a relatively clear picture

of the synoptic-scale setting for the afternoonsand evenings developments.

B. Upper Air Chart Analysis

If the analyst has the option of contouring theconstant pressure level charts, rather than simplyenhancing the facsimile (or AFOS) products, the

A. General Remarks

It must be pointed out immediately that thenetwork of upper air observations is entirelyinadequate for any true mesoanalysis. Withroutine soundings over the U.S. only availableevery 12 h, at an average separation of about 400km, no analysis can be considered mesoscale.

Nevertheless, this is where mesoanalysis shouldbegin. It cannot be overemphasized that a

forecast should start with a 4-dimensional mentalpicture of the atmosphere. Thus, some of theanalysts most important efforts should be directedtoward developing this 4-dimensionalunderstanding. With the development andapplication of sophisticated remote sensing tools(specifically, radar and satellite imagery), newunderstanding of many aspects of convection hasbeen obtained rapidly. It should be completelyobvious that analysis should not be done withoutexamination of all the available data. The processof analysis is, in no small part, heavily dependent

on the skill of the analyst at integrating a varietyof data into a unified picture (i.e., a synthesis).Although these notes by themselves cannotprovide the reader with all the necessaryknowledge to interpret remote sensing data, someelements will be presented in those areas wheresuch data can be crucial in the analysis process.

Remote sensing data can have a real impact onthe upper-air analyses, in two related ways. First,the position and strength of upper air systems canbe refined, based on the cloud and precipitation

patterns. Second, and more importantly,information from the data-void areas (e.g., overthe oceans) may have a real impact, eitherdirectly (e.g., a feature in the Gulf of Mexicowhich can move onshore later in the forecastperiod) or indirectly (e.g., a misanalyzed shortwave trough which results in a faulty numericalprognosis [Hales, 1979a]). See Anderson et al.(1974) or Weldon (1979) for applications of


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basic process is relatively straightforward. At 850and 700 mb, the Severe Local Storms ForecastUnit of NSSFC (SELS) analyzes for height (30 mcontour interval), temperature (2 deg C isotherminterval) and dewpoint temperature (2 deg Cisodrosotherms, starting with 8 deg C at 850 mband 0 deg C at 700 mb). At 500 mb, heights (60 m

contours) temperatures (2 deg C isotherms) and12-h height changes (30 m isallohypses) areanalyzed. At 250 mb, isotachs (20 kt interval) andaxes of maximum wind are depicted. Examples ofSELS-type analyses shall be shown in III.V.

Within some limits, the development of this basicset of charts follows standard analysis practice(see Saucier, 1955, ch. 4). As described by Miller(1972), the analyst should avoid drawing closedisopleths whenever possible, even at theoccasional expense of creating long, narrow

ribbons. There is good evidence that theatmosphere really does tend to create suchfeatures and the basic idea is to emphasize thesource regions.

An important departure from synoptic scalepractice is a heavy emphasis on 12-h changes inthe observations. The SELS routines which plot theupper-air data provide a 12-h change for allplotted variables, including the winds. Rather thanemphasizing chart-to-chart continuity, the severeweather analyst needs to recognize the

significance of the chart-to-chart changes. Ofcourse, some effort should be made to developtime continuity, but the upper air data bythemselves are too sparse in space and time toprovide a clear picture of the often subtle featureswhich move through the synoptic-scale patterns.Short wave troughs, wind maxima, vorticitylobes and small-scale temperature anomaliesare frequently too small to be analyzed in detailunless 12-h height changes, backing/veeringpatterns of the wind, and thermodynamic changesare examined.

There are two complicating factors in evaluatingthe change fields: normal diurnal variations (e.g.,Harris, 1959) and the contamination of therawinsonde observations by convection. Theanalyst should know and recognize the expecteddiurnal changes (e.g., high 700 mb temperaturesat 0000 GMT over the mountains; roughly 20 m12-h height rises at 1200 GMT or falls at 0000GMT in mid-latitudes at 500 mb). While diurnal

effects are at least conceptually easy to accountfor, convection can produce large changes thatare less easy to adjust. Studies by Ninomiya(1971a,b), Maddox (1979a, 1980a), and othershave shown that large thunderstorm complexes(up to 500,000 km2, often lasting for 8 hr or more)can have a dramatic influence on even synoptic-

scale rawinsonde networks. Since the effects ofconvection cannot be isolated, the correction ofconvectively contaminated data is basically notpossible. Radar and satellite data should beexamined routinely during analysis so that theanalyst can exercise caution in interpreting thedata within convective regions.

Most, if not all, of the effort spent by a severeweather analyst forecaster in examining upper-airdata is directed toward finding where upwardvertical motion will occur in regions of moist,

unstably stratified air (Beebe and Bates, 1955).This being the case, the real job of analysis shouldbe directed toward this end, not merely drawinglines on the charts.

1. Vertical Motion

By way of introduction, one might ask thephysical reason for a meteorologistspreoccupation with vertical motion. The

production of weather requires condensationand the most common way the atmosphereproduces condensation is adiabatic cooling byexpansion. This results from lowering thepressure. Since in horizontal motion parcels tendto travel parallel to isobars, no important changein pressure results. Local pressure falls do, ofcourse, occur but their magnitude is so small incomparison to what is required to saturate parcelsthat their effect is not significant (but pressure fallsare important in other ways, of course; see III.D).Since pressure surfaces are so closely packed inthe vertical through the troposphere, a smallvertical displacement can result in a large changein pressure. Naturally, this is reflected in thenormal state of large-scale hydrostatic balance,where the relatively large vertical pressuregradient force is, compensated for by gravitationalacceleration. What small vertical accelerationsoccur are quite negligible in comparison, but stillare our primary source of weather. For


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meteorologists the physical significance ofvertical motion is ultimately the reduction ofpressure following a parcel which results incondensation.

