Quasigeostrophic Forcing of Ascent in the Occluded Sector of Cyclones and the Trowal Airstream

19 Pages·1998·0.65 MB·English

70 MONTHLY WEATHER REVIEW VOLUME127
Quasigeostrophic Forcing of Ascent in the Occluded Sector of Cyclones and the Trowal
Airstream
JONATHAN E. MARTIN
DepartmentofAtmosphericandOceanicSciences,UniversityofWisconsin—Madison,Madison,Wisconsin
(Manuscriptreceived21October1997,infinalform27January1998)
ABSTRACT
Anumericalmodel-basedanalysisofthequasigeostrophicforcingforascentintheoccludedquadrantofthree
cyclones is presented based upon a natural coordinate partitioning of the Q vector into its along- and across-
isentropecomponents,Q andQ ,respectively.TheQ componentdescribesthegeostrophiccontributiontothe
rate of change of the masgnituden of (cid:61) (cid:117)(traditional fnrontogenesis), whereas the Q component describes the
geostrophic contribution to the rate ofpchange of direction of (cid:61) (cid:117)(rotational frontosgenesis). It is shown that
p
convergence of Q simultaneously creates the isobaric thermal ridge characteristic of the thermal structureof
s
occluded cyclones and provides the predominant dynamical support for ascent within the occluded quadrant.
The absence of significant Q convergence there suggests that quasigeostrophic (Q-G) frontogenesis plays a
n
subordinate role both in forcing vertical motions and in affecting three-dimensional structural changes in the
occludedsectorofpost-maturephasemidlatitudecyclones.
A cyclonically ascending, cloud- and precipitation-producing airstream that originates in the warm-sector
boundarylayerandflowsthroughthetrowalportionoftheoccludedstructureissupportedbytheupwardvertical
motionsimpliedbytheidentifiedQ-Gforcing.Thisairstreamisreferredtoasthe‘‘trowalairstream’’anditis
showntoberesponsiblefortheproductionofthe‘‘wraparound’’cloudandprecipitationcommonlyassociated
withoccludedsystems.Therelationshipofthetrowalairstreamtopreviouslyidentifiedcloudandprecipitation
producingairflowsincyclonesisdiscussed.
1. Introduction the cold front overtaking, and subsequently ascending,
thewarmfrontalsurface.Oneofthemainresultsofthis
The relationship between thethree-dimensionalther-
processwastheproductionofawedgeofwarmairaloft,
mal structure and the distribution ofcloudsandprecip-
displaced poleward of the surface warm and occluded
itation in cyclones was first suggested by Bjerknesand
fronts.Thecloudinessandprecipitationassociatedwith
Solberg (1922) in their conceptual model of the mid-
thedevelopmentofthewarmocclusionweresuggested
latitude cyclone, which has come to be known as the
to result from lifting of warm air ahead of the upper
Norwegian Cyclone Model (NCM). According to their
coldfrontandwereconsequentlydistributedtothenorth
account,theamplificationofthecyclonewavedistorted
and west of the sea level pressure minimum. Further,
the polar front into a cold front and a warm front and
as a result of the gradual squeezing of warm air aloft
leftaregionofhomogeneouswarmairextendingdown-
betweenthetwofrontalsurfaces,thehorizontalthermal
wardtothesurfacebetweenthetwofronts.Thisregion
structure of warm occlusions was characterized by a
was known as the warm sector and theairthereknown
thermal ridge connecting the peak of the warm sector
as warm sector air.
to the geopotential or sea level pressure minimum. In
OneofthemoreintriguingelementsoftheNCMwas
nature,thisthermalridgeisoftenmanifestedasa1000–
the notion of occluded fronts first devised by Tor Ber-
geron(Jewell1981).Occludedfrontswerehypothesized 500-hPathicknessridgeor asanaxisofmaximum(cid:117)or
to develop late in the cyclone life cycle and occurred (cid:117)e in a horizontal cross section.
in two varieties: the cold occlusion and the warm oc- Theobservationthatthecloudinessandprecipitation
clusion. The warmocclusiondescribedtheverticaldis- characteristicoftheoccludedquadrantofcyclonesoften
placementofwarmsectorsurfaceairthatresultedfrom occurs in the vicinity of thethermalridgeledscientists
at the Canadian Meteorological Service (Crocker et al.
