Mesoscale Meteorology METR 4433
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Hurricanes Observations and Dynamics Houze Section 101 Holton Section 97 Emanuel K A 1988 Toward a general theory of hurricanes American Scientist 76 371379 web link httpww2010atmosuiucede Gh guide smtrhurrhomerxml De nition Hurricanes are intense vortical rotational storms that develop over the tropical oceans in regions of very warm surface water Hurricanes are called typhoons when they occur over the western Pacific Before they reach the hurricanetyphoon strength when winds near the center of vortex is gt 32 ms they are called tropical cyclones Horizontal scale 500 km vertical depth 10 15 km Although hurricanes have radial scales of several hundred kilometers the horizontal scale of the region of intense convection and strong winds in a hurricane is typically only about 100 km in radius Thus it is reasonable to classify hurricanes as mesoscale systems Regions of fnrmzdnn Between 5 and 20 iantude but not at the equator need Coriolis force Seasnrfaeeternperature gt 26 5 80F Moderately conditionally unstable atmosphere Weakvertteai shear Locations offorrnatton over a 2 ear enod Figure um Locnttnns nr tropical cyclone formation over st mycat period From Gray mu eprinled with permission from titc Rayal Melcurological SociuyJ Tracksunrug alcgcluneszmdse surface temperature Figure 102 Tracks of tropical Cyclones in relation In mean seasurface Aemperalure CL September temperarures arc taken fur the Norlhern Hmlsphercv March lemperalures are taken for In Southern Hemisphere me Bergeron 1954 Reprinled with perml ion from the Royal Meteorological Society General Patterns of Cloud and Precinitation in Hurricanes Figure 128 V 39 39 39 quot39 quot quot quot0 quot of Frank D Marks 1er F I 04 nnuul 39 39 of Fig 103 Comours are for 25 and 40 dBZ From Marks and Hum m7 Reproduced wnh pcrmission from he American Meiwrologicul Society 5 Figure um Schcmnlic rum xcnmuun uhhu Iypxculccho paucrn n w z 39 AIndavi n r w n mucmd nl URJI In h gh nn 1 3 v t Rt wih permimun rmquot me Annnun Mulcnrnlngicnl Sucicly Major Features Cyclonic spiral convergent bands at the lowlevels and anticyclonic outward spiral cirriform clouds at the upper levels Hurricane eye typically a cloud free center of 1050 km in diameter Eye wall deep convection surrounding the eye Slopes outward with height Twoeyewall structures had been observed Rainbands typically spiral bands of clouds outside the eye wall Often propagate outwards from the eye Re ectivity even in eye wall Rmax 45 50 de 3035 typical In server thunderstorms R 55 70 de The winds 7 In the horizontal Cros section v w was man ms sa snw39 Figure 105 Lawlcvcl 900 Mb wind cld assocmcd with Hurricane Gloria I935 m w 39 39 39 uml in In m uu Highresolulian wind unaly s in which wavclcnmh Icss Ian abuut 6s 28 and 44 km have bun ltered cm in he Ihree successively larger domains whose boundaries are indicated by lick marks 39 39 39 39 39 39 r39 Courtesy ofJames Franklin Hurrican Rcsearch Divisions us Nauunal Oceanic and Atmospheric Adminlsln iun 9 15 msnw Flure 10 Ur ptrlncl coo mbl wlml ml Jasmulzd wim Humrm Glnnn mm Horizontal Distribution of Winds symmetric in terms of system relative winds Asymmetric in total winds due to the hurricane motion stronger on the quotforwardquot side V 0V Vortlclty E a m cylmdr1cal coordmates r SOms 50km 1x10 3s 1 Typical value The winds 7 In the Vertical crossrsection radial wind 6 0 r latitude Figure 1417 Figlue 106 Figure 106 Vcrllcul cm secliuu of th mean rudiul wind u in wcslcrn Allnnlic hurricanes Anal ais is u Campanile of data collcclcd in many slorms From Gray 1979 Reprinled Mlh permlxsion from he Rnyul Mclcol39olnllical Sucicly Venicnl cm smion or lhc Inch mngenml componcnl n m wind v in Paci c n a composite nruma culluclcd in ma y storms From Frank I977 Reprinted lgur Iyphuum Anuly9i from me American Mcxcurumicm Smitty wnh pcrmiwun 11 tangential wind Maximum tangential wind at the edge of eye wall Max speed 05 15 km above sfc Vertical shear lt 00 since the thermal wind opposes the observed wind throughout the troposphere Why because hurricanes have warm code see next figure The vertical shear is relatively weak due to vertical momentum mixing by Cb clouds Maxrmum wmds I m eye wan Mmimum pressure and wmds m eye wmds can be cam gt ngher Wmds Pressure Them odm amic Structure 5 3 g m E g 5 3 E U m 9 LU I a I 5 RAD US Figure 1011 Radial crms section lhmugh an idculizcd umlly symmelri hurricane 0n lcfl lmes on ngm langcmial velocity in m s i indicated by ltolid lines and Iempcmlurc in C by Ihc dashed lines From Wallace and Hobbs I977 as udupled mm Pulm n and Nwlon I969 Temperature departure from the mean 10 15 warmer inside eye due to subsidence Warm core causes surface lowpressure hydrostatic balance Be in hurricane more potentially stable than outside since instability has been released Be in eye much higher 15 30 more Note a If one starts with Ge 350K and go up along moist adiabat and psfc lOOOmb typical for most tropical disturbances we can show Apsfc 25 ABS b Air from outside hurricane where p lOOOmb going towards the center where p 950 mb should normally cool adiabatically but observed temperature stays the same or increases slight This is due to sensible heat flux from the sea surface 9 Ge increases substantially The airsea interaction theory of Emanuel further points out that the latentheat flux from the sea surface as the air ow towards the center at large wind speed is another major energy source Presence of warmcored eye is a key feature of hurricanes which causes pressure drop at the center Landfall greater frictional convergence convection may actually intensify because of enhanced Ekman pumping effect but less high Ge air from the surface cause pressure to rise wind damage from large scale tangential winds but also from convective downdrafts weak to moderate tornadoes are common after landfall sfc winds now about 50 of 1 km winds vs 70 over ocean so vertical shear increases significantly CAPE in hurricanes relatively small Damages Strong Winds convective