In examining upper-air data to locate features, abasic problem is the diagnosis of regions ofupward vertical motion. Upward motion on thescale of the upper air data is in the range of a fewcm s-1 . This illustrates the essentially horizontalnature of large-scale flow, since the verticalcomponent can be less than a tenth of onepercent of the horizontal wind. However, sincethis upward motion is sustained for long periods, itcan have dramatic effects. If one maintains a 5cm s-1 upward motion for 24 hr, the net vertical liftis more than 4 km! Further, if the parcel started ata pressure of 1000 mb, that amount of lift reducesthe pressure to about 600 mb. Since the surface ofthe earth and the tropopause act effectively asbounding surfaces for vertical motions, a region ofupward vertical motion must have convergenceat its base and divergence at its summit. This is a

consequence of the law of mass continuity. Thus,divergence undergoes a change in sign withheight, leading to the concept of the so-calledlevel of nondivergence. Actually, this level israrely at the same height from place to place andtime to time. Rather, it is typically a slopingsurface (Fig. 2.1), as described by Charney (1947).Therefore, the axis of strongest vertical motionsmay be somewhat tilted away from the vertical.The interest in divergence is, therefore, an

extension of the need to assess large-scalevertical motion.

A basic effort in analysis is to infer upper leveldivergence from such features as short-wavetroughs, jet maxima, vorticity advection, and soforth (see McNulty, 1978; or Kloth and Davies-

Jones, 1980 for discussions on these topics).Owing to several difficulties, we often must relyon such subtle approaches to diagnosedivergence. One basic problem is that we haveavailable only 12-hourly samples: in the morningwhen mesosystems may not be well developed,and again in the evening when convection isusually already underway. Organized regions ofupper-level divergence are hard to follow as aresult. Another, frequently mentioned problem isexemplified if we consider a 5 cm s -1 upwardmotion at a height of 5 km. This implies that the

average low-level convergence in the layer fromthe surface to 5 km is 10-5 s-1. This, in turn,suggests horizontal wind differences in the rangeof 1 m s-1 over a distance of 100 km. Smallchanges in the data (say 10% of the observedwind speed) can result in a large change (in therange of 100%) in the calculated divergence and,hence, the vertical velocity.

Given the small magnitude of synoptic-scalevertical motion and the modest changes inhorizontal wind needed to produce it, the role of

quasigeostrophic theory becomes more clear. Formost purposes, and specifically for horizontaladvection, the geostrophic flow is good enough.The divergence needed for vertical motion is notcontained in the geostrophic wind, but the theorycan be used to evaluate it. In effect, the verticalmotion is the result of a secondary flow (muchweaker) which is required to maintain a state ofnear-geostrophic (and hydrostatic) balance. Thissecondary circulation is a cornerstone ofquasigeostrophic theory (and explains why theterm is quasigeostrophic) and its validity is seen in

its value for diagnosis of real weather systems.

Vorticity advection is widely accepted as anindirect means of locating large-scale upwardmotion. By vorticity advection, we mean a patternof height contours and vorticity isopleths as shownin Fig. 2.2. For this indirect method to work, avariety of assumptions is necessary. The first twoassumptions are that the actual winds are closelyapproximated by the geostrophic winds (which

Fig. 2.1. Vertical cross section (after Fleagle,

1948) of horizontal divergence relative to trough

and ridge lines (dotted and dash-dotted lines,

respectively). Divergence contours in units of 10 -6

s-1.


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parallel the contours) and that the vorticity field isderived from the height field (i.e., is essentiallygeostrophic) and so is moving slower than thewinds. Under these restrictions, a parcel movesthrough the vorticity pattern, and finds its originalvorticity different from that of its environment.Another assumption is that the basic process bywhich the parcel changes its vorticity isdivergence (or convergence), so if a parcel ismoving into regions of lower vorticity (as in aregion of positive vorticity advection [PVA]) theremust be a tendency for divergence to bring theparcels vorticity down to that of ite environment.

Petterssen (1956a, p. 299ff) presents the PVAarguments as follows: at lower levels, vorticityadvection is weak since the flow is very nearlyparallel to the vorticity isopleths. Therefore, atthose levels, vorticity changes are dominated bydivergence effects. Regions of increasing vorticity

must be convergent (and vice versa) at low levels.At upper levels, vorticity advection is large butlocal changes are small in comparison. Air passesthrough the vorticity pattern since wind speedsare high, so the arguments (above) apply whichsuggest that PVA implies divergence. At middlelevels (500 mb), divergence is small and vorticityis very nearly conserved local changes invorticity are dominated by advection. Historically,this is why 500 mb was chosen for earlynumerical forecasting models (the Barotropicmodel). Vorticity changes implied by PVA at 500mb produce convergence below and divergenceabove that level - hence, vertical motion.Panofsky (1964, p.114ff) also gives an excellentdescription of how to infer vertical motion fromvorticity concepts.

This simple physical picture is subject to manyrestrictions because so many assumptions are

Fig. 2.2. Schematic showing vorticity advection by the geostrophic wind (Vg). Solid lines are height

contours (z), dashed lines are contours of absolute vorticity (in units of 10 -5 s-1). Where the height and

vorticity contours intersect, they form quadrilaterals (with curved sides). The strength of the advection is

proportional to the number of such quadrilatarals per unit area. Where vorticity and height contours are

parallel, no advection is occurring. The hatched quadrilateral is in a region of negative vorticity advection

(NVA) by Vg, since V

gis pointing from lower to higher vorticity. The stippled quadrilateral is in a region of

positive vorticity advection (PVA) by Vg.