1947; Godson 1951; Penner 1955; Galloway 1958,
1960)toregardtheessentialfeatureofawarmocclusion
Corresponding author address: Dr. Jonathan E. Martin, Dept. of to be the trough of warm air that is lifted aloft ahead
AtmosphericandOceanicSciences,UniversityofWisconsin—Mad-
of the upper cold front, not the position of the surface
ison,1225W.DaytonSt.,Madison,WI53706.
E-mail:[email protected] occludedfront.Thesestudiessuggestedthatthelocation
(cid:113)1999AmericanMeteorologicalSociety
JANUARY1999 MARTIN 71
ofafeaturecalledthetrowal(troughofwarmairaloft) of a westward slope to the crests of the thermal wave
bore a closer correspondence to the cloud and precip- at successive heights in occluded cyclones. Noting the
itation features of occluded cyclones in North America samefeature,Godson(1951)drewattentiontoitsthree-
than did the often weak surface warm occluded front. dimensional structure by referring to it as a ‘‘sloping
This relationship was understood, however, in termsof valley of tropical air’’ (high (cid:117)or (cid:117)) in the occluded
e
relative flow along the frontal surfaces comprising the quadrantofthecyclone.Penner(1955),whonamedthe
occluded structure and not as a consequence of some feature, stated that the ‘‘trowal marks the crest of the
characteristic dynamical process. warm air aloft.’’ Consistent with each of the abovede-
Compelling evidence supporting these observational scriptions,thetrowalmarksthethree-dimensionalslop-
findings comes from a number of recent finescale nu- ing intersection of the upper cold frontal portion ofthe
mericalmodelingstudiesofoccludedcyclones(Schultz warm occlusion with the warm frontal zone and could
and Mass 1993; Reed et al. 1994; Martin 1998a,b) that therefore be said to represent a refined, three-dimen-
have illustrated the structure and thermal evolution of, sional description of the warm occluded structure pre-
andairflowthrough,theoccludedquadrant.Thesestud- sented by Bjerknes and Solberg (1922) and not a new
ies have identified a coherent airstream, originating in structure.Aschematicillustratingthetrowalconceptual
the warm sector boundary layer, that ascends cycloni- model is given in Fig. 1.
cally in the occluded quadrant of the cyclone. Martin ConsistentwiththedefinitiongivenbyPenner(1955)
(1998b), noting a spatial relationship between the path andthedescriptiongivenbyGodson(1951),thetrowal
taken by this airstream and the trowal in his case, re- can be approximately located either as a ridge of high
ferred to this airflow as the ‘‘trowal airstream.’’ The (equivalent)potentialtemperatureonahorizontalcross
resultsofthesemodel-basedanalyseshavenot,however, section,ormorepreciselylocatedasathree-dimensional
been fortified by a dynamical explanation of the rela- slopingcanyoninanisosurfaceof(equivalent)potential
tionship between the developmentofthethermalstruc- temperature. These complementary methods of identi-
ture in the occluded quadrant of cyclones and the as- fying the trowal are illustrated in Fig. 2 for a case de-
sociated ascent that supports this airstream. scribed in detail by Martin (1998a).1 The relationship
In the present paper a quasigeostrophic (Q-G) anal- of the trowal to the ‘‘wrap around’’ cloud and precip-
ysis of the forcing for ascent in the occluded quadrant itationinoccludedcyclonesisrecognizedbysomepre-
ofthreecyclonesispresentedbaseduponapartitioning sent-dayforecastersinCanada.Theyidentifythetrowal
oftheQvector(Hoskinsetal.1978)suggestedbyKurz astheregionnorthandwestofthenorthernedgeofthe
(1988b,1992)andKeyseretal.(1992).Itisshownthat dryslot where the frontal cloud shield of a mature cy-
a single component of the forcing (convergence of the clone wraps into the comma head (J. Anderson 1997,
along-isentrope component of Q, which represents the personal communication).