gusts Sea level rise by 12 in due to low pressure Storm surge 2 10 m strongest in the right front quadrant Waves Tornadoes Flooding from rains Damage eaused by numeanes Wrm numeanes berng as powerful as they are r rs not surpnsrng that upon landfall mey eause damage an esvmenon Even when are numeane has yet to make landfall its effects ean be dangerous Hovvever most ofthe damage causedto man and nature oeeur as a numeane makes landfall Shogg Wmds Eaen ofthe above phenomena ean tum a numeane into a nomeevvreeker a naturer destroyer and even a Idler ome aopreal storms that make landfall eause damage rn mese vvays but very rarely do they do so rn as sxgn cant a manner as do numeanes Stro ds determmes me mtensxty ofa humcane mwentedxt The scale 15 hsted below 27 177 A 07 27 88 5 5 9201 gt115 gt118 2717 gt1135 The Sa iprmpson scale categonzes humcanes on a scale 30m 1 to 5 Category 1 humcanes are k V F rr F r w m r h 0111 been two category 5 humcanes that made 1mm on me mama U s Flonda Keys 1935 and Camilla 1969 Recent mtense humcanes to make 1mm on me Umted States were Opal m 1995 and Franm 1996 18 Hurricane Dynamics Hurricane vortex cannot be understood without including the rotation of the earth in the vorticity balance The rapid rotation is produced by concentration of the vertical component of absolute vorticity by vorteX stretchinghorizontal convergence Maximum tangential Wind speeds range typically from 50 to 100 m s39l Centrifugal force cannot be neglected compared to the Coriolis force The azimuthal tangential velocity in a steadystate hurricane is in gradient Wind balance with the radial pressure gradient force Hydrostatic balance holds on the hurricane scale which implies that the vertical shear 0f the azimuthal tangential velocity is a function of the radial temperature gradient thermal Wind balance The kinetic energy of hurricanes is maintained in the presence of boundary layer dissipation by conversion of latent heat energy acquired from the underlying ocean This potential energy conversion is carried out by a transverse secondary circulation associated with the hurricane as shown below Tvade Inversion 51 Fig 914 cane Air spirals in toward me cyc mgmn 5 in the boundary lzycr region 0 ascends along wnsznlM surfaces in me eycwnll cloud regmn 1 and slowly subsides and dries in regions 2 and 1mm Emanuel 1933 Hurricane Formation Theories Two main theories CISK Conditional Instability of the Second Kind Theory and the Airsea interaction theory CISK gConditional Instabili of the Second Kind Theogv 1960 s 1970 s Represents a cooperation between convection and largescale convergence Weak disturbances containing vorticity Ekman layer BL convergence through Ekman pumping Increased convection Latent heat release Temperature increase Sfc pressure falls Increased vorticity Increased convergence A feedback loop instability Linear analysis to capture the above instability process has not been very successful however since there is little evidence that such interaction leads to a growth rate maximum on the observed scale of hurricanes 21 Another problem is as is pointed out by Emanuel handout that the tropical atrnos here is on average included Therefore net buoyancy within a convective cloud is srnall relative to its environrnent It is hurricane circulation 2cm Prassure mh 70 Va Temperature 390 Ainsez interactinn hang Emanuel 1983 handum A sea inmmc un Lhenry between the sznsphere and the underlying mean a 5 m in quotwar rm Trade Inverslnn Sea su ace Fig 939 I V V V k e Air spirals in inward nu 2y region 5 in UN boundary layer region 4 ascends slung cor anlM surfaces 1 me ycwall cloud region I and slowly subsides and dries In regions 2 and 3 Arm Emanuel 193339 The airsea interaction theory views energetics of the steadystate hurricane as an example of a Carnot cycle heat engine in which heat is absorbed in the form of water vapor from the ocean at temperature TS and expelled by radiative cooling to space at temperature T0 at the top of the storm With this theory the circulation is driven by AT between region 1 5 and region 2 The temperature in region 1 is higher because of increase of water vapor of BL air as it owed inward towards the eye and that in region 5 due to subsidence Quantitative investigation of energy source Hoe does total moist entropy increase Recall dry entropy ds Cp dln9 Rcp where 6 T gt P dln6dlnT Rdelnp or deln szdlnT Rdlnp Now for moist processes we can show that C pd ln6 equation for moist adiabat T 24 so moist entropy is defined as ds delnT de Rdln T I7 As air moves toward the hurricane center entropy increases due to increase in moisture dwS term Via latent heat uxes and p decrease but temperature stays the same as sensible heat flux from the ocean balances the expected adiabatic cooling isothermal expansion heat input at high T As the air ascends in the eye wall region region 1 in Figure s is conserved S decreases outside the hurricane at the upperlevels due to radiative cooling at point 0 to O Carnot s Theorem says total mechanical energy of the system is E 8T5sc sa c for center and a for ambient outside where 8 is the thermodynamic efficiency of the heat engine Since TS 300 K and TO 200 K the efficiency of the heat engine can be as high as 30 ie as much as 30 heat acquired at the low levels can be converted into kinetic energy Since the primary balance in hurricane BL is between PGF and frictional dissipation In a steady state hurricane the mechanical energy generated E balances frictional dissipation 25 Equating the work done by the PGF to E gt pr ems sgt a P or R lnp 8T5sc sa 17 Solve for pc gives the minimum possible central pressure Fig7 in Emanuel is obtained this way Since the airsea interaction model depends on the sea surface fluxes which depend on the wind speed It has bee demonstrated in a numerical model that the initial vortex has to have sufficient intensity wind speed is large enough a hurricane to form See Fig9 The real difficulty is in determining which tropical disturbance can gain sufficient intensify to develop into a hurricane This is a still an unsolved