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involved. Although the winds are not usually toofar from geostrophic, it is often those cases oflarge ageostrophic departures which producesignificant weather [recall the geostrophic wind isessentially non-divergent!]. Also, occasionally,the vorticity pattern may move faster than thewinds, reversing the convergence/divergencepatterns associated with vorticity advection.Finally, it is not at all clear that 500 mb levelparcels conserve their vorticity, that divergence isthe only mechanism by which parcels changetheir vorticity, and that 500 mb is always near the

level of nondivergence.

Nevertheless, in spite of all these potentialproblems, PVA patterns often prove useful. Thecareful analyst should be aware of those situationswhere PVA is less likely to tell the whole story. Anexcellent discussion of large scale vertical motioncan be found in Holton (1979, p. 136ff.). In thisdiscussion the role of PVA in producing verticalmotion is clarified. Specifically, there are two

sources for vertical motion in quasigeostrophicsystems. Rising motion is proportional to (a) therate of increase with height of PVA and (b) thestrength of warm thermal advection.1

Note that PVA must increase with height forupward vertical motion to result. This is anessential consequence of the law of masscontinuity we have described and is consistentwith the physical picture presented above. If thedivergence (related directly to PVA) does notincrease with height, then the air is not likely tobe rising, even if PVA exists at the standard 500mb level. Hales (1979b) has recently emphasizedthis important point.

The contribution of warm advection to upwardmotion is often neglected. The physicalsignificance of this effect can be described in avariety of ways. Consider the well-knownrelationship that the thickness of a layer (usuallybounded by pressure surfaces) is proportional tothe mean temperature in that layer. Thus, warmadvection is essentially related to thicknessadvection. A common situation wherein warmadvection plays a role is with a warm front. Thesoutherly flow, nearly perpendicular to thethickness contours, produces strong warm(thickness) advection, which tends to increase thethickness at a point. The vertical motion (upward)acts to cool the column by lifting and, therefore,

tends to compensate for the warming. Upwardmotion induced by warm advection is oftenerroneously attributed to overrunning.

Most of the confusion about overrunning andthe effects of warm advection result from taking a2-dimensional, rather than a 3-dimensional view.Fig. 2.3 shows a cross section through a frontalzone, with potential temperature (theta) surfaces(isentropes). The actual winds are acting to pushthe theta surfaces from left to right, by advection.However, the vertical motion also acts to lift those

surfaces, which displaces them opposite to thecontribution by advection. If the 3-dimensionalwind happens to be exactly parallel to the thetasurfaces, there is no horizontal movement, despitea horizontal wind component across the surfaces.In general, the flow is not exactly isentropic,usually giving a net horizontal displacement lessthan the normal component of the horizontalwind. This also explains why warm fronts tend tomove more slowly than cold fronts. It happens that

Fig. 2.3. Schematic illustration of how the 3-

dimensional wind acts to displace isentropic (theta

= constant) surfaces. The effect of the horizontal

wind component (\VH

) is to push the theta surfaces

from left to right. Three different vertical

components are illustrated; \V1

is the typical

example, which makes the theta surfaces rise,

displacing them from right to left at any given level,

such that the net displacement is less than thatindicated by the \V

Hcontribution, but still from left

to right. In the second case, \V2

is such that the 3-

dimensional flow is parallel to the theta surface,

yielding no net displacement. For the third case,

which is rare, the vertical component of \V3

is so

large that the net displacement by vertical motion is

larger than the \VH

contribution, giving a net

movement from right to left.


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analysis on isentropic surfaces is a good way tosee this on a 2-dimensional chart, subject to thelimitation that the actual flow may not be exactlyalong isentropes. Note that in some unusualcases, the contribution by vertical motion canexceed that by advection, so the front couldback up, into the horizontal flow!

Recently, Trenberth (1978) and Hoskins et al.(1978) have pointed out that the PVA andthickness advection effects have a tendency tocancel each other. This can also be seen in thediscussion by Holton (1979, p. 139). Trenberth hasproposed a solution to this dilemma by using theadvection of vorticity by the thermal wind. Thosefamiliar with the pioneering work of Sutcliffe (e,g.,Sutcliffe, 1947 or Sutcliffe and Forsdyke, 1950)should recognize this approach. This requiresdoing the same thing that is currently done withPVA, but using thickness contours (to infer the

thermal wind) rather than height contours.Sangster (personal communication) has verifiedthe validity and value of this approach on a day-to-day basis. Sangsters estimates of 850 and 700mb vertical motion are derived by using thevorticity and isotherms at each level. Theisotherms at each level ought to be fairly goodapproximations to thickness contours (for a layercontaining that level), so this is quite similar tovorticity advection using the thermal wind.

Since this revised method for locating areas ofupward motion includes both the PVA and thermaladvection terms, it has clear advantages. WithAFOS, overlaying the thickness and vorticityfields is relatively simple.

There are other ways to estimate the verticalmotion field, including the model output fields,which show forecast vertical motion directly.Since the model-generated vertical motion

Fig. 2.4. Vorticity advection by the thermal wind (VT)

. Thickness countours (T) are dashed lines, while solid

lines are contours of absolute vorticity (as in Fig. 2.2). Note that thickness contours and height contours

usually do not coincide, so that VT

differs from Vg.