rotational component of the quasigeostrophic vector Although extensive examination of the trowal was
frontogenesisfunction)simultaneouslycreatesthether- made by the aforementioned Canadian investigators,
mal ridge characteristic of occluded cyclones and pro- none of those studies attempted to place this structure
vides the vast majority of the Q-G forcing for upward in a dynamical context. Morris (1972) identified the
vertical motion within the thermal ridge. trowal as ‘‘a discontinuity in the thermal advection
The paper is organized in the following manner. In field’’ and correctly pointed out that such a featurehas
section 2 a review of the trowal conceptual model and dynamical significance with respect to the diagnosisof
itsrelationshiptotheclassicalwarmocclusionisgiven. vertical motion. He employed the traditional quasi-
The numerical model used to simulate the three cases geostrophicomegaequationtodiagnosetheverticalmo-
examinedinthisworkisdescribedinsection3.Amod- tion associated with the trowal portion (i.e., occluded
el-based synoptic overview of each of the three cases quadrant)ofamodestAtlanticcyclone.Heascribedthe
along with selected model-based trajectories for each observed patterns of vertical motion totheinfluenceof
case are also presented there. In section 4 the quasi- the thermal advection term. Martin (1998b) provided
geostrophic forcing forascentintheoccludedquadrant evidence that the lower-tropospheric ascent manifested
of each cyclone is discussed and related to the support in the trowal airstream in his case was supported by
of the trowal airstream. A discussionoftheimportance low-level frontogenesis (calculated using the full wind
of the trowal airstream in the midlatitude cyclone and vector) along the warm frontal portion of a warm oc-
thenatureoftheverticalmotionforcingintheoccluded cludedstructure.Withtheexceptionofthesetwocases,
quadrant are given in section 5. A summary and con- no published work has focused on elucidating the dy-
clusions are offered in section 6. namical processes responsible for forcing ascent in the
2. The trowal and its relationship to the warm
occlusion 1Animationofthe309K(cid:117)surface,whichdemonstratesthestruc-
e
tural evolution of the trowal through the cyclone life cycle, can be
Theconceptofthetrowalwasintroduced(thoughnot
viewedatthefollowingWorldWideWebaddress:
named)byCrockeretal.(1947),whonotedtheubiquity http://marrella.meteor.wisc.edu/occlusion.html.
72 MONTHLY WEATHER REVIEW VOLUME127
FIG.1.Schematicillustrationofthetrowalconceptualmodel.Thelightlyshadedsurfacerep-
resentsthewarmedgeofthecoldfrontalbarocliniczone.Thedarkershadedsurfacerepresents
thewarmedgeofthewarmfrontalbarocliniczone.Thethickdashedline(marked‘‘TROWAL’’)
represents the three-dimensional sloping intersection between the cold and warm frontal zones
characteristicofwarmocclusions.Schematicprecipitationbandisindicatedasarethepositions
ofthesurfacewarm,cold,andoccludedfronts.
occludedquadrantofmidlatitudecyclones.Thepresent ing a second-order enstrophy-conserving leapfrog
paper offers such a diagnosis of three storms. The di- scheme (Sadourny 1975). Model physics include a ra-
agnosisbeginswithasynopticoverviewofeachcyclone diation parameterization that predicts longwave and
given in the next section. shortwave radiative transfer in a cloudy atmosphere
(Chen and Cotton 1983), and a predictive soil model
with surface energy budget (Tremback and Kessler
3. Case studies
1985). Liquid and ice processes are represented in the
Inthissection,threecasesofoccludedcycloneswith model by an explicit microphysics package, which de-
trowal structures are briefly described. An overviewof scribes the evolution of cloud water, rainwater,pristine
thestructureof thesecyclones,aswellasasnapshotof crystals, snow crystals, aggregate crystals, andgraupel
theirprecipitationdistributionisgiven.2Theanalysisof (Cotton et al. 1986; Flatau et al. 1989). A version of
these cases relied upon a numerical simulation of each the Emanuel (1991) convective parameterization was
performed using the University of Wisconsin-Nonhy- employed, modified such that the convection equili-
drostatic Modeling System (UW-NMS) described by brateswiththecycloneandfrontal-scaleverticalmotion
Tripoli (1992a,b). forcing.
Themodelemploysatwo-wayinteractive,moveable The two grids used in the simulationshadhorizontal
nesting scheme that allows for the simultaneous simu- resolutions of 160 km and 80 km, respectively. Only
lation of planetary/synoptic-scale forcing as well as the80-km griddatawereusedinthisstudy.Themodel
frontal-scaleforcing.Prognosticvariablescarriedbythe employed geometric height as the vertical coordinate
model include u, (cid:121), w, (cid:112)(Exner function), ice-liquid with discretely blocked-out topography similar to that
potential temperature ((cid:117)), total water mixing ratio, as
il used in the National Center for Environmental Predic-
well as the mixing ratios for a variety of precipitation
tion’s (NCEP’s) Eta model. Forty vertical levels were
particles.
usedwiththeverticalgridspacingof200minthelowest
Advectionofthescalarvariablesisaccomplishedus-
five grid levels and a gradual geometric stretching (by
ing a sixth-order Crowley scheme (Tremback et al.
a factor of 1.07)abovethat suchthatthenext18levels
1987), whereas the dynamic variables are advectedus-
had an average spacing of 404 m and the top 17 levels
had a spacing of 700 m. The model top was located at
19.2 km.