problem 26 rnmv 39 39 r w v Thepmum LU k 39 1 wilh39mlt The 39 vIv 39 mum omquot 39 um E as 39 hw emam39zs S 2 u 32 n E E o 3 25 39 a i U 24 20 0 30 gt60 9CI 420 450 Lower slramspheric lemperalure 39C Fugue 8 A more gmenl wzy to c When plasmas modded with hnnicana IS dunnoth this 39 sh W e 39 39 um ble m llilhbals nf knpial mums alth hum F4 5 as a human hull loner annulment The ambient sulme Ida ve humidin is mined quotkW beans the uudunial may pmdumd by hummhmmgineissomgeupmmbehhmd Hahn Jane The iniquity a Madman in this legal Wald be Iimibed by inmIul Imbalan dissipation of Idne c any pmbly a way high wind speed 28 40 E 3 5 g 30 o n a u 5 K g 20 E x a 2 1o 0 0 50 100 1 50 Time m ngu 9 tompuxu models pmvide n partial m m nu qns an abundant clergy m lppon lhcm 11quot graph shows an evallm39on will time In he maximum mg wind speed produced by on 1 e e ans an of wuk rundown noise rather a m of su denl amplide musl be pmvided by independent mun u h middleblind continent 29 References Emanuel K A 1986 An air sea interaction theory for tropical cyclones Part I Steady state maintenance J Almos Sell 43 585604 Rotunno R and K A Emanuel 1987 An airsea interaction theory for tropical cyclones Part II An evolutionary study using a hydrostatic aXisymmetric numerical model J Almos Sell 44 543561 30 Chapter 2 Planetary Boundary Layer and PBLrelated Phenomena In the chapter we will first have a qualitative overview of the PBL We will then discuss several applications of the boundary layer concepts including the development of mixed layer as a preconditioner of server convection low level jet and dryline phenomena The emphasis is on the applications Main references Stull R B 1988 An Introduction to Boundary LayerMeteorology Kluwer Academic 666 pp 2 1 Planetary boundary layer and its structure The planetary boundary layer PBL is defined as the part of the atmosphere that is strongly in uenced directly by the presence of the surface of the earth and responds to surface forcings with a timescale of about an hour or PBL is special because we live in it it is where and how most of the solar heating gets into the atmosphere it is complicated due to the processes of the ground boundary boundary layer is very turbulent others In this section we discuss some aspects of the planetary boundary layer that are important for the understanding of boundary layer related phenomena such as dryline and noctumal lowlevel jet Day time boundary layer is usually very turbulent due to groundlevel heating as illustrated by the following gure Range rmm rm km Lider Imares orthe aerosolladen bounda layer oblalned during the FIFE vein experimani In Kansas a nvective mixed layer observed al 1030 Inc me on July 1537 when winds were generally less than 2 ms 1 SliuhlIyslable boundary layer with shear eneraied turbulence observed ai 53D local lime on 7 July 1587 rnds ranged from 5 ms nearthe surlace lo 15 ms near the top oi the boundary la er Fhol raphs irom Ina Univ 0 Wisconsin Iidar are counesy oi Eloranla undary Layer Research Team Flange lram lldar km The layer above the PBL is referred to as the free atmosphere BH39IRJTI if Tropepausa quot 7 quotquot Free Airmaphare 3E1 km Earlh Fig 11 The Imposphera can be divided inm tum pans a haundary layer shaded near the Surlaca and tl wl res atrmsphere above it omnarison of boundary layer and the free 39 characteristics Table 11 Comparison of boundary layer and tree atmosphere characteristics r ert Boundary Laye Frgg Atmosphere Turbulence 0 Almost continuously turbulent Turbulence in convective clouds over its whole depth and sporadic CAT in thin layers of large horizontal extent Friction Strong drag against the earth s surlace Large Small viscous dissipation energy dissipation Dispersion Flapid tufoulent mixing in Small molecular ditiusion Oiten rapid the vertical and horizontal horizontal transport by mean wind Winds Near logarithmic wind speed Winds nearly geostrophio proiile in the surtace layer Subgeostrophic cross isobaric flow common Vertical Transport Turbulence dominates Mean wind and cumulusscale dominate Thickness Varies between 100 m to 3 km Less variable 848 km in time and space Slowtime variations Diurnal oscillations over land Diurnal evolution of the BL 2000 Free Atmosphere Entrainment Zone Capping Inversion V Entrainment Zone Residual Layer Height in onvec ve lxed Layer Stable Nocturnal Boundary Layer Surface Layer Mldnlght Sunrlu Local Time Fig 17 The boundary layer in high pressure regions over land consists of three major parts a very turbulent mixed layer a lessturbulent residual layer containing former mixedlayer air and a nocturnal stable boundary layer of sporadic turbulence The mixed layer can be subdivided into a cloud layer and a subcloud layer Time markers indicated by 8186 will be used in Fig 112 The above figure shows the typical diurnal evolution of the BL in highpressure regions ie without the development of deep cumulus convection and much effect of vertical lifting At and shortly after sunrise surface heating causes turbulent eddies to develop producing a mixed layer whose depth grows to a maximum depth in late morning In this mixed layer potential temperature and water vapor mixing ratio are nearly uniform At the sunset the deep surface cooling creates a stable nocturnal boundary layer above which is a residual layer basically the leftover part of the daytime mixed layer At all time near the surface is a thin surface layer in which the vertical uxes are nearly constant It is also called constant ux layer N xed layer development Free AEnmphera Entraian mm M intad Law Surface Lam I39m 4r Lquot quot 39E39v M E Fig 15 Iwical daytime murilea ulmean vi ual potential tern mature Eu Eind speed M where M24114 water vapor maing ram r and pulluftanl cancentratiun c Turbulence in the mixed layer is usually convectively driven ie driven by buoyancy due to instability Strong wind shear can also generate turbulence however The Virtual potential temperature it determines the buoyancy is nearly adiabatic ie constant with height in the middle portion of the mixed layer NIL and is