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patterns are not perfect, it is in the analyst/forecasters interest to have as many differentestimates of where upward motion is (or is goingto be) occurring as possible. This includesempirical rules as well as more objectivemethods, since no single approach appliesequally well under all conditions. Most severe

convection depends on larger-scale forcing todevelop (and/or maintain) its severity. It is worthnoting that this supportive large-scale upwardmotion may not always be obvious fromindications in mid-troposphere (about 500 mb).There is evidence (e.g., Hales, 1979b) that duringthe warm season, the upper support may onlybe detectable above 500 mb. Also, the forcingcan be confined to levels below 500 mb (Doswell,1977; Maddox and Doswell, 1982), as well.However, it should be recalled, that upperdivergence and lower convergence are mostfrequently related, as we have discussed. This isan essential element in the work of Uccellini and

Johnson (1979), in which the coupling of upperand lower jet streaks is stressed, and which isdiscussed further in III.F.3.

2. Production of Unstable ThermodynamicStratification

Vertical motion, by itself, obviously is insufficientto develop severe thunderstorms or heavyconvective rain. In fact, large-scale vertical

motion produces large-scale regions ofcondensation. It can be argued that the major roleplayed by large-scale upward motion is toprepare the environment for convection. Onebasic property of convection is that it requires anunstable thermodynamic stratification.2 Therefore,a substantial effort in the interpretation of upper-air charts is directed also toward questions of theinstability of the air mass. Note that it is unusualfor severe storms to occur in a true air massregion, i.e., one with horizontally uniformproperties. Thus, it is somewhat misleading to

speak of the unstable air mass in which severeconvection develops. This is especially the casesince the vertical structure associated with severestorms (to be discussed later) usually revealsdifferent source regions for the air at differentlevels.

Fig. 2.5. Schematic illustration of differential advection (after Newton, 1980). Frontal symbols are

conventional. Long-dashed lines are 500 mb isotherms while short-dashed lines are isotherms of low-level

parcels lifted to 500 mb (proportional to theta-w). Note that the eastward progression of the 500 mb thermal

trough and the northward progression of high theta-w air at low levels creates a condition of instability at

time to### + dt### in the hatched region. That is, low-level parcels in the hatched region, when lifted to 500

mb, are warmer than their environment.


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The means by which the classic severe stormsounding develops is often the result of a processof differential advection. This process, describedby McNulty 1980, Whitney and Miller (1956), andAppleby (1954) among others, is simply the resultof vertical differences in the horizontal advectionof atmospheric properties (see Fig. 2.5). If

differential advection acts to warm the lowerlayers relative to those above (or, equivalently, tocool the upper layers relative to those below), theresult is a net decrease in the stability of the aircolumn. Typical values in severe weathersoundings suggest that differential advection mayincrease the lapse rate of a sounding by as muchas 1 deg C km-1 every 3 hr (recall the dryadiabatic lapse rate is about 10 deg C km -1). Asevidence of the importance of instability changes,Newton (1980) has shown that an average parcelbuoyancy increase of 1 C over the depth of thetroposphere cap increase the cloud maximumvertical velocity by 7-12 m s-1.

Further, if differential advection results in a netmoistening of the lower layers, and/or a net dryingof the middle and upper troposphere, theconvective potential is also enhanced. In fact, anincrease in moisture content by 1 g kg-1 is aboutequivalent to increasing the temperature by 3.5deg C, if all the latent heat ran be released.McNulty (1980) has combined the influences oftemperature and moisture by considering thedifferential advection of wet-bulb potentialtemperature (theta-w)3 , since convectiveinstability is defined to exist when wet-bulbpotential temperature decreases with height.McNultys study was not directed beyond theshort-range correlation of differential advectionwith observed severe storms, so no clear-cutresults concerning the relationship were found.Nevertheless, over a period of days, differentialadvection must play a substantial role in creatingareas of unstable stratification. In most cases, the

modification of stratification necessarily involvesthe process of differential advection. This does notimply that, once a basically unstable region hasdeveloped, differential advection is an ongoing,important process. McNultys conclusions supportthis view, since he suggested that during thespring, differential advection is not effective atseparating non-severe from severe storms, while itis more valuable at separating convective fromnon-convectiveregions. Because instability is

confined to relatively small regions during thespring, the additional destabilization fromconcurrent differential advection was notsignificant. In summer, the opposite conclusionwas drawn i.e., differential advection isvaluable for delineating areas of severe weather,

but not effective for locating convective regions.As NcNulty states (1980, p. 288), in summer,Further destabilization is unnecessary forconvection and appears to contribute only tosevere convection development.

When discussing differential advection, it isperhaps appropriate to digress briefly andexamine the concept of the thermal wind. If oneexamines the upper air charts, it is quite clear thatthe height contour pattern (and hence, thegeostrophic wind) generally varies with height at

any given location. The difference between thepatterns at any two levels is simply the thicknessbetween the pressure surfaces. A relationshipknown as the Hypsometric Law can be stated asfollows: the thickness between any two pressuresurfaces is proportional to the mean virtualtemperature4 in that layer (see Table 1). Thus, thethickness contours can be regarded as isotherms,as we have already mentioned.

Since the contour patterns change with height, sothen does the geostrophic wind. By definition, the

change in the geostrophic wind with height is thethermal wind.5 Figure 2.6 shows how the thermalwind can be derived from the geostrophic windsat two pressure levels. Observe that we have twoquantities which are related to the change ofcontour patterns with height: the thickness and thethermal wind. It is logical to assume that thesequantities are related in some way to each otheras well. This is, in fact, the case. Specifically, thethermal wind blows parallel to the thicknesscontours (i.e., to the layer average isotherms),with speed proportional to the thickness gradient,

and with low thickness (temperature) to its left.This is totally analogous to the geostrophic windsrelationship to height contours (recall Fig. 2.4).