The model was initialized for each case by interpo-
2Radar reflectivity data were not available for the 7 November
1996case. lating directly from the 90.5-km NCEP Eta initializa-
JANUARY1999 MARTIN 73
gridpoints.Datawerethenverticallyinterpolatedtothe
model grid levels. The lateral boundarieswereupdated
every 6 h from the Eta gridded forecasts using a Ray-
leigh-type absorbing layer. In all three cases,36-hsim-
ulations were employed in order to keep the output vi-
sualization datasets at a manageable size. Twelve and
18-h forecast data were used in the study (as opposed
to 0- and 6-h forecasts) to ensure that the occluded
structures present in each case developed within the
model simulation.
Airparceltrajectorieswerecalculatedusingu,(cid:121),and
w from the model output, using a forward differencing
schemewithatimestepof24.5min.Additionalanalysis
of these data was performed using the General Mete-
orologicalAnalysisPackage.Briefdescriptionsofeach
of the three cases used in this study are given below.
a. 23 October 1996
At 0600 UTC 23 October 1996, an occluded surface
low pressure center with a sea level pressureminimum
of 992 hPa was locatedovereast-centralIowa.Afairly
welldefined axisofmaximumsurface(cid:117)extendedfrom
extremenortheastIowasouth-southwestwardintonorth-
central Missouri (Fig. 3a). The geopotential minimum
at 850 hPa was centered in southeast Iowa (Fig. 3b)
withanassociatedaxisofmaximum(cid:117)locatedinroughly
the same geographic area as, although more elongated
than,itssurfacecounterpart.Thegeopotentialminimum
axis tilted to the south-southwestwithheight.Theaxes
ofmaximum(cid:117)inthemiddletropospherewerenotnearly
as well defined as at lower tropospheric levels, as evi-
denced by the weaker axis of high (cid:117)at 700 hPa (Fig.
3c)thatextendedfromnorthcentralWisconsintonorth-
west Missouri. Nonetheless, these thermal axes exhib-
ited a northwestward tilt with height. An axis of max-
imum (cid:117)was barely detectable at 500 hPa (Fig. 3d).
Averticalcrosssectionthroughtheoccludedportion
of this cyclone (not shown) revealed the 315 K (cid:117) sur-
e
FIG. 2. (a) Isobaric topography of the 309 K (cid:117)e surface from an face to be appropriate for further analysisof thetrowal
18-h forecast of the University of Wisconsin-Nonhydrostatic Mod- structure.Theisobarictopographyofthatsurfaceisgiv-
eling Systemvalid at 1800 UTC 19 January 1995. Shading depicts en in Fig. 4a. The trowal position, identified by con-
isobariclevelsat100-hPaintervalswithlightestshadingrepresenting
nectingthecrestsofthevariousisobaricsurfacesinthe
the 1000–900-hPa layer and darkest shading representing the layer
above 400 hPa. Thick solid/dashed line is plan view of the trowal ridge of high pressure, stretched from the Iowa/Min-
position, dashed to indicate where the 309 K (cid:117) surface overhangs nesota/Wisconsin border southwestward to south of
e
the trowallocation. (b) Elevated viewfrom the north of the 309 K Kansas City, Missouri. An elevated, northern view of
(cid:117)esurfacefroman18-hforecastoftheUW-NMSvalidat1800UTC the 315 K (cid:117) surface offers another perspective of the
19January1995.Thedashedlineindicatesthetrowalposition,which e
slopesupwardfromnearthesurfaceto(cid:59)8km.Positionofthesurface trowalstructureinthiscase(Fig.4b).Theunusualextent
cold front is also indicated. (c) Equivalent potential temperature at of the ‘‘wrap around’’ precipitation exhibited by this
2kmfroman18-hforecastoftheUW-NMSvalidat1800UTC19 storm (Fig. 4c) was directly related to ascent in the
4JanKu.aTryhi1c9k9d5a.sShoedlidlinlieneissathree(cid:117)axe,islaobfelmedaxiinmKuman(cid:117)d ccohnatroauctreerdisetivceroyf trowal portion of the cyclone (to be shown later). In
e fact, betweenOmaha,Nebraska,andKansasCity,Mis-
awarmoccludedcycloneandusedtoapproximatelylocatethetrowal.