superadiabatic in the surface layer At the top of the lL there is usually a stable layer to stop the turbulent eddies from rising further When the layer is very stable so that the temperature increases with height it 395 usually called capping inversion This capping inversion can keep deep convection from developing When the surface heating is sufficient so that the potential temperature of the entire ML is raised above the maximum potential temperature of the capping inversion convection breaks out assuming there is sufficient moisture in the BL This usually occurs in the later afternoon The best time for tornado chasing The boundary layer wind is usually subgeostrophic due to surface drag and vertical mixing of momentum The water vapor mixing ratio is nearly constant in the ML with atypical diumal cycle the PBL wellmixed layer in particular grows by a 4rphase process 1 Formation ofa shallow ML burning 01f ofthe nocturnal inversion 1039 to 10039 meter deep 7RanirlM1 mwth 39 39 39 quot L r C 394 layer quot p ML 39 Growth l u ii 39 4 Decay ofturbulence at sunset as the layerbeeorries convectively stable as t agroundbasedlidar Fig 1110 Evolulton a he entrainment zone measuved by Igtdar at lhe LXBJ eld slle luv 15 n 1983 The and Height m U bottom lines represent me lop and 0 am of 6 c a mi alehnersme 5m avevagemlxedlaye1 Gapini Aner Wilde el al 1985 D Smhle Brnlmlar L2 2139 Fran a1n1osvbera Farmer annalnmem zone Residual Laynr sxaus Boundary Layer 7v Fig 111 Mean virtual potential lemperatuve 5V and wind speed in pro les 10 an Ideallzed stable boundary layer in a highpressure reg on As the night progresses the bottom portion of the residual layer is transformed by its contact with the ground into a stable boundary layer This is characterized by statically stable air with weaker sporadic turbulence Although the wind at ground level frequently becomes lighter or calm at night the Winds aloft may accelerate to supergeostrophic speeds in a phenomenon that is called the lowlevel jet or nocturnal jet The statically stable air tends to suppress turbulence while the developing nocturnal jet enhances Wind shears that tend to generate turbulence As a result turbulence sometimes occurs in relatively short bursts that can cause mixing throughout the SBL During the nonturbulent periods the ow becomes essentially decoupled from the surface As opposed to the day time lL which has a clearly defined top the SBL has a poorlydefmed top that smoothly blends into the RL above Fig 110 and 111 The top of the NE is defined as the base of the stable layer while the SBL top is defined as the top of the stable layer or the height where turbulence intensity is a small fraction of its surface value SBLs can also form during the day as long as the underlying surface is colder than the air These situations often occur during warmair advection over a colder surface such as after a warm frontal passage or near shorelines Virtual Potential Temnerature Evolution how is virtual temperature de ned and what s its signi cance Flg L12 Prohies 0 mean W quotl m ra we 6v shawing the SBL bounqaryiaypr each sounding M n With an associated launch time l dlCaled m f m 1 0 Virtual potential temperature profile evolution at time 81 through S6 indicated in Fig 17 o The structure of the BL is clearly evident from these profiles ie knowledge of the virtual potential temperature lapse rate is usually suf cient for determining the static stability 0 An exception to this rule is evident by comparing the lapse rate in the middle of the RL with that in the middle of the ML Both are adiabatic yet the NE corresponds to statically unstable air while the RL contains statically neutral air One way around this apparent paradox for the classification of adiabatic layers is to note the lapse rate of the air immediately below the adiabatic layer If the lower air is superadiabatic then both that superadiabatic layer and the overlying adiabatic layer are static ally unstable Otherwise the adiabatic layer is statically neutral m crinlher am Fx39 are ya 4 mmpmw oj ve a emaan mm Um saunath b mmmm mm mm pmducm damagmg 39 t l 3971 RangcarelzafCallmldn I an the n39g t and c dew 170ml Empemm The mundmg atypiculoflhe type fenvllanm 1mm dung dwith rgenm my quotmy I 5Camtena x Avmbeusociae n C 983 The Warming shawl AM Elmrurlenmc deep dry ed me th my mum w 2 rule 9squotc km quot Upped by a aria layer hm de an y mumtloud e wpm39nldepresw39ll An examnle morning sounding showing the surface inversion stable law that develon ed due to niglrtime surfac cooling Such a shallow stable law can usual he guich removed after sunrise Fygm 917 4 m mmwa uundmg m m Fig 9d 17m taken in mu morning 1200 UTC 031 Mm mu shuwmg he kum ofslmlla mvmim near the mu m m usually dimpymr I 1 r in mg da m 39g reby m try mimbmm Pater m r c a Thlxmnmling Wm mm ribml 7 how 2 u micmhum rclmd ItemMutian m Smplemn mm uanonnlmrpun E Horizontal Convective Rolls METR 4433 Mesoscale Meteorology Spring 2006 r daytime heating undarylayer The ro11s tend to align themselves with the vertical shear vector socalled longitu 39n mode I Rm quot uvll 39L 4 39 39 Ilnnllinn quot u location Air li ed by the roll updra s can saturate forming aregnlar arrangement of quotcloud streetsquot aligned along the ro11s r r Pm depthi 39 M t M common n n Vemcal vetentty vemcal mnd wu b npnnatt dullnde tmstacuan mlslssclnn Visual Structure on Satellite and Radar 10 August 1991 1TODQT MAY1996 WECKWERTH ET AL 773 a 39 him lt V FIG 2 CP3 suIveillzmce scan from 3 at 1715 UTC 17 August showing a re ectivity 11323 and 1 Doppler velocity m 5quot Corresponding scales are beneath each panel Range rings are every 5 km and azimuth lines are every 0 FIG 3 CP3 RHI scan nearly perpendicular to the roll axes at 1645 U39l39C 2 August showing a rncclivlty dBL and 1 Doppler velocity m s Arrows mark the lucaliuna ul lowilcvel convergence due to the roll updraft rcginns Corresponding scales are beneath each panel Tick marks are every 2 km Thermodynamic Variability Caused by HCRs Because HCRs have ascending and descending branches they can locally destabilize