So how does all of this apply to the subject ofdifferential advection? Examine Fig. 2.6 andconsider the winds relationship to the thicknesscontours. If these contours are given theirinterpretation as isotherms, then it can be seenthat there is a component of the winds in the layer


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Table 1. Factors, which when multiplied by the mean virtual temperature (Tv) in a layer for which the

bounding pressures have the given ratio, yields the thickness (in m) of that layer. Thus, for example if Tv

=

0 deg C = 273.16 deg K in the 850-700 mb layer, then the thicknees dZ### is simply 5.687 x 273.16 =

1553.5 m.

Pressure RatioP

bot/P

topExamples Factor

2.0 (1000/500, 500/250, etc) 20.3021.70 (850/500) 15.5421.6667 (500/300, 250/150, etc) 14.9621.50 (300/200, 150/100, etc) 11.8761.4286 (1000/700) 10.4471.40 (700/500) 9.8551.3333 (400/300, 200/150, etc) 8.4261.25 (500/400, 250/200, etc) 6.5361.2143 (850/700) 5.6871.20 (300/200) 5.3401.1765 (1000/850) 4.760

which is blowing across the isotherms. Thiscomponent, curiously enough, is the same ateither level! That is, the normal component (to theisotherms can be determined from the geostrophicwind at either level. The implication is that achange in geostrophic wind direction with heightis always associated with thermal advection. Asshown in Fig.2.6, when the geostrophic windbacks with height (turns counterclockwise , cold

advection is implied, while veering of thegeostrophic wind with height indicates warmadvection. Perhaps now the reason for thisdigression is clear. Thermal advection canactually be diagnosed simply by examining thechange in the contour pattern with height, even ifisotherms are not available. In fact, subject to thelimitation that the real wind may differ markedlyfrom geostrophic (especially at low levels), onecan infer temperature advection merely byknowing the profile of winds aloft, over a singlestation! See also Oliver and Oliver (1945) formore details.

Given the geostrophic thermal advectioncontribution through several layers (or at severallevels), one might be tempted to conclude thatone could diagnose the differential thermaladvection. After all, advection at any level isdominated by the geostrophic contribution.Unfortunately, this does not work. One cannotinfer destabilization when the 850 mb geostrophic

Fig. 2.6. Schematic illustration showing

temperature advection as implied by the change in

geostrophic wind with height. Geostrophic winds atthe lower and upper levels are denoted by V

Land

VU, respectively, while the resultant thermal wind is

given by VT. Implied thickness contours are shown

by dashed lines. The component of either VL

or VU

normal to the thickness lines is VN

. In the case

where the geostrophic wind veers with height (turns

clockwise in the Northern Hemisphere, warm

advection is implied. Conversely, winds backing

with height imply cold advection.


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thermal advective change is positive and thecorresponding 500 mb term is negative. In orderto see why this is so, consider how thegeostrophic advection changes with height. Sincethe geostrophic wind change is simply the thermalwind, which is parallel to the layer meantemperatures, the differential advection by the

geostrophic wind must essentially vanish.Therefore, differential advection must beaccomplished by the ageostrophic wind. Whilethe ageostrophic wind may not be the largest partof the wind itself, it has two very important roles --it supplies the significant divergent part of thewind field and it provides the means to changethe stratification via differential advection. Anexcellent discussion of how changes in stabilityoccur can be found in Panofskys (1964, p. 105ff)textbook.

As a final observation on differential advection, ithas often been suggested that cold air advectionat, say, 500 mb is an important contributor tosevere weather potential. Observations do notsupport this on a day-to-day basis. While casestudies certainly exist (e.g., Barnes, 1978) whichshow that cooling aloft as a result of coldadvection did play a role, it is more frequentlyfound that the environmental soundings show onlyweak thermal advection at 500 mb (either warmor cold) in the threat area. This is especially trueduring the late spring and summer (Hales, 1982).

A major contributor to the development ofinstability is the large-scale vertical motion itself.Regions undergoing large-scale lifting mustnecessarily approach an adiabatic lapse rate. Thedemonstration of this is available in any textbook(e.g., Hess, 1959, p. 102). By means of lifting,even an initially stable environment can becomefavorable for convection.

Since the classic pre-severe storm sounding(discussed in Miller, 1972) often has an inversion

capping the moist layer, the lifting process may beessential for development of storms even whenthe atmosphere is already convectively unstable.For the typical storm environmental sounding,about 6 h of synoptic-scale lift (at about 5 cm s -1)is capable of eliminating the cap (i.e., about 1 kmof net vertical lift).

Note that the negative area for the soundingassociated with the cap can be interpreted in an

interesting way. This area happens to beproportional to the square of vertical motion(Petterssen, 1956b, p. 136)! That is, for negativeareas, an upward vertical motion equal to thesquare root of twice the area is needed to cancelthat amount of negative buoyancy.

When the capping inversion is too strong to bebroken by the available sources of lift, noconvection may occur even under conditions ofextreme instability above the inversion. Thus, acoupling between dynamics andthermodynamics frequently must be present forsevere storms. The capping inversion acts toenhance severe potential by confining moisture tolow levels (Williams, 1960; Carlson and Ludlam,1968) until it can be released. Although daytimeheating from below may sometimes be sufficientto eliminate the inversion, the unmistakable

relationship between severe thunderstorms andsome source of upward motion (fronts, short-wavetroughs, etc.) suggests that in most cases, theinversion is eliminated by lifting.