souri, the precipitation fell in the form of snow and
providedthatareawithitsmostsignificantearlyseason
tion, which has 50-hPa vertical resolution. Horizontal snowstorm in history (National Climatic Data Center
windcomponents,geopotentialheight,temperature,and 1996).
relative humidity were interpolated horizontally along Of the several coherent airstreamssubjectivelyiden-
constantpressuresurfacestothelocationsofthemodel tifiedinthiscasethroughuseofmodel-basedtrajectory
74 MONTHLY WEATHER REVIEW VOLUME127
FIG.3.(a)Sealevelisobars(solidlines)and1000-hPapotentialtemperature(dashedlines)froman18-hforecastoftheUW-NMSvalid
at 0600 UTC23 October 1996. Isobars are labeled in hPa and contoured every 4 hPa. Isentropes arelabeledin K and contouredevery 2
K. (b) 850-hPa geopotential height (solid lines) and potential temperature (dashed lines) from an 18-h forecast of the UW-NMS valid at
0600UTC23October1996.Geopotentialheightlabeledinmandcontouredevery30m.PotentialtemperatureanalyzedasinFig.3a.(c)
AsforFig.3bexceptfor700hPa.(d)AsforFig.3bexceptfor500hPawithgeopotentialheightcontouredevery60m.
analysis, two are highlighted in Fig. 5. Trajectory B is a rapid, cyclonic ascent in the trowal.3 Trajectory A
representativeofanairstreamthatoriginatedeastofthe represents the trowal airstream in this cyclone.
surface cold front in the warm sector boundary layer.
Itsurgednorthwardinalow-leveljetandroseabruptly
b. 7 November 1996
uponbecomingincorporatedintoavigoroussquallline.
As it rose it turned anticyclonically thus fitting the de- At 1200 UTC 7 November1996, asurfacelowpres-
scriptionofthewarmconveyorbelt(BrowningandHar- sure center with a minimum sea level pressure of 987
rold 1969; Harrold 1973; Carlson 1980). Trajectory A hPawaslocatedincentralOntarioatthecrestofaridge
is representative of an airstream that also originatedin of high surface (cid:117)(Fig. 6a). The geopotentialminimum
thewarmsectorboundarylayer.Itwasextremelymoist at 850 hPa was located directly atop the center of the
(mixingratioof11gkg(cid:50)1initially)anditsurgednorth- surface disturbance (Fig. 6b). A ridge of high (cid:117)at that
ward east of the surface cold front as well. However,
this airstream was not involved in the squall line as
parcels transported within it had moved too far north
by the time the squall line became organized. Instead, 3Combinedanimationofthisairstreamandthe315K (cid:117)esurface
for this cyclone, with similar animations of the other two storms
this airstream rose gently until reaching the trowal
reviewedhere,isavailableforinspectionatthefollowingWorldWide
((cid:59)0600 UTC 23 October) at which timeitcommenced Webaddress:http://marrella.meteor.wisc.edu/trowal.html.
JANUARY1999 MARTIN 75
FIG.5.Representative27-hforwardtrajectoriesoriginatinginthe
warmsectorboundarylayerat1200UTC22October1996calculated
fromtheUW-NMSmodeldata.Widthofthetrajectoryarrowindi-
catesheightoftheairparcelaccordingtothelegend.Tickmarkson
trajectoryarrowsrepresent3-hourlypositionsofairparcels.Seetext
fordiscussionofAandB.
the position of the geopotential minimum at 700 hPa
(Fig. 6c) and 500 hPa (Fig. 6d). More importantly, at
these midtropospheric levels the ridge of high (cid:117)was
located progressively farther north and west.
Vertical cross section analyses (not shown) revealed
the 309 K (cid:117) surface to be near the warm edge of both
e
thecoldandwarmfrontalzonesintheoccludedportion
of this cyclone. The isobaric topography of the 309 K
(cid:117) surface at 1200 UTC 7 November is shown in Fig.
e
7a. Based upon this analysis, the trowal position
stretchedfromnorthofLakeHuronthroughJamesBay
to northwest Ontario. An elevated eastern perspective
of the 309 K (cid:117) surface (Fig. 7b) clearly demonstrates
e
the three-dimensional nature of the trowal structure as
a ‘‘sloping valley’’ of high (cid:117) air. The position of the
e
trowal bears an obvious relationship to the UW-NMS
forecasted 1-h precipitation total ending at this time
(Fig. 7c).