a region of the atmosphere and lead to rapid horizontal variations in temperature and moisture ie CAPE relative cloud bases and depths predicted from measurements directly beneath them actual cloud FIG 10 Schematic diagram summarizing results of this study Gray lines indicate roll circulations Thick black lines are contours of moisture with the maxima existing within the roll updraft regions Actual cloud base and depth are shown by the solid cloud Dashed clouds represent relative cloud bases and depths expected if stability parameters were estimated from CBL moisture values directly be neath those clouds 17 August1991 Mobile 1642 UTC 9 f 1700 UTC 9 1642 170J 1 r a a 70 UTC urc 4 Ascent v r 0 Rate quot654 5 a 7 a 910 FIG 5 Mobile CLASS sounding cumpariSous taken on 17 August within the roll updraft region 1642 UTC called M1642 in the text thick lines and between a roll updraft and downdraft 1700 UTC culled M1700 in the text thin lines These balloon launch locations are shown schemati cally in the center relative to the boundary layer roll circulations See Fig 4 for exact launch locations relative to radar re ectivity eld Schematic cloud indicates cloud penetration by M1642 The ascent rates m squot for each sonde are shown on the left Horizontal wind speeds are shown on the right full barb5 m 5quot half bar bils m 5quot Dynamics of HCRs HCRs represent an instability in the atmosphere resulting from the combined effects of vertical shear and surface heating The relative importance of these factors can be examined by looking at the turbulent kinetic energy budget from classical boundarylayer theory d d 7 u w U 7 Wu V 7 D dz dz B SA SC where the primes denote the perturbation quantities due to the rolls the overbars denote the spatially averaged means is the mean virtual poten l temperatureW is the mean thermodynamic ux Mnquot is the mean along roll momentum ux v w is the mean cross roll ino mentum ux and D is the loss due to viscous dissi pation The rst term on the right denotes the production of energy by buoyancy B and represents roll forcing by thermal instability and the second and third terms denote the production of roll kinetic energy by the along roll SA and cross roll wind shear SC com ponents In this study the SA and SC terms were com bined to represent roll forcing due to a generic shear instability S genaal concluslons can be made PBL for rolls to exxst Rolls bend to be abgned mm the Dn ectlona Lhe PBL Rolls are Lhepref amb lent wmd 1 shear 15 not requned for rolls to exxst ened convectwe mode as opposed w more unorgamzed convectlon when a mucal surface heat ux has been achleved Inmmc un Between HCRs and the Sea Breeze convergmce thexr mtaacuon can lead to convectwe initiation 55F mental oud ism mm m mu anmdn pm M m 55 chum lmnksn mam we mum e we meme n Hewemmn ngml we myan ewe us a mm W mfm cummus mm m mum cumuh enhanced K Penudnaw along m lnstablllty tn the ar wtthln the roll updratts Recall that the roll clrculatlons cause vanath tn CAPE across the rolls pnnclpally b ecause the roll up dm s ll molsmre lntersectlon locales Note the absence of cloudlness at the downdm lntersectlon polnts The spatlal to the m uence of roll downdratt Suppresslon as roll updratt enhancernent once they d Mn anks ll Thu create thatyanablllty Detailed Stages of Interaction and Convective Initiation well beyond represent descent along w boundary tn blue The leadlng edge of the latter ls the sea breeze lth cloud water contours tn red and the cool rnanne alr 39ont W x ml The gure beluw depde me mtermedlate stage whmh mcumpasses themust dmmauc SEFVHCR enebumer the are mll lumled abuve x 1m ebnbnues m intensify spawmng a deep and Strung ebnveebve duudahuve n Nuts am thaws me SEF with me mll up dra us duud and me duwndm that had appared m between abuve me 5m breeze frunt and mu chuked bmbe 5m breeze frunt duud By me laslume huwn mere 15 vmuany nu duud remarmrrg rrgmabbve me 5m breeze frunt x Jmm r Wm r H Fw V speed rrrereases th me absmce uf cundensa un mug shame the 39nnL the pressure mi m R w updraa stranthEns alugcal cunsequence quhe fasterpmnganun Ths uparea mi m much cundensanun wermmg that me seabreeze 39nnt pmpaga un speed sluws Ind 1 actually retxugades dunng the 1m few ume peneas depicted m me gure HCR Interaction with Other Local Circulations The complex physiography in the vicinity of Cape Canaveral makes forecasting weather for Space Shuttle launches a notable challenge Local landwater contrasts can lead to highly complex circulations that under the proper circumstances can initiate convection 288N 286N MAINLAND FLORIDA a 5 284N 808w 806W 804w FIG I Physiography near Cape Canaveral FL This region was simulated with the OU ARPS model at very ne grid spacing down to 100 m with the domains shown below The Indian River Breeze KH instability and HCRs all interacted to produce regions of enhanced upward motion and vertical vorticity 26 8N 28v v39 quotV PM 808w 806W 501w FIG 2 lucmmns of he Ilncc gnd rlonmms unli7crl for numcncnl annulmmn huh D DI mm D crmlznn lmrlmnlnl rcmlunons of 6 t 4 Iml ll km rcspccllwl 700 b 600 7 500 7 400 E300 200 100 v O r 2838N 28 39N 284N 2841N 2842N 28 43N 1m 0 m Vamcm monon un c y m 52 m move me suer mm um mm m xx m mm 1 M nmv 2 1mm Mr 1R m M mmmnn hwum v1 mummd Hunt lmmn mqu 2me Mann mm up m y m u m m m s W Mung A2 A1 2 L39ummu mmml L 1 n m w Wm range m squot Lmulmn 01 me an mum 15 Magnum x m m my mum Numbm 5 mm vmllmh m m R x 7 0 MF IR K G X5 X7 28412N m 23mm MEOY E m 28 404N 3 5 x3 th5 80 SW 80 75W 80 76W 803974W he 7 J Am A emczu nmunn m c an i m Abmu ms mm mm m mm mm m m m m s Ammmk pomou m I 0x umm m my mug from a l m M m 5quot mm A wmmu Anan um I m gt Lam x X3 7 dcnolc um wcnuns 5mm m 171g mm 0 HM Ml 4nd R m as m Mg Iv HCRs and the May 3rd Tornado Outbreak It has been proposed that the rst tomadic storms in the May 3 1999 outbreak were initiated by a horizontal convective roll Shown below is the base re ectivity from the WSR88D radar at Frederick OK KFDR The re ectivity band appeared to be confined to the PBL It was not apparent in KFDR imagery above approximately 1370 