It should be pointed out that layer lifting in thetraditional sense described by Hess occurs onlyfor layers of small thickness. That is, the processHess describes involves lifting the top and bottomof a layer by an equal amount. While thiscertainly has the effect described, one shouldremember that vertical velocity normally has its

largest magnitude in middle levels (say, around500 mb). Thus, layers of significant thickness willundergo stretching (or compression) whichamplifies any changes in stability. Further, it isworth emphasizing that the more stable the layeris to begin with, the greater is the change in itsstability as a result of lifting and stretching. Ineffect, the large-scale lifting process tends to drivelapse rates toward the dry adiabatic value. Alayer which is already stratified nearly dryadiabatically will not undergo much change,whereas a very stable layer is altered rapidly by

the lifting and stretching mechanisms.

Clearly, the source of vertical motion can be ondifferent scales in different situations. A case likethat of April 3-4, 1974 (Hoxit and Chappell, 1975)may be driven by large-scale lifting process.Doswell (1977) has shown that at timessubsynoptic scale lifting may provide the meansfor breaking the inversion. Beebe (1958) haspresented serial soundings where the inversion


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clearly rises and the moist layer deepens in amesoscale area. As the scale of a translatingvertical motion source decreases, the requiredaverage upward speed must increase, since it hascorrespondingly less time to act. That is, the timescale generally decreases with size scale.Mesoscale systems can develop vertical motions

in the range of several m s -1, but their life cyclescan be completed in 6 h. Naturally, such detailcan be unavailable to the operational forecaster,but it is clear that the existing instability (say, at1200 GMT) in a region may not reflect accuratelywhat the sounding will look like at the time ofconvection. The Lifted Index6 (Galway, 1956)represents an adjustment of the soundingsstability parameter to account for diurnal heating.The analyst/forecaster needs to provide furtheradjustments based on the upper level charts, usingthe concept of differential advection and thepossible effect of vertical motion.

3. Some Kinematic Considerations

As discussed before, many empirical rules forinterpretation of upper level winds are indirectefforts to diagnose and forecast vertical motion.

McNulty (1978) and Kloth and Davies-Jones(1980) have evaluated several of these ideas, asrelated to jet maxima. Hales (1979b) hasconsidered the use of anticyclonic (horizontal)shear in this context. It is pretty clear thatmesoscale features exist aloft, even ifconventional rawinsonde data are generally

insufficient to reveal them. This insufficiency isrelated to the data density, to errors in the data(which tend to increase with height), to roundingwinds to 5 deg direction intervals, and to theanalysts bias toward recognition of winddirection changes more readily than actual vectorwind changes. The smaller scale details of thewind field can be inferred to some extent from thesatellite images, especially when animated loopsare available. The basic principle involved is thatwhere there is cloud, there is upward verticalmotion, and where there is vertical motion there issome feature which is forcing it (see Doswell,1982a).

Perhaps the most successful application of thisprinciple is the location of the jet stream axis(Whitney et al, 1966; Whitney, 1977). However,the often very sharp cloud edge near the jetstream axis (e.g., Fig. 2.7) may not be the result of

Fig. 2.7. Visible (a) and enhanced infrared (b, next page) satellite images showing anticyclonically curved

band of cirrus across Texas, Oklahoma, southeastern Kansas and Missouri. Such bands are associated

writh upper level jet streams, with the jet axis from 1 deg to 5 deg poleward of the sharp cloud edge.

a b


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the deep vertical motions associated with jetstream secondary circulations (such as thosedescribed by Cahir, 1971). Rather, the edgemechanism appears to be an interface betweenshallow vertical circulations, basically confined tocirrus levels (Weldon, 1975). Details of thismechanism remain unclear.

Unfortunately, conventional data do not alwaysrelate well to cloud masses observed in satelliteimagery. An interesting phenomenon whichreveals the type of problems inherent in satelliteinterpretation is the large mesoscale convectivecomplex (MCC) described by Maddox (1980b)(e.g., Fig. 2.8). As the MCC grows to maturity ithas an increasingly obvious influence on therawinsonde-sensed observations. Thedevelopment of a diverted flow around thenorthern side of an MCC creates the illusion of a

short-wave trough or vort max upstream,which may have no previous or subsequenthistory. It is an effect rather than a cause,since it has a convective origin. In order todiscriminate valid mesoscale features in the largerscale fields, the satellite imagery should, ifpossible, be supplemented with corroborativeconventional data.

C. Sounding Analysis andInterpretation

1. General Remarks

Part of the early morning upper-air analysis shouldinclude an examination of plotted soundings. Thissubject has also suffered from declining interest,along with other aspects of synoptic meteorology.It seems obvious that considerable usefulinformation is available in the soundings. Anabundance of literature (Showalter, 1953;Fawbush and Miller, 1954b; Galway, 1956;House, 1958; Prosser and Foster, 1966; Miller,1972; Doswell and Lemon, 1979) exists whichstresses the detailed vertical structure, boththermodynamic and kinematic, of the

environment in which convection develops. Anautomated sounding analysis, such as thatproduced at SELS (Doswell et al., 1982), can helpto decide which soundings to examine. However,such parameters as moisture depth, inversionstrength, and wind directional variation aredifficult to automate and can be helpful indeveloping a clear picture of the synopticsituation. Nothing can or should replace anexamination of the individual soundings. Such anexamination can also help to evaluate and correctany erroneous data that may have crept into theconstant level analyses.