FIG. 4. (a) Isobaric topography of the 315 K (cid:117)e surface from an Of the several coherent airstreamssubjectivelyiden-
18-hforecastoftheUW-NMSvalidat0600UTC23October1996.
Isobariclayersshadedandcontoured,andtrowalpositionindicated, tified in this storm through use of model-based trajec-
as in Fig. 2a. (b) Elevated, northern perspective of the 315 K (cid:117) tory analysis, two are presented in Fig. 8. TrajectoryB
e
surface from an 18-h forecast of the UW-NMS valid at 0600 UTC is representative of an airstream that originated in the
23October1996.Dashedlineindicatestrowalposition,whichslopes lower troposphere ((cid:59)1.7 km) east of the cold frontal
upward from the surface to (cid:59)6 km. (c) National Weather Service
(NWS)manuallydigitizedradarreflectivityat0635UTC23October zone. This airstream rose only slightly until encounter-
1996. Shading indicates echo/precipitation rate intensity fromlevel ingthewarmfrontalzoneatwhichtimeitroseabruptly
1tolevel5signifyinglight,moderate,heavy,veryheavy,andintense to(cid:59)7km.TrajectoryAisrepresentativeofanairstream
precipitation,respectively.Thickdashedlineindicatestrowalposition
that also originated east of the cold frontal zone in the
asshowninFigs.4aand4b.
lowertroposphere((cid:59)1.5km).Thisairstreamrosegently
until encountering the lower portion of the trowal
level extended through the geopotential minimum in a ((cid:59)1200 UTC 7 November) after which time it begana
semicirclefromnearJamesBay,Ontario,tosouthcentral rapid, cyclonically turning ascent through theoccluded
Ontario.Asinthepreviouscase,theaxisofgeopotential quadrantofthestorm.TrajectoryArepresentsthetrowal
minima tilted southward with height as evidenced by airstream in this cyclone.
76 MONTHLY WEATHER REVIEW VOLUME127
FIG. 6. (a) As for Fig. 3a except for 12-h forecastfrom UW-NMS valid at 1200 UTC7 November 1996. (b) As for Fig. 3b except for
12-h forecast from UW-NMS valid at 1200 UTC 7 November 1996. (c) As for Fig. 3c except for 12-h forecast from UW-NMS valid at
1200UTC7November1996.(d)AsforFig.3dexceptfor12-hforecastfromUW-NMSvalidat1200UTC7November1996.
c. 1 April 1997 850 hPa extending from south of Nova Scotia to south
of Long Island.
Oneofthemostmemorablesnowstormsinthehistory
Even moredramatic distortionofthebarocliniczone
ofsouthernNewEnglandoccurredon31March–1April
associated with this cyclone was evident at 700 hPa
1997. At 0600 UTC 1 April, a surface low pressure
center was located (cid:59)400 km south of Nantucket,Mas- where the ridge of high (cid:117)extended cyclonically from
justsouthofNovaScotiawestwardacrosssouthernNew
sachusetts, and had a minimum sea level pressure of
England and southward to the west of the geopotential
981 hPa (Fig. 9a). A secondary surface cold front ex-
minimum,whichwaslocateddirectlyaboveits850-hPa
isted along the Atlantic Coast of the United States,
counterpart(Fig.9c).Theprimarycoldfrontalzonewas
whereas the primary surface cold front associatedwith
even stronger at thislevel than at850hPa,whereasthe
thiscyclonewaswelltotheeastouttosea.Thesurface
warm front, located south of Nova Scotia at this time, warm frontal zone was more diffuse. No evidence of
was a robust feature of this cyclone. the lower-tropospheric secondary cold front existed at
The geopotential minimum at 850 hPa was located 700 hPa.
directly above the surface disturbance (Fig. 9b). The At 500 hPa (Fig. 9d) an extraordinarily lengthy axis
primary cold frontal zone was more vigorous at this of maximum (cid:117)was evident from the Gulf of Maine,
level than at the surface. The secondary cold frontal throughsouthernNewEngland,andsouthwardtoChes-
zoneofftheCarolinacoastalongwiththewarmfrontal apeake Bay. An intense baroclinic zone bordered the
zonesouthofNovaScotiawerealsowelldefinedatthis geopotential height minimum at this level, particularly
level. An incipient axis of high (cid:117)was also evident at on its southern and eastern edges.