m 4500 ft AGL This height corresponded well with the top of the PBL as determined from modified soundings The possible HCR was not observed by radars farther away at Oklahoma City and Fort Worth whose beams scanned above the PBL Also the HCR s re ectivity pattern disappeared farther north and south as the 5 and 15 elevation KFDR beams scanned above the CBL Although the re ectivity band was quasistationary throughout its appearance in KFDR imagery small waves formed and moved northward along its axis As a few of these waves forced the re ectivity axis across the Oklahoma Mesonet site in eastern Tillman County the wind direction veered from southsoutheast to southsouthwest with little speed change before backing again behind the wave crests 990503 2012 urns 1 m EASE REFLECT 150 0m For further information see httpwwwspcnoaagovpublicationsedwardshcr3mayhtm 12 99050312027 TIDE 1 m ans REFLECT 150 mas Chapter 1 Introduction In this class we will examine atmospheric phenomena that occurs at the mesoscale including some boundary layer processes convective storms and hurricanes We will emphasize the physical understanding of these phenomena and use dynamic equations to explain their development and evolution First we will start with the definition of MESOSCALE 11 De nition of Mesoscale We tend to classify weather system according to their intrinsic or characteristic time and space scales Often W enter into the definition as well Two commonly used approaches for defining the scales Dynamical and scaleanalysis approach Dynamical The dynamical approach ask questions such as the following o What controls the time and space scales of certain atmospheric motion 0 Why are thunderstorms a particular size 0 Why is the planetary boundary layer PBL not 10 km deep 0 Why are raindrops not the size of baseball 0 Why most cyclones have diameters of a few thousand kilometers not a few hundred of km 0 Tornado and hurricanes are both rotating vortices what determine their vastly different sizes There are theoretical reasons for them There are many different scales in the atmospheric motion Let look at a few examples Hemi spherical plot of 500mb height color and MSL pressure contours showing planetary scale waves and surface cyclones lows at 00UTC 15 Jan 2002 A quot um i 39 u x 12 i 1 a xquot A wane A F V y 39 39 seamX I nuns 39 gt i A312 A 1 A V V m I 1 m ANALYSIS HEIGHTSTEMFER man i ESOME i illy 2 m National Weather Service 850mb computer generated synopticscale weather chart for northern America for 6pm CST January 15 2002 A cyclonelow is located over eastern US Most features shown are considered synoptic scale as fine scale features are often missed by standard upperair observation networ ARPS Cnn nentzl Scale Fnreczsl dx40km Similar fureczsts can be fuund at htqwwwczpsuueduwx 15 hr lorecast valid Wed 17 Jan 2001 am CST 1a 500 mb Height Abs Vonicity zuaa m mm 2003 7 m w Max VFmd ave1 Sun mu Med Mn 79 Max1923 s k cpu Hgt sub mh cuntnun Mmz i mam nwzeo m 15 hr lorecast valid Wed 17 Jan 2001 9 am CST 1E SeaLevel Pmssure Clouds Precip Rate MKIK 1 0 mm me me ma mm mm Cover mm Mmn Mux EIEI z Premp Rule mm Mn 0 Max115 SLP comour Mmmm Max 039 mw4 mb Max Wmd L 273 Ma 15 hr lorecast valid Wed 11 Jan 2001 9 am CST 1E Weather Ram E omng 5m HotHumid Fog mom m shim m gt I 1 won an Max24 m 2mm 1 Weather syn Med m HER H um HER H L w I M ED 1am CST January 17 2001 12001 Thu 2 NEW 2mm TE 4 s 24DUIW P500m MB 111 1 25600 d a quot 15360 1021 0 5120 LEI 39 quot 39 I10 1024161 39 39 30720 dBBB nun h 41Dm SHADEDKZDNTDUR MIN539E MAXSBB3 lncdJ JI Cl LHI rjml s BARE UMIN 1TEE UMM29 K vmln 3EI32 wnaxd3d i 12002 Thu 2 Now mm 1TE840I3 5 240000 Furs level anemia ground surface In 1 1 J 3mm 391 L 1 250 t I 2Equot T5 394 5 quot f 25 2021300 lt quotEaC an i 15 V i quotlimo f w F 5 HEAD 2 I 512 3 I125 L11 H 1rJ EIil2 3930 V V r V V 39 quot quot 0339quot 0 dL IBEIJ Sea Level Pressure mtg CUNTUUR MINg925 Mama inc25jj UV mfg BARE UMIN1 EI1 LIMAK13JI1 mum154 ma a96 MINEI J D MM9IVSIJ Tidal precip rat imm h SHADEDJ 24 h forecasts by ARPS for November 2 2000 at 32km resolution 10 no on nm 2 Nov 2000 mm mm mow cnouumsumuxm 1 anmnmuv mmlmmm swuw smwm muumlmb comwgg urvmw mum UnunAa mama Da12000m MIN 1 m man mm DMAxrwm mm 500 Umwu usvmm My mm 57 we a quotM m snADEDcomoum mrs 5mm umum m7 001 m 2 mum Ham u 5 mm am we on ME 154 quotn n was 5 MAXVSEE 1mm we Uvnaxzzstzvmxngt1525 vaz z as 2 cm W 2 Nov 2000 mama a g 24 an no my LEVEL ABOVE GROUND SURFACE 2 col Whu 2 NDV 25m pawn n s 24 an am Mon nn ME W E 55 41 0 vs ranawm valutmmm SHADEga39 m SaaLmal mssmLlmb caNT w MWEHNMAX nvumjmnmcomoum mums amax umngt252 Umax2920megtz 22vm uv um umm umuFZMIUmM szasa lt mm Dan 7 aquot vmmu a Lkm A 500mb plot showing smalliscale disturbances associated with thunderstorms in the 9km7resolution forecast oi ARPS Atmospheric Energy Spectrum There are a few dominant time scales in the atmosphere as is shown by the following plot of the kinetic energy spectrum plotted as a function of time Free Atmosphere 60 Ground 5m 5 400 E 1 300 200 we 39 39 39 a x i y 107 loquot mquot vo m7 m1 IO 10 lday year I man 1 day 1 hour 1 mm 1 52 Average kinetic energy of westeast Wind component in the free atmosphere solid line and near the ground dashed line After Vinnichenko 1970 See also Atkinson Chapter 1 There is a local peak around 1 day associated with diurnal cycle of solar heating and a large peak near 1 year associated with the annual cycle due to the change in the earth s rotation aXis relative to the sun These time scales are mainly determined by forcing external to the atmosphere There is also a peak in the a few days up to about 1 month range These scales are associated with synoptic scale cyclones up to planetaryscale waves There isn t really any external forcing that is dominant at a period of a few days this peak must be related to the something internal to the atmosphere it is actually scale of most unstable atmospheric motion such as those associated with baroclinic and barotropic instability There is also a peak around 1 min This appears to be associated with smallscale turbulent motion