Newton (1980) has presented the three types ofsoundings associated with thunderstorms (Fig.2.9). Newtons Type A corresponds to Millers(1972) Type IV tornado air mass, which isgenerally characteristic of High Plains severeweather situations. Newtons Type B is MillersType I tornado air mass, which is the classicalloaded gun sounding of the Great Plains.Finally, Newtons Type C corresponds to MillersType II tornado air mass, typically identified withthe Gulf Coastal regions of the southeasternUnited States. Newton does not explicitlydescribe Millers Type III sounding and itssimilarity to the Type II profile (except for lowertemperatures) suggests that it is a subset of theType II (or Newtons Type C) situation.

Fig. 2.8. Enhanced infrared satellite image

revealing Mesoscale Convective Complex (MCC)

over Illinois and Indiana.


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2. Sounding Thermodynamics

First consideration of sounding analysis is anassessment, usually via a single parameter, of thestability of the thermodynamic stratification. Thismight be the Showalter Stability Index (Showalter,1953), the Lifted Index (Galway, 1956), or theTotals Indices (Miller, 1972). These parameterskey on the amount of buoyancy available to alifted parcel at 500 mb, and have been in use for a

considerable time. The SWEAT index developedby Miller (1972) attempts to incorporate somekinematic properties, specifically the shearbetween 850 and 500 mb. The need for and valueof these parameters are well-known and arestraightforward.

There are other factors which can be evaluatedfrom the soundings, some of which are not soeasily automated. One important example is thedepth of the moist layer. While some soundingstypify the classical loaded gun severe weather

sounding (Fawbush and Miller, 1954b) in that theyhave a well-defined, inversion-capped moistlayer, surmounted by a substantially drier layerwith a steep lapse rate, this is not always thecase. The depth of the moisture has a large impacton the subsequent events. If the moisture is tooshallow (say, less than 50 mb deep) there may beinsufficient water vapor to support severeconvection. If the moist layer is exceptionallydeep (say, 200 mb or more), the likelihood of non-

severe heavy rainstorms is greater. Further, asdescribed in Schaefer (1974a), moist layer depthhas a dramatic influence on dryline motion (seeIII.B.5).

The occasional occurrence of a very deep layerof essentially saturated conditions to, say, above500 mb can result from convection contaminationand, hence, be unrepresentative. However, it alsocan indicate some severe potential, especially inthe southern part of the United States (Newtons

type C). In many such cases, the occurrence ofdry air aloft upstream from the threat area iscommon (Miller, 1972). This dry air typically hasarisen from subsidence (but may have otherorigins e.g., Carlson and Ludlam, 1968) andthus is also relatively warm, so a dry intrusion isfrequently also indicative of warm advection (seeIII.E). The complete absence of dry air generallyimplies an increase in heavy rain potential and acorresponding decrease in the likelihood ofsevere thunderstorms.

However, moisture aloft in the absence of low-level moisture does not preclude severe weather,since high-based severe storms in such a situationare not uncommon, especially in the High Plainsregion of the United States (Newtons type A). Asimple argument can show that such storms havea high potential for strong surface wind gusts.Further, when a shallow, surface-based moistlayer is found in such soundings, tornadoes canresult from High Plains thunderstorms (Doswell,

Fig. 2.9. Schematic of three distinctive soundings associated with severe convection in the U.S. (after

Newton, 1980). Type A is an inverted V sounding typical of the High Plains or desert severe storms. Type

B is the classical. loaded gun sounding characteristic of Great Plains or central U.S. severe weather

outbreaks. Type C is common over Gulf coastal states and in summer east of the Mississippi River. Dash-

dotted lines correspond to moist adiabats associated with low-levels and dashed lines to moist adiabats in

lower middle levels (600-700 mb).


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1980, Mahrt, 1977) since a few storms may beable to tap this low-level moisture by developingupdrafts with surface roots.

The reader should have realized by this time thatthe existence of dry air, generally in the mid-troposphere, is an important factor in much severeconvection. This has long been recognized(Ludlam, 1963). It appears that the enhancementof the downdraft potential, created by evaporationof cloud and precipitation into dry environmentalair, plays a key role in developing the stormstructures associated with severe weather (Lemonand Doswell, 1979),

Although it is not easily evaluated from a simpleplotted sounding, the vertical profile of wet-bulbpotential temperature (theta-w) is worth someexamination, Since theta-w incorporates bothtemperature and moisture, its vertical distributionprovides key clues about convective instability. Infact, by definition, if theta-w decreases withheight in a layer, that layer is convectivelyunstable. As noted previously, the loaded gunsounding is the archetypical example ofconvective instability, since its moisture andtemperature profiles combine to produce aminimum in theta-w in middle levels.

It has been argued that the difference between thetheta-w minimum at mid-levels and the theta-wmaximum at low levels (often at the surface)represents the total energy available to a severestorm (Darkow, 1968; Morgan and Beebe, 1971).This concept has been tested by Doswell andLemon (1979). They found that, for a sample ofsevere thunderstorm environmental soundingsbefore and then near severe storm occurrence, aparameter based on this difference did not seemtoo effective at delineating the region of mostsevere convection. However, they note thatduring the time from the sounding well before thestorm to the sounding closest to storm occurrence,

the minimum theta-w value actually increasesslightly (about 1.5 deg C) and the height of theminimum rises (by about 80 mb). This can beinterpreted as a reflection of the action of upwardvertical motion. That is, the moist layer deepensand rises during the period before storms (Beebe,1958).