JANUARY1999 MARTIN 77
FIG. 8. Representative 24-h forward trajectories initializedinthe
warmsectorboundarylayerat0000UTC7November1996.Width
of the trajectory arrow indicates height of the air parcel according
to the legend. Tick marks on trajectory arrows represent 3-hourly
positionsofairparcels.SeetextfordiscussionofAandB.
thusplacedonacyclonicallycurvinglinethatstretched
from well south of Nova Scotia through southern New
England at this time.
An elevated, northeastern view of this three-dimen-
sional moist isentropicsurfaceprovidesadifferentper-
spective of the structure of the trowal in this cyclone
(Fig. 10b). Although radar coverage was limited off-
shore, a widespread region of precipitation was occur-
ring from southeast Maine southwestward to the Del-
marva peninsula at this time in association with ascent
FIG. 7. Isobaric topography of the 309 K (cid:117)e surface from a 12-h in the trowal portion of the cyclone (Fig. 10c).
forecast of the UW-NMS valid at 1200 UTC 7 November 1996. Two representative trajectories involved in the pro-
Pressurelayersshadedandcontoured,andtrowalpositionindicated,
asinFig.2a.(b)Elevated,easternviewofthe309K(cid:117)surfacefrom duction of clouds and precipitation in this cyclone are
a 12-h forecast of the UW-NMS valid at 1200 UTCe7 November shown in Fig. 11. Trajectory B originated at lowlevels
1996. Thick dashed line indicates the trowal position. (c) Forecast in the warm sector and remained below 1 km until en-
of accumulated 1-h liquid equivalent precipitation ending at 1200 countering the surface warm front at (cid:59)0000 UTC 1
UTC7November1996fromtheUW-NMS.Precipitationtotalsare
April. After this time trajectory B rose abruptly to 6.6
contouredandshadedevery1mm(beginningat1mm).Thickdashed
km as a portion of the warm conveyor belt airstream
lineindicatestrowalpositionasdeterminedinFigs.7aand7b.
responsibleforproducing the easternportionofthecy-
clonecommaheadcloudshield(notshown).Trajectory
Vertical cross sections through the ridge of high (cid:117) A,thetrowalairstreaminthiscyclone,originated(cid:59)200
(not shown) revealed that the 312 K (cid:117) surface formed mabovethesurfaceinthewarmsectorandhadamixing
e
the warm edges of both the cold and warm frontalpor- ratio of 12 g kg(cid:50)1 at its origin. It also remained quasi-
tions of the warm occluded structureofthisstorm.The horizontal until (cid:59)0000 UTC 1 April at which time it
location of the trowal was determined by considering began a rapid ascentin thetrowalto(cid:59)7km.Theenor-
the topography of the 312 K (cid:117) surface. A plain view mous snowfall totals that visited many locations in the
e
of the isobaric topography of this (cid:117) surface is shown northeasternUnitedStatesinassociationwiththisspring
e
inFig.10a.Asinthepreviouscases,thetrowalposition in blizzard (National Climatic Data Center 1997a,b)
was determined by connecting the crests of thevarious were a direct result of the rapid ascent of the trowal
isobaric surfaces in the ridge of high pressure and was airstream associated with this cyclone.
78 MONTHLY WEATHER REVIEW VOLUME127
FIG. 9. (a) As for Fig. 3a exceptfor 18-h forecastfromUW-NMS valid at 0600 UTC1 April1997. (b) As forFig.3b exceptfor 18-h
forecastfromUW-NMSvalidat0600UTC1April1997.(c)AsforFig.3cexceptfor18-hforecastfromUW-NMSvalidat0600UTC1
April1997.(d)AsforFig.3dexceptfor18-hforecastfromUW-NMSvalidat0600UTC1April1997.
[ ]
4. Quasigeostrophic forcing of ascent in the (cid:49) (cid:93)2(cid:50) (cid:93) (cid:49)1 (cid:50)
vicinity of the trowal (cid:115)(cid:185)2 (cid:49) f2 (cid:118)(cid:53) f V ·(cid:61) (cid:185)2(cid:102)(cid:49) f
o(cid:93)p2 o(cid:93)p g f
o
Intheprevioussection,threecasesweredescribedin
[ ]
which a coherent airstream underwent ascent, while (cid:49) (cid:93)(cid:102)(cid:50)
turning cyclonically, in the vicinity of the trowal. The (cid:49) (cid:185)2 Vg·(cid:61) (cid:50)(cid:93)p (1)
ascent manifested in these important precipitation pro-
ducing airstreams was a result of the distribution of (Holton 1992). As demonstrated by Trenberth (1978),
vertical motion accompanying the individual cyclones. some cancellation exists between the two terms on the
Inthissection,aquasigeostrophicdiagnosisoftheforc- rhs of (1). By expanding the expressions on the rhs of
ingforthesupportingverticalmotionsisundertakenby (1) and neglecting the deformation term, Trenberth ar-
examining the divergence of the Q vector (Hoskins et rived at the following approximate f-plane form of the
al. 1978) and considering its decomposition in relation Q-G omega equation,
to the horizontal potential temperature gradient.