including those found in convective thunderstorms and planetary boundary layer The figure also shows that energy spectrum of the atmospheric motion is actually continuous There appears to be a gap between several hour to half an hour there remain disputes about the interpretation of this gap This gap actually corresponding to the mesoscale that is the subject of our study here We know that many weather phenomena occur on the mesoscale although they tend to be intermittent in both time and space The intermittency unlike the ever present largescale waves and cyclones may be the reason for the gap Mesoscale is believed to play an important role in transferring energy from the large scale down to the small scales Quoting from Dr A A White of British Met Office quotat any one time there is not much water in the out ow pipe from a bath but it is inconvenient if it gets blockedquot It s like the midlatitude convection it does not occur every day but we can not do without it otherwise the heat and moisture will accumulate near the ground and we will not be able live at the surface of the earth Energy Cascade As We go down scales We see ner and ner structures Many ofthese structures are due to certain types of instabilities that inherently limit the size and duration of the phenomena Also there exist exchanges of energy eat moisture and momentum among all scales Example A thunderstorm feeds off convective instabilities as measured by CAPE created by eg synopticscale cyclones A thunderstorm can also derive part o its kinetic energy from the mean ow The thunderstorm in turn can produce tornadoes by concentrating vorticity into small regions Strong Winds in the tornado creates turbulent eddies Which then dissipate and eventually turn e kinetic energy into heat Convective activities can also feed back into the large scale and enhancing synoptic scale cyclones 2 I nrn zennv 7r new 35 D59 L we Figure 55 Disphy of Doppler rndu du mm a Lamadxc m cm on 20 May 1917 Top re ectivlty bottom Bowie velocity Elcvnuou mic is 007 n t v rmlnr 39I39Iu dhlplny w ammonium from m 39J391 I 39mi RUSS dupluy m that occurred nan mm 16 a 39 up Law We can the energy transfer among sca1es energy cascade Energy W cascade large swall scale What does this have to do with the mesoscale A 39 39 39 Histnn39can ya in early 139 Rough De nition of Mesoscale The scale for which both ageostrophic advection and Coriolis parameter f are important which is smaller than the Rossby radius of deformation L NHf lOOOkm Does that help you For now let s use a more Qualitative definition and try to relate the scale to something more concrete Consider that the word mesoscale defines meteorological events having spatial dimensions of the order of one to two states not an individual thunderstorms or cumulus clouds and not a synopticscale cyclones whose scale is on the order of several thousands of km Typical thunderstorms are actually submeoscale scale we call their scale the convective scale Orlanski39s classi cation of scales see more discussions on this table in Atkinson Chapter 1 I I l I II u I MONTHUI I DAY 1 I mugs l I MINursI IzI I sac I I I MAGIon 5mm uuntcns no WI WI ms SCALE 0000 39 Km 39 39 I I A Mum I MACRO2 quotVquot I SCALE 1000 39 Km I I I M550 39 s39 SCALE m I Km m w WJIVI ILQE MESO 5 I w nau mj SCALE quotMm 20 m Km Iwamgvm x I m I M550 I U I SCALE mm 2 l I Km mmms I M I MICRO Imam I 3quot I SCALE 200 In vat I III I USI I quot L MICRO 5 INN SCALE m mm m FIUMIS WWESS r SCALE wquENu rIIMATnInIrn 39 SYNOPTIC 39MESO PROPOSED 0539 SCALE PLgr 39ERY39SCALEA M39CRO39SCALE DEFINITION 19 1mm um hulk Drlnnskl L Lifequ n mu new 975 Plucm mmmphuncuhunnmenl s I mmm Mann u Mxmu Gmudtun allm Mum nrmnn 39i M r Maura Muma Synnpvkcyclmvm n 200ka mm y n Moon Mm anlL immune x 21mm lazy M E Mum7 Mm LawIcch Jib rumian mm s uummnm mm and mus m H mm mm nnuluunns 20km M I n f Mm Hurry numkmnmxlurwmmdmm a 2km an n MunA Cummu mam 1mm mm M mu m 34 mm l i M 1 mm mm mmwmmmmi Limb mm Inun 7 mm 7m n M Mmm Tllybultnpc munuwave r Minnb o a Atmospheric scale de nitions Where L is hoIizonlal scale length proposed by Thunis and BoIstein 1996 De nition of scales via scale analysis on equations of motion Read Chapter 1 of Atkinson Fujita also has a chapter on this topic in book edited by Ray 1985 Some time and spatial scales in the atmosphere are obvious Time scales diurnal cycle annual cycle inertial oscillation period due to earth rotation the Coriolis parameter f advective time scale time taken to advect over certain distance Spatial scales 0 global related to earth s radius 0 scale height of the atmosphere related to the total mass of the atmosphere and gravity 0 scale xed geographical features mountain height width width of continents oceans lakes Scale analysis you should have learned this tool in Dynamics 1 is a very useful method for establishing the importance of various processes in the atmosphere and terms in the governing equations Based on the relative importance of these processesterms we can deduce much of the behavior of motion at such scales 21 Let s look at a simple example duauuauLap dt at 0x pax What is this equation Can you identify the terms in it With scale analysis we try to assign the characteristic values for each of the variables in the equation and estimate the magnitude of each term then determine their relative importance du Au U For example dt At T where U is the velocity scale typical magnitude or amplitude if described as a wave component and T the time scale typical length of time for velocity to change by Au or the period for oscillations It should be emphasized here there it is the typical magnitude of change that defines the scale which is not always the same as the magnitude of the quantity itself The absolute temperature is a good example the surface pressure is another For different scales the terms in the equation of motion have different importance leading to different behavior of the motion so there is a dynamic significance to the scale Synoptic Scale Motion Let s do the scale analysis for the synoptic scale motion since we know pretty