Another factor that should be evaluated fromselected soundings is the so-called negative area

in the lower part of the parcels ascent profile. Ifthe parcel is negatively buoyant, energy must besupplied to lift the parcel through those layers. Assuggested earlier, negative area can act toenhance severe potential by capping the releaseof energy until the optimum time (usually near thetime of maximum surface heating). The Lifted

Index can account for the contribution of surfaceheating to cap erosion by using a forecastmaximum surface temperature. When substantialnegative area remains after accounting for diurnalheating (if applicable -- at 0000 GMT, surfacecooling will occur), the forecaster/analyst shouldtry to determine whether there is a source ofsufficient lift (e.g., a source of low-levelconvergence or some feature supplying upwardmotion) to eliminate the cap (recall II.B.2, above).

Also valuable in operational study of soundings is

the determination of the equilibrium level for therising air parcels. The equilibrium level (EL) iswhere the rising, buoyant parcel re-crosses theenvironmental sounding curve. It is this level,rather than the tropopause, that is physicallysignificant. Anvil cloud material tends toaccumulate here, rather than at the tropopause,since it is where rising parcels are (naturally) inequilibrium with their environment. Penetrationsof the EL are indicative of strong updrafts, and theEL can be well below, near, or well above thetropopause. Naturally, depending on thecharacteristics of the tropopause, a storm whichreaches above the tropopause is usuallysignificant. However, when the EL is far belowthe tropopause, storms with tops which remainbelow the tropopause can still be severe (Burgessand Davies-Jones, 1979). Similarly, a storm whichpenetrates the tropopause may still be below theEL .

Positive area should also be evaluated. If a smallcalculator is available, the positive area can bedetermined from the hypsometric equation as the

difference in thickness between the observedheights and the heights using the parcel ascentcurve (between the LFC and the EL). As discussedearlier, this can be used to determine the parceltheory vertical motion associated with the amountof positive area. Such a vertical motion speed isgenerally an overestimate (see II.II.A), but isrepresentative of peak updraft speeds in the mostsevere storms.


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In the past, some attempts have been made toforecast the maximum gust potential and/or themaximum hail size possible with a given sounding(Foster and Bates, 1956; Foster, 1958; Fawbushand Miller, 1954a; and Fawbush and Miller, 1953).Doswell et al., (1982) suggest that the automatedestimates previously used in SELS (Prosser andFoster, 1966) do not have much skill in predictionof observed gust speeds and hail sizes. Shown inTable 2 are the average gust speed errors fromthat study, based on 1978 severe storm reports. Ofsignificance is the fact that well over half of thereported gusts occurred when the predicted valuefrom the nearest rawinsonde was for no gusts. Byexcluding the no gust forecasts, it can be seenthat reported gusts under 65 knots were actuallyoverforecast while those 65 knots or greater wereconsistently underforecast.

In Table 3, the same sort of calculation is shownfor predicted maximum hailstone size.Underforecasting is the general rule, even whenexcluding the (roughly) one-fourth of reportedevents which occurred with a no hail forecast.Based on these statistics, it seems clear thatrelatively little skill is apparent.

Sophisticated cloud models, using soundings asinput, might be able to provide better quantitativeestimates (Chisholm, 1973), but they are notcurrently practical for operational use. Further,there are simply too many important factors in

Table 2. Errors in predicted gust speeds: 01 Apr 30 Jun 1978, for reported gusts 50 kt or greater in the

two categories shown. Values are the mean difference (in knots) of (observed-predicted) +### the

associated standard deviation. The number of cases is in parentheses. Values under Preceding refer to

predictions from the sounding preceding the report by more than 6 hr; whereas Next refers to predictions

from the sounding immediately following. Values are given for All predictions and also excluding cases

when the prediction is no gusts.

TABLE 2

Less than 65 kt 65 kt or Greater

Preceding Preceding Next

All: 30.5 30.0 (167) 41.3 29.6 (45) 48.1 30.9 (43)

Excl 0s: -5.7 6.1 (62) 12.9 8.8 (22) 13.2 10.5 (19)

105 23 24

105/167 = 62.9% observed gusts 50 =< V < 65 kt with 0 calculated (Preceding)

23/45 = 51.1% observed gusts V >= 65 kt with 0 calculated (Preceding)

24/43 = 55.8% observed gusts V >= 65 kt with 0 calculated (Next)

producing hail and surface wind gusts that arepoorly understood, much less routinely observed.

An example of a plotted sounding is shown in Fig.2.10 with relevant features labelled. Any textbook(e.g., Hess, 1959) provides enough understandingto plot and analyze the typical sounding. Thereare several aspects of this sounding worth noting.First, it is interesting to observe that the moisturecuts off just below 850 mb, so that the ShowalterIndex is unrepresentative of the soundingsconvective instability the Showalter Index hasa value of +0.2 deg C, whereas the Lifted Index(based on a forecast surface temperature of 100 F)is -6.3 C! Further it can be seen that even at asurface temperature of 100 F, a substantialnegative area remains to be overcome before theconvective instability can be released. Also, notethe large positive area in this sounding. The sizeof the positive area may be a more relevantparameter than 500 mb buoyancy, since updraft

speed is only crudely related to the accelerationat any (arbitrary) single level. As discussed inII.III.A.3, the updraft speed is probably a goodmeasure of storm severity.

This sounding also shows an equilibrium levelsomewhat above the tropopause. Thus, a stormwhich slightly overshoots the tropopause in thisenvironment is not necessarily severe. In fact, thesounding suggests that a storm which realizes


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most of the energy

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