(cid:49) (cid:93)2(cid:50)
(cid:115)(cid:185)2 (cid:49) f2 (cid:118)(cid:248) F (cid:53) 2f V ·(cid:61)(cid:122), (2)
a. The quasigeostrophic omega equation o(cid:93)p2 TR o T g
The diagnosis of vertical motions on the synoptic where V is the thermal wind ((cid:93)V /(cid:93)p) and (cid:122) is the
T g g
scale is made possible through use of the quasigeo- geostrophic relative vorticity. This relationship, in
strophic (Q-G) omega equation: which synoptic-scale vertical motion is controlled by
JANUARY1999 MARTIN 79
FIG.11.Representative24-hforwardtrajectoriesinitializedinthe
warmsectorboundarylayerat1200UTC31March1997fromthe
UW-NMS.Heightofairparcelsindicatedbywidthoftrajectoryarrow
according to legend. Tick marks identify 3-hourly positions of air
parcels.SeetextfordiscussionofAandB.
F (cid:53) (cid:50)2(cid:61)·Q , (3)
TR TR
where Q (cid:53) f (cid:103)(cid:122)(k(cid:246) (cid:51) (cid:61)(cid:117)) and
TR o g
R (cid:49)P (cid:50)c(cid:121)/cp
(cid:103)(cid:53) o
f P P
o o
and is constant on isobaric surfaces. This form of F ,
TR
wheretheforcingdependsontheconvergenceofavec-
tor field that is everywhere parallel to the (layermean)
isentropes, demonstrates that this forcing can never be
distributed in bands parallel to the isentropes. Thus, it
FIG.10.(a)Isobarictopographyofthe312K(cid:117)esurfacefroman doesnotdescribetheforcingofbandedverticalmotions
18-h forecast of the UW-NMS valid at 0600 UTC 1 April 1997. paralleltobarocliniczonessuchasoccursatfronts.The
Pressurelevelsshadedandcontoured,andtrowalpositionindicated, Trenberth forcing, therefore, could be said to describe
asinFig.2a.(b)Elevated,northeasternperspectiveofthe312K(cid:117)
e onlythenonfrontal,synoptic-scaleforcingforQ-Gver-
surfacefroman18-hforecastoftheUW-NMSvalidat0600UTC1
tical motion.
April 1996. Thick dashed line indicates the trowal position, which
slopesupwardfromthesurfaceto(cid:59)8km.(c)AsforFig.4cbutfor A complete solution to the Q-G omegaequationwas
0635UTC1April1997. introduced by Hoskins et al. (1978). They showed that
the synoptic-scale vertical motion is controlled by the
divergence of the Q vector defined as
the advection of geostrophic relative vorticity by the [ ]
(cid:49)(cid:93)V (cid:50) (cid:49)(cid:93)V (cid:50)
thermal wind, is a close relative of the development Q (cid:53) (cid:50)f (cid:103) g·(cid:61)(cid:117) i(cid:246)(cid:49) g·(cid:61)(cid:117) j(cid:246) . (4)
equation forwarded by Sutcliffe (1947). Both the Sut- o (cid:93)x (cid:93)y
cliffe(1947)andTrenberth(1978)versionsof(1)retain
Foradiabatic,geostrophicflow,theQvectorrepresents
theirsimplifiedformsattheexpenseofneglectingterms
therateofchangeofthevector(cid:61) (cid:117)alongageostrophic
involving the deformation of the horizontal flow. De- p
trajectory:
formation is important in baroclinic regions, such as
fronts, and thus, potentially important information re- d
garding omega is lost in these simplified expressions. Q (cid:53) f (cid:103) (cid:61) (cid:117), (5)
o dt p
HoskinsandPedder(1980)showedthatF couldbe g
TR
written in a vector divergence form as where d/dt (cid:53) (cid:93)/(cid:93)t (cid:49) V ·(cid:61) (the subscript g denotes
g g p