well about synoptic scale motion correct V 10 m s actually the typical variation or change in horizontal velocity over the typical distance W 01 m s typical magnitude or range of variation of vertical velocity 22 L 1000 km 106 m about the radius of a typical cyclone H 10 km depth of the troposphere T LV 105 s the time for an air parcel to travel for 1000 km f 10394 s391 for the midlatitude p l kgm3 Ap in horizontal 10 mb 1000 Pa about the variation of pressure from the center to the edge of a cyclone note that it is the typical variation that determines that typical scale not the value itself as in this example Using the scale of 1000mb will give you wrong result 6 ua u wgz ia p fi2 at 0x 02 p 3x K a E Ap W 9 T L H pL 2 3 1O5 01x410 104X10 10 10 10 10 10 4 10 4 10 4 10 3 10 3 It turned out that the time tendency and advection terms are one order of magnitude smaller for synoptic scale ows The pressure gradient force and Coriolis force are in rough balance what kind of ow do you get in this case The guasigeostrophic ow Similar scale analysis can be performed on the vertical equation of motion Ap over vertical length scale H 1000 mb 105 Pa 23 aw aw 6w 1 ap u w g at 0x 02 p 02 K E WW Ap T L H pH g 01 10x01 01x0l 105 5 6 4 4 10 10 10 10 1x10 10 6 10 6 10 6 10 10 Clearly the vertical acceleration is much smaller than the vertical pressure gradient term and the gravitational term which are of the same order of magnitude The balance between these two terms gives the hydrostatic balance and this balance is a very good approximation for synoptic scale flows Also the vertical motion is much smaller than 6v 6w the horizontal motion We can deduce the latter from the mass continuity equation lg 27 m 0 x y 2 Therefore we obtain based on the scale analysis along the following basic properties of flows at the synoptic scale ows such ows are quasitwodimensional quasigeostrophic and hydrostatic We saw a good example of horizontal scale determining the dynamics of motion In summary synoptic and up scale flows are quasitwo dimensional because w ltlt u hydrostatic we can see it by performing scale analysis for vertical equation of motion Coriolis force is a dominant term in the equation of motion and it is in rough balance with the PGF the flow is quasigeostrophic 24 Mesoscale Motion What about the mesoscale We said earlier we define the mesoscale to be on the order of hundreds of kilometers in space and hours in time Repeat the scale analysis done earlier 6 ua u wa Ll fix at 0x 02 p 0x V W WV A p T L H pL 2 2 1 2 L140 Q 10 4x10 10 10 10 10 10 3 10 3 10 3 10 3 10 3 we see that the all terms in the equation are of the same magnitude none of them can be neglected we no longer have geostrophy For the vertical direction the hydrostatic approximation is still reasonable good for the mesoscale In the vertical direction 25 aw aw 6w 1 ap u w g at 0x 02 p 02 K E WW Ap T L H pH g L 10x1 E 105 10 104 105 104 1x104 10 4 10 4 10 4 10 10 Therefore mesoscale motion is not geostrophic ie ageostrophic component is significant see earlier definition the Coriolis force remains important and hydrostatic balance is roughly satisfied The motion is quasi twodimensional wltltu or V This can be a dynamic definition of the mesoscale or in Orlanski s definition the mesoB scale In summary meso scale ows are 0 quasitwo dimensional o nearly hydrostatic o Coriolis force is nonnegligible When we go one step further down the scale looking at cumulus convection or even supercell storms L 10 km V 10 ms T 1000 s we get 26 0 6 wau at 0x 02 p 0x V W WV A P W T L H pL 10 102 102 102 104 x 10 103 104 104 104 10 2 10 2 10 2 10 2 10 3 Now we see that the Coriolis force is an order of magnitude smaller it can therefore be neglected when studying cumulus convection that lasted for an hour or so Again the acceleration term is as important as the PGF The scale analysis of the vertical equation of motion based on the Bousinessq equations of motion see e g page 354 of Bluestein is as follows aw aw 6w 1 0p 6quot u w g at 0x 02 p 02 9 K E WW AP A6 T L H 5H 60 g n E E 102 1x10 103 104 104 05x104 300 10 2 10 2 10 2 2 x 10 2 3 x 10 2 Here we are using the vertical mean density as the density scale in PGF term The Bousinessq form of equation is used because it is the residual between the PGF and buoyancy force terms that drives the vertical motion therefore we want estimate the terms in terms of the deviationsperturbations from the hydrostatically balanced base state 27 Clearly the vertical acceleration term is now important therefore hydrostatic approximation is no longer good According to Orlanski s definition this falls into the mesoy range sometimes it s referred to as small scale or convective scale At this scale the flow will be agostrophic nonhydrostatic and three dimensional w u and v In summary meso y small or convective scale ows are 0 three dimensional o nonhydrostatic o ageostrophic and the Coriolis force is negligible As one goes further down to the microscales the basic dynamics becomes similar to the small scale ows the flow is 0 three dimensional o nonhydrostatic o ageostrophic and the Coriolis force is negligible 28 Summary There are more than one way to define the scales of weather systems The definition can be based on the time or space scale or both of the system It can also be based on certain physically meaningful nondimensional parameter for example Rossby number based on Lagrangian time scale as advocated by Emanuel 1986 The most important is to know the key characteristics associated with weather systemsdisturbances at each of these scales as revealed by the scale analysis The scale analysis can lead to nondimensional parameters in non dimensionalized governing equations Physically the last approach that based on nondimensional parameters makes most sense Reference Emanuel K A 1986 Overview and definition of mesoscale meteorology In PS Ray Editor Mesoscale Meteorology and Forecasting American Meteorological Society Boston 117 with some coverage on mesoa and microa scale gegI